Volume Volume Volume Volume- -- -37 37 37 37 Number 1 Number 1 Number 1 Number 1www.nsa2010.gpgcrishikesh.com Ultrasonics Proceeding of National Proceeding of National Proceeding of National Proceeding of National Symposium on Accoustic Symposium on Accoustic Symposium on Accoustic Symposium on Accoustic Number 1 Number 1 Number 1 Number 1 2010 2010 2010 2010 www.nsa2010.gpgcrishikesh.com Ultrasonics Proceeding of National Proceeding of National Proceeding of National Proceeding of National Symposium on Accoustic Symposium on Accoustic Symposium on Accoustic Symposium on Accoustic 1 | P a g e ISSN 0973-3302 2010 Proceeding of National Proceeding of National Proceeding of National Proceeding of National Symposium on Accoustic Symposium on Accoustic Symposium on Accoustic Symposium on Accoustic 2 | P a g e Journal of Acoustical Society of India The Refereed Journal of the Acoustical Society of India (JASI) The journal of Acoustical Society of India is a refereed journal of the Acoustical Society of India (ASI). The ASI is a non-profit national society founded in 31 st july,1971. The primary objective of the society is the advance the science the science of acoustics by creating an organization that is responsive to the needs of scientists and engineers concerned with acoustics problems all around the world. Manuscripts of articles, technical notes and letter to the editor should be submitted to the Chief Editor. Copies of articles on specific listed above should also be submitted to the respective. Associate Scientific Editor. Manuscripts are refereed by at least two referees and are reviewed by Publication Committee (all editors) before acceptance. On are refereed by at least two referees and are reviewed by Publicatin Committee (all editors) before acceptance. On acceptance revised articles with the text and figures scanned as separate files on a diskette should be submitted to the Editor by express mail Manuscripts of articles must be prepared in strict accordance with the author instructions. All information concerning subscription new books journals conferences etc. Should be submitted to Chief Editor Acoustics Section, National Physical Laboratory, Dr. KS Krishnan Road New Delhi 110 012 Tel: +91.11.4560.9319. Fax:+91.11.4560.9310, e-mail:
[email protected] The journal and all articles and illustrations published herein are protected by copyright. No part of this journal may be translated reproduced stored in a retrieval system or transmitted in any form or by any means electronic ,mechanical, photocopying, microfilming recording or otherwise, without written permission of the publisher. Copyright @2007, Acoustical Society of India ISSN 0973-330 Printed at Alpha Printers BG-2/38C Paschim Vihar, New Delhi-110063 Tel:9811848335, JASI is sent to ASI members free of charge. CHIEF EDITOR Mahavir Singh Acoustics Section National Physical Laboratory Dr. KS Krishnan Road New Delhi 110 012 Tel +91-11-45609319 Fax +91-11-45609319 E-mail:
[email protected] ASSOCIATE SCIENTIFIC EDITOR Applied Acoustics Trinath Kar Technology Lead Editorial Office: MANAGING EDITOR Omkar Sharma ASSISTANT EDITORS Yudhisther Kumar Anil Kumar Nain Naveen Garg Acoustics Section National Physical Laboratory Dr. KS Krishnan Road New Delhi 110 012 Tel +91-11-45609319 Fax +91-11-45609319 E-mail:
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[email protected] 3 | P a g e MAHAVIR SINGH Chief Editor OMKAR SHARMA Managing Editor TRINATH KAR Associate Scientific Editor Youdhishter kumar Anil Kumar Nain Assistant Editor Naveen Garg Assistant Editor EDITORIAL BOARD M L Munjal IIsc Banglore India S Narayanan IIT Chennai India V Rajendran KSRCT Erode India R J M Craik HWU Edinburg. UK Trevor RT Nightingle NRC Ottawa, Canada B V A Rao VIT Vellore, India P Narang NMI Lindfield, Australia E S R Rajagopal IISc Banglore, India V Bhujanga Rao NSTL Vizag, India AL Vyas IIT Delhi, India V Bhujanga Rao NSTL Vizag, India Yukio Kagawa NU Chiba Japan S Datta LU Loughborough UK Sonoko Kuwano OU Osaka Japan KK Pujara IIT Delhi (Ex) India AR Mohanty IIT Kharagpur India Ashok Kumar NPL New Delhi India V mOhanan NPL New Delhi ,India 4 | P a g e Sound Transmission through Building Enclosures The article deals with sound transmission through building enclosures including different forms of predominantly lightweight wall construction. It gives guidance on how walls comprising a number of separate element can be assessed. Sound transmission from outside to inside the reader should also see BS EN 12345-4:2000 if they are concerned with containment of sound within a building. The performance of a wall or roof has to be considered in terms of the internal spaces. The aim is to provide a building envelope that gives the required sound pressure levels within a room or other internal space. The noise level within a room will depend on the amount of sound energy transmitted through the wall and interreflection of sound inside the room. The room effect is usually determined by the amount of sound absorbing material in the room. Sound transmission of an assembly of components can be calculated provided the wall can be analysed as discrete areas for each of which the Sound Reduction Index is known. This applies to windows in walls and collections of windows but note that sound transmission through interface components such a joining mullions between windows may not be known. Sound transmission through a whole wall Is established by calculating an apparent sound reduction index (SRI) for the wall. This is used to determined the difference in sound between the outside and inside. The procedure is to calculate the sound power reduction for each element of the wall. The total sound power reduction can then be calculated and converted to an apparent reduction index. When sound of intensity 1W/m 2 falls on a wall the sound power (in watts) transmitted by an element is given by: Wi =Si 10 Where Si is the area of an element (m 2 ) Ri is the sound reduction Index of that element (dB) (Mahavir Singh) 5 | P a g e 1 US-1 Velocity and Thermodynamic properties of Binary liquid mixtures of Methanol, Ethanol with Ethylacetoactate P. Paul Divakara, A. Madhusudhanacharyulua & Mrs. K. Samathab 8-13 2 US-2 Study of Solvation number and related parameters of Ammonium bifluoride in non-aqueous medium A. Beulah Mary, J.H.Rakini Chandrasekaran, G. Bharathi & K.Ganthimathi 14-19 3 US-3 Study of Internal pressure and Equivalent conductance of solutions of calcium fluoride in non-aqueous medium A. Beulah Mary, J.H.Rakini Chandrasekaran, G. Bharathi & K.Ganthimathi 20-22 4 US-4 Effect of electronegativity on free volume and vanderwaals constant of binary and ternary liquid mixtures K. VIJAYALAKSHMI, C. Ravidhas 23-27 5 US-5 Ultrasonic studies of nn'-methylene bis-acrylamide in water T.Mathavan, S.Umapathy, M.A.Jothi Rajan, A. Alfred Nobel Antony, X.Dolour Selvarajan, J.Hakkim, V.Stephen Raja & T.S.Vivekanandam 28-33 6 US-6 Determination of ultrasonic interaction parameter for Poly (acrylic acid) in water T.Mathavan, S.Umapathy, M.A.Jothi Rajan, B.Valarmathi & T.S.Vivekanandam 34-38 7 US-7 Ultrasonic investigations of n-methylpyrrolidone in 1-propanol T.Mathavan, S.Umapathy, M.A.Jothi Rajan, S.Gokila, M.Abirami, S.K.Dravida Selvi, R.Hemalatha & T.S.Vivekanandam 39-44 8 US-8 A study of solvation effect of some sodium salts in non-aqueous medium using ultrasonic velocity Padmavathy. R, Jasmine Vasantha Rani. E, Seethalakshmi. K & Rahmathunnisa. R 45-50 9 US-9 Thermo - acoustic and spectroscopic study of polymer salt in non- aqueous medium using ultrasonic velocity Jasmine Vasantha Rani.E, Padmavathi.R, Radha.N, Kannagi. & Lavanya.N 51-56 10 US-10 Ultrasonic investigations of peg (400) in toluene-clay mixture T. Mathavan, S.Umapathy, M.A.Jothi Rajan, M. Megala & T.S.Vivekanandam 57-62 11 US-11 Acoustical Study on Thermo dynamical and Excess parameters of binary and ternary mixtures M.M. Armstrong Arasu & Dr. I.Johnson 63-69 12 US-12 Study of Thermo Acoustical Parameters of Some Binary Mixtures from volume Expansivity Data M.M. Armstrong Arasu & Dr. I.Johnson 70-76 13 US-13 A comprehensive analysis of solvation number of some organic acid salts in non- aqueous medium Jasmine Vasantha Rani E & Suhashini Ernest 77-82 14 US-14 Ultrasonic study on binary mixtures of ethyl benzoate with benzene and substituted benzenes at different temperatures B. Nagarjuna, Y.V. V Apparaoa, G.V Ramaraob, A.V Sarmaa & C. 83-88 6 | P a g e Rambabuc 15 US-15 Study of non linear parameter (b/a) and thermo acoustic parameter of binary mixture at different frequencies G. Nath & R. Paikaray 89-94 16 US-16 Thermo-acoustic Studies on Ternary Mixtures of Methyl Iso-butyl Ketone, Acetyl acetone and butanols with carbon tetrachloride (CCl4) T.Karunamoy, S. K Dash, S.K.Nayak & B B Swain 95-100 17 US-17 Glueckauff’s model for lowering of dielectric constant of electrolytic solutions & Isentropic Compressiblity Studies with aqueous electrolytic solutions using Ultrasonics –IONS PAIRS (CHLORIDES) V.Brahmajirao , T. Gunavardhan Naidu , P.Rajendra , T.Srikanth & Shanaz Batul 101-110 18 US-18 Glueckauff’s model for lowering of dielectric constant of electrolytic solutions & Isentropic Compressiblity Studies with aqueous electrolytic solutions using Ultrasonics –IONS PAIRS (SULPHATES) V.Brahmajirao , T. Gunavardhan Naidu, T.Srikanth , P.Rajendra & Shanaz Batul 111-121 19 US-19 Tempareture variation of velocity in cow milk at different Ultrasonic frequencies Kailash, S. N. Shrivastava & Poonam Yadav 122-128 20 US-20 Ultrasonic Study of some Organic Pathological Compounds Kailash, S. K. Shrivastava & Jitendra Kumar 129-133 21 US-21 High Temperature Study of Anharmonic Properties of TeO Kailash, Jitendra Kumar & Virendra kumar 134-138 22 US-22 Orientation Dependence of Ultrasonic Attenuation for Calcium Oxide in High Temperature Range Kailash, S. K. Shrivastava & Jitendra Kumar 139-143 23 US-23 Molecular radii of Pyridine/quinoline with phenol in benzene using acoustical methods at different temperatures Anjali Awasthi, Bhawana S. Tripathi, Rajiv K. Tripathi & Aashees Awasthi 144-149 24 US-24 Ultrasonic and theoretical study of binary mixture of DEHPA(Di-(2- ethyl-hexyl) phosphoric acid) with n-hexane at different temperatures Sujata Mishra & Rita Paikaray 150-155 25 US-25 Acoustical Studies of Molecular Interactions in Binary Liquid System of Cinnamaldehyde and N-N Dimethylaniline at 303 K Padmanabhan G, Kumar R, Jayakumar S & Kannappan V 156-163 26 US-26 Characterization of Nanofluid of Platinum Virendra Kumar, Kailash and Jitendra Kumar 164-169 27 US-27 Ultrasonic Behaviour of Mixed Crystals Virendra Kumar, Kailash and Bharat Singh 170-175 28 US-28 Temperature Dependence of Ultrasonic Attenuation in Strontium Oxide Crystal Kailash, Virendra Kumar, and D.D. Gupta 176-181 29 US-29 Ultrasonic Wave Propagation in Refractory Materials Devraj Singh , P. K. Yadawa, Ravi S. Singh and S. K. Sahu 182-188 30 US-30 Ultrasonic Wave Propagation in II-VI Hexagonal Semiconductor 189-200 7 | P a g e Compounds Pramod Kumar Yadawa & Devraj Singh 31 US-31 Sound Velocity And Density Studies To Find The Effect of PEG on Aqueous Anionic Surfactant (SDS) S. CHAUHAN, M.S. CHAUHAN & R.S. THAKUR 201-208 8 | P a g e VELOCITY AND THERMODYNAMIC PROPERTIES OF BINARY LIQUID MIXTURES OF METHONOL, ETHANOL WITH ETHYLACETOACTATE AS COMMON SOLVENT P. Paul Divakar *, A.S. Madhusudanacharyulu* and Mrs. K. Samatha # * Research Scholars, Department of Physics, Andhra University, Visakhapatnam – 530 003 # Professor, Department of Physics, Andhra University, Visakhapatnam – 530 003 email:
[email protected] ABSTRACT: Ultrasonic velocity(U), density(ρ) and viscosity(η) measurements were made in two binary liquid mixtures for methanol and ethanol with ethylacetoacetate as a common solvent at 303, 308, 313 and 318 K with increasing mole fraction of ethylacetoacetate using single crystal variable path ultrasonic interferometer at 2 MHz frequency. The experimental data have been used to calculate adiabatic compressibility, inter molecular free length, free volume, internal pressure, molar volume and enthalpy. The excess values of the above parameters have been evaluated and discussed in the light of molecular interactions. KEYWORDS: Adiabatic compressibility, Inter molecular free length, Free volume, Internal pressure, Molar volume and Enthalpy. INTRODUCTION: The ultrasonic velocity measurements are very important and playing vital role not only in characterizing the behaviour of liquid mixtures but also in the study of molecular interactions. In recent times ultrasonic velocity has been adequately employed in understanding the nature of molecular interaction in pure liquids and binary mixtures. Most of the work on binary mixtures is channelized towards the estimation of thermodynamic parameters like adiabatic compressibility, free length etc., and their excess values so as to relate them towards explaining the molecular interactions and hydrogen bonding taking place between the components of the binary liquid mixtures [1-5]. 9 | P a g e The present study involves the binary mixtures of methanol and ethanol with ethylacetoacetate of various mole fractions at four different temperatures 303, 308, 313, 318 K. The excess values of some acoustical and thermo dynamical parameters have been calculated from the experimentally measured values i.e., ultrasonic velocity, density and viscosity of the mixtures. The excess values are made to use for the explanation of the intermolecular interactions, intramolecular interactions and also hydrogen bonding. EXPERIMENTAL DETAILS: The chemicals used in the present work are AR grade of purity 99% from E- Merck. The densities and viscosities were measured and compared at the working temperature with the corresponding literature values. Speeds of sound measurement were made with a single crystal variable path ultrasonic interferometer (Model F-81; Mittal enterprises) at 2 MHz frequency with an accuracy of ±0.01%. The densities were measured using specific gravity bottles by relative measurement method with accuracy of ±0.01kg/m. The weight of the samples were measured using a single pan balance (electronic, Keroy). An Oswald viscometer (5ml) was used for the viscosity measurements and efflux time was determined using a conventional stop-watch. A constant temperature bath has been used to circulate water through the measuring cell made-up of steel containing the experimental liquid at the desired temperature with an accuracy of ±0.1K. THEORY AND CALCULATIONS Various Physical and thermo dynamical parameters are calculated. (1) Adiabatic Compressibility βad = 1/(ρU 2 ) cm 2 / dyne (2) Intermolecular free length Lf = k( βad ) 1/2 A 0 where k is a temperature dependent constant. Its values are 627×10 –6 , 631.5×10 –6 , 636×10 –6 and 640.5×10 –6 respectively at 303, 308, 313 and 318K. (3) Molar volume V = Meff /ρeff cm 3 / mole where Meff is the molecular weight of the mixture in which Meff = ∑ mi xi where mi and xi are the molecular weight and the mole fraction of the individual constituents respectively. (4) Internal Pressure Πi = bRT (Kη/U) 1/2 [ (ρ) 2/3 / (Meff) 7/6 ] dynes / cm 2 where b is the cubic packing which is assumed to be 2 for all liquids and solutions, η is the viscosity, R is a gas constant and T absolute temperature K is the temperature dependent constant is equal to 4.28 X10 9 for all liquids. 10 | P a g e (5) Free volume Vf = ( Meff U / Kη ) 3/2 cm 3 / mole (6) Enthalpy H = ΠiV cal / mole Excess values of the above parameters can be evaluated using A E = Aexp - Aid Where Aid = ∑ Ai xi where Ai is any acoustical parameter and xi is the mole fraction of the liquid component. RESULTS AND DISCUSSIONS The experimental values of ultrasonic velocity, density and viscosity for the two binary liquid systems at 303, 308, 313 and 318K are given in Table 1. The excess values of acoustical and thermo dynamical parameters are presented in tables 2-3. Table 1 : Values of Ultrasonic Velocity(U), Density (ρ ) and viscosity(η ) for mole fraction X of ethylacetoacetate System I : Methanol +Ethylacetoacetate X U x 10 4 cm/sec ρ x 10 3 gr/cm 3 η centi poise 303K 308K 313K 318K 303K 308K 313K 318K 303K 308K 313K 318K 0.0000 1088.5 1070.3 1055.30 1034.20 0.7809 0.7709 0.7656 0.7605 0.4968 0.4747 0.4478 0.4236 0.0381 1097.8 1081.6 1067.85 1048.26 0.8224 0.7976 0.7931 0.7881 0.5548 0.5124 0.4756 0.4548 0.0818 1108.6 1092.4 1080.52 1061.17 0.8650 0.8228 0.8181 0.8127 0.6140 0.5571 0.5110 0.4889 0.1324 1120.9 1105.9 1093.32 1074.63 0.9083 0.8471 0.8418 0.8358 0.6692 0.6073 0.5481 0.5275 0.1919 1135.3 1119.9 1107.53 1089.20 0.9502 0.8704 0.8650 0.8583 0.7239 0.6617 0.5940 0.5709 0.2626 1151.1 1135.6 1123.13 1105.43 0.9900 0.8929 0.8870 0.8795 0.7796 0.7190 0.6411 0.6181 0.3482 1168.2 1152.2 1139.68 1123.34 1.0281 0.9138 0.9075 0.8994 0.8383 0.7726 0.6940 0.6681 0.4539 1188.9 1172.8 1159.75 1143.01 1.0621 0.9340 0.9273 0.9184 0.9019 0.8251 0.7420 0.7200 0.5876 1215.6 1199.7 1186.15 1169.69 1.0914 0.9543 0.9470 0.9373 0.9704 0.8791 0.7928 0.7668 0.7622 1251.6 1235.7 1221.24 1204.98 1.1131 0.9750 0.9670 0.9562 1.0480 0.9416 0.8540 0.8083 1.0000 1303.0 1286.1 1270.00 1253.00 1.1298 0.9960 0.9870 0.9750 1.1391 1.0192 0.9250 0.8443 System II : Ethanol + Ethylacetoactate X 303K 308K 313K 318K 303K 308K 313K 318K 303K 308K 313K 318K 0.0000 1132.1 1116.2 1098.5 1080.8 0.7806 0.7763 0.7718 0.7676 0.9856 0.8970 0.8299 0.7670 0.0539 1141.9 1142.0 1144.6 1132.0 0.8199 0.8073 0.8037 0.7998 1.0025 0.9090 0.8389 0.7750 0.1135 1152.7 1153.0 1172.0 1160.9 0.8587 0.8370 0.8334 0.8285 1.0189 0.9222 0.8530 0.7839 0.1180 1164.8 1169.0 1194.4 1181.0 0.8978 0.8653 0.8610 0.8567 1.0366 0.9366 0.8643 0.7951 0.2546 1178.1 1184.0 1212.8 1197.4 0.9373 0.8932 0.8871 0.8826 1.0540 0.9531 0.8783 0.8072 0.3387 1193.2 1195.0 1225.0 1209.9 0.9769 0.9192 0.9124 0.9067 1.0692 0.9685 0.8911 0.8208 0.4345 1210.3 1211.0 1236.0 1220.0 1.0157 0.9424 0.9360 0.9297 1.0816 0,9761 0,8964 0.8243 0.5445 1229.4 1235.0 1245.1 1231.0 1.0522 0.9630 0.9577 0.9499 1.0936 0.9843 0.9020 0.8276 0.6720 1250.4 1255.0 1252.0 1238.7 1.0828 0.9785 0.9720 0.9629 1.1076 0.9949 0.9075 0.8313 0.8218 1274.6 1267.0 1260.8 1247.3 1.1082 0.9902 0.9819 0.9719 1.1230 1.0058 0.9156 0.8373 1.0000 1303.0 1286.0 1270.0 1253.0 1.1298 0.9960 0.9870 0.9750 1.1391 1.0192 0.9250 0.8443 11 | P a g e The ultrasonic velocity values increases with increase in concentration of ethylacetoacetate in both the systems. An increase in the ultrasonic velocity with increase in concentration appears to be associated with an overall increase in the cohesion in both the systems. The viscosity values from observations are regularly increasing without having any maxima with the increase of mole concentration of ethylacetoacetate at all the temperatures. Moreover it has been decreasing with increase in temperature for both the binary systems. The linear increase in િ with mole fraction concentration of ethylacetoacetate confirmed the increase of cohesive forces because of strong molecular interactions. In order to substantiate the presence of interaction it is essential to study the excess parameters such as internal pressure, free volume and enthalpy apart from excess adiabatic compressibility, excess free length, and excess molar volume. Table 2: Excess values of adiabatic compressibility (βad E ) , Free length ( Lf E ) and Molar volume (V E ) for mole fraction X of ethylacetoacetate System I : Methanol +Ethylacetoacetate X βad E cm 2 / dyne Lf E x10 -8 cm V E cm 3 / mole 303K 308K 313K 318K 303K 308K 313K 318K 303K 308K 313K 318K 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0381 -5.048 -3.962 -4.636 -5.271 -0.014 -0.011 -0.013 -0.014 -0.350 -0.568 -0.639 -0.688 0.0818 -9.521 -7.384 -8.531 -9.815 -0.027 -0.020 -0.024 -0.026 -0.746 -1.119 -1.241 -1.326 0.1324 -13.19 -10.08 -11.466 -13.260 -0.038 -0.028 -0.032 -0.035 -1.185 -1.638 -1.785 -1.891 0.1919 -15.83 -11.88 -13.221 -15.121 -0.047 -0.033 -0.037 -0.041 -1.654 -2.107 -2.249 -2.359 0.2626 -17.16 -12.58 -13.605 -14.759 -0.051 -0.036 -0.039 -0.042 -2.120 -2.493 -2.605 -2.701 0.3482 -16.95 -12.09 -12.583 -11.446 -0.052 -0.035 -0.036 -0.038 -2.517 -2.760 -2.821 -2.891 0.4539 -15.15 -10.50 -10.464 -4.610 -0.048 -0.030 -0.030 -0.031 -2.720 -2.849 -2.862 -2.907 0.5876 -12.05 -8.311 -8.104 -4.010 -0.039 -0.024 -0.023 -0.024 -2.511 -2.665 -2.674 -2.718 0.7622 -8.091 -6.038 -6.427 -3.250 -0.025 -0.017 -0.018 -0.019 -1.590 -1.980 -2.063 -2.146 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 System II: Ethanol +Ethylacetoacetate X 303K 308K 313K 318K 303K 308K 313K 318K 303K 308K 313K 318K 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0539 -3.855 -6.111 -9.998 -11.454 -0.011 -0.018 -0.030 -0.035 -0.330 -0.510 -0.620 -1.710 0.1135 -7.056 -10.418 -16.874 -19.128 -0.020 -0.031 -0.052 -0.059 -0.682 -1.023 -1.184 -1.343 0.1180 -9.516 -12.887 -20.575 -22.992 -0.028 -0.039 -0.062 -0.071 -1.046 -1.528 -1.684 -1.892 0.2546 -11.14 -13.580 -21.212 -23.249 -0.033 -0.042 -0.067 -0.073 -1.406 -1.999 -2.106 -2.343 0.3387 -11.86 -12.750 -19.243 -20.562 -0.036 -0.040 -0.063 -0.066 -1.730 -2.400 -2.430 -2.680 0.4345 -11.63 -10.880 -15.985 -15.985 -0.036 -0.034 -0.052 -0.053 -1.973 -2.675 -2.631 -2.882 0.5445 -10.45 -8.325 -11.463 -11.359 -0.033 -0.028 -0.040 -0.039 -2.056 -2.741 -2.661 -2.909 0.6720 -8.328 -6.929 -8.469 -8.4969 -0.026 -0.023 -0.030 -0.030 -1.873 -2.465 -2.642 -2.662 0.8218 -5.117 -5.404 -6..689 -7.4241 -0.016 -0.017 -0.022 -0.025 -1.260 -1.650 -1.710 -1.900 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 12 | P a g e The excess adiabatic compressibilities (βad E ) are negative as observed for both the systems. The excess adiabatic compressibilities are not only negative but also vary non-linearly with increase in temperature, i.e., it reaches negative maximum till the mole concentration reaches 0.5 (approx) then again begins to increase as the mole fraction increases. Fort et.al [2] found that the negative values of excess compressibilities indicates greater interaction between the components of the mixtures. So the βad E is associated with a structure forming tendency. In the present case the mutual breaking of hydrogen bonds in alcohols with ester leading to decrease in free lengths in the mixture contributing to negative deviation in the adiabatic compressibility for both the systems. It indicates strong molecular interactions in liquid mixtures. Sridevi et.al [6] suggested that the negative excess values have been due to closely packed molecules which account for strong molecular interactions Table 3: Excess values of Internal pressure (Πi E ), free volume (Vf E ) and Enthalpy( H E ) for mole fraction X of ethylacetoacetate System I : Methanol +Ethylacetoacetate X Πi E dyne / cm 2 Vf E cm 3 / mole H E cal / mole 303K 308K 313K 318K 303K 308K 313K 318K 303K 308K 313K 318K 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0381 -181.1 -337.3 -409.5 -357.4 -0.444 -0.283 -0.150 -0.366 -7157 -2712 -784 -1200 0.0818 -393.0 -652.0 -781.8 -738.6 -0.823 -0.636 -0.394 -0.765 -12313 -6128 -2022 -3189 0.1324 -633.9 -932.7 -1101. -997.1 -1.116 -1.048 -0.734 -1.261 -15046 -10205 -3731 -6017 0.1919 -897.2 -1166. -1350 -1252. -1.306 -1.520 -1.162 -1.836 -15011 -14765 -5870 -9643 0.2626 -1163. -1334. -1509 -1437. -1.379 -2.015 -1.638 -2.470 -12126 -19322 -8246 -13791 0.3482 -1392 -1420. -1558 -1529. -1.335 -2.462 -2.074 -3.113 -6940 -22911 -10421 -17789 0.4539 -1508 -1402. -1487 -1498. -1.208 -2.716 -2.287 -3.637 -1275 -23743 -11507 -20200 0.5876 -1378 -1259. -1294 -1311. -1.070 -2.521 -1.980 -3.761 -1131 -19096 -10017 -18506 0.7622 -834.9 -922.3 -946.0 -905.6 -0.941 -1.543 -0.870 -2.905 -36470 -7077 -4546 -9867 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 System II: Ethanol +Ethylacetoacetate X 303K 308K 313K 318K 303K 308K 313K 318K 303K 308K 313K 318K 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0539 -346.83 -453.4 -520.90 -528.08 -0.2759 -0.1942 -0.0632 -0.0469 -7674 -11165 -16409 -17579 0.1135 -640.81 -813.6 -924.40 -932.67 -0.5510 -0.4459 -0.2115 -0.2134 -14182 -19182 -27899 -29612 0.1180 -874.18 -1073.5 -1202.9 -1206.8 -0.8166 -0.7403 -0.4331 -0.4828 -19365 -24007 -34394 -36064 0.2546 -1037.6 -1277.3 -1351.9 -1347.8 -1.0522 -1.0494 -0.7032 -0.8202 -23031 -25761 -36088 -37230 0.3387 -1122.8 -1275.0 -1375.5 -1360.1 -1.2530 -1.3286 -0.9787 -1.1653 -25010 -24886 -33692 -34024 0.4345 -1122.9 -1204.6 1289.17 -1264.7 -1.3716 -1.5135 -1.1925 -1.4285 -25165 -22211 -28563 -28108 0.5445 -1031.7 -1090.9 -1119.7 -1092.6 -1.3697 -1.5177 -1.1255 -1.4883 -23357 -18919 -22713 -21903 0.6720 -841.10 -887.2 -895.26 -875.7 -1.1884 -1.2495 -1.0648 -1.2186 -19350 -16055 -18179 -17808 0.8218 -526.08 -586.5 -596.20 -593.5 -0.7548 -0.6715 -0.5736 -0.5900 -12394 -12673 -14427 -15102 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 13 | P a g e The excess intermolecular free length (Lf E ) is negative at all temperatures over the entire composition range for both the systems. Also the Lf E decreases with increase in the mole fraction of ethylacetoacetate. This ascribes dominant nature of hydrogen bond interaction between unlike molecules. Hence it represents the existence of greater interactions. Spencer et.al [7] have also reported a similar observation on the basis of excess values of free length. The excess values of enthalpy( H E ) are negative for both the systems over the entire mole fraction range is observed. This negative trend of H E indicates that strong interaction between the unlike molecules besides dipole-dipole interactions are predominant. In the present study the excess internal pressure (Πi E )for both the systems shows negative values and reaches a maximum at middle concentration as mole fraction of ethylacetoacetate goes on increasing . Moreover the Πi E values increases with increase in temperature. This trend shows a pre-dominance of repulsive forces. The excess free volume (Vf E ) values are found to be negative for both the systems studied over the entire mole fraction range and at all the temperatures. Fort et.al 2 noticed that the negative Vf E trend is due to decrease in the strength of the interaction between the unlike molecules. The excess molar volumes also exhibit a similar trend as that of Vf E and are in good agreement with the aforesaid observations, i.e., weakening of intermolecular forces between the components. CONCLUSION The excess parameters of non-ideal binary mixtures have been satisfactorily used in explaining the extent of interactions between mixing components [8, 9]. The negative deviation of high magnitude of Vf E and negative values of Π E and H E indicate the existence of strong interaction such as hydrogen bond formation between hetero molecules in both the systems. These conclusions are good in agreement with those parameters derived from ultrasonic measurements. References: 1. Kinocid, J. Am. Chem.Soc., S1, 2950 (1929) 2. R.J.Forte and W.R.Moore, Trans.Faraday soc, 61, 2102 (1965) 3. S.B.Kasare and B.A.Patadi, Indian J. Pure & Appl. Phys 25, 180 (1987) 4. Mehra.K Sanjami, Indian J. Pure & Appl. Phys 38, 760 (2000) 5. Y Marcus, Introduction to Liquid state Chemistry, Wiley-inter science, NY (1977) 6. U. Sridevi, K. Samatha, A Viswanadha Sarma, J. pure & Appl. Ultras 26, 1 (2004) 7. J N Spencer, E Jeffery & C Robert J. of Phys.chem. 83, 1249 (1979) 8. A.Pal and Anil Kumar J. Chem.Eng. Data 50, 856 (2005) 9. Rita Mehra and Pancholi J. Indian Coun. Chem, 22 ,32 (2005) 14 | P a g e STUDY OF SOLVATION NUMBER AND RELATED PARAMETERS OF AMMONIUM BIFLUORIDE IN NON-AQUEOUS MEDIUM A. Beulah Mary 1 , G. Bharathi 2 , K.Ganthimathi 2 and J.H. Rakini Chandrasekaran 3 1. Department of Physics, Bishop Heber College, Tiruchirappalli. 2. Department of Physics, Holy Cross College, Tiruchirappalli. 3. Department of Physics, Govt. Arts College. Pudukottai. ABSTRACT The passage of ultrasonic waves through liquids, disturb the equilibrium between the solute and solvent molecules. Ultrasonic velocity measurement is used to throw light on various aspects of solvation chemistry including ion-ion and ion-solvent interactions. In the present study, computation of solvation number for Ammonium bifluoride in Dimethyl sulfoxide is undertaken for highlighting the existing interactions. For such study, density and ultrasonic velocity through the non-aqueous solutions of various concentrations are measured at different temperatures ranging from 35°c to 55°c.From Adiabatic compressibility, solvation number and its related parameters namely Apparent molal compressibility, Apparent molal volume, and Apparent solvated volume are calculated. All these parameters are temperature and concentration sensitive .Hence the variation of all these parameters with respect to temperature and concentration are analyzed. These parameters provide the sufficient information about the interaction between the ions and molecules of solvent. KEY WORDS: Adiabatic compressibility, Apparent molal volume, molar solvation number, apparent molal compressibility, molar solvated volume. 1. INTRODUCTION Study of non-aqueous solutions of electrolytes is interesting for the physical understanding of the ion-solvent interactions. A primary solvation number can be defined as the number of solvent molecules, which have surrendered their own translational freedom and remain with the ion when it moves relative to the surrounding solvent. It can also be defined as the number of solvent molecules, which are aligned in the force field of the ion. The forces will cause some of the solvent molecules to break away from the solvent network and attach themselves to the ion [1]. 15 | P a g e Solvent has been described as having an open framework structure with many holes in it. When pressure is applied, the solvent molecules can break out of the solvent network and enter interstitial space due to the close packing, the volume decreases. In addition to this, on the introduction of ions into the solvent, solvent molecules are wrenched out of the solvent framework so as to envelop themselves with solvent sheaths. Because the molecules are oriented in ionic field, the solvent is more packed in primary solvation sheath as compared to the packing if the ion were not there. The origin of the influence of the ion is the electric field of the ion. Thus the electric field causes compression of the material upon which they exert their influence, due to the phenomenon known as electostriction [2]. 2. EXPERIMENTAL STUDY Dimethyl sulfoxide solutions of various concentrations upto saturation of Ammonium bifluoride are prepared with AnalaR grade substances. The density of the solution is measured with 10 ml specific gravity bottle. Ultrasonic velocity of the solution is measured with a Mittal type ultrasonic interferometer with an accuracy of ±2m/s. The temperature is maintained from 35˚C to 55˚C with an accurate thermostat. 3. CALCULATIONS The simplest but accurate method of determining the adiabatic compressibility is through ultrasonic study [3]. From the adiabatic compressibility (β), the solvation number (n h ) can be found [4]. The adiabatic compressibility can be computed using standard relation as given below: β = 1/ (u 2 ρ) ---------------------- (1) The molar solvation number is calculated using Barnartt’s [5] relation n h = [ n 1 - βN/ β o ] / n 2 -----(2) where β o is the compressibility of solvent, n1 is the number of moles of the solvent present in 1000 cc of solution of molar concentration n2 and N is the number of moles of the solvent in 1000 cc of the solvent. The molal solvation number nh' has been computed through Passynsky’s [6] equation nh '= [1 - β/β o ] N' / n2' -------------------- (3) where n₂ʹ is the total molal concentration of the solution and N´ is the number of moles of solvent in 1000 g of the solvent. The apparent molal volume of the solution (φv) is defined as the volume of the solution containing one mole of the solute minus the volume of the solvent. It is calculated using the relation (4) φ v = V1 [N n ' h / n1 - nh] -------- (4) It is also computed by the traditional method using the equation, 16 | P a g e φ v = [1000 (ρo -ρ ) / n2 ρo] + M2 / ρo ------ (5) The apparent molal compressibility is the compressibility of an amount of solution containing one mole of the solute minus the compressibility of the solvent. It has been calculated using the relation (6) φ k = - V1 βo nh -------- (6) and the traditional equation. φ k = [1000 (ρo β – βo ρ ) / n2 ρo ] + M2 βo / ρo ---------- (7) The molar solvated volume (φs) is defined as the volume of the solvated part that comprises the solute and bound solvent. It is calculated from the following equations φ s = φ v + nh V1 --------- (8) φ s = V (β – β0) / n2 β0 ------- (9) 4, RESULTS AND DISCUSSION: The computed values of solvation numbers, apparent molal compressibility, apparent molal volume and molar solvated volume of Dimethyl sulfoxide solutions of Ammonium bifluoride are given in Tables 1-2. The values of apparent molal compressibility, apparent molal volume and molar solvated volume calculated using solvation number and traditional formula are found to be in agreement. Solvation number is found to decrease with concentration. A gradual decrease of Solvation number from lower to higher concentrations is observed standing in agreement with the statement ‘the more dilute the solution the greater the solvation of the ion’ [7].The value of solvation number decreases with temperature upto 50⁰C and then increases to a higher value at 55⁰C.Positive Solvation number suggests that compressibility of the solution will be less than that of the solvent. Table No.1 Molar solvation number and Apparent molal volume of NH₄ ₄₄ ₄HF₂ ₂₂ ₂+DMSO System Temparature ⁰c Molality n₂' nh nh' Фv*10^6 m³/Mole Фv*10^6 m³/Mole By Equation(4) By Traditional method 35 0.1 10.4167 9.6014 -63.731 -63.731 0.2 6.2352 5.6268 -48.239 -48.239 0.3 4.9958 4.4001 -48.032 -48.032 0.4 4.6827 3.9281 -62.202 -62.202 0.5 4.2182 3.5055 -59.716 -59.716 40 0.1 10.1655 9.2993 -67.885 -67.885 17 | P a g e 0.2 5.9032 5.3721 -42.142 -42.142 0.3 4.8899 4.2748 -49.681 -49.681 0.4 4.5949 3.8257 -63.495 -63.495 0.5 4.0664 3.3361 -61.037 -61.037 45 0.1 9.2469 8.4563 -61.759 -61.759 0.2 5.8912 5.4261 -37.079 -37.079 0.3 4.9907 4.3735 -50.171 -50.171 0.4 4.6095 3.8694 -61.423 -61.423 0.5 4.1116 3.3952 -60.253 -60.253 50 0.1 8.7246 7.9941 -56.999 -56.999 0.2 5.1041 4.6692 -34.321 -34.321 0.3 4.4337 3.8497 -46.956 -46.956 0.4 4.1762 3.4451 -59.924 -59.924 0.5 3.7731 3.0571 -59.477 -59.477 55 0.1 10.8186 10.0651 -60.041 -60.041 0.2 6.0015 5.6505 -28.259 -28.259 0.3 5.1033 4.5187 -48.001 -48.001 0.4 4.7441 4.0331 -59.727 -59.727 0.5 4.2455 3.5417 -59.965 -59.965 Apparent molal volume values are found to change with concentration as well as with temperature. It is found to be maximam at 0.2 molality and at all temperatures. The decrease in the apparent molal volume suggests that there is strong ion-ion interaction and increase in apparent molal volume with respect to concentration supports the solute-solvent interactions. Apparent molal compressibility increases with concentration at all temperatures and it decreases upto 50⁰C and then decreases at 55⁰C for all concentrations. Table No.2 Apparent molal compressibility and Molar solvated volume of NH₄ ₄₄ ₄HF₂ ₂₂ ₂+DMSO System Temparature ⁰c Molality n₂' Фk*E7 m³ Фk E7m³ Фs*10^6 m³/Mole Фs*10^6 m³/Mole By Equation(6) By Traditional method By Equation(8) By Traditional method 35 0.1 -3.281 -3.281 689.51 689.51 0.2 -1.964 -1.964 402.63 402.63 0.3 -1.573 -1.573 313.22 313.22 0.4 -1.475 -1.475 276.41 276.41 0.5 -1.329 -1.329 245.31 245.31 40 0.1 -3.278 -3.278 670.92 670.92 0.2 -1.904 -1.904 386.89 386.89 0.3 -1.577 -1.577 305.71 305.71 -80 -60 -40 -20 0 0 0.5 1 A p p a r e n t M o l a l V o l u m e E + 6 m ³ / M o l e Molality NH₄HF₂+DMSO M o l a r S o l v a t e d V o l u m e E + 6 M ³ / M o l e 0.4 0.5 45 0.1 0.2 0.3 0.4 0.5 50 0.1 0.2 0.3 0.4 0.5 55 0.1 0.2 0.3 0.4 0.5 Fig :1 Fig : 2 Fig : 3 Molal Solvation number of NHHF+DMSO System Apparent Molal Volume of NHHF+DMSO System 1 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C -40 -30 -20 -10 0 0.2 0.4 0.6 A p p a r e n t M o l a l C o m p r e s s i b i l i t y M ³ Molality NH₄HF₂+DMSO 100 300 500 700 900 0 0.2 0.4 0.6 Molality NH₄HF₂+DMSO 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C -1.482 -1.482 270.45 -1.311 -1.311 234.51 -3.066 -3.066 612.82 -1.953 -1.953 392.69 -1.655 -1.655 313.91 -1.528 -1.528 274.85 -1.363 -1.363 239.69 -2.928 -2.928 581.2 -1.713 -1.713 339.04 -1.488 -1.488 277.36 -1.402 -1.402 245.56 -1.266 -1.266 216.51 -3.761 -3.761 734.19 -2.087 -2.087 412.33 -1.774 -1.774 326.65 -1.649 -1.649 288.56 -1.476 -1.476 251.72 Fig :1 Fig : 2 Fig : 3 Fig :4 Molal Solvation number of +DMSO System Molar Solvation numb NHHF+DMSO System Apparent Molal Volume of +DMSO System Apparent Molal Compressibility of NHHF+DMSO System Molar Solvated Volume of NHHF+DMSO System 18 | P a g e 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C 270.45 234.51 612.82 392.69 313.91 274.85 239.69 581.19 339.04 277.36 245.56 216.51 734.19 412.33 326.65 288.56 251.72 Molar Solvation number of System Apparent Molal Compressibility of +DMSO System 19 | P a g e Fig : 5 The molar solvated volume is found to decrease in concentration as in the case of salvation number. This shows that solvation number plays an important role in deciding the value of molar solvated volume. The above results show that there is strong solvent-solute interaction. REFERENCES 1. John O. M. Bokris and Amulya K. N. Reddy, Modern Electrochemistry A Plenum/Rosetta Edition Vol.1, (1977). 2. Suhashini Ernest Ph.D., Thesis submitted to Bharathidasan University 2010. 3. Jacobson B., Acta. Chem. Scand, 6, 1485 (1952). 4. Pia Thomas and Ganthimathi K., Hydration Number and Apparent Molal Compressibility From Ultrasonic Measurements, J.Acoust.Soc. Ind., Vol. 27 No. 1–4, (1999) pp 331–333. 5. Barnartt S.J., Chem. Phys., 20, 278 (1952). 6. Passynsky A., Acta Physiochem. 8, 385 (1930). 7. Christian Riechardt “Solvent and Solvent effects in organic chemistry”Wiley VCH Third Edition 2003, 20 | P a g e STUDY OF INTERNAL PRESSURE AND EQUIVALENT CONDUCTANCE OF SOLUTIONS OF CALCIUM FLUORIDE IN NON-AQUEOUS MEDIUM A. Beulah Mary 1 , J.H. Rakini Chandrasekaran 2 , G. Bharathi 3 and K.Ganthimathi 3 1. Department of Physics, Bishop Heber College, Tiruchirappalli. 2. Department of Physics, Govt. Arts College. Pudukotta 3.Department of Physics, Holy Cross College, Tiruchirappalli. ABSTRACT Thermodynamic and electrochemical properties of electrolytes find extensive application in characterizing physico-chemical properties. This paper deals with the thermodynamic and electrochemical behaviour of solutions of calcium fluoride in dimethyl formamide. Measurement of density, viscosity and ultrasonic velocity leads to the determination of internal pressure which tells about the interaction between molecules and ions. Specific conductance values are also measured for studying ionic behaviour of the solutions. All the measurements are carried out for various concentrations of the solutions in the temperature range from 35˚C to 55˚C. The relation between equivalent conductance and internal pressure of the solutions are studied. KEY WORDS: Ultrasonic velocity, Internal Pressure, Equivalent Conductance, Concentration potential. 1. INTRODUCTION Dimethyl formamide is a protic solvent and it has very high dielectric constant and dipole moment (=3.86D, ε=36.7&µ=1.4305) compared to other protic solvents. The high values indicate the existence of appreciable non specific coulombic interactions and specific forces like hydrogen bonding resulting in dimers [1]. Internal pressure is a measure of cohesive force in a solution and is considered as a rational basis to understand thermodynamics of electrolytic solutions [2]. Internal pressure is due to coulumbic interaction between ions with net charges leading to long range interaction. The ionic behaviour of the solutions is explained by the equivalent conductance of the solutions. Cohesive energy barrier which is the product of internal pressure and molar volume also depends on the equivalent conductance. When we examine values of the equivalent conductance Λc with the variation of concentration potential Cp, in all the electrolyte solutions Λc decreases with increase in concentration potential [3].The internal pressure is found to decrease with concentration for some electrolytes and to increase for some other solutions. Based on this theory C.V. Suryanarayana found the relation [4], πi V=Λc exp (m₁Cp+k₁) -------------- (1) to hold good in the case of electrolyte solutions at constant temperature where m1 and k1 are constants. C.V. Suryanarayana formulated a similar equation for the variation of (πiV/Λc) with temperature, concentration remaining constant. (i.e) πi V=Λc exp (m₂T+k₂) --------------- (2) The validity of these equations is checked for dimethyl formamide solutions of calcium fluoride. 2. EXPERIMENTAL PROCEDURE AND COMPUTATIONS 21 | P a g e Solutions of various concentrations of calcium fluoride in dimethyl formamide are prepared with AnalaR grade substances. The density of the solution is measured with 10 ml specific gravity bottle. Ultrasonic velocity of the solution is measured with a Mittal type ultrasonic interferometer with an accuracy of ±2m/s. Viscosity is measured with the help of Oswald viscometer. Specific conductance values are also measured using conductivity meter with a cell constant 1.0. The temperature is maintained from 35˚C to 55˚C with an accurate thermostat. Internal pressure and equivalent conductance values are computed using the following formulae. Internal Pressure atmos M ρ u kη bRT Π 6 7 eff 3 2 2 1 i = ----------- (3) Equivalent conductance N 1000 k c c × = ∧ ----------- (4) Where, the terms carry the usual meaning. 3. RESULTS AND DISCUSSION The computed values of internal pressure and equivalent conductance of the electrolyte solutions are given in table (1&2.). The variation of internal pressure and equivalent conductance with concentration of the solutions is shown in Figs (1&2). In this solution the internal pressure values increase with concentration and decrease with temperature. This shows that calcium fluoride has structure making nature in dimethyl formamide. The equivalent conductance is found to decrease with concentration and increase with temperature. Variation of Ln(πiv/Λ) with Cp and Temperature of solutions are shown in Figs (3&4).They are linear. It proves the validity of the equations (1&2). Thus, the equivalent conductance depends directly on cohesive energy barrier and inversely on the exponential function of concentration potential or temperature [5&6]. Table No.1 Internal Pressure of CaF₂ ₂₂ ₂+DMF System in Atmos Cp 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C 0.00 4285.39 4247.75 4227.99 4183.18 4160.36 0.15 4364.37 4393.29 4407.89 4375.46 4284.89 0.30 4526.47 4548.88 4547.09 4539.65 4405.31 0.45 4715.52 4682.75 4669.87 4648.75 4544.94 0.60 4881.94 4884.71 4893.27 4854.91 4776.42 0.75 4988.41 4985.62 5054.13 4977.67 4890.32 0.90 5133.99 5090.54 5140.88 5097.75 5011.47 1.00 5256.91 5169.61 5223.81 5135.45 5104.55 Table No.2 Equivalent Conductance of CaF₂ ₂₂ ₂+DMF System in cm²/ohm Cp 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C 0.15 23.4955 28.8283 33.4849 36.5429 43.6699 0.30 21.4581 25.4338 27.8562 30.9453 32.2826 0.45 16.5792 20.0249 21.4906 23.9589 25.7584 0.60 14.9031 18.0374 19.8382 21.9684 23.7329 0.75 14.2359 16.1376 17.3905 20.1298 21.3225 Internal Pressure of CaF+DMF System Variation of Ln(πiv/Λ) with Cp of 4000 4500 5000 5500 0 0.5 1 I n t e r n a l P r e s s u r e A t m o s Concentration Potential CaF₂+DMF 0.90 12.4907 1.00 12.6085 Fig :1 Fig 3 Fig 4 REFERENCES 1. John E. Mc Grady, Michael.P.and Mingos D.J.Chem. Soc. Perkin Trans., 2 (1995), 228. 2. Suryanarayana, CV.J.IndianchemSoc (1982)562 3. Glasstone S. Introduction to Electrochemistry’ Litton educational Publishing Inc.New York, 82, (1942) 4. Suryanarayana, C.V.Aruna, P. and Natarajan, s.: Ind. J. Tech.Vol.29, 327 5. Ganthimathi k. ‘Proton Relaxation Rate, Free Volume and Equivalent Conductance as functions of Internal Pressure in Aqueous Electrolytes’ , Ph.D.Thesis, Bharathidasan University (1992) 6. Dhanalakshmi A.Lalitha V.and Ganthimathi K., J. Acoust. Soc. Ind.Voi.XXI, 1993, 219 Internal Pressure of +DMF System Equivalent Conductance of CaF+DMF System Λ) with Cp of Variation of Ln(πiv/Λ Temperature of CaF+DMF 8.5 9 9.5 10 10.5 30 40 50 L n ( π i v / Λ ) Temperature ⁰c CaF₂+DMF 10 20 30 40 50 0 0.5 E q u i v a l e n t C o n d u c t a n c e c m ² / o h m Concentration Potential CaF₂+DMF 1 Concentration Potential 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C 14.6493 16.2358 18.4618 13.9104 15.4907 17.3378 Fig 2 Fig 3 Fig 4 E. Mc Grady, Michael.P.and Mingos D.J.Chem. Soc. Perkin Trans., 2 (1995), 228. Suryanarayana, CV.J.IndianchemSoc (1982)562 Glasstone S. Introduction to Electrochemistry’ Litton educational Publishing Inc.New York, una, P. and Natarajan, s.: Ind. J. Tech.Vol.29, 327-333 (1991). Ganthimathi k. ‘Proton Relaxation Rate, Free Volume and Equivalent Conductance as functions of Internal Pressure in Aqueous Electrolytes’ , Ph.D.Thesis, Bharathidasan University (1992) kshmi A.Lalitha V.and Ganthimathi K., J. Acoust. Soc. Ind.Voi.XXI, 1993, 219 22 | P a g e Equivalent Conductance of m iv/Λ) with +DMF System 50 60 Temperature ⁰c 0 . 3 0 . 6 0 . 9 1 Concentration Potential 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C 20.0501 18.7657 E. Mc Grady, Michael.P.and Mingos D.J.Chem. Soc. Perkin Trans., 2 (1995), 228. Glasstone S. Introduction to Electrochemistry’ Litton educational Publishing Inc.New York, 333 (1991). Ganthimathi k. ‘Proton Relaxation Rate, Free Volume and Equivalent Conductance as functions of Internal Pressure in Aqueous Electrolytes’ , Ph.D.Thesis, Bharathidasan University (1992) kshmi A.Lalitha V.and Ganthimathi K., J. Acoust. Soc. Ind.Voi.XXI, 1993, 219-222 23 | P a g e EFFECT OF ELECTRONEGATIVITY ON FREE VOLUME AND VANDERWAALS CONSTANT OF BINARY AND TERNARY LIQUID MIXTURES K. Vijayalakshmi and C.Ravidhas Department of physics, Bbishop Heber College, Tiruchirappalli, Tamil nadu, India Abstract Ultrasonics is an interesting field of study which makes an effective contribution to many areas of human endeavor. In the recent years many attempts have been made in the field of physical acoustics and ultrasound on solids, liquids and gases . One of two fundamental types of solute–solvent intermolecular interactions are the specific interactions, such as hydrogen bonding complexation between solute and solvent. The free volume is an important quantity that determines the nature and strength of various inter molecular interaction in binary and ternary liquid mixtures.In the present work,the ultrasonic velocity measurements of binary and ternary liquid mixtures of Dioxane, Lactic acid and n-alcohols have been carried out at 25 0 C temperature using Interferometer technique. From the measured values of density, viscosity and ultrasonic velocity, the thermodynamic and acoustic parameters such as free volume Vf and Vander waals constant b have been evaluated. These parameters were successfully employed to understand the nature of molecular interaction between the interacting components in the mixtures. In Lactic acid – Alcohol systems ,the free volume increases with percentage of alcohol due to mutual destruction of association between Lactic acid and alcohol molecules. In all the other ternary systems, Vf decreases throughout the entire concentration and the Vander waals constant curves are non linear It was observed that the depolymerisation increases the free volume and electrostatic attraction and association reduces the free volume. Moreover an increase in the value of b due to increase in the hydro carbon chain shows a reduction in the free volume. Keywords: Thermodynamic parameters, molecular interaction, Hydrogen bonding. 1 Introduction Ultrasonics is an interesting field of study which makes an effective contribution to many areas of human endeavor. In the recent years many attempts have been made in the field of physical acoustics and ultrasound on solids, liquids and gases .Ultrasonic velocities and derived thermodynamic parameters are of considerable interest in understanding the nature and strength of various intermolecular interaction, formation of Hydrogen bonding etc. [1]. In the present case, work undertaken is to study the thermo- 24 | P a g e acoustical behavior of binary and ternary liquid mixtures of n-alcohols with Lactic acid and Dioxane from the variation of Vanderwaal’s constant b and Free volume Vf. 2. Materials and Methods Binary liquid mixtures of n-alcohols (from Methanol to Hexanol) with Dioxane and Lactic acid and ternary mixtures of Lactic acid, Dioxane and n-alcohols of various proportions are prepared by volume. Ultrasonic velocity of the mixtures are measured using Mittal type Ultrasonic Interferometer of fixed frequency 2MHZ [2]. Using Specific Gravity bottle and Kenon-Fenske Viscometer, density and viscosity of the mixtures are measured. A constant temperature bath with a compressor unit is used for maintaining the temperature constant at 25°C. 3.Theory From the measured values of density ρ, viscosity η and ultrasonic velocity u, the Free volume and Vander waals constant are computed [3]. Free Volume Vf = 2 3 η K Mu Vander Waals constant b = | | ¹ | \ | − + − 1 3RT Mu 1 Mu RT 1 ρ M 2 2 where M is the effective molecular weight of the mixtures, k a constant = 4.28 x 10 9 independent of temperature and nature of the system, R the universal gas constant and T the absolute temperature. 4. Results and Discussion Free volume is the free space available for the molecule to move. The free volume is the effective volume in which the molecules in the liquid can move and obey perfect gas law. The change in the size and shape of the molecules results in structural rearrangement of the molecules in the mixture. These structural changes feature in different types of interaction between like and unlike molecules, during the mixing of liquids [4]. The free volume of Lactic acid is less and Dioxane is more. However the free volume of n-alcohols decreases as the hydrocarbon chain increases. Due to overall increase in size of the molecules, their 25 | P a g e Brownian motion may be affected [5]. Since the molecules are large, they occupy more volume and hence the free space for their movement is reduced. So the free volume available for their movement is decreased as the chain length increases from Methanol to Hexanol .This is reflected in the values of Vander waals constant b, since b may be even 4 times greater than the molar volume [6]. So an increase in the value of b suggests a reduction in the free volume Vf of the alcohols. Alcohol-Dioxane system shows an exponential increase in the value of free volume (Fig.1). As the free volume of alcohols is in the order Methanol > Ethenol > Propanol > Butanol > Pentanol > Hexanol, the Vf curve goes low as we go from Methanol to Hexanol. The variation of Vanderwaals constant b (Fig. 2), indicates the specific interaction between alcohol and Dioxane molecules. In Lactic acid – Alcohol systems [Fig. 3], the free volume increases with percentage of alcohol due to mutual destruction of association between Lactic acid and alcohol molecules [7].The variation of Vanderwaals constant b is non-linear in Lactic acid - Alcohol Systems [Fig 4]. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 140 0 10 20 30 40 50 60 70 80 90 100 M : D E : D 1. FIG. 1 FREE VOLUME OF Fig. 2 Vander Waal’s Constant of Alcohol – Dioxane system 2 . F R E E V a n d e r W a a l ’ s C o n s t a n t ( b ) 26 | P a g e % of Alcohol by volume 8. FIG . 7 FREE VOLUME 6 . F R E E % of Dioxane by volume 11. FIG. 5 FREE VOLUME 1 0 . F R E E 60 65 70 75 80 85 90 0 10 20 30 40 50 60 70 80 90 100 L: D % of Dioxane by volume 9. FIG. 6 VANDER WAAL’S V a n d e r W a a l ’ s C o n s t a n t ( b ) 40 45 50 55 60 65 70 75 80 85 90 0 10 20 30 40 50 60 % of Alcohol by volume 7. FIG. 8 VANDER WAAL’S V a n d e r W a a l ’ s C o n s t a n t ( b ) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 10 20 30 40 50 60 70 80 90 100 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 10 20 30 40 50 60 L:D:M L: D:E L: D:P L: D:B L:D:P e L: D:H 27 | P a g e The variation of free volume and Vander waals constant in Lactic acid – Dioxane system [Fig 5, 6], indicates the possible breaking of hydrogen bonds at higher Dioxane contents[8].That is the variation of Vf and b with % of solvent shows an exponential behavior, indicating the possible breaking of hydrogen bonds at higher Dioxane contents. In Lactic acid – Dioxane - Alcohol systems the free volume rise initially at 10% o Methonal and thereafter Vf decreases. In all the other ternary systems, Vf decreases throughout the entire concentration (Fig 7), and the Vander waals constant curves are non linear (Fig 8). From the above observation, it is found that the depolymerisation increases the free volume and electrostatic attraction and association reduces the free volume [9]. Moreover an increase in the value of b due to increase in the hydro carbon chain shows a reduction in the free volume. 5. References 1. Rahmat Sadeghi, Roushan Khoshnavazi and Hana Parhizkar, Fluid Phase Equilibria, 260 (2007) 335. 2. Beyer R T and Letcher S V, (1969),Physical Ultrasonics, Academic Press,65. 3. Papadakis E P,(1976), Physical Acoustics:Principles and Methods, Academic Press New York,12,277-374. 4. Manish S. Kelkar, Jake L. Rafferty, Edward J. Maginn , and J. Ilja Siepmann, Fluid Phase Equilibria 260 ( 2007) 218. 5. Neena Jaggi and Jaiswal R M P.,(2001), Ind J Pure and Appl phys, 39, 122-129. 6. Lalitha, V., (1998), J. Acoust. Soc. Ind. Vol. XXVI, No. 324, pp. 133-138. 7. Baral K K and Mandal R K.,(1998), J Pure and Appl Ultrasonics, 20 , 39 8. Thakare J B., Dongre D T and Deogaonkar,(2000), J Acoust Soc Ind, 28, 365 9. Vijayalakshmi K., (2001), J Acoust Soc Ind, 29, 136 28 | P a g e ULTRASONIC STUDIES OF NN'-METHYLENE BIS-ACRYLAMIDE IN WATER T.Mathavan 1* , S.Umapathy 2 , M.A.Jothi Rajan 3 , A. Alfred Nobel Antony 1 , X.Dolour Selvarajan 1 , J.Hakkim 1 , V.Stephen Raja 1 1 Department of Physics, NMSSVN College, Nagamalai, Madurai - 625 019, India. 2 School of Physics, Madurai Kamaraj University, Madurai – 625 021, India. 3 Department of Physics, Arul Anandar College, Karumathur – 625 514, India. Corresponding author. E-mail address:
[email protected] ABSTRACT: NN'-Methylene bis-acrylamide (NN'MBA) is dissolved in water and its physical parameters such as isentropic compressibility(Ks), adiabatic modulus(B), intermolecular free length(Lf), relaxation time(τ), absorption coefficient(α/f 2 ), attenuation constant(α), molar volume(V), free volume(Vf), internal pressure(πi), acoustic impedance(Z), Gibbs energy(G), Rao’s number(R) and Wada’s constant(W) were determined and studied. The acoustic measurements were carried out for four different concentrations at temperatures 308 K, 313 K, 318 K and 323 K. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions. KEYWORDS: Thermodynamics, ultrasonic velocity and viscosity. 1. 1. INTRODUCTION The ultrasonic studies are extensively used to estimate the thermodynamic properties and predict the intermolecular interactions of binary mixtures [1-3]. The sound velocity is one of those physical properties that help in understanding the nature of liquid state. Hence an attempt is made to study the interaction of NN'MBA in water. 29 | P a g e 2. EXPERIMENTAL ANALAR GRADE (AR) SAMPLE OF NN'MBA SUPPLIED BY S.D.FINE-CHEM. LTD., (BOISAR 401501) HAVING MOLECULAR WEIGHT 154.17G/MOLE AND CHEMICAL FORMULA (CH2:CH.CO.NH)2CH2 WAS USED AS SUCH WITHOUT FURTHER PURIFICATION. WATER, DOUBLY DISTILLED OVER ALKALINE PERMANGANATE IN ALL GLASS APPARATUS WAS USED AS THE SOLVENT FOR PREPARING THE SOLUTION. SINGLE FREQUENCY ULTRASONIC INTERFEROMETER (M/S. MITTAL ENTERPRISES, DELHI, INDIA, MODEL F81, 2 MHZ) AND CONSTANT TEMPERATURE WATER BATH (M/S. TOSHNIWAL BROTHERS, INDIA) TO AN ACCURACY OF 0.01 C WERE USED FOR ULTRASONIC VELOCITY MEASUREMENTS. THE REQUIRED CONCENTRATIONS OF THE SOLUTION (0.5, 1.0, 1.5, 2.0ML -1 ) WERE PREPARED AND THE MEASUREMENTS WERE TAKEN FOR 308 K, 313 K, 318 K AND 323 K OBTAINED BY WEIGHING THE SOLUTE BY A DIGITAL BALANCE (ACCURACY 0.001G) AND MIXING WITH THE ALREADY PURIFIED WATER IN GLASS BEAKERS, WHICH WERE CLEANED AND DRIED BEFORE USE. Densities of the solutions were measured by specific gravity bottle of capacity 5ml to an accuracy of 0.1 kgm -3 . Viscosities of the solutions were measured by pyknometer to an accuracy of 0.05%. 3. ACOUSTICAL PARAMETERS The ultrasonic velocity (U), viscosity( and density( measurements are extensively used to study the physical, chemical behavior of liquid solutions. In this work the following parameters were determined. 1. Isentropic compressibility Ks = (U 2 ) -1 ----- (1) 2. Adiabatic bulk modulus B = 1/ Ks ----- (2) 3. Intermolecular Free length Lf = k/( U 2 ) ----- (3) k is the temperature dependent constant. 4. Relaxation time = 4 / 3 U 2 ----- (4) 5. Absorption co-efficient /f 2 = 8 2 /3U 3 ----- (5) 6. Attenuation co-efficient = 8 2 f 2 /3U 3 ----- (6) 7. Molar volume (V) V= Meff/ ----- (7) Meff = X1M1+X2M2 30 | P a g e where is the density of the solution, Meff is the effective mass of the binary liquid, X1 is the mole fraction of the water, X2 is the mole fraction of NN'MBA, M1 is the molecular weight of water, and M2 is the molecular weight of NN'MBA. 8. Free volume (Vf) Vf = (Meff U/k) 3/2 ----- (8) 9. Internal pressure i = bRT(k/U) 1/2 2 / 3 / Μ 7/6 eff ----- (9) where R is the universal gas constant and b=1.78 (fcc). 10. Specific Acoustic Impedance Z= U ----- (10) 11. Gibbs free energy G = RT ln (V/hNa) ----- (11) where h is the Planck’s constant and Na is the Avogadro number. 12. Rao’s number R = Meff U 1/3 / ----- (12) 13. Wada’s constant W = Meff K -1/7 / ----- (13) 4. RESULTS AND DISCUSSION Ultrasonic velocity (U) in the solution varies according to the molecular interactions in it. Ultrasonic velocity in water of NN'MBA shows a general increase in temperature (Fig.1), indicating breaking up of hydrogen bonds as temperature rises. It is observed from the fig. 2 that Ks varies linearly for 308 K and 318 K for all concentrations, whereas Ks varies non-linearly for temperatures 313 K and 323 K for all concentrations. The non-linear increase and decrease in Ks values with concentration indicates significant molecular interactions (association) between the component unlike molecules [4, 5]. In the present investigation as shown in figure 3, it has been observed that intermolecular free-length decreases as concentration increases for all temperatures (308 K, 318 K) except for the temperatures 313 K and 323 K where the free length decreases up to 1%, 1.5% concentrations respectively, and then increases as concentration increases. The minimum observed at 313 K in the concentration 1.5% is shifted to the concentration 1% when the temperature is increased to 323 K. The difference in free length of 0.01A between these two temperatures indicates significant interactions between the components unlike molecules. Therefore Lf decreases with increase in the volume of water in the solution [6, 7]. Relaxation occurs in liquids and can be either thermal relaxation type as found in gases or of the type due to structural rearrangement of the molecules which are usually associated with longer chain molecules. Longitudinal propagation of waves involves the compressional modulus, which is generally considerably larger than the shear modulus. The classical absorption of ultrasound arises because the propagating wave loses energy in overcoming the shear viscosity and thermal conductivity of liquids. However the attenuation due to shear 31 | P a g e viscosity will be a significant contribution. In the present investigation the relaxation time fluctuates in between 9.4 x 10 -5 s for 313 K and 8.5 x 10 -5 s for 323 K, for low and high concentrations respectively as shown in fig 4. In the present study the absorption coefficient α/f 2 decreases with increase in concentration of the solution in general. But it is observed for the temperatures 313 K at 1.5% there is a minimum and at 323 k at 1.0% there is a minimum respectively. There is a shift of 1.5% to 1% with the corresponding shift in absorption coefficient of 0.01x10 -10 Nms -2 as shown in fig. 5. As the ultrasonic waves pass through the experimental solution, the hydrogen bonds are weakened or broken during compression. The variation of the attenuation coefficient with respect to the variation of concentration and temperature is as shown in fig. 6. The molar volume almost remains constant with increase in the concentration of the solution as in fig. 7. Even when the temperature is increased there is a very small increase in the molar volume for various concentrations. Free volume of NN'MBA solution shows a general increase in raise of temperature but the free volume almost remains constant for all the concentration range as shown in fig. 8. When free volume is minimum it is inferred that close packing of molecules inside the shell which may be brought about by the formation of associated complexes due to hydrogen bonding [8]. Internal pressure is a single factor, which appears to vary due to all the internal interactions [9]. Variations of internal pressure of aqueous solutions of NN’MBA at various concentrations and at different temperatures were shown in fig. 9. Internal pressure shows a general decrease with increase in temperature. These suggest that cohesive forces decrease with increase in temperatures [10]. Specific acoustic impedance is similar to the index of refraction in optics. In the present investigation the specific acoustic impedance increases with increase in concentration almost linearly as shown in fig. 10. The same trend is observed when the temperature is increased except for 323K where there is a maximum at 1% concentration. The decreasing trend after 1% of concentration may be due to the change of dielectric constant of the medium (solute-solvent). From the fig. 11 it is observed that the Gibbs free energy increases slightly with increase in concentration. There is appreciable increase in the Gibbs free energy with the increase in temperature for a constant concentration of the solution. This agrees very well with the theory. Rao’s number gives an idea of how the molecular interactions change (i.e., from weak to strong and vice-versa). An analysis of the experimental data shows that Rao’s constant is almost constant up to 1.75% of the solution and thereafter decreases abruptly as shown in Fig.12. This indicates that the strength of the bond is slowly shifting from higher strength to lower strength. Wada’s 32 | P a g e 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1520 1525 1530 1535 1540 1545 1550 1555 1560 1565 1570 1575 V e lo c it y , m s -1 Mole concentration,M 308K 313K 318K 323K constant also gives an idea of the changing nature of the molecular interaction i.e., they are weak or strong interactions (fig. 13). 2. 5. CONCLUSION For NN'MBA in water for different concentrations the velocities of ultrasonic waves were determined at a fixed frequency 2MHz, for four different temperatures. The various parameters calculated in this work are the premises of the study of interactions and complex formation in solutions. Figure 1 Acoustic velocity Vs Mole concentration . Figure 2 Adiabatic compressibility Vs Mole concentration. Figure.3 Free length Vs Mole concentration . Figure.4 Relaxation time Vs Mole concentration. Figure.5 Absorption coefficient Vs Mole concentration. Figure.6 Attenuation constant Vs Mole concentration. Figure.7 Molar Volume Vs Mole concentration. Figure.8 Free volume Vs Mole concentration . Figure.9 Internal pressure Vs Mole concentration. 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 4.0 4.2 4.4 4.6 4.8 5.0 A d ia b a tic c o m p r e s s ib ility x 1 0 -1 0 m 2 N -1 Mole concentration,M 308K 313k 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 R e la x a tio n tim e x 1 0 -1 0 S Mole concentration,M 308k 313K 318k 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.404 0.406 0.408 0.410 0.412 0.414 0.416 0.418 0.420 0.422 0.424 0.426 0.428 F re e le n g th , A 0 Mole concentration,M B C D E 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.106 0.108 0.110 0.112 0.114 0.116 0.118 0.120 0.122 0.124 0.126 0.128 A b s o r p tio n c o e ffic ie n tx 1 0 -1 0 m s -2 Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 43 44 45 46 47 48 49 50 51 A tte n u a tio n c o n s ta n t Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.0176 0.0177 0.0178 0.0179 0.0180 0.0181 0.0182 0.0183 0.0184 0.0185 M o la r v o lu m e m l/ m o l Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 70 72 74 76 78 80 82 84 86 88 F r e e v o lu m e x 1 0 -1 0 m l/ m o l Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 3.32 3.34 3.36 3.38 3.40 3.42 3.44 3.46 3.48 In te r n a l p r e s s u r e x 1 0 7 a m u Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1.50 1.52 1.54 1.56 1.58 1.60 A c c o u s tic a l im p e d a n c e x 1 0 -6 k g m -2 s -1 Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 6.42 6.44 6.46 6.48 6.50 6.52 6.54 6.56 6.58 6.60 6.62 6.64 6.66 6.68 6.70 6.72 G ib b 's e n e r g y X 1 0 4 R T u n its Mole concentration,M 308K 313K 318K 323K 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.203 0.204 0.205 0.206 0.207 0.208 0.209 0.210 0.211 0.212 0.213 0.214 0.215 0.216 0.217 0.218 0.219 0.220 R a o 's c o n ta n tx m 3 m o l -1 m s -1 Mole concentration,M 308K 313K 318K 323K 33 | P a g e Figure.10 Acoustical impedance Vs Mole concentration. Figure.11 Gibb’s energy Vs Mole concentration . Figure.12 Rrao’s constant Vs Mole concentration. Figure.13 Wadd’s constant Vs Mole concentration. 6. References 1. A V Rao, G K Raman and A V Rajulu, ‘Acoustical parameters of polystyrene in Binary mixture’, Asian Journal of Chemistry, Vol 5, p 582, 1993. 2. Kch Rao, A V Rajulu and S V Naidy, ‘Acoustical parameters of poly (trinyl pyrrolidone)’, Acta Polymer, Vol 40, p 743, 1989. 3. S Das, R P Singh and S Math, ‘ultrasonic velocities and Rao formalism in Solutions of Poly (ester - imides)’, Polymer Bulletin, Vol 2, p 400, 1980. 4. R J Fort and W R Moore, Trans. Faraday Society, 61, p 2102, 1965. 5. B Garcia, R Alcalde, J M Leal and J S Matos, Journal of Chemical Society, Faraday Trans, 92, p 3347, 1996. 6. Subba Rao and R Gopal Krishnan, Journal of Acoustical Society of India, Vol 7, p 5, 1979. 7. S M Gaour, J S Tomav and R P Varma, Indian Journal of Pure and Applied Physics, Vol 24, p 602, December 1986. 8. K Ganapathy and D Anbanathan, “Ultrasonics Investigations of Organic Liquid Mixtures”, Journal of Acoustic Society of India, 15,1:pp 213-220, 1987. 9. E Jasmine Vasnatha Rani and R Padmavathy, “Analysis of Thermodynamical and Electrochemical Properties of Potassium Bromide in Formamide”, Journal of Acoustical Society of India, 28, 1-4, pp 329-332, 2000. 10. D Muraliji, S Sekar, A Dhanalakshmi and A R Rankuna, “Internal Pressure and free Volume in Phenols”, Journal of Acoustical Society of India, 29, 2-4:270-274, 2001. 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0.384 0.386 0.388 0.390 0.392 0.394 0.396 0.398 0.400 0.402 0.404 0.406 W a d d 's c o n s t a n t x m 3 m o l -1 N m -2 Mole concentration,M 308K 313K 318K 323K 34 | P a g e DETERMINATION OF ULTRASONIC INTERACTION PARAMETER FOR POLY (ACRYLIC ACID) IN WATER T.Mathavan 1* , S.Umapathy 2 , M.A.Jothi Rajan 3 , B.Valarmathi 2 1 Department of Physics, NMSSVN College, Nagamalai, Madurai - 625 019, India. 2 School of Physics, Madurai Kamaraj University, Madurai – 625 021, India. 3 Department of Physics, Arul Anandar College, Karumathur – 625 514, India. * E-mail:
[email protected] ABSTRACT: Ultrasonic interaction parameter measurements have been made for poly (acrylic acid) in water solutions at 1MHz, 4MHz and 5MHz. We report the results for weight concentrations 0.12, 0.36, 0.60 and 0.84 g/100ml at various temperatures 35 0 C, 40 0 C, 45 0 C and 50 0 C. In this work it has been found that the effect of interchain forces strengthened interaction between polymer- solvent molecules, which serve to vary the interaction parameter. Neverthless, remarkable similarities exist between the interaction parameters obtained from viscometric and relaxation time values. The decreasing interaction parameter values have shown the effects of increasing temperatures. 1. INTRODUCTON Ultrasonic absorption measurements for Poly (acrylic acid) (PAA) in water can be attributed to shear viscosity and possibly, to structural relaxation, which relates to the complex molecular formation [1-4]. In this report, the study of interaction parameter using the change in Gibb’s free energy employing the viscosity and relaxation- time values is reported [5]. For a high polar polymer, PAA in a high polar solvent, water, the ultrasonic investigations have shown the interesting result of strengthening in association and the interaction effects and the influence of a macromolecule on the other molecules. The measurements have been discussed about the interaction of molecules indirectly [1-4]. We report here the interaction 35 | P a g e parameter values for PAA in water which exist the structure changes for increasing concentration and also present the effects of varying the temperature of the system. 1.1 Theory The properties of polymer solution depend both on the nature and size of the polymer chains and also on the interaction between polymer and solvent molecules. The interaction parameter χ measures the extent with which the polymer interacts with the solvent. Flory-Huggins proposed the method of estimation of the interaction parameter from relative vapour pressure and by osmotic pressure of solution [5]. The thermodynamic property Gibb’s free energy is used to estimate the interaction parameter, which can be expressed as ∆G-G1Φ1 χ = ------------------ n1Φ2 where ∆G is the free energy per unit mole of the solution, G1 is the free energy of the solvent, n1 is the number of solvent molecules, Φ1 and Φ2 are the respective volume fractions of the solvent and the polymer [6]. The literature values of viscosity and relaxation time and the estimated values of χ were shown in tables I - IV. Table I. Calculated interaction parameter values of PAA in water at 35° °° °C. Frequency ΜΗz Concentration Weight % Viscosity η * 10 3 Nsm -2 Relaxation time τ * 10 12 sec χ From η from τ 1 0.0 0.7194 0.4178 - - 1.2 1.2928 0.74781 0.0492 0.0412 3.6 1.5694 0.90667 0.0157 0.0130 6.0 1.6968 0.97847 0.0093 0.0077 8.4 1.9483 1.1267 0.0064 0.0053 4 0.0 0.7194 0.41638 - - 1.2 1.2928 0.75493 0.0492 0.0409 3.6 1.5694 0.91702 0.0157 0.0129 36 | P a g e 6.0 1.6968 0.99431 0.0093 0.0076 8.4 1.9483 1.1355 0.0064 0.0052 5 0.0 0.7194 0.41290 - - 1.2 1.2928 0.75255 0.0492 0.0404 3.6 1.5694 0.91010 0.0157 0.0128 6.0 1.6968 0.97285 0.0093 0.0075 8.4 1.9483 1.198 0.0064 0.0052 Table II. Calculated interaction parameter values of PAA in water at 40° °° °C. Frequency ΜΗz Concentration Weight % Viscosity η * 10 3 Nsm -2 Relaxation time τ * 10 12 sec χ From η from τ 1 0.0 0.6529 0.37524 - - 1.2 1.0772 0.61701 0.0455 0.0377 3.6 1.4138 0.80928 0.0142 0.0116 6.0 1.5526 0.88609 0.0083 0.0068 8.4 1.7606 1.0094 0.0058 0.0046 4 0.0 0.6529 0.37711 - - 1.2 1.0772 0.61573 0.0455 0.0380 3.6 1.4138 0.82472 0.0142 0.0116 6.0 1.5526 0.89423 0.0083 0.0068 8.4 1.7606 1.0186 0.0058 0.0047 5 0.0 0.6529 0.37047 - - 1.2 1.0772 0.61460 0.0455 0.0370 3.6 1.4138 0.82147 0.0142 0.0113 6.0 1.5526 0.88655 0.0083 0.0066 8.4 1.7606 1.02730 0.0058 0.0045 Table III. Calculated interaction parameter values of PAA in water at 45° °° °C. Frequency ΜΗz Concentration Weight % Viscosity η * 10 3 Nsm -2 Relaxation time τ * 10 12 sec χ From η from τ 0.0 0.5960 0.33877 - - 1.2 0.9514 0.54348 0.0416 0.0535 3.6 1.1574 0.65702 0.0132 0.0172 6.0 1.3771 0.78369 0.0075 0.0099 8.4 1.6120 0.92001 0.0051 0.0068 4 0.0 0.5960 0.34181 - - 37 | P a g e 1.2 0.9514 0.54094 0.0416 0.0344 3. 1.1574 0.66599 0.0132 0.0107 6.0 1.3771 0.78635 0.0075 0.0061 8.4 1.6120 0.91666 0.0051 0.0041 5 0.0 0.5960 0.33667 - - 1.2 0.9514 0.54052 0.0416 0.0335 3.6 1.1574 0.66451 0.0132 0.0104 6.0 1.3771 0.77943 0.0075 0.0059 8.4 1.6120 0.92216 0.0051 0.0040 Table IV. Calculated interaction parameter values of PAA in water at 50° °° °C. Frequency ΜΗz Concentration Weight % Viscosity η * 10 3 Nsm -2 Relaxation time τ * 10 12 sec χ From η from τ 1 0.0 0.5468 0.30825 - - 1.2 0.9263 0.51812 0.0369 0.0295 3.6 1.1003 0.62414 0.0117 0.0092 6.0 1.3209 0.75545 0.0066 0.0051 8.4 1.5217 0.86244 0.0045 0.0035 4 0.0 0.5468 0.31207 - - 1.2 0.9263 0.52527 0.0369 0.0301 3.6 1.1003 0.63429 0.0117 0.0091 6.0 1.3209 0.75880 0.0066 0.0052 8.4 1.5217 0.85489 0.0045 0.0036 5 0.0 0.5468 0.30873 - - 1.2 0.9263 0.52500 0.0369 0.0295 3.6 1.1003 0.62236 0.0117 0.0092 6.0 1.3209 0.74206 0.0066 0.0052 8.4 1.5217 0.86558 0.0045 0.0035 2. DISCUSSION An important finding in this investigation was giving the result in numerical scale of inter/intra molecular interactions as a single parameter χ although the other parameters were there. The negative values of χ reveal explicitly the strong attractive interaction between interchain molecules [6]. As both PAA and water are strong polar molecules, it might be expected to show decreasing values of χ for increasing 38 | P a g e concentrations. Similar behaviour is seen with the χ values of increasing temperatures. This interaction χ is a measure of the polymer-solvent interaction [7]. Here the interaction may be between (monomer) units or groups of (monomer) units. In more concentrated solutions, direct segment-segment interactions may exist 3. CONCLUSION The interaction parameter values obtained from thermodynamic property Gibbs free energy for poly (acrylic acid) in water which exhibits structure changes for increasing concentration. The effects of varying the temperature of the system are also reported. 4. REFERENCES 1. J.H.So, R.Esquivel-Sirvent, S.S.Yun and F.B.Stumpf, “Ultrasonic velocity and Absorption Measurements for Poly (acrylic acid) and Water Solutions”, J Acoust. Soc. Am. 98 (1), 659-660 (1995). 2. S.K.Hassun, Acoustics Letters, 12(9), 161-165(1989). 3. P.Vigoureuse, Ultrasonic, John Wiley & Sons, New York, 32(1951). 4. B.Valarmathi, “Ultrasonic Investigations of Poly (acrylic acid) in water ”, M.Phil Dissertation, School of Physics, Madurai Kamaraj University, India, (1997). 5. S.Kalyanasudaram and J.Hemalatha, “Ultrasonic studies on PVC in Chlorobenzene,” J.Plym.Mater.14, 285-289(1997). 6. P.J.Flory, “Thermodynamics of High Polymer Solutions,” J.Chem.Phys.10, 51(1942). 7. R.A.Orwoll and P.A.Arnold, “Phys Prop Poly.Hand Book,” AIP Press, Newyork, 170(1996). 8. A.M.Bell, W.North, R.A.Pethrick and P.B.Jeik, J.Chem.Soc.Faraday Trans 11, 75, 1115(1979). 39 | P a g e ULTRASONIC INVESTIGATIONS OF N-METHYLPYRROLIDONE IN 1-PROPANOL T.Mathavan 1* , S.Umapathy 2 , M.A.Jothi Rajan 3 , S.Gokila 1 , M.Abirami 1 , R.Hemalatha 1 , S.K.Dravida Selvi 1 1 Department of Physics, N.M.S.S.Vellaichamy Nadar College, Nagamalai, Madurai - 625 019, India. 2 School of Physics, Madurai Kamaraj University, Madurai – 625 021, India. 3 Department of Physics, Arul Anandar College, Karumathur – 625 514, India. * Corresponding author. E-mail :
[email protected] 3. Abstract: LOW POWER ULTRASONIC TECHNIQUE IS ONE OF THE MOST POWERFUL AND USEFUL NONDESTRUCTIVE TESTING TOOLS TO INVESTIGATE PROPERTIES OF SOLUTIONS. THE LOW POWER ULTRASONIC MEASUREMENTS ARE CARRIED OUT AT FIVE DIFFERENT CONCENTRATIONS AND AT TWO DIFFERENT TEMPERATURES FOR N-METHYLPYRROLIDONE IN 1-PROPANOL. THE ACOUSTICAL AND THERMODYNAMICAL PARAMETERS ARE COMPUTED ON THE BASIS OF EXPERIMENTALLY DETERMINED VALUES OF ULTRASONIC VELOCITY, DENSITY AND VISCOSITY. N-METHYLPYRROLIDONE (NMP) IS MIXED WITH 1-PROPANOL AND ITS PHYSICAL PARAMETERS SUCH AS DENSITY, VISCOSITY AND VELOCITY WERE MEASURED EXPERIMENTALLY. FROM THESE VALUES THE EXCESS PROPERTIES SUCH AS η E , βA E , LF E , V E AND ПI E ARE FOUND OUT AND THESE GIVE INSIGHT ABOUT THE NATURE OF THE INTERMOLECULAR ASSOCIATION BETWEEN THE NMP AND 1- PROPANOL. KEYWORDS: NMP, 1-Propanol, low power ultrasound, Thermodynamical parameters, Excess parameters. 40 | P a g e 4. 1. INTRODUCTION N-Methylpyrrolidone (NMP) is a dipolar aprotic solvent. Large amounts of NMP are consumed in the polymer industry as a medium for polymerization and as a solvent for finished polymers. The study of propagation of ultrasonic waves in liquids and liquid mixtures is well established for examining the nature of molecular interactions [1-7]. Ultrasonic velocity studies on NMP in 1-propanol may reveal its suitability of being used as coating agent in aircrafts under high pressure and various atmospheric conditions. In this work an attempt is made to study the interaction of NMP in 1-propanol for five different concentrations and two different temperatures by measuring the various thermodynamics parameters. 2. Experimental 2.1. Apparatus Analar grade sample of NMP supplied by s.d.fine-chem. Ltd., (BOISAR 401501) having molecular weight 99.13g/mole and chemical formula (CH2: CH.CO.NH)2CH2 is used as such without further purification. 1-Propanol, doubly distilled over alkaline permanganate was used as the solvent for preparing the solution. Single frequency (2 MHz) ultrasonic interferometer (M/S. Mittel Enterprises, Delhi, India, Model F81) was used for ultrasonic velocity measurements and the measured intensity was 5.5W/cm 2 . This works on the principle of piezo-electric effect and imparts ultrasonic waves into the solution in a 12 ml thermostatic cell. The solutions of different concentrations were prepared by weighing the solute by a digital balance (accuracy ±0.001g) and mixed with the already purified 1-propanol in cleaned and dried glass beakers. The required amount of the solution was placed in the cell and maintained at a predetermined temperature using a constant temperature water bath (M/S. Toshniwal Brothers, India) to an accuracy of ±0.01 ° C. Thus, velocity measurements were made for five different concentrations (0.2, 0.4, 0.6, 0.8 and 1.0 ML -1 ) of the experimental solution. For each concentration of the solution velocity measurements were made for two different (constant) temperatures (308 K and 313 K). Densities of the solutions were measured by specific gravity bottle of capacity 5ml to an accuracy of ±0.1 Kgm -3 . Viscosities of the solutions were measured by Oswald viscometer to an accuracy of ±0.05%. 2.2. Theory The ultrasonic velocity, viscosity and density measurements are extensively used to study the physical and chemical behavior of liquid solutions. Studies of excess thermodynamic functions such as excess viscosity, excess free length, excess adiabatic compressibility, excess molar volume and excess 41 | P a g e internal pressure are useful in understanding the nature of intermolecular interactions in liquid mixtures [1- 4]. The excess value of the above parameters provides the nature and strength of the interactions [5-7]. The non-zero values confirm the presence of interaction i.e., excess values are the indicators of magnitude of the relative strength of interaction. In this work the following parameters were determined: Excess viscosity (η E ) The excess viscosity is given by η E = η exp – [X1η1 + X2η2] ----- (1) where η exp is the viscosity of the solution, X1 is the mole fraction of NMP, X2 is the mole fraction of 1- propanol, η1 is the viscosity of pure NMP and η2 is the viscosity of pure 1-propanol. Excess free length (Lf E ) The excess free length is given by Lf E = Lf exp – [X1Lf1 + X2Lf2] ----- (2) where Lf exp is the free volume of the solution, X1 is the mole fraction of NMP, X2 is the mole fraction of 1- propanol, Lf1 is the free length of pure NMP and Lf2 is the free length of pure 1-propanol. Excess adiabatic compressibility (β E ) The excess adiabatic compressibility is given by β E = β exp – [X1β1 + X2β2] ----- (3) where β exp is the adiabatic compressibility of the solution, X1 is the mole fraction of NMP, X2 is the mole fraction of 1-propanol, β1 is the adiabatic compressibility of pure NMP and β2 is the adiabatic compressibility of pure 1-propanol. Excess Molar volume (V E ) The excess molar volume is given by V E = V exp – [X1V1 + X2V2] ----- (4) where V exp is the molar volume of the solution, X1 is the mole fraction of NMP, X2 is the mole fraction of 1- propanol, V1 is the molar volume of pure NMP and V2 is the molar volume of pure 1-propanol. Excess internal pressure (Пi E ) The excess internal pressure is given by Пi E = Пi exp – [X1Пi1 + X2Пi2] ----- (5) where Πi exp is the internal pressure of the solution, X1 is the mole fraction of NMP, X2 is the mole fraction of 1-propanol, Πi1 is the internal pressure of pure NMP and Πi2 is the internal pressure of pure 1-propanol. 3. Results and discussion 42 | P a g e The excess viscosity η E calculated shows the reverse trend of β E as shown in the Fig. 1. The excess free length of NMP with 1-propanol at two different temperatures 308K and 313K are found out. The variation of ultrasonic velocity in a solution depends upon the increase or decrease of intermolecular free length after mixing the components. In the present work the positive values of Lf E signify decreasing dipole- dipole interactions due to decreasing proton donating abilities. The positive Lf E values decrease with increase of temperature suggesting a decrease in hetero-association of molecules at elevated temperatures (Fig. 2) [8, 9]. The excess adiabatic compressibility of NMP with 1-propanol for two different temperatures 308K and 313K are studied (Fig. 3). The β E decreases as temperature increases. Positive values in excess properties correspond mainly to the existence of dispersion forces and a positive β E tending towards a negative one shows that the strength of interaction increases. In this case the tendency of change from positive values to negative values indicating the strong interaction between the unlike molecules [10]. The partial molar volume as a function of X1 suggests that these values are positive in the NMP+1- propanol system. In this system there may be a strong interaction between the 1-propanol molecules due to hydrogen bond and the addition of NMP may weaken the interactions. The observed value of V E can be qualitatively explained by considering the factor, which influences this excess function, namely the mutual disruption of associates present in the pure liquid (Fig.4). This factor contributes to positive value of V E , and also suggests that this effect is due to break up of dipolar association of NMP+1-propanol predominates over that of hydrogen bonding between unlike molecules making V E values positive (Fig. 4). The positive V E values can also be attributed to the weak dipole-dipole interaction leading to weak complex formation between unlike molecules [8]. The increase in negative values of Πi E suggests the predominance of hydrogen bonded interactions over the interstitial accommodation of component molecules at higher concentration of 1-propanol (Fig. 5) [11]. 4. Conclusion Acoustic investigations were carried out for five different mole concentrations of NMP+1-propanol system. When the concentration of the solution is increased, correspondingly its various physical parameters change considerably. Similar changes in physical parameters are also observed when the temperature of the solution is varied. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions. 43 | P a g e Fig. 1 Mole concentration vs Excess viscosity. Fig. 2 Mole concentration vs Excess freelength. Fig. 3 Mole concentration vs β E Fig. 4 Mole concentration vs V E 0.2 0.4 0.6 0.8 1.0 -0.050 -0.045 -0.040 -0.035 -0.030 -0.025 -0.020 -0.015 -0.010 -0.005 0.000 E x c e s s v i s c o s i t y , N s m -2 Mole concentration 308 K 313 K 0.2 0.4 0.6 0.8 1.0 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 L f E , A o Mole concentration 308 K 313 K 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 β β β β E , 1 0 - 1 0 m 2 N - 1 Mole concentration 308 K 313 K 0.2 0.4 0.6 0.8 1.0 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 V E , 1 0 -4 M -1 Mole concentration 308 K 313 K 0.2 0.4 0.6 0.8 1.0 -0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 π π π π Ε Ε Ε Ε , 1 0 1 0 a t m Mole concentration, M 308 K 313 K 44 | P a g e Fig. 5 Mole concentration vs П E 5. REFERENCES 1. A.V. Rao, G.K. Raman and A.V. Rajulu, ‘Acoustical parameters of polystyrene in Binary mixture’, Asian Journal of Chemistry, 5, (1993), 582. 2. Kch Rao, A.V. Rajulu and S.V. Naidy, ‘Acoustical parameters of poly (trinyl pyrrolidone)’, Acta Polymer, 40, (1989), 743. 3. S. Das, R.P. Singh and S. Math, ‘ultrasonic velocities and Rao formalism in Solutions of Poly (ester – imides)’, Polymer Bulletin, 2, (1980), 400. 4. R.A. Pethrick, ‘Acoustic studies of Polymer solutions’, Journal of Macromolecule Science Review, Macromolecule, Chemistry, C9, (1973), 91. 5. J. I. Dunbar, A.M. Pethnik and D.B. Steinhauer, ‘Acoustic Absorption of dilute solution of polystyrene in Toluene and cyclohexane’, Journal of Polymer Science, Physics Edition, 15, (1977), 263. 6. T. Boubbik, ‘Statistical Thermodynamics of Molecules’, Molecular Physics, 27, (1974), 1415-1477. 7. S.X. Sheng, J.Y. Huang, J. Li and O.P. Guo, ‘Phase Behavior and Properties of PMMA- Polyvinyl acetate’, Journal of Applied Polymer Science, 699(4), (1998), 675. 8. Amalendu Pal, B.R., Harsh Kumar, Arbad and A.B. Tekale, Indian J. of Pure and Applied physics, 41, (2003), 113-120. 9. A.V. Narashimham and A.T. Seshadri, Indian Journal of Physics, 65B (3), (1992), 44-48. 10. A.V. Narashimham, Indian Journal of Physics, 65B (4), (1991), 312-318. 11. Rita Mehra, Rekha Israni, J. Acous. Soc. India, 30, (2002), 72. 45 | P a g e A STUDY OF SOLVATION EFFECT OF SOME SODIUM SALTS IN NON-AQUEOUS MEDIUM USING ULTRASONIC VELOCITY Padmavathy.R 1 , Jasmine Vasantha Rani. E 2 , Seethalakshmi.K 3 , Rahmathunnisa.R 4 123 Department of Physics, Seethalakshmi Ramasami College, Trichy-2, Tamil Nadu 4 Department of Physics, Govt. Arts College, Pudukkottai, Tamilnadu 5. ABSTRACT Ultrasonic studies of solutions yield valuable information about the ionic interactions, the nature and strength of the interactions. Velocity of sound waves in a medium is fundamentally related to the binding forces between the molecules. The ultrasonic velocity data combined with density constitute the standard means of determining the compressibility of the system. When an electrolyte is added to a solvent the volume of the solvent changes and hence there is a change in compressibility. These changes have been determined quantitatively as solvation number. In the present case, the effect of temperature and concentration on solvation is analyzed for some sodium salts in non acqueous medium, thus various interactions taking place between the solute and solvent are interpreted. Keywords: solvation number, solute - solvent interaction, structure maker/breaker 1.Introduction The passage of ultrasonic waves through solutions and liquids disturb the equilibrium between the solute and solvent molecules. The velocity of such a wave is a thermodynamic quantity and it is related to the physio-chemical properties of the medium. Ultrasonic velocity measurement is used to throw light on various aspects of solvation chemistry including ion-ion and ion-solvent interaction. By measuring the fundamental quantities such as density and ultrasonic velocity of sodium citrate, sodium molybdate, sodium 46 | P a g e salicylate and sodium calcium edetate in formamide from 5 o c to 55 o c at different concentration, the solvation number were computed. From the analysis of solvation, the sodium salts in formamide reveals the structural interaction taking place in the solutions. 1.1 Experimental technique Solutions of sodium citrate, sodium molybdate, sodium salicylate and sodium calcium edetate of various concentrations are prepared in formamide with (AR/BDH) salt. Density of the solutions is measured using 25ml specific gravity bottle with an accuracy of .001gm/cc. Mittal’s interferometer of frequency to 2MHz, with an accuracy of ±2m/s is used for the measurement of ultrasonic velocity. The solvation number was calculated using the formula: )] / ( 1 )[ / ( o i s h n n n β β − = 1.1(a)Results and Discussions Solvation is the attraction and the association of the molecules of a solvent with molecules or ions of the solute. The solvation numbers reflect the dynamic situation of the ion as it moves around in the solution. The structure of the solvent near an ion will be having three regions. In the primary or structure enhanced region next to the ion, the solvent molecules are immobilized and oriented by the ionic field. Then there is a secondary or structure broken region, in which the normal bulk structure of the solvent is broken down in various degrees. The in-between solvent molecules, however, do not partake of the translational motion of the ion. The structural changes in the primary and secondary regions are generally referred to as the solvation.[1] The general observations made on solvation number of the system studied in relation to temperature and molality are as shown in figs.(1,2,3,4). The solvation number is positive at a high temperature, it is negative at low temperature and no abrupt change in solvation number is found at higher molalities. At lower molalities, the solvation number changes from negative values to the positive values. Solvation number is decided by relative values of compressibility of solution and solvent. Constant values of solvation number only indicates that no change occurs in the compressibility value of the solvent when the solution is formed. This may be due to ion solvent interaction energy equal to intermolecular interaction energy. Therefore no change in compressibility. Negative values of solvation number at lower molalities, emphasizes that solutions are more compressible than solvent, hence the negative sign for the solvation 47 | P a g e number. Positive solvation number of the solution suggests that the compressibility of the solution at high temperature and at low molalities will be less than that of the solvent. But however a fall in the solvation number at high temperature or rise in solvation number from negative maximum towards zero at low temperature may be attributed to decreasing ion-solvent interactions[2]. The solvation approach is used to interpret ion - solvent interaction[3]. The negative solvation number for various molalities is reported in literature[4,5,6]. The decrease in solvation number with increasing molality is due to either not enough solvent molecules available for ions or preferentially ion - pairing occurred[7]. 1,1(b)Conclusion: In the present investigation, the solvation number of the sodium salts reveal very high solvation number in formamide. The solvation number of an ion depends on the solvent. The concept of solvation is a measure of the ionic force field and ion - solvent interaction energy of the solutions. Structural elucidation of the solute in the solvent. i.e. sodium citrate& sodium molybdate in formamide acts as structure makers and sodium salicylate & sodium calcium edetate in the solvent acts as structure breakers fig(5,6,7,8). 48 | P a g e 2. Figures and Tables Solvation Number Table –1 Sodium citrate Molality(m) 5°C 15°C 25°C 35°C 45°C 55°C 0.001 -137.24 -17.53 -198.70 70.93 318.38 329.58 0.005 -21.16 -4.12 -22.58 33.03 83.37 77.64 0.010 -0.77 1.75 -21.59 11.82 33.87 33.41 0.025 3.40 7.95 -2.27 8.56 18.18 18.47 0.050 5.23 10.40 2.74 6.71 12.97 12.17 Table – 2 Sodium molybdate Molaity(m) 5°C 15°C 25°C 35°C 45°C 55°C 0.001 -300.10 -26.10 -232.44 -24.22 235.92 266.51 0.005 -43.95 19.09 -31.70 2.07 79.53 73.51 0.010 -6.41 16.16 -4.34 6.30 45.77 44.58 0.050 1.83 3.94 0.85 5.17 10.63 13.71 0.100 3.67 4.67 2.56 5.73 7.92 8.97 0.150 4.19 5.66 3.56 5.25 6.30 7.10 Table – 3 Sodium salicylate Molality(m) 5°C 15°C 25°C 35°C 45°C 55°C 0.001 -592.58 -436.84 -1236.30 -784.00 -146.83 419.33 0.005 112.37 -22.75 -1.17 87.32 174.44 192.54 0.010 20.55 63.63 -5.06 -1.36 9.01 57.80 0.050 -0.75 5.75 -1.42 3.13 9.33 10.78 0.100 -9.22 -4.01 -1.25 5.84 12.48 6.30 0.200 9.53 9.58 5.18 8.45 11.48 6.85 Table – 4 Sodium calcium edetate Molality(m) 5°C 15°C 25°C 35°C 45°C 55°C 0.001 485.01 752.59 745.61 1457.11 1438.94 1355.54 0.005 -4.51 -13.26 -191.44 -65.98 30.30 96.27 0.010 -186.06 -190.16 -189.96 -148.22 -107.64 -65.46 0.020 -9.02 -1.12 0.19 27.86 23.50 33.92 0.030 57.94 59.43 59.82 60.53 85.72 108.72 49 | P a g e 6. SOLVATION NUMBER Fig – 1 SODIUM CITRATE Fig – 2 SODIUM MOLYBDATE 7. IG – 3 SODIUM SALICYLATE FIG – 4 SODIUM CALCIUM EDETATE Fig - 5 Fig - 6 Molality Vs Solvation number -1400 -1200 -1000 -800 -600 -400 -200 0 200 400 600 0 0.01 0.01 0.05 0.1 0.2 Molality(m) S o l v a t i o n n u m b e r 5°C 15°C 25°C 35°C 45°C 55°C Molality Vs Solvation number -400 -200 0 200 400 600 800 1000 1200 1400 1600 0.001 0.005 0.01 0.02 0.03 Molality(m) S o l v a t i o n n u m b e r 5°C 15°C 25°C 35°C 45°C 55°C Molality Vs Solvation number -300 -200 -100 0 100 200 300 400 0.001 0.005 0.01 0.025 0.05 Molality(m) S o l v a t i o n n u m b e r 5°C 15°C 25°C 35°C 45°C 55°C Molality Vs Solvation number -400 -300 -200 -100 0 100 200 300 0 0.01 0.01 0.05 0.1 0.15 Molality (m) S o l v a t i o n n u m b e r 5°C 15°C 25°C 35°C 45°C 55°C 50 | P a g e Fig - 7 Fig - 8 3. References: 1. John O.M. Bockris and Amulya K.N. Reddy, “Modern Electrochemistry”, A Plenum / rosetta Edition, Vol 1, (1997) 2. Bhullar.k, Bhavneet.K.Bakshi. M.S., Jasbir.S., Sharma S.C. and Joshi I.M.Acoustica. Vol.73(1991)292. 3. Padova J, Isr At. Energy Comm,(1963) IA – 823, (16PP), A-830(23PP) 4. Lit vinenko, Zh.Strukt, Khim.,4(1963) 830 5. Rao M.G.S. and Rao B.R., J.Pure and applied Phys.,1(10) (1963) 362. 6. Rajkotia, et.al.,J.Pure and Appl. Ultrasonics, 21(1999)132-135 7. KuppuswamiJ.,Lakshmanan A.S., Lakshminarayanan R. Rajaram N., and Suryanarayana C.V.Bull. Chem. Soc. Japan , 38, (1965) 1610. 51 | P a g e THERMO - ACOUSTIC AND SPECTROSCOPIC STUDY OF POLYMER SALT IN NON -AQUEOUS MEDIUM USING ULTRASONIC VELOCITY * JASMINE VASANTHA RANI.E, * PADMAVATHY.R, # RADHA.N, @ KANNAGI.K, & LAVANYA.N *Department of Physics, #Department of Chemistry @ Dr. Kalaignar arts and science college, Lalgudi. Seethlakshmi Ramaswami College, Trichirapalli-2, Tamil Nadu, INDIA
[email protected]&
[email protected] ABSTRACT Polyaniline (PANI) is an organic metal. Its thermo power has been classified as metallic. In this present investigation acoustic and thermodynamic properties are studied for poly aniline perchlorate in Formamide from 5° °° °C to 55° °° °C at different molalities using ultrasonic velocity. Various molecular interactions have been analyzed and these interactions indicate the structural enhancement of this material in formamide. This results are also confirmed by FTIR and UV spectra. Keywords: Thermodynamic properties, ultrasonic velocity, FTIR, UV. 1. Introduction: Polymers conduct electric current without the addition of inorganic dopants. It has unlimited worldwide commercial availability. PANI is an organic metal, its specific conductivity are semi-metallic. Its thermo power has been classified as metallic. Polyaniline salts have been synthesized by chemical oxidative polymerization of aniline in the presence of phenoxy acetic acid.[1] PANI is one of the most widely studied materials.[2] A wide range of technological applications have been associated with polyaniline. In electrostatic dissipation, anticorrosion coatings in various optoelectronic devices and as an antistatic material, polyaniline salts are used.[3][4] The present work dealt with the acoustic and spectroscopic study of polyaniline perchlorate in formamide. Density, viscosity and ultrasonic velocity are determined at various molality from 5°C to55°C. Using the above values, internal pressure , free volume and acoustic parameters at different concentrations and at different temperatures are evaluated. 1.1.Experimental technique and computation: 52 | P a g e Formamide is taken as the solvent for preparing polyaniline perchlorate solution. It is unusual in its properties. It has high dielectric constant 109 with low molecular weight 45.04. The experiment has been carried out at various temperatures and at different molalities (0.001m, 0.005m, 0.01m, 0.015m, and 0.02m). Significance of thermodynamics such as internal pressure and free volume in liquids had been emphasized by Richards, Hildebrand and others. Internal pressure (πi) and the free volume (Vf) and various acoustic parameters, Rao’s (R) Wada’s (W),van der Waal’s (b) constants and adiabatic compressibility (βad) are computed using the following formulae πi = bRT(kη/u) 1/2 *(P 2/3 / Meff 7/6 ) atms Vf = (Meff * u/kη) 3/2 cc R = Meff (u) 1/3 / ρ W = Meff (βad) -1/7 / ρ b = (Meff/ρ) ((1-RT)/ Meff u 2 ) (1+( Meff u 2 /3RT-1)) 1/2 βad = 1/u 2 ρ dynes/cm 2 The values are given in the Tables 1-6 1.2. Results and discussion: 1.2 (a) Thermodynamic study: Internal pressure is the single factor which varies due to all the internal interactions. Internal pressure is the measure of cohesive energy. In the present investigation, the internal pressure increases with concentration. The variations are shown in Figure-1. This increase in internal pressure suggests that there is a strong solute and solvent interaction.[5] But, at higher temperatures, when the temperature is increased there is a tendency for the ions to move away from each other, hence there is a reduction in internal pressure[6]. This result is also confirmed from the study of free volume. It is shown in Figure-2. The variations of adiabatic compressibility with respect to concentration and temperature are given in Figure3.The irregular behaviour of Rao’s constant, Wada’s constant and van der Waal’s constant supports that there is a strong ion-solvent interaction occurring in the solution.[7] These non-linear variations emphasize that there is an association between molecules of the solution.(Figures 4-6) 1.2 (b) Spectroscopic study: Infrared spectroscopy is the subset of spectroscopy that deals with the infrared region of the electromagnetic spectrum. Solution of Polyaniline perchlorate (PAPC) in formamide is prepared using AR grade salts and IR spectra have been taken at St.Joseph’s college [ACIC center Nadu. The molecular structures of formamide and polyaniline are given below (I& II). I. Structure of Formamide II From the IR spectrum of formamide, occurs at 3416.98cm -1 .At 2886.82 cm 1686.35 cm -1. Well defined peaks are observed at 1390.36, 1308.77 cm group. The low frequency absorption of amide I band is due to the resonance in the amide functional group. Also these shifts indicate the presence of hydrogen bonding, between the C=O and N=H groups in formamide and confirm the cage structure[6] . absorption at 601.89 cm -1 . When PAPC is added to formamide(figure shifted to 3417.45 cm -1 . (i.e.) towards higher frequency side by 1 cm cm -1 . (i.e.) towards higher frequency side by 1.99 cm due to the tightening of hydrogen bonds in the caged structure. No shift is observed in N bending. The deviations in the peaks support the tightening of hydrogen bonds in the caged structure of formamide. This confirms that structure making nature of the solutes in the solvent[7] The same results are reported from the thermodynamic study[8]. non-aqueous solvent, It promotes a thermodynamically more stable chain[9]. PAPC exhibits peak at λmax=349.94 nm and another peak at 677.82 nm. These two peaks in PAPC are the characteristics of the benzenoid and quinoid moieties. The ratio of the intensities of the quininoid to benzenoid peak is 0.5. This indicates PAPC has more benzenoid forms than that quinoid forms.(figure In the present study, the structure making nature of the PAPC is confirmed from the spectr and thermodynamic studies. It is found to be in good agreement with the result reported in literature. 2. Figures and Tables: Figure – 1 y is the subset of spectroscopy that deals with the infrared region of the Solution of Polyaniline perchlorate (PAPC) in formamide is prepared using AR grade salts and IR spectra have been taken at St.Joseph’s college [ACIC center], Tiruchirapalli, Tamil Nadu. The molecular structures of formamide and polyaniline are given below (I& II). I. Structure of Formamide II-structure of polyaniline From the IR spectrum of formamide, (figure-7 and Table-7) a strong N-H stretching absorption .At 2886.82 cm -1 , C=O stretching absorption known as amide I band is observed at Well defined peaks are observed at 1390.36, 1308.77 cm -1 this confirms the presenc The low frequency absorption of amide I band is due to the resonance in the amide functional group. Also these shifts indicate the presence of hydrogen bonding, between the C=O and N=H groups in formamide and confirm the cage structure[6] .In the spectrum there is also an N-H out of plane bending When PAPC is added to formamide(figure -8) the N-H stretching absorption is . (i.e.) towards higher frequency side by 1 cm -1 . C=O stretching is shi . (i.e.) towards higher frequency side by 1.99 cm -1 . These slight deviations in the absorption peaks are due to the tightening of hydrogen bonds in the caged structure. No shift is observed in N n the peaks support the tightening of hydrogen bonds in the caged structure of formamide. This confirms that structure making nature of the solutes in the solvent[7] The same results are reported from the thermodynamic study[8]. It is already confirmed that, when PANI is dissolved in polar aqueous solvent, It promotes a thermodynamically more stable chain[9]. PAPC exhibits peak at =349.94 nm and another peak at 677.82 nm. These two peaks in PAPC are the characteristics of the moieties. The ratio of the intensities of the quininoid to benzenoid peak is 0.5. This indicates PAPC has more benzenoid forms than that quinoid forms.(figure -9). In the present study, the structure making nature of the PAPC is confirmed from the spectr and thermodynamic studies. It is found to be in good agreement with the result reported in literature. Figure - 2 53 | P a g e y is the subset of spectroscopy that deals with the infrared region of the Solution of Polyaniline perchlorate (PAPC) in formamide is prepared using AR ], Tiruchirapalli, Tamil H stretching absorption , C=O stretching absorption known as amide I band is observed at this confirms the presence of C-H The low frequency absorption of amide I band is due to the resonance in the amide functional group. Also these shifts indicate the presence of hydrogen bonding, between the C=O and N=H groups in H out of plane bending H stretching absorption is . C=O stretching is shifted to 1688.34 . These slight deviations in the absorption peaks are due to the tightening of hydrogen bonds in the caged structure. No shift is observed in N-H out of plane n the peaks support the tightening of hydrogen bonds in the caged structure of formamide. This confirms that structure making nature of the solutes in the solvent[7] The same results are hat, when PANI is dissolved in polar aqueous solvent, It promotes a thermodynamically more stable chain[9]. PAPC exhibits peak at =349.94 nm and another peak at 677.82 nm. These two peaks in PAPC are the characteristics of the moieties. The ratio of the intensities of the quininoid to benzenoid peak is 0.5. This In the present study, the structure making nature of the PAPC is confirmed from the spectroscopic and thermodynamic studies. It is found to be in good agreement with the result reported in literature. Figure – 3 Figure – 5 IR Spectrum Figure – 7 Molality(m) FTIR SPECTRUM ACIC St.Joseph's College ( Autonomous ) Trichy-2 Spectrum Name: Sam = Formamide.sp Date: 08-1-2010 Sam = Formamide.pk SAM_FO~1.SP 3601 4000.00 400.00 7.94 100.00 4.00 %T 5 0.50 REF 4000 99.42 2000 98.83 600 3416.98 7.94 2886.82 33.27 2771.58 71.90 2691.97 82.59 2366.52 94.37 2197.03 92.51 1686.35 8.77 1390.36 22.60 1308.77 18.43 1054.13 61.42 601.89 21.04 4000. 0 3000 2000 1500 1000 400.0 0.0 10 20 30 40 50 60 70 80 90 100.0 cm-1 %T 3416.98 2886.82 2771.58 2691.97 2366.52 2197.03 1686.35 1390.36 1308.77 1054.13 601.89 Figure – 4 Figure – 6 IR Spectrum UV Spectrum Figure – 8 Figure Table -1 Internal Pressure (atms) 5° °° °C 15° °° °C 25° °° °C 35° °° °C 45° °° °C 55° °° °C FTIR SPECTRUM ACIC St.Joseph's College ( Autonomous ) Trichy-2 Spectrum Name: SRC-PAPC.sp Date: 07-1-2010 SRC-PAPC.pk SRC-PAPC.s p 3601 4000.00 400.00 6. 44 100.00 4.00 %T 5 1.00 REF 4000 99.61 2000 98.53 600 3417. 45 7.73 2889.86 47. 94 2774.31 81. 47 2395.44 97.62 2191.63 93.95 1688. 34 6.44 1605.34 16. 69 1390.26 23. 96 1311.27 23.36 1052.87 72.97 601.82 23.93 4000.0 3000 2000 1500 1000 400.0 0.0 10 20 30 40 50 60 70 80 90 100.0 cm-1 %T 3417.45 2889.86 2774.31 2395.44 2191.63 1688.34 1605.34 1390.26 1311.27 1052.87 601.82 ACIC St.Joseph's College( Autonomous) Trichy-2 Spectrum Name: PAPC.SP Instrument Model: Lambda 35 250.0 300 400 500 600 0.000 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.800 A 349.94,0.27985 257.05,0.52332 254.05,0.55516 54 | P a g e UV Spectrum Figure - 9 St.Joseph's College( Autonomous) Trichy-2 UV spectrum Date: 1/8/2010 700 800 900 1000 1100.0 nm 677.82,0.22060 55 | P a g e .001 19178 16357 13412 12678 11396 10450 .005 19453 16542 13664 13178 11862 11056 .01 19933 16848 13945 12931 11951 10823 .015 19987 16953 13312 13282 11434 11502 .02 20458 17084 13592 13387 11913 11238 Table- 2 Free Volume (cc) Molality(m) 5° °° °C 15° °° °C 25° °° °C 35° °° °C 45° °° °C 55° °° °C 0.001 0.32 0.59 1.03 1.67 2.07 2.6 0.005 0.22 0.49 0.87 1.42 1.69 2.53 0.01 0.21 0.48 0.82 1.34 1.56 2 0.015 0.21 0.48 0.8 1.28 1.5 1.87 0.02 0.19 0.46 0.74 1.21 1.39 1.78 Table - 3 Adiabatic Compressibility (10^-13) Molality(m) 5° °° °C 15° °° °C 25° °° °C 35° °° °C 45° °° °C 55° °° °C .001 361 353 344 360 344 334 .005 377 360 347 378 398 379 .01 354 353 362 344 384 334 .015 367 358 281 361 315 401 .02 377 359 293 370 363 378 Table - 4 Rao’s Constant Molality(m) 5° °° °C 15° °° °C 25° °° °C 35° °° °C 45° °° °C 55° °° °C .001 2116 2143.5 2166 2165 2213 2243 .005 2132 2136.8 2162 2154 2160 2196 .01 2127 2140.8 2149 2185 2171 2237 .015 2134 2139.4 2240 2169 2247 2156 .02 2104 2136.6 2221 2161 2193 2200 Table - 5 Wada’s Constant Molality(m) 5° °° °C 15° °° °C 25° °° °C 35° °° °C 45° °° °C 55° °° °C .001 1221 1234.5 1245 1245 1269 1283 .005 1229 1231.1 1244 1240 1243 1260 .01 1226 1233.1 1237 1255 1248 1281 .015 1230 1232.4 1282 1247 1285 1241 .02 1215 1231.1 1273 1243 1259 1262 Table-6 van der Waal’s constant Molality(m) 5° °° °C 15° °° °C 25° °° °C 35° °° °C 45° °° °C 55° °° °C .001 118.9 119.5 119.9 115.1 118.5 119.8 .005 118.0 118 119.1 112 107.7 110.3 .01 120.7 119.3 116.1 118.9 110.2 119.5 .015 119.5 118.5 136.5 115.3 125.6 105 .02 115.9 118.2 132.5 113.5 114.4 110.8 Table-7 Polyaniline perchlorate (PAPC) Wave number in cm -1 Possible functional groups 56 | P a g e 3417.45 N-H Stretching 2889.86 Intermolecular hydrogen bond O-H Stretching 2774.31 C-H Stretching 2395.44 N + H2 and N + H Stretching 1688.34 C=O Stretching 1390.26 Inplane O-H bending 1311.27 C=O Symmetric Stretching 1052.87 C-O Stretching 601.82 N-H out of plane bending 3. References: 1) Lynne.A; Samuelson Althea Angnostopoulos; K.Shridhara Alva; Jayant Kumar and Sutant; K. Tripathy. Macromolecules 1998, 31, 4376-4378. 2) Li-MingHuanga; Cheng-Hou Chena and Ten-Chin Wen Electrochimica Acta; 2006,51,(26)5858- 5863. 3) P.C.Ramamurthy; W.R.Harrell; R.V.Gregory, B.Sadananda and A.M.Rao;Polymer Engineering Science.,44,28,2004 4) Gilbert R.G, Pure and Applied Chemistry, 2002, 74, 857- 867. 5) Ravichandran.G;Srinivasa Rao.A and Nambinarayanan. T.K;Indian Journal of Pure and Applied Physics., vol. 32, 1994. 6) Jasmine Vasantha Rani, E.Suhashini Ernest., Padmavathy.R, Radha.N ,An investigation of solvation number, Electrochemical and Thermodynamical properities of Calcium lactate solution using ultrasonic velocity –(2005). 7) Analysis of internal pressure, Free volume and also some acoustical parameters of sorbiton monosterate – J.Acoustic Soc. India vol xxx pp23-25 NSA 2002. 8) Jasmine Vasantha Rani , E.Suhashini Ernest,Study of molecular interactions of calcium pantothenate in non-aqueous medium through ultrasonic speed measurement and spectroscopic analysis .(2005). 9) Bidhan C.Roy,Maya Dutta Gupta, Leena Bhoumik, Spectroscopic investigation of water-soluble polyaniline copolymers – Synthetic Metals 130(2002) 27-32. 57 | P a g e ULTRASONIC INVESTIGATIONS OF PEG (400) IN TOLUENE-CLAY MIXTURE T.Mathavan 1 , S.Umapathy 2 , M.A.Jothi Rajan 3 , M. Megala 1 1 Department of Physics, NMSSVN College, Nagamalai, Madurai - 625 019, India. 2 School of Physics, Madurai Kamaraj University, Madurai – 625 021, India. 3 Department of Physics, Arul Anandar College, Karumathur – 625 514, India. Corresponding author. E-mail address:
[email protected] ABSTRACT: Low power ultrasonic technique is one of the most powerful and useful non-destructive testing tools to investigate properties of polymer/clay composite solutions. When the concentration of the solution is increased, correspondingly its various physical parameters change considerably. Similar changes in physical parameters are also observed when the temperature of the solution is varied. Poly(ethylene glycol)-400 (PEG-400) in toluene-bentonite clay mixture solution and its physical parameters such as adiabatic compressibility, intermolecular free length, acoustic impedance, adiabatic bulk modulus, relaxation time, Rao’s number, absorption coefficient, surface tension and refractive index are determined. The acoustical and thermodynamic parameters are computed based on experimentally determined values of ultrasonic velocity, density and viscosity. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions. 1. INTRODUCTION The main aim of this study is to bring out the structural changes, if any in association with the formation of mixture of a polymer solute and clay-solvent mixture due to molecular interaction between them. Ultrasonic studies in polymer solutions have drawn the attention of several investigators in the recent years [1-5]. The present study is undertaken on the ultrasonic study of PEG (400) in Toluene-Bentonite (Clay) mixture at several concentrations for four different temperatures (30 0 C, 35 0 C, 40 0 C and 45 0 C). Toluene is chosen because it is a good solvent. It is important to select favorable reaction media for use of enzymes in organic synthesis. In recent years, aqueous polymer solutions have found widespread applications, mostly because of their use in two-phase aqueous systems for separation of biomolecule mixtures. Specially, solutions of polyethylene glycol (PEG) in water have attracted much attention. These solutions have been used in bio-chemistry and biochemical engineering to separate and purify biological products, biomaterials, proteins, enzymes from the complex mixtures in which they are produced. Bentonite is a lightly absorbent clay-like substance that helps to lift impacted waste matter which has accumulated on the walls of the gastrointestinal tract. In this report ultrasonic method is used to study the physical parameters and investigate the associative nature, if any between the solute and solvent-clay mixed molecules. 58 | P a g e 2. EXPERIMENTAL Analar grade (AR) sample of PEG (400), toluene supplied by Merck, India and clay (Aldrich) were used as such in the sample preparation. Water, doubly distilled over alkaline permanganate in all glass apparatus was used as the solvent for preparing the solution. Single frequency ultrasonic interferometer (M/S. Mittal Enterprises, Delhi, India, Model F81, 2 MHz) and constant temperature water bath (M/S. Toshniwal Brothers, India) to an accuracy of ±0.01 ° K were used for ultrasonic velocity measurements. The required concentrations of the solution (0.5, 1.0, 1.5, 2.0 ML -1 ) were prepared and the measurements were taken for 308 K, 313 K, 318 K and 323 K obtained by weighing the solute by a digital balance (accuracy ±0.001g) and mixing with the already purified water in glass beakers, which were cleaned and dried before use. Densities of the solutions were measured by specific gravity bottle of capacity 5ml to an accuracy of ±0.1 Kgm -3 . Viscosities of the solutions were measured by pyknometer to an accuracy of ±0.05%. 3. ACOUSTICAL PARAMETERS The ultrasonic velocity (C), viscosity ( and density ( measurements are extensively used to study the physical and chemical behavior of liquid solutions. In this work the following parameters were determined: 1. Isentropic compressibility βd = (C 2 ) -1 ----- (1) 2. Intermolecular Free length Lf = k/( C 2 ) ----- (2) k is the temperature dependent constant. 3. Specific Acoustic Impedance Z= C ----- (3) 4. Adiabatic bulk modulus K = 1/ βd ----- (4) 5. Relaxation time = 4 / 3 C 2 ----- (5) 6. Rao’s Number (R) is given by R = C 1/3 V ----- (6) Where V is the molar volume which is equal to molecular weight/density of the solution. 7. Absorption co-efficient /f 2 = 8 2 /3C 3 ----- (7) 8. Surface tension (C 3/2 ) X (6.3×10 -4 ) X ----- (8) 59 | P a g e 4. RESULTS AND DISCUSSION The variation of the measured and derived parameters for various concentration(0.1M, 0.2M, 0.3M, 0.4M, 0.5M, 0.6M, 0.7M, 1M) of polyethylene glycol (400) in toluene-bentonite clay mixture at for different temperatures (30 0 C, 35 0 C, 40 0 C, 45 0 C) were studied and shown graphically in figures 1-10. Variation of ultrasonic velocity in any solution generally indicates nature of the interaction existing in between molecules in them [1]. The ultrasonic velocity increases with increasing concentration. This is due to formation of more hydrophobic character with increase in concentration as result of solute-solvent-clay interaction. And also it shows non-linear behavior. It indicates that, there is complex formation between the unlike molecules [2]. The ultrasonic velocity decreases with increasing temperature. It indicates that weak polymer solvent interactions between PEG in Toluene-clay mixture. In this, non-linear increase in velocity may be due to the molecule-clay association. The variation of the acoustic velocity is given by graph in figure 1. The isentropic compressibility (βd) values of the solutions of different concentrations were calculated from the density and the ultrasonic velocity. The βd value decreases with increase of concentration and increases with increase of temperature. The value of isentropic compressibility decreases in all system which indicates the presence of molecular interaction in these systems (fig. 2) [3]. In this work, it indicates that there is a complex formation between the solute and solvent-clay mixture. One of the important properties of a liquid is the free length (Lf) between the surfaces of the neighboring molecules and is the distance covered by the propagating acoustic waves between two neighboring molecules. It directly gives information about complex formation between solute and solvent (fig. 3) [4]. The experimental solution shows a decrease in intermolecular free length with increase in concentration and it increases with temperature; and hence an increase in ultrasonic velocity is observed. The velocity deviation depends upon the increase or decrease in the freelength in the solution after mixing [5]. It indicates significant interaction between solute and solvent-clay molecules due to which to structural arrangement [6] in the neighborhood of constituent ions are considerably affected. The experimental solution shows an increase in acoustical impedance with increasing concentration and also it shows a decreasing value of acoustical impedance with increasing temperature (fig. 4). This is in agreement with requirement both ultrasonic velocity and density increase with increase in concentration and also due to effective solute solvent-clay interaction [7]. The adiabatic compressibility decreases with increasing concentration and increases with increase in temperature (fig. 5). This is due to strong molecular interaction of PEG (400) in toluene-clay mixture. 60 | P a g e Relaxation time gives the orientation of the molecules in a particular direction. For increase in concentration, the structure of the solution changes by forming association of molecules and clay layers (fig. 6). This result in high viscous nature and hence the time taken for the flow of ultrasonic wave in the viscous medium increases [8, 9]. It may be understood that this relaxation is a structural relaxation. The value of Rao's constant shows decrease with increase in temperature and also increases with increase in concentration (fig. 7). This variation confirms the changes in molecular interactions. The classical absorption factor of experimental polymer-toluene-clay mixture shows increase of concentration and decreases with increase of temperature and it is characteristic of polymer solvent-clay interaction (fig. 8). It shows the value of classical absorption factor of the experimental solution, increases while increasing the concentration and decreases while increasing the temperature. Surface tension value increases with increase of concentration and decreases with increase of temperature. The variation of surface tension is shown in figure 9. The value of surface tension is plotted against concentration for four different temperatures (30 0 C, 35 0 C, 40 0 C, 45 0 C). The value of the refractive index decreases with increase of concentration and increases with increase of temperature. The variation of refractive index with concentration has been plotted in fig. 10. From the figure, it is clearly evident that the variation is non-linear. 5. CONCLUSION Acoustic investigations were carried out for different mole concentrations of polymer/clay mixture in toluene. When the concentration of the solution is increased, correspondingly its various physical parameters change considerably. Similar changes in physical parameters are also observed when the temperature of the solution is varied. Poly(ethylene glycol)-400 (PEG-400) in toluene-bentonite clay mixture solution and its physical parameters such as adiabatic compressibility, intermolecular free length, acoustic impedance, adiabatic bulk modulus, relaxation time, Rao’s number, absorption coefficient, surface tension and refractive index were determined. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions. Fig 1. acoustic velocity Vs Mole concentration. Fig 2. Isotropic compressibility Vs Mole concentration. Fig 3. Free Length Vs Mole concentration. 0.0 0.2 0.4 0.6 0.8 1.0 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 β d X 1 0 -1 0 N -1 m 2 MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 0.0 0.2 0.4 0.6 0.8 1.0 1220 1240 1260 1280 1300 1320 1340 1360 1380 C ( m /s ) Mole concentration 30 0 C 35 0 C 40 0 C 45 0 C 0.1 0.2 0.3 0.4 0.5 0.6 0.7 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 L f X 1 0 -1 1 m MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 61 | P a g e 0.0 0.2 0.4 0.6 0.8 1.0 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 K X 1 0 1 0 N m -2 MOLECONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C Fig 4. Acoustic impedance Vs Mole concentration. Fig 5. Adiabatic bulk modulus Vs Mole concentration. Fig 6. Relaxation time Vs Mole concentration. Fig 7. Rao’s Number Vs Mole concentration. Fig 8. Classical Absorption Factor Vs Mole concentration. Fig 9.Surface tension Vs Mole concentration. Figure 10. Refractive index Vs mole concentration. 0.0 0.2 0.4 0.6 0.8 1.0 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 Z X 1 0 6 K g /m 2 s MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 0.0 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10 12 14 16 18 τ X 1 0 -1 2 s e c MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 0.0 0.2 0.4 0.6 0.8 1.0 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 R X 1 0 3 MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 α /f 2 X 1 0 -14 m /s 2 MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 0.0 0.2 0.4 0.6 0.8 1.0 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 γ X 1 0 4 N m -1 MOLE CONCENTRATION 30 0 C 35 0 C 40 0 C 45 0 C 0.0 0.2 0.4 0.6 0.8 1.0 1.455 1.460 1.465 1.470 1.475 1.480 1.485 1.490 1.495 1.500 n Mole concentration 30 0 C 35 0 C 40 0 C 45 0 C 62 | P a g e 6. REFERENCES 1. Vijayalakshmi T.S & Naidu P.R, Indian J Pure and Appl. Phys., 28, 215, (1990). 2. Nomoto O, J. Phys. Soc., Japan, 8, 553, (1953). 3. Velmurugan S, Nambinarayanan T.K, Srinivasa Rao A and Krishnan B, Indian J. Phys., 61B, 105, (1987). 4. Kalyana Sundram S, Manuel Stephen A and Gopalan.A, J Polym. Materials, 12, 177, (1995). 5. Sosamma S, Nambinarayanan T.K and Srinivasa Rao A, Indian J. Phys., 62B, 31, (1988). 6. Singh R.P, and Srivastava T.N, Proc. Net. Acad sci. India, 57(A), 285-291, (1987). 7. Sheo Prakash S, Srinivastar B and Prakash O.M, Indian J. Pure and Appl. Phys., 13, 191, (1975). 8. Narashimham A.V, Indian J. Phys, Vol 65 B, No.4, 312-318, August (1991). 9. Narashimham A.V and Seshadri A.T, Indian J. Phys., Vol.65 B, No.3, 44-48, (1992). 63 | P a g e ACOUSTICAL STUDY ON THERMO DYNAMICAL AND EXCESS PARAMETERS OF BINARY AND TERNARY MIXTURES M.M. Armstrong Arasu and Dr. I. Johnson Centre for Nano Science and Applied Thermodynamics, Dept. of Physics, St. Joseph’s College, Trichy – 620 002, India. ABSTRACT: Industry demands reliable and accessible reference data on the physical and chemical properties of a wide variety of compounds. These data are required in the development of process design and efficiency and in the evaluation of possible environmental impacts. 1. INTRODUCTION In this paper density, viscosity and speed of sound is measured for binary mixture of Propanol + Ethyl acetate for temperatures 308.15K. The density, viscosity and speed of sound for ternary mixture of Propanol + Ethyl acetate + water were measured at 303.15K. The excess volume, Wada constant, ultrasonic relaxation time, deviations enthalpy, ultrasonic velocity, adiabatic compressibility viscosity, free length, internal pressure, acoustic impedance, free volume& Gibb’s free energy were calculated for binary mixture at the constant temperature of 308.15K, for ternary mixture at the constant temperature of 303.15K. 2. EXPERIMENTAL The binary and ternary mixtures were prepared by mass, by mixing the calculated volumes of liquid components in airtight glass bottles. In all the measurements, INSREF thermostat with a constant digital temperature display accurate to ±0.01K was used. For all the mixtures and pure solvent, triplicate measurements were performed and the averages of all values were considered in the calculation. The mass measurements (±0.0001g) were made using an electronic balance. The accuracy of density measurements was 0.0001g.cm -3 . A set of 18 and 11 compositions were prepared for ternary and binary mixtures respectively and also their physical properties were measured. Viscosity is measured by calibrated Ostwald’s Viscometer. The speed of sound was determined using a constant frequency (2MHz) ultrasonic interferometer with an accuracy of ± 2 m.s -1 . 3. THEORY The excess molar volume V E was calculated from the density data by the relationship V E = VM –Σ xiVi , (1) i where Vi represents the molar volume, xi the mole fraction of the ith component and VM is the molar volume of the mixture, given as VM = (x1M1+x2M2) /ρm , (2) where ρm is the density of the liquid mixture. The adiabatic compressibility βa was obtained from sound velocity and density measurements as βa= 1/(u 2 ρ) (3) The excess adiabatic compressibility was calculated as βa = βa m –Σφi βai , i (4) where the φi is the volume fraction of the ith liquid, 64 | P a g e φi = xiVi/ΣxiVi , (5) i The excess viscosity is obtained as η = ηm – Σxiηi , (6) i where ηm and ηi refer to the viscosity of the mixture and pure components respectively . The Wada’s constant was calculated using the formula W = (Meffβa -1/7 )/ρ (7) The inter molecular free length was calculated using the formula given by Jacobson et al. Lf = KJ √ βa , (8) where KJ is Jacobson’s constant. KJ is the temperature dependent parameter which varies directly with the square root of the absolute temperature i.e., K J α √T (9) The excess free length is given as Lf = Lf mix – (ΣxiLfi) (10) i where xi and Lfi, are the mole fractions and inter-molecular free lengths of the respective components. Lfmix is the free length of the ternary mixture. The acoustic impedance is given as Z = ρu, (11) where u is the ultrasonic velocity and ρ the density. The excess acoustic impedance is given as Z = Zmix - Σxizi (12) i The free volume of a liquid and liquid mixture can be calculated using the formula Vf = [Mu/Kaη] 3/2 , (13) Where M is the molar mass of the liquids, u is the ultrasonic velocity, Ka is the constant having value of 4.28x10 9 , independent of the temperature and nature of the liquids and η is the viscosity. On the basis of the dimensional analysis using the free volume concept, Suryanarayana suggested the expression for the internal pressure as Pi = bRgT [Kaη/u] 1/2 ρ 2/3 /Meff 7/6 , (14) where b is the space packing factor (equal to 2 in the present case) ,Rg ,is the gas constant and T is the temperature in degree Kelvin . Equations (13) and (14) are used for mixtures for which parameters such as M, u, ρ and η corresponds to those mixtures. The excess free volume of the mixture is given as 3 Vf = Vfmix - Σ xiVfi (15) i=1 The excess internal pressure of the mixture is obtained using the relation 3 Pi = (Pi)mix –Σ xiPi (16) i=1 The dispersion of the ultrasonic velocity in this system should contain information about the characteristic time τ of the relaxation process that causes the dispersion. The relaxation time τ is estimated from the following relation 65 | P a g e τ = 4η/3ρu 2 (17) From the Eyring’s rate process theory, the Gibb’s free energy of activation for the relaxation process ∆G was obtained as 1/τ = KT/h) exp (-∆G/kT), (18) where k is the Boltzmann’s constant and h is the Planck’s constant. The excess enthalpy of a binary mixture is obtained from the fundamental relation 3 H= Σ (xiPij Vj - (Pi)mixVm. (19) i=1 The classical absorption or relaxation amplitude is given by (α/f 2 )cl= (8∏ 2 η/3ρu 2 ) (20) 4. RESULTS AND DISCUSSION In reference with table 1and 2 gives experimental results density, viscosity and speed of sound for 35 0 C for the system of binary mixtures of Ethyl acetate + Propanol and the excess volume, Wada constant, ultrasonic relaxation time, deviations in enthalpy, ultrasonic velocity, adiabatic compressibility, viscosity, free length, internal pressure, acoustic impedance, free volume & Gibb’s free energy are calculated at the constant temperature of 308 K. For the system of binary mixtures Ethyl acetate + Propanol the excess adiabatic compressibility and excess volumes values are also positive which indicates that influence of -OH bonding interaction or chemical forces. V E , βa E are negative indicate interstitial accommodation of one liquid molecule into another. L E f are positive which shows that there is increase in free length and compressibility. The excess internal pressure is negative which shows the presence of cluster formation. The free volume plays an important role in ultrasonic wave propagation in liquids. It has been found that the free volume of liquid molecules depends on the particular temperature of the liquid at which it is measured. The trend of variation of Vf is opposite to the change in the Pi. The Vf values are positive while V E f are negative. The mathematical relations for specific acoustic impedance, Z = uρ adiabatic compressibility, βa = 1/ (u 2 ρ) shows that the behaviour is opposite. Specific acoustic impedance is the complex ratio of the effective sound pressure at a point to the effect particle velocity at that point. The relaxation amplitude and Gibbs free energy also positive in most of the mixture. When the mole fraction of any one of the three liquids kept constant and the mole fraction of the other three liquids have been varied Wada’s constant variation is linear. For the system of ternary mixtures (Ethyl acetate+ Propanol + Water) at 303.15.K (Table 3&4), the η E values are positive in most of the combinations of the ternary system studied. According to Fort and Moore η E values are negative in system of unequal molecular size which is very much evident. η E are negative and positive, the negative value suggest that the force between pairs of unlike molecules are less than the forces between the forces of like molecules while positive value suggest that the force between pairs of unlike molecules are greater than the forces between pairs of like molecules . L E f are negative and positive. The negative values suggest that there is a decrease in free length and compressibility. The positive values suggest that there is a increase in free length and compressibility .The excess internal pressure is negative which shows that the presence of cluster formation. The free volume plays a important role in ultrasonic wave propagation in liquids found that the free volume of liquid molecules depends on the particular temperature of the liquid at which is measured. The relaxation amplitude and Gibbs free energy also negative in most of the mixture. When the mole fraction of any one of the three liquids kept constant and the mole fraction of the other three liquids have been varied Wada’s constant variation is nonlinear. Excess volumes are positive which proves the influence of – OH bond interactions over dispersion type interactions. The excess adiabatic compressibility values are also positive which confirms 66 | P a g e the above fact.. The V E and βa E are negative indicate interstitial accommodation of one liquid molecule into another. The free volume plays an important role in ultrasonic wave propagation in liquids found that the free volume of liquid molecules depends on the particular temperature of the liquid at which is measured. βa = 1/ (u 2 ρ) shows that the behavior is positive .Specific acoustic impedance is the complex ratio of the effective sound pressure at a point to the effect particle velocity at that point. The relaxation amplitude and excess Gibbs free energy also positive in most of the mixture. When the mole fraction of any one of the three liquids kept constant and the mole fraction of the other two liquids have been varied. Table -1 Ethyl Acetate +Propanol Table -2 Ethyl Acetate + Propanol S. NO X(i) ρ x10 -3 kgm -3 η N.sm -2 U ms -1 W τD x10 2 pa ∆G KJ/mole Z x10 5 Kgm -2 s -1 Z x10 5 Kgm -2 s -1 P i x10 6 pa Pi x10 6 Pa 1 1.0000 0.8244 0.00048 1085 2855 0.0007 - 7.2012 8.9447 0.000 0.1055 0.0000 2 0.9002 0.8209 0.00049 1090 2778 0.0007 -7.1946 8.9478 5.3501 0.1101 -0.0051 3 0.7999 0.8085 0.00054 1096 2726 0.0007 -7.1514 8.8612 1.7534 0.1186 -0.0063 4 0.7001 0.8005 0.00056 1100 2659 0.0008 -7.1348 8.8055 1.2305 0.1247 -0.0099 5 0.6002 0.7991 0.00058 1107 2574 0.0008 -7.1246 8.8460 10.332 0.1317 -0.0126 6 0.5001 0.7866 0.00061 1112 2517 0.0008 -7.1002 8.7470 5.4862 0.1393 -0.0147 7 0.4004 0.7747 0.00063 1118 2458 0.0009 7.0846 8.6611 1.9396 0.1462 -0.0176 8 0.3002 0.7703 0.00067 1123 2376 0.0009 -7.0598 8.6505 5.9352 0.1570 -0.0165 9 0.1980 0.7549 0.00070 1129 2320 0.0010 -7.0371 8.5228 1.665 0.1660 -0.0174 10 0.1003 0.7493 0.00081 1134 2240 0.0011 -6.9756 8.4971 0.6958 0.1863 -0.0066 11 0.0000 0.7403 0.00088 1140 2166 0.0012 -6.9397 8.4394 0.0000 0.2026 0.0000 67 | P a g e Table: 3. Ethyl Acetate + Propanol + Water at 303.15 K S. NO X(i) V E x10 6 cm 3 /mol βa x10 -10 m 2 n -1 U ms -1 H KJmol -1 G Kg mol -1 α/f 2 x10 -15 M -1 s -2 Vf x 10 6 m 3 /mol Vf x 10 m 3 /mol Lf x10 6 m 3 /mol Lf x 10 6 m 3 /mol 1 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1055 0.0000 64.6100 0.0000 2 0.9002 -0.3853 -0.0578 -0.4890 0.0031 -0.9407 -0.4890 0.1101 -0.0051 64.4506 -0.1875 3 0.7999 0.3108 -0.0216 -0.0055 0.0024 0.0567 -0.0055 0.1186 -0.0063 64.5874 -0.0790 4 0.7001 0.4028 -0.0019 -1.4945 0.0046 -0.5124 -1.4945 0.1247 -0.0099 64.6733 -0.0212 5 0.6002 -0.357 -0.1224 0.0110 0.0062 -1.1328 0.0110 0.1317 -0.0126 64.3206 -0.4020 6 0.5001 0.1794 -0.0618 -0.4945 0.0076 -1.3814 -0.4945 0.1393 -0.0147 64.5382 -0.2127 7 0.4004 0.5836 -0.0247 0.0221 0.0101 -2.1084 0.0221 0.1462 -0.0176 64.6829 -0.0960 8 0.3002 0.0405 -0.0676 -0.4890 0.0094 -2.1129 -0.4890 0.1570 -0.0165 64.5786 -0.2286 9 0.1980 0.6888 0.0207 -0.1100 0.0111 -2.6259 -0.1100 0.1660 -0.0174 64.8873 0.0513 10 0.1003 0.1970 -0.0044 -0.4835 0.0033 -0.4720 -0.4835 0.1863 -0.0066 64.8422 - 0.021 11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2026 0.0000 64.8918 0.0000 S. No X (i) Y (i) βa x10 -10 m 2 n - V x10 6 m 3 H Kg mol -1 G Kg mol -1 η x10 -3 m 2 s -2 U ms -1 Lf x10 3 A 0 Pi x 10 6 Pa Z x10 5 Kgm -2 s -1 1 0.7214 0.1005 -0.849 -7.751 -0.0094 5.0567 0.0000 -19.367 -1.206 -0.1029 -45.0507 2 0.6277 0.1013 -0.843 -7.129 -0.0115 7.4368 0.0000 -28.411 -0.451 -0.1526 -23.8818 3 0.5056 0.0978 -0.056 -3.654 -0.0058 7.9435 0.0000 -65.872 3.0749 -0.2233 -67.1043 4 0.4206 0.0977 0.1923 1.0247 -0.0026 10.540 0.0001 -46.903 4.4056 -0.2642 -130.728 5 0.3195 0.0988 -1.272 0.3595 -0.0048 13.331 0.0001 46.183 -0.188 -0.2905 -54.6449 6 0.2129 0.0963 -0.208 0.9844 -0.0418 22.368 0.0005 -23.433 3.6783 -0.2142 -137.012 7 0.1005 0.0982 -1.954 1.7183 -0.0011 12.979 0.0002 164.332 -3.398 -0.2749 -7.1016 8 0.0992 0.2048 -1.669 0.8048 -0.0154 15.910 0.0003 115.777 -2.201 -0.2456 -26.0531 9 0.1010 0.3084 -1.409 0.8051 -0.0081 13.140 0.0002 92.543 -1.431 -0.2505 -41.4531 10 0.1001 0.4105 -0.375 0.9399 -0.0115 11.996 0.0002 12.969 1.8625 -0.2161 -96.7512 11 0.0988 0.5128 -0.645 1.0809 -0.0037 9.1613 0.0001 38.350 0.4016 -0.1926 -63.2401 12 0.0971 0.6374 -0.359 0.9648 -0.0025 6.6955 0.0001 20.018 0.6575 -0.1391 -52.2058 13 0.0962 0.7296 -0.110 0.8286 -0.0083 6.6639 0.0001 4.2955 0.9078 -0.0855 -42.9605 14 0.0994 0.8116 0.1595 0.9700 -0.0027 3.1532 0.0001 -10.096 1.2242 -0.0484 -35.9857 15 0.1890 0.7254 0.8763 1.0948 0.0021 0.901 -0.0001 -55.817 3.5664 -0.0552 -68.4114 16 0.3051 0.6114 1.1157 1.8614 0.0068 -0.436 -0.0001 -65.827 4.3443 -0.0619 -81.2803 17 0.3998 0.5166 0.5194 1.7196 0.0087 -0.407 -0.0001 -34.074 2.4920 -0.0653 -54.2248 18 0.5156 0.3973 0.4136 1.2972 0.0110 -1.320 -0.0001 -31.199 2.1951 -0.0706 -47.9292 68 | P a g e Table: 4. Ethyl Acetate + Propanol + Water at 303.15 K S. N o X (i) Y (i) ρ x10 -3 kgm -3 η N.sm -2 U ms -1 βa x10 -10 m 2 n W τD x10 2 ps G Kg mol - Z x10 5 Kgm -2 s -1 Pi x 10 6 Pa Lf x10 3 A 0 1 0.7214 0.1005 0.9063 0.00067 1129 0.0483 2200 0.0008 -7.0109 10.2321 0.1599 58.7083 2 0.6277 0.1013 0.9113 0.00071 1131 0.0342 1994 0.0008 -6.9904 10.3068 0.1842 58.4435 3 0.5056 0.0978 0.8831 0.00070 1108 0.0082 1769 0.0009 -6.9660 9.7847 0.2133 60.6017 4 0.4206 0.0977 0.8277 0.00077 1137 -0.0098 1689 0.0010 -6.9206 9.4109 0.2403 61.0004 5 0.3195 0.0988 0.8438 0.00087 1242 -0.0314 1471 0.0009 -6.9515 10.4800 0.2937 55.3080 6 0.2129 0.0963 0.8433 0.00130 1185 -0.0580 1205 0.0015 -6.7438 9.9931 0.4567 57.9856 7 0.1005 0.0982 0.8393 0.00099 1386 -0.0641 999 0.0008 -6.9870 11.6327 0.4842 49.6944 8 0.0992 0.2048 0.8311 0.00110 1336 0.0265 1147 0.0010 -6.9080 11.1035 0.4385 51.8079 9 0.1010 0.3084 0.8093 0.00100 1311 0.0713 1323 0.0010 -6.9210 10.6099 0.3582 53.5022 10 0.1001 0.4105 0.7911 0.00099 1230 0.0935 1472 0.0011 -6.8623 9.7305 0.3205 57.6778 11 0.0988 0.5128 0.7767 0.00093 1254 0.1042 1653 0.0010 -6.8970 9.7398 0.2720 57.0959 12 0.0971 0.6374 0.7661 0.00091 1234 0.1089 1849 0.0010 -6.8868 9.4537 0.2379 58.4213 13 0.0962 0.7296 0.7602 0.00097 1217 0.1094 1991 0.0011 -6.8453 9.2516 0.2264 59.4668 14 0.0994 0.8116 0.7533 0.00090 1201 0.1122 2131 0.0011 -6.8617 9.0471 0.2025 60.5344 15 0.1890 0.7254 0.7613 0.00079 1146 0.1784 2177 0.0011 -6.8815 8.7245 0.1858 63.1054 16 0.3051 0.6114 0.7656 0.00071 1124 0.2238 2271 0.0010 -6.9123 8.6053 0.1679 64.1597 17 0 3998 0.5166 0.7757 0.00068 1146 0.2325 2350 0.0009 -6.9521 8.8895 0.1567 62.5170 18 0.5156 0.3973 0.7898 0.00062 1137 0.2134 2414 0.0008 -6.9917 8.9800 0.1443 62.4468 69 | P a g e 5. 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[10] Ambinabhavi ,M and Virupakashagouda , 1998,J.Chem.Eng.Data 43,(497) Books [1]Riddick,J.A., Bunger,W.B., Sanako,T.K., 1986, Physical properties and methods of purification , John Willy & Sons ,New York, [2] Hirschfelder, J.O, Curtio, and Byron bird .R., 1950,Molecular theory of gases and liquids.John Willy & Sons, New Yark. Others [1] R.N.Fort and W.R.Moore – 1965Trans.Faraday Society 61,(2102) [2] Handbook of Chemistry and Physics, 1984, The Chemical Rubber Company, USA, [3] Zorebski,E Zak, A Z.1999 Physikalis che Cheie. 210,(223). [4] Chauhan , M.S. Sharma, K.C et al .1995 Acoustics letters 18,12,(223) [5] Mukhrejee,A.Kamila ,S et al ,1999, Acoustics letters 23,1,(17) [6] Belsae, N.s. Akhare, V.P and Deogaonkar, V.S, 1990, Acoustic letters 14,2,(37) 70 | P a g e STUDY ON THERMO-ACOUSTICAL PARAMETERS OF SOME BINARY MIXTURES FROM VOLUME EXPANSIVITY DATA M.M. Armstrong Arasu and Dr. I. Johnson Centre for Nano Science and Applied Thermodynamics, Dept. of Physics, St. Joseph’s College, Trichy – 620 002, India. ABSTRACT: Researches have previously shown that the contribution of internal pressure and the temperature coefficient of volume to the sound velocity in the condensed phase is significant and that volume expansivity is the controlling factor for satisfactory description of the various parameter which describe the thermo-acoustic properties of polycrystalline solid, metal, alkali halide salt, polyatomic ionic liquid and organic liquid mixtures. Such a description employs only volume expansivity data. From the volume expansivity data the isothermal, isobaric and isochoric acoustical parameters, Moelwyn-Hughes parameter, fractional free volume, Huggin’s parameter, sharma’s parameters and repulsive exponent in Mie’s potential have been evaluated. Keywords: volume expansivity , Gruneisen parameter, Moelwyn-Hughes parameter, fractional free volume, Huggin’s parameter and Sharma’s parameters. 1. INTRODUCTION The volume expansivity data is highly useful for evaluating Gruneisen parameter which is a useful quantity in studying the internal structure, molecular order and thermo acoustical properties of liquids and polymers. The important of volume expansivity in evaluating various thermo acoustical properties has been amply demonstrated earlier. In this paper an attempt is made to analyze the relationship between different parameters that are used for system description like Moelwyn-Hughes parameter, fractional free volume, Huggin’s parameter, Sharma’s parameters and repulsive exponent in Mie’s potential have been evaluated in the mixtures Ethyl acetate + n-propanol and Methyl acetate + n-propanol at 308.15K. It is interesting to note that all these thermo acoustical properties are linked to a single experimentally determinable quantity, volume expansivity. 2. EXPERIMENTAL The binary mixtures were prepared by mass, by mixing the calculated volumes of liquid components in airtight glass bottles. In all the measurements, INSREF thermostat with a constant digital temperature display accurate to ±0.01K was used. For all the mixtures and pure solvent, triplicate measurements were performed and the average of all values was considered in the calculation. The mass measurements (±0.0001g) were made using an electronic balance. The accuracy of density measurements was 0.0001g.cm -3 . A set of 11 compositions was prepared for binary mixtures and their physical properties were measured. Viscosity is measured by calibrated Ostwald’s Viscometer. The speed of sound was determined using a constant frequency (2MHz) ultrasonic interferometer with an accuracy of ± 2 m.s -1 . 3. THEORY The volume expansivity is given by | ¹ | \ | = = dT d 1 V 1 ρ ρ α dT dV (1) 71 | P a g e Let V, and respectively molar volume, Volume expansivity and isothermal compressibility. If * and V* are the characteristic compressibility and volume (at absolute zero temperature and zero pressure), the their reduced values are given by, C1 ~ ~ V * = = β β β (2) ( ) 3 ~ T 1 3 T 1 * V V + + = α α V (3) The Moelwyn-Hughes parameter is ( ) T 3 4 3 13 dlnV dln 1 1 α α β + + = = − T C (4) The Sharma’s parameters are expressed as, ( ) T 4 3 V T 2 1 ~ C1 0 α α + | | ¹ | \ | + = S (5) T 3 4 1 * α + = S (6) ( ) | ¹ | \ | + + = T 3 4 1 T 2 1 * 0 α α S (7) Huggin’s parameter F is given in terms of Sharma’s parameters given above as, ( ) T S S F α 1 - S * 2 * 1 0 + − = (8) Eqns. (1)-(8) demonstrate the importance of in the evaluation of the parameters V, C1, S, S0, S0* and F, since all the parameters involved therein may be determined from the knowledge of alone. The volume dependence of sound speed in liquids at constant pressure and at constant temperature is represented by isobaric and isothermal acoustical parameters k and k’ respectively, due to Rao, Carnevale and Litovitz. While examining the relationship between sound velocity u and density in liquids and determining the difference between k and k’ in liquids, Aziz, and Sharma have shown that the isochoric acoustical parameter k’’ is given by. k’ = k = k’’ (9) In which P k | ¹ | \ | ∂ ∂ = | ¹ | \ | ∂ ∂ = T lnu 1 - V ln lnu - P α (10) T k | ¹ | \ | ∂ ∂ = | ¹ | \ | ∂ ∂ = P lnu 1 - V lnu - T ' β (11) T P T u k | ¹ | \ | ∂ ∂ − | ¹ | \ | ∂ ∂ = = = P lnu 1 ln 1 k k ' " β α (12) Alternatively, the isobaric and isochoric acoustical parameters may be expressed in terms of α as 3 2 2 1 3 5 T T k α α + + = (13) 72 | P a g e ( ) 1 1 1 " 1 T 2 - C C V V k − − − + − = α (14) Using these calculated values of k and k’’, the isothermal acoustical parameter k’ can then be calculated for the binary liquid mixtures, using eqn(9). The sound speed can be expressed as u 2 = s, where = Cp/Cv, Cp and Cv are respectively the isobaric and isochoric heat capacity of the liquid. The fractional free volume f which is a measure of disorder due to the increased mobility of molecules in a liquid and can be expressed as, f = Va/V = (k’+1) -1 (15) The repulsive exponent n in the Mie’s potential is given by, n = 3 (2k’ -3) (16) The equation (13) can be rearranged to give the dimensionless thermo acoustic parameters A* and B* as, A* = 1+ ' k f (17) B* = 1+ k f (18) The pseudo-Gruneisen parameter used for structural study of liquids is usually expressed as ( ) T C Mu C V p v s α γ α β α 1 2 − = = = Γ (19) The Gruneisen parameter is an important quantity of current interest because of its usefulness in studying the internal structure, molecular order and other thermo acoustic properties of polymers and liquids. We have a distinct relationship between the microscopic isothermal Gruneisen parameter ’ (as a measure of anharmonicity of the normal mode frequency v of the molecular vibrations), and the conventional thermodynamic Gruneisen parameter ’ (used for the structural study of liquids). There are two distinct modes are of low frequency and are anharmonic. They are characterized by high values of ’. The low frequencies of these modes are determined almost entirely by the weak intermolecular forces. The intra molecular optical modes of vibration are of high frequency and are harmonic. They are characterized by low values of , and arise from the strong intra molecular forces which are altered little by pulling the molecules apart. The anharmonic (microscopic isothermal) Gruneisen parameter ’ is determined primarily by the intermolecular vibration, while is an average over all modes of vibration, including intermolecular and intra molecular vibrations which employ capacities of the liquid. As relatively little is known about the influence of the intermolecular vibration, while r is an average over all modes of vibration, including intermolecular and intra molecular vibrations which employ thermodynamic parameters such as the isochoric Cv and isobaric Cp heat the intermolecular vibrations on the heat capacity Cp in quasi spherical molecular liquids and fluorocarbon fluids, the analysis of the theoretical foundations of the relationship between ’ and t is essential for this class of liquids. The ratio of the Gruneisen parameters (/’) is utilized to measure the intermolecular isobaric heat capacity and the adiabatic bulk modulus due to the molecular vibrations in these liquids. Much confusion has existed in literature to recognize the difference between ’ and for liquids. It may be clearly pointed out that the concept of ’ and is appropriate to all the solids, molten metals, liquids, liquefied gases and polymers which show anharmonicity of molecular vibrations. However, K.M. Swamy overlooked the basic conceptual aspect that and ’ may not have the same values for different substances. It was shown that ’ and in case of organic liquids differ from one another. For organic molecules, experimentally it is observed that ’> which implies that a certain fraction of the molecules in a molecular liquid has a finite and common fractional frequency dependence on the volume at a constant temperature and the remaining modes are unaffected by volume changes. Following Hart-mann, this fact can be explained by noting that not all the normal mode contributions to heat capacity Cp also contribute to the volume change of the sound speed (molecular rotation, for example). The analogous situation in the case of polymeric materials has already been noted. In order for to be as large as ’, only a fraction Cp’ of the total cp that is taken up by the molecular vibrations which interact with volume, should be used in eqn.(15). 73 | P a g e Thus ’u α/Cp’ (20) From eqns (19) and (20) it follows that X -1 = /’ = Cp’/Cp (21) Eqn(21) shows that the quantity X = /’ is of some interest since it gives a simple method to measure the ration C’p / Cp for a complex liquid and hence Cp which refers to that part of the isobaric heat capacity taken up by molecular vibrations which interact with volume. The Andeson-Gruneisen parameters has been expressed as 1 2 1 + = | ¹ | \ | ∂ ∂ = ∆ k T in P s β α (22) Beyer’s nonlinearity parameter B/A of liquids can be obtained from the distortion of the finite amplitude waves, and from the variation with pressure and temperature of the sound velocity. The B/A is a particular combination of the temperature and pressure derivation of the sound of speed is a given by P P T T u C T u T u u A B | ¹ | \ | ∂ ∂ | | ¹ | \ | + | ¹ | \ | ∂ ∂ = α ρ 2 2 (23) which can be rewritten as B/A = (B/A)’ + (B/A)” (24) Where (B/A)’ = (C1-1) (25) (B/A)” = - ( -1) (-1) (26) Eqns (23) - (26) lead to a way to determine the Beyer’s nonlinear parameter theoretically. 4. RESULTS AND DISCUSSION In the table 1to 4 give the calculated values of , s, C, ~ ,S, So, S*, F, k, k”, f, N, A*, B* and k/ k’, for binary liquid mixture of Propanol + Ethyl acetate and Methyl Acetate + n-proponol using only the experimental data of density at three different temperatures. It may be absorbed from table 1 and 2 that C values vary from 6.8 to 9.8 for the liquid mixture studied in agreement with the value of C, in other non- associated of the liquids. This signifies the non –linear variation of volume expansivity of the liquids with mole fraction. The value of reduced compressibility s ranges from 5.2 to 13.1 as compared to the range from about 5 to 14 for the molen alkali halides and 4 to 6 for polymers. The value of So remains fairly constant within the experimental error. The estimated values of So are on the average, lie the range 1.2 to 1.49. The Sharma’s parameter So may be termed a molecular constant which varies its constancy for a wide verity of binary mixtures for investigating thermo acoustic and an harmonic properties. The calculated values of S* are around 1.1 to 1.2 for the binary mixture as compared to 1.5 for polymers .It may be interesting to note that So* is equal to 1.1 to 1.2 similar to that of poly crystalline solids. The Value of the Huggin’s parameter ranges from about 0.4 to 1.3 which is of the same order as observed for polymers, crystalline and molten alkali halides, liquid alkali metals and ionic liquids. The Calculated acoustical parameter k range from 0.2 to 4.4 in the mixtures, the value of the ratio k/k’ is close to about unity, for liquid. The value of n is found to 13.3 to 18.8 with different mole fraction, which is the same order as reported by Sockiewies. The average values of the dimensionless parameters A* and B* for the liquid mixtures examined have the value 1.03 to 1.07 respectively in the case of fluorocarbon fluids. This means that on the average the approximate relationship A* = B* = 1.05 for holds for these liquids mixtures as compared to A* =B* =1.05 for fluorocarbon fluids. 74 | P a g e Table -1 Nonlinear parameter of Ethyl Acetate + proponol (Temp=30,35and 40 0 C) Note: x(i) is Mole fraction of Ethyl Acetate Table -2 Nonlinear parameter of Ethyl Acetate + proponol (Temp=30,35and 40 0 C) Note: x(i) is Mole fraction of Ethyl Acetate Table -3 Nonlinear parameter of Methyl Acetate and n-proponol (Temp=30,35and 40 0 C) Note: x(i) is Mole fraction of Methyl Acetate X(i)1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 1.3616 1.3328 1.2335 1.3286 1.2373 1.2145 1.1930 1.2189 1.1219 1.0978 1.0349 V ~ 1.3256 1.3203 1.3014 1.3195 1.3022 1.2978 1.2936 1.2986 1.2795 1.2746 1.2618 C 7.2760 7.3156 7.4708 7.3216 7.4644 7.5042 7.5435 7.4964 7.6867 7.7404 7.8940 ~ 7.7766 7.6355 7.1609 7.6149 7.1785 7.0724 6.9730 7.0926 6.6506 6.5438 6.2702 S 1.1064 1.1075 1.1111 1.1077 1.1110 1.1118 1.1125 1.1116 1.1146 1.1153 1.1168 So 1.5594 1.5476 1.5068 1.5459 1.5083 1.4990 1.4901 1.5008 1.4609 1.4510 1.4252 S* 1.1793 1.1769 1.1681 1.1765 1.1685 1.1664 1.1644 1.1668 1.1577 1.1554 1.1491 F 0.9135 0.9294 0.9848 0.9318 0.9827 0.9954 1.0075 0.9930 1.0476 1.0613 1.0972 k 3.1380 3.1578 3.2354 3.1608 3.2322 3.2521 3.2718 3.2482 3.3434 3.3702 3.4470 k” 0.7181 0.7096 0.6766 0.7083 0.6780 0.6697 0 6613 0.6713 0.6321 0.6213 0.5904 k’ 3.8562 3.8674 3.9121 3.8691 3.9102 3.9218 3.9336 3.9195 3.9756 3.9915 14.037 f 0.2059 0.2054 0.2035 0.2053 0.2036 0.2031 0.2020 0.2032 0.2009 0.2003 0.1985 n 14.137 14.204 14.472 14.215 14.461 14.531 14.600 14.517 14.853 14.949 15.225 A* 1.0533 1.0531 1.0520 1.0530 1.0520 1.0518 1.0515 1.0518 1.0505 1.0501 1.0491 B* 1.0652 1.0650 1.0629 1.0649 1.0630 1.0624 1.0619 1.0625 1.0601 1.0594 1.0575 k/k’ 81376 0.8165 0.8270 0.8169 0.8266 0.8292 0.8318 0.8287 0.8409 0.8443 0.8537 X(i) (B/A)’ (B/A)” (B/A) 1.0 7.27615 1.692 1.64924 10.61914 -4.34309 6.27603 0.9 7.31574 1.65691 1.59940 10.46456 -4.14892 6.31563 0.8 7.47094 1.62270 1.63815 10.50033 -4.02948 6.47084 0.7 7.32172 1.58901 1.43861 10.04519 -3.72356 6.32162 0.6 7.46449 1.55469 1.45479 10.05019 -3.58580 6.46439 0.5 7.50428 1.51888 1.38637 9.879134 -3.37495 6.50418 0.4 7.54363 1.48480 1.31869 9.715938 -3.17239 6.54354 0.3 7.49654 1.45090 1.20045 9.425764 -2.92932 6.49644 0.2 7.68684 1.41481 1.19984 9.460561 -2.77381 6.68674 0.1 7.74051 1.38008 1.12354 9.302373 -2.56194 6.74042 0.0 7.89416 1.345 1.08175 9.272562 -2.37848 6.89407 X(i) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 2.2874 2.1791 2.0784 1.9747 1.8565 1.7460 1.6201 1.4903 1.3683 1.2414 1.0991 V ~ 1.4734 1.4579 1.4434 1.4280 1.4098 1.3921 1.3713 1.3488 1.3268 1.3030 1.2749 C 6.6918 6.7178 6.7486 6.7880 6.8441 6.9093 7.0020 7.1230 7.2671 7.4573 7.7373 75 | P a g e Table-4 Nonlinear parameter of Methyl Acetate and n-proponol (Temp=30,35and 40 0 C) Note: x(i) is Mole fraction of Methyl Acetate ~ 13.355 12.588 11.904 11.228 10.493 9.8372 9.1257 8.4303 7.8099 7.1979 6.5499 S 1.0499 1.0583 1.0656 1.0728 1.0806 1.0873 1.0943 1.1007 1.1061 1.1109 1.1152 So 1.9398 1.8953 1.8539 1.8113 1.7627 1.7173 1.6656 1.6123 1.5622 1.5100 1.4516 S* 1.2422 1.2362 1.2303 1.2239 1.2163 1.2088 1.1998 1.1899 1.1799 1.1689 1.1555 F 0.4210 0.4769 0.5292 0.5835 0.6459 0.7043 0.7723 0.8422 0.9095 0.9804 1.0606 k 2.8459 2.8589 2.8745 2.8940 2.9220 2.9546 3.0010 3.0615 3.1339 3.2287 3.3686 k” 0.8720 0.8614 0.8504 0.8377 0.8214 0.8038 0.7806 0.7522 0.7201 0.6794 0.6219 k’ 3.7179 3.7203 3.7247 3.7318 3.7434 3.7585 3.7817 3.8138 3.8537 3.9082 3.9906 f 0.2119 0.2118 0.2116 0.2113 0.2108 0.2101 0.2091 0.2077 0.2060 0.2037 0.2003 n 3.3085 13.322 13.348 13.390 13.460 13.551 13.690 13.882 14.122 14.449 14.943 A* 1.0570 1.0569 1.0568 1.0566 1.0563 1.0559 1.0553 1.0544 1.0534 1.0521 1.0502 B* 1.0744 1.0740 1.0736 1.0730 1.0721 1.0711 1.0696 1.0678 1.0657 1.0631 1.0594 k/k’ 0.7654 0.7684 0.7716 0.7755 0.7805 0.7861 0.7935 0.8027 0.8131 0.8261 0.8441 X(i) (B/A)’ (B/A)” (B/A) 1.0 6.691925 1.692 .9817346 9.630624 -3.938812 5.691812 0.9 6.717931 1.656918 .9782763 9.474034 -3.756214 5.717821 0.8 6.748702 1.622704 .9722448 9.328334 -3.57974 5.748593 0.7 6.788105 1.58901 .9679546 9.197252 -3.409254 5.787998 0.6 6.844169 1.554692 .9695939 9.085779 -3.241714 5.844065 0.5 6.909399 1.518882 .964404 8.975575 -3.066279 5.909297 0.4 7.002077 1.484806 .9710738 8.911823 -2.909846 6.001978 0.3 7.123152 1.450904 .9817998 8.884011 -2.760957 6.123055 0.2 7.267194 1.414816 .9837708 8.866835 -2.599735 6.2671 0.1 7.457465 1.380082 .9935296 8.911737 -2.454365 6.457373 0.0 7.737373 1.345 1.018563 9.061678 -2.324394 6.737284 76 | P a g e 5. REFERENCES: Periodicals [1] I. Johnson, M.Kalidoss and R.Srinivasamoorthy, 2001, Acoustical investigation of some binary and ternary liquid mixtures – Proceedings of the 17th international congress on Acoustics (ROME), ,Vol.I,Physical Acoustics – Part B,(12). [2] Pandey,J.D. and Ashok kumar, 1994,Ultrasonic velocity in pure liquids, J. Pure and Applied Ultrasonic, 16(63). [3] J.P.E.Grolier, and A.Viallard, 1971, J. chem. phys. 68(1442) [4] J.ortaga, J.A.Pena, M.I. Paz-Andrade, and E.Jimnez, 1985 J. Chem. Thermodyn.17 (1127). [5] V.D.Gokhale and N.N.Bhagavat, 1989, Evaluation of Ultrasonic Velocities in some Binary Liquid Mixtures by Rao Specific Sound Velocity. J.Pure and Appl.Ultrasonic., 11(21). [6] C.V Sorianarayan , 1976 ,J Acoustics Soc. Of India, 4 (76). [7]Senanayake,P.C., Gee,N. and Freeman, R.G.1987 Can. J. Chem. Eng.Data,65(2441). [8] Kalidoss.M and Srinivasamoorthy .R, 1997 J.Pure and Appl.Ultrasonic 19,(9). [9] Viswanatan, S, and Anand rao,M, 1999.J.Chem. Eng.Data 45, (764). [10] Ambinabhavi, M and Virupakashagouda, 1998, J.Chem.Eng.Data 43,(497) [11]K.M. Swamy, Acoustic (Germany) 29,197(1973) Books [1]Riddick,J.A., Bunger,W.B., Sanako,T.K., 1986, Physical properties and methods of purification , John Willy & Sons ,New York, [2] Hirschfelder, J.O, Curtio, and Byron bird, R., 1950, Molecular theory of gases and liquids.John Willy & Sons, New Yark. Others [1] R.N.Fort and W.R.Moore – 1965Trans.Faraday Society 61,(2102) [2] Handbook of Chemistry and Physics, 1984, The Chemical Rubber Company, USA, [3] Zorebski,E Zak, A Z.1999 Physikalis che Cheie. 210,(223). [4] Chauhan , M.S. Sharma, K.C et al .1995 Acoustics letters 18,12,(223) [5] Mukhrejee,A.Kamila ,S et al ,1999, Acoustics letters 23,1,(17) [6] Belsae, N.s. Akhare, V.P and Deogaonkar, V.S, 1990, Acoustic letters 14,2,(37) 77 | P a g e A COMPREHENSIVE ANALYSIS OF SOLVATION NUMBER OF SOME ORGANIC ACID SALTS IN NON- AQUEOUS MEDIUM Jasmine Vasantha Rani E ^ and Suhashini Ernest * ^ Dept. of Physics, Seethalakshmi Ramaswamy College, Trichy-620002, India. *Dept. of Physics, Urumu Dhanalakshmi College, Trichy-620019, India. E mail:
[email protected] [email protected] Ultrasonic measurement can be used as a powerful probe to study the structural, physical and chemical properties of matter. In the present study, measurements of ultrasound velocities, and densities for various concentrations of non-aqueous formamide solutions of calcium salts of some organic acids for different temperatures have been made in order to investigate the compressibility behaviour in the solutions. Calculation of solvation number of the solutions is undertaken to highlight the interactions existing in the solutions. The result obtained from compressibility method is seen to agree well with the results from different theoretical and experimental methods. Keywords: Solvation number, formamide, calcium salts of some organic acids INTRODUCTION Ultrasonic measurements have gained momentum in recent years for the study of liquids, liquid mixtures, aqueous and non-aqueous electrolytes solutions. The ultrasonic velocity data combined with density constitute the standard means for determining the compressibility of the system under consideration. The compressibility of the system throws light on the ion- ion and ion-solvent interactions. The samples chosen are calcium salts of carboxylic acids and its derivatives. The study of molecular interactions existing in the non-aqueous solutions of calcium salts has been made through ultrasonic velocity measurements. EXPERIMENTAL PROCEDURE AND COMPUTAION Ultrasonic velocity (u) of AR grade Calcium salts in Formamide is measured at the frequency of 2 MHz with a Mittal Interferometer with an accuracy of ± 2 m/s. The density (ρ) measurements are made with accuracies of ±0.001gm/cc. Solvation number (ns) is computed using the following formula Solvation number ns = (nf /ni) (1-(β / β0)) 78 | P a g e where u the ultrasonic velocity, ρ the density , β , β0 the adiabatic compressibility of the solutions and the solvent and nf , ni is the number of moles of solvent formamide and number of ions solvated. 8. RESULT AND DISCUSSION Passynski has taken consideration of the adiabatic compressibility of the solute and solvent for deriving solvation number[1]. The study of solvation number is used to interpret ion-solvent interactions. The solvation number is defined as the number of solvent molecules per ion, which remain attached to a given ion long enough to experience its translational movements. The values of solvation number for various values of temperatures and molalities are presented in Table 1 The decrease in the solvation number with increasing concentration reveals that either there is not enough solvent for all the ions or preferably ion pairing has occurred. The positive solvation number for the solutions suggests that the compressibility of the solution at high temperatures may be less than that of solvent. However, the fall in solvation number at high temperatures and the rise in solvation number from negative maximum towards zero at low temperatures may be attributed to the decreasing ion-solvent interactions but with further increase in concentration, it remains constant. This may be due to the dominant effect of intermolecular attraction of solutes over ion- solvent interactions.The general observations on solvation number of the system studied in relation to temperature and molality may be summarized as follows. • The solvation number is positive above room temperature and is negative below room temperature. • Gradual increase of solvation number from lower to higher concentrations is observed. • The solvation number values are approximately found to be zero near higher concentration of 0.1m and 0.15m mostly at lower temperature. • The sign of the solvation number indicates the relative values of compressibility of solution and the solvent. 79 | P a g e The negative values of solvation number at temperatures emphasize that the solutions are more compressible than the solvent. This may be attributed to the mobility of the ion being low at the low temperatures. Therefore solution is more compressible than the solvent and hence the negative sign for the solvation number. Positive solvation number suggests that compressibility of the solution at high temperatures at all molalities will be less than that of the solvent supporting the fact that ions gain high mobility and have more probability of contacting solvent molecules. Therefore an increase in interaction between ion and solvent molecules is expected. Zero value of solvation number indicates that no change occurs in the compressibility value of the solvent when the solution is formed [2]. The rise in solvation number from negative value towards zero at low temperatures and fall in solvation number at higher temperature with increasing concentration may be attributed to decreasing solute-solvent interaction. The constant values of solvation number at higher concentrations and higher temperatures may be due to the strong ion-ion attractions between the electrolyte molecules than the ion-solvent interactions[3]. The perusal of Table 2 shows that the number of solvent molecules in the coordination sphere varies with anions [4]. An inspection of Table.1 stands in agreement with the fact that ‘the more dilute the solution ,the greater the solvation of a given ion’[5].Table.3 presents the solvation number computed from different methods, which agree with the values calculated in the present measurements. CONCLUSION The solvation number of calcium ion calculated from the compressibility study for sample solutions agree well with the values reported from other methods. 80 | P a g e REFERENCES 1. Passynski A, (Acta Physicochem.8, 385.,)1930. 2. Kuppuswami J., Lakshmanan A.S., Lakshminarayanan R., Rajaram N. and Surayanarayana C.V. (Bull. Chem. Soc. Jap 38, 1610.,)1965. 3. Bhuller S.K., Bhavneet K., Bakshi M.S. Jabir S., Sharma S. C and Joshi I.M., (Acoustica, Vol. 73, 292.,)1991. 4. Kothai S and Kannapan V.,(Proceedings of National Symposium on acoustics,437-441.,) 2007. 5. Christian Riechardt,’Solvent and solvent effects in organic chemistry,(Wiley VCH Third Edition,35.,)2003. 6. Samoilov O.Ya., ‘Structure of Aqueous Electrolyte solutions and hydration of numbers at 25 O C’, (Consultants Bureau New York, N.Y.,) 1965. 7. Yasutiro Umebayashi, Yutaka Mune, Taiga Tsukamoto Yue Zhang, Shin Chi Ishiguro. ( J. mol. liquids vol.118, issues 1-3, pp. 45-49.,) 2008. 8. Ulström, Ann-Sofi Warminska, Dorata Person Ingmar.,( vol.158, Number 7, 12,pp 611-612.,) 2005. 9. Anan Tongraar, Kritsana Sagarik, Bernd Michal Rode.,( phys. chem. chem. phys, 4, 628-634.,) 2002. 10. Asada M., Fujimori.T., Kanzaki,K.,Umebayashi, R., Ishiguro,S.,(J. of Raman spectroscopy vol. 38, no.4.,)2007. 11. Meyes Jünde Grosz Tamas Radnai Tamas Bako Imrl Palinkas Gabor,(J. Phys. Chem. vol.108, No.35, pp 7261-7271.,) 2004. 12. Gapon, E.N., Z. Anorg.,(Allg. chem., 168, 125.,) 1927. 13. Ulich H,( Trans Faraday Soc 23, 392.,)1927. 14. Passynski .,( A., Acta Physicochim U.R.S.S 8,385.,)1938. 15. Azzam A. M., (Can .J.Chem. Vol 38, 993-1002.,) 1960. 81 | P a g e Table - 1 SOLVATION NUMBER C A L C I U M L A C T A T E Molality (m) 5˚ C 15˚ C 25˚ C 35˚ C 45˚ C 55˚ C 0.001 -168 -94 -244 34 250 377 0.005 -133 -17 -36 28 73 91 0.01 -34 5 -12 -6 24 35 0.05 -9 1 -1 3 3 7 0.1 -3 2 1 3 4 5 C A L C I U M P A N T O T H E N A T E 0.001 -818 -391 -168 -84 153 366 0.005 -138 -51 10 -8 61 123 0.01 -30 -6 12 22 48 47 0.05 -6 2 1 -4 11 6 0.1 1 4 4 4 8 18 9 . C A L C I U M A S C O R B A 0.001 -449 77 -481 21 254 274 0.005 -110 -38 -25 15 73 70 0.01 -43 -10 -8 59 10 44 0.05 -5 5 -15 9 2 28 0.1 5 3 7 11 11 5 0.15 4 6 5 6 8 8 C A L C I U M A C E T A T E 0.001 -268 -88 -247 -486 84 -63 0.005 -44 25 -6 -21 53 84 0.01 -4 19 9 11 32 75 0.05 -8 -1 -2 1 6 10 0.1 -2 1 0 4 5 9 0.15 0 -1 -1 1 2 4 C A L C I U M P R O P I O N A T E 0.001 -640 -396 -298 200 754 817 0.005 -228 -53 -53 76 165 243 0.01 -64 -42 -5 53 110 110 0.05 -12 3 -2 10 18 24 0.1 -10 0 -2 4 12 4 0.15 -6 -3 -1 7 9 4 C A L C I U M L A C T O B I O N A T E 0.001 -534 -417 -457 117 603 1151 0.005 -91 -44 -83 83 74 248 0.01 -91 -12 -10 9 62 88 0.05 -10 -5 -5 8 23 31 0.1 -4 4 2 7 7 17 C A L C I U M C I T R A T E 0.001 -629 -97 -327 -149 114 381 0.005 -84 -7 -9 8 49 101 0.0075 -57 -18 -35 -4 30 70 0.01 -33 3 -14 20 28 51 0.0125 -41 -3 -33 0 12 18 C A L C I U M L E V U L I N A T E 0.001 -255 -281 -260 -153 214 230 0.005 -18 -32 -37 3 68 -48 0.01 -17 6 -11 18 52 8 0.05 -4 -1 -3 -1 8 10 0.1 -1 6 -1 2 3 1 0.15 0 1 0 2 3 2 82 | P a g e Table 2 The solvation number for Ca 2+ ion in formamide at 35 O C and 0.1m for all the samples Sample Solvation number Calcium levulinate 2 Calcium lactate 3 Calcium pantothenate 4 Calcium acetate 4 Calcium propionate 4 Calcium lactobionate 7 Calcium ascorbate 11 Table 3 The solvation number of Ca 2+ reported from different studies in different solvents. Study Solvation number. From Aqueous solutions at 25 O C [6] 4 CaClO4 in DMPA at 298 (from Raman spectroscopy)[7] 6 Calcium ion in DMS (LAXS)[8] 6 Ca 2+ in Aq. Ammonium solutions (QM/MM simulation)[9] 7.2 Ca 2+ in DMF & DMA (Raman Spectroscopy & DFT calculations)[10] 7 CaCl2 in water and methanol solutions (X-ray Diffraction and ab initio calculations[11] 8 (water) 6 (Methanol) Ca 2+ in water at 25 O C (diffusion methods)[12] 9 Mobility Experiments[13] 7.5-10.5 Compressibility Study[14] 16 Theoretical studies on divalent ions at 25 O C[15] 12.3 83 | P a g e Ultrasonic study on binary mixtures of ethyl benzoate with benzene and substituted benzenes at different temperatures B. Nagarjun a , Y.V. V Apparao a , G.V Ramarao b , A.V Sarma a , C. Rambabu c a Department of Physics, Andhra University, Visakhapatnam. b Department of Physics, DAR college, Nuzvid. c Department of Chemistry, ANU, Dr.M.R.Appa Row Campus, Nuzvid. ABSTRACT : Densities, ultrasonic velocities and viscosities of ethyl benzoate + benzene, + Chloro benzene, + nitrobenzene have been measured at temperatures 303.15 – 318.15K. The measured data used to compute adiabatic compressibility (βad), deviation in adiabatic compressibility (∆βad), deviation in viscosity (∆η), intermolecular free length (Lf) and molar volume (Vm). The excess molar volume (Vm E ) and excess free length (Lf E ) are also evaluated for all the systems. These results were satisfactorily correlated by Redlich-Kister polynomial. The excess parameters are used to discuss molecular interactions between unlike molecules. KEYWORDS: Ultrasonic velocity, excess properties. 1. Introduction The thermodynamic study of esters has attracted increasing interest because these chemicals have an extensive variety of applications [1,2,3 Ultrasonic velocity together with density, viscosity data furnish a wealth of information about the sum total of interactions between ions, dipoles, H- bonding, multi polar and dispersion forces[4-7]. The extensive uses of polymeric materials in technology have prompted ultrasonic studies to help to understand the structures of polymers and molecular interactions in solutions and nature of polymers[8,9] The present paper deals with the study in the binary liquid mixtures of ethyl benzoate (1) + benzene (2), + chlorobenzene (2), + nitrobenzene(2) at 303.15K, 308.15K, 313.15K and 318.15K. Further the data has been obtained at different temperatures with a view to understand the effect of temperature on these properties. 2. Experimental Details Ethyl benzoate (EB), benzene, Chlorobenzene and nitrobenzene were purified using fractionating column[10,11,12]. 84 | P a g e The accuracy in the measurement of density employing the specific gravity bottle method is better than + 0.01%. Viscosity was determined by Ostwald’s viscometer,. The values are accurate to +0.001c.p. Velocities were determined using single crystal ultrasonic interferometer (Model M-81, Mittal enterprises, India) working at 2 MHz. 3. Theoretical considerations Assuming that ultrasonic absorption is negligible, adiabatic compressibilities can be obtained from the densities and ultrasonic sound velocities using the relation βad = (ρu 2 ) -1 ……….. 1 The molar volumes of the binary mixtures were calculated using the equation V = (X1M1+X2M2 ) / ρ ……….. 2 Intermolecular free length (Lf) was calculated from the measured density and ultrasonic velocity by using the following relation Lf = K/ uρ 1/2 ………… 3 where K is the temperature dependent Jacobson constant 13 and T is the absolute temperature. The excess properties such as ∆βad, V E , ∆η and Lf E have been calculated using the equation Y E = Ymix - (X1Y1+X2Y2) ……………. 4 where Y E is βad or V E or ∆η or Lf E , and X represent mole fraction of the component and subscripts 1 and 2 stand for the components1and 2. 4. Results and Discussion On the basis of a model for sound propagation proposed by Eyring and Kincaid[13], ultrasonic velocity should decrease if the intermolecular free length increases as a result of mixing of components. This fact is observed in the present investigation for Ethyl benzoate+ Benzene and Ethyl benzoate + Chlorobenzene systems. In Ethyl benzoate + Nitrobenzene system, velocity decrease as free length increases with concentration of ethyl benzoate. The ultrasonic velocity varies non - linearly with concentration without any maxima or minima at all temperatures [14] as evident from Table 1. The deviations in adiabatic compressibility are negative for all the three systems of ethyl benzoate with benzene, chlorobenzene and nitrobenzene as shown in Figs. 1.2, 2.2 and 3.2. The adiabatic compressibility is proportional to strength of interaction between unlike molecules. The ∆βad values fall in the order Benzene > Chlorobenzene >Nitrobenzene 85 | P a g e The sign of deviation in adiabatic compressibility and excess free length plays a vital role in assessing the compactness due to molecular interactions in liquid mixtures through charge transfer, dipole-dipole interactions, dipole-induced dipole interactions, interstitial accommodation and orientation ordering leading to more compact structure [15] The V E values become more negative at higher temperature( Figs.1.1,2.1,3.1), suggesting an increase in interaction between component molecules[16,17] Excess molar volumes for ethylbenzoate + nitrobenzene system are more negative than that of ethylbenzoate + chlorobenzene system or ethylbenzoate + benzene system ( Figs.1.1,2.1,3.1) The general trend in variation of excess molar volume of the mixtures follows the sequence. Benzene> Chloro benzene>Nitro benzene. As temperature increases dissociation of associated species takes place releasing more and more free molecules but because of favorable packing of ethyl benzoate and benzene or substituted benzene molecules into each other’s structure [18,19] . The values of ∆η for the whole mole fraction range for all the three systems are positive as evident from Figs. 1.4, 2.4 and 3.4. For the systems where dispersion and dipolar interactions were operating the values of viscosity deviations are found to be negative where as specific interactions tend to make deviations positive[20]. The ∆η values have the following trends for binary mixtures with ethyl benzoate as common component, Nitro benzene > Chloro benzene > Benzene 86 | P a g e -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 D e v i a t i o n i n a d i a b a t i c c o m p r e s s i b i l i t y ( ∆ β a d ) Molefraction of Ethyl benzoate Fig 1.2- Variationof deviation in adiabatic compressibility with molefraction Ethyl benzoate for Ethyl benzoate + Benzene system 303.15K 308.15K 313.15K 318.15K -1.5 -1.0 -0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 E x c e s s m o l a r v o l u m e ( V E ) Molefraction of Ethyl benzoate Fig 1.1 - Variation of excess molar volume with molefraction of Ethyl benzoate for Ethyl benzoate + Benzene system 303.15K 308.15K 313.15K 318.15K 0.00 0.05 0.10 0.15 0.20 0.0 0.2 0.4 0.6 0.8 1.0 D e v i a t i o n i n v i s c o s it y ( ∆ η ) Molefraction of Ethyl benzoate Fig 1.4 - Variation of Deviation in viscosity with molefraction of Ethyl benzoate for Ethyl benzoate + Benzene system 303.15K 308.15K 313.15K 318.15K -0.014 -0.012 -0.010 -0.008 -0.006 -0.004 -0.002 0.000 0.0 0.2 0.4 0.6 0.8 1.0 E x c e s s i n t . m o l . f r e e l e n g t h ( L f E ) Molef raction of Ethyl benzoate Fig 1.3 - Variation of excess intermolecular free length with molefraction of Ethyl benzoate for Ethyl benzoate + Benzene system 303.15K 308.15K 313.15K 318.15K -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 D e v i a t i o n i n a d i a b a t i c c o m p r e s s i b i li t y ( ∆ β a d ) Molef raction of Ethyl benzoate Fig 2.2 -Variation of deviation in adiabatic compressibility with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system 303.15K 308.15K 313.15K 318.15K -1.5 -1.0 -0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 E x c e s s m o l a r V o l u m e ( V E ) Molefraction of Ethyl benzoate Fig 2.1 - Variation of excess molar volume with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system 303.15K 308.15K 313.15K 318.15K 0.0 0.1 0.2 0.0 0.2 0.4 0.6 0.8 1.0 D e v i a t i o n v i s c o s i t y ( ∆ η ) Molef raction of Ethyl benzoate Fig 2.4-Variation of deviation in viscosity with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system 303.15K 308.15K 313.15K 318.15K -0.020 -0.015 -0.010 -0.005 0.000 0.0 0.2 0.4 0.6 0.8 1.0 E x c e s s i n t . m o l . f r e e l e n g t h ( L f E ) Molefraction of Ethyl benzoate Fig 2.3 -Variation of excess inter molecular free length with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system 303.15K 308.15K 313.15K 318.15K 87 | P a g e -5.0 -4.0 -3.0 -2.0 -1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 D e v i a t i o n a d i a b a t i c c o m p r e s s i b i l i t y ( ∆ β a d ) Molefraction of Ethyl benzoate Fig 3.2 -Variation of deviation in adiabatic compressibility with molefraction of Ethyl benzoate for Ethyl benzoate +Nitro benzene system 303.15K 308.15K 313.15K 318.15K -1.6 -1.2 -0.8 -0.4 0.0 0.0 0.2 0.4 0.6 0.8 1.0 E x c e s s m o l a r V o l u m e ( V E ) Molefraction of Ethyl benzoate Fig 3.1-Variation of excess molar volume with molefraction of Ethyl benoate for Ethyl benzoate + Nitro benzene system 303.15K 308.15K 313.15K 318.15K 0.00 0.50 1.00 1.50 2.00 0.0 0.2 0.4 0.6 0.8 1.0 D e v i a t i o n i n v i s c o s i t y ( ∆ η ) Molefraction of Ethyl benzoate Fig 3.4 -Variation of deviation in viscosity with molefraction of Ethyl benzoate f or Ethyl benzoate + Nitro benzene system 303.15K 308.15K 313.15K 318.15K -0.020 -0.016 -0.012 -0.008 -0.004 0.000 0.0 0.2 0.4 0.6 0.8 1.0 E x c e s s i n t . m o l . f r e e l e n g t h ( L f E ) Molefraction of Ethyl benzoate Fig 3.3 -Variation of excess inter molecular free length with mole fraction of Ethyl benzoate for Ethyl benzoate + Nitro benzene system 303.15K 308.15K 313.15K 318.15K 88 | P a g e References 1. Reddy B R & Reddy D L, Indian J Pure & Appl Phys, 37, 13(1999). 2. Perez E, Cardoso M & Mainar A M, Parde J I & Urieta J S, J.Chem Eng Data, 48, 1306(2003). 3. Nayak J N, Aminabhavi T M & Aralaguppi, M I, J Chem Eng Data, 48, 1112(2003). 4. Wankhede D S, Lande M K& Arbad B R, J Chem Eng Data, 50, 455(2005). 5. Pal A, Sharma H K& Singh W, Indian J Chem, 34A, 987(1995). 6. Oswal S L & Patel N B, J Chem Eng Data,40, 845(1995). 7. Aminabhavi T M & Gopala Krishna B, J Chem Eng Data,40, 856(1995). 8. Nikam P S & Kharat S J, J Chem Eng Data, 50, 455(2005). 9. Chen J-T, Shiah I-M & Chu H-P, J Chem Eng Data, 50, 1038(2005). 10. Vogel A I, A text book of practical organic chemistry, 5 th Edn (John Willey, New York)(1989). 11. Riddick, J A, Bunger W B & Sokano T K, Techniques in Chemistry, Vol 2, Organic solvents, 4 th Edn (John Willey, NewYork) (1986). 12. Weissberger A, Proskaner E S, Riddick J A & Toops E E Jr, Organic Solvents, Vol II 2 nd Ed, Weissberger A Ed, Wiley Interscience, New York (1955). 13. Eyring H, Kincaid J F, J Chem Phys, 6, 620(1996). 14. Appa Rao Y V V, Ph.D Thesis, Andhra University, October (2009). 15. Thirumaran S, Earnest Jayakumar, Indian J Pure Appl Phys, 47, 265, (2009). 16. Babu P, Sekhar G C & Rao N P, Indian J Pure Appl Phys, 38, 425(2000). 17. Anil Kumar Nain, Rajni Sharma, Anwar Ali & Swarita Gopal, J Mol Liq,144, 124(2009). 18. Ali A, & Tariq M, J Mol Liq, 137, 64(2008). 19. Nandhibatla V Sastry, Rakesh R, Thakor & Mitesh C Patel, J Mol Liq, 144, 13(2009). 20. Subhash C Bhatia, Rachna Bhatia & Gyan P Dubey, J Mol Liq, 144, 163(2009). 89 | P a g e STUDY OF NON LINEARITY PARAMETER (B/A) AND THERMO ACOUSTIC PARAMETER OF BINARY MIXTURE AT DIFFERENT FREQUENCIES G. Nath 1 and R. Paikaray 2 1 Dept. of Engg. Physics, Dhaneswar Rath Institute of Engg. and Management Studies (D.R.I.E.M.S.), Tangi, Cuttack -754022, Odisha, India. 2 P.G.Dept. of Physics, Ravenshaw University, Cuttack -753003, Odisha, India. ABSTRACT: Experimental data on speed of sound(C) values at 303K for different frequencies like 1MHz, 3MHz and 5MHz are presented for the binary mixture of di isopropyl ether (DIPE) and xylene (XY). From these experimental data for sound speed and density (ρ) of the binary mixture the thermo acoustic parameter like isentropic compressibility (βs), isothermal compressibility (βT), coefficient of thermal expansion (α) are calculated for different frequencies. The experimental values of sound speed have been fitted Ballou’s and Hartmann’s equation for non linearity parameter and variation of these parameters with the frequencies has been discussed in the context of molecular interactions. KEYWORDS: Ultrasonic speed, binary mixture, isentropic compressibility isothermal compressibility, coefficient of thermal expansion, heat capacity ratio, non linearity parameter 1. Introduction: The propagation of acoustic waves of infinitesimal amplitude has been used to deduce most of the parameters involved in ultrasonic studies. But when a sound wave of high amplitude propagates, non-linear effects occur such as harmonic distortion and acoustic scattering. It has become of much interest to predict the extent of various kind of non-linear effects which are due to deviation from nonlinearity in ordinary acoustics [1-4].A number of information about some physical properties [5-6] of the liquid such as internal pressure, intermolecular spacing, clustering, acoustic scattering, wave form distortion and structural behaviour etc.can be obtained from the knowledge of this parameter. Researchers found that the acoustic non linearity parameter (B/A) was not only the parameter describing the degree of non linearity, but also the parameter which may provides some structure and state information of media.[7].Now a days the acoustic nonlinearity parameter B/A is of potential possibility to be treated as a new parameter in tissue characterizing,dignosis and imaging .Obviously the study of acoustic nonlinearity parameter B/A in liquid binary mixture is very helpful in discovering the mixture law of acoustic nonlinearity parameter B/A in biological tissue as well as in developing and computing the theory of medical 90 | P a g e ultrasonic and the theory of nonlinearity acoustics. During recent years [8-10 ] a no. of experimental and theoretical studies have been performed on the nonlinearity parameter of liquid and liquid mixture but also to the best of our knowledge, computation of B/A at different frequencies has not been done so far. The present work deals with the computation of thermodynamic parameters in one binary liquid mixture at different frequencies and at temperature 303K. In addition with this we have taken an attempt to compute acoustic nonlinearity parameter B/A of the binary mixture using two different method like Ballou’s empirical relation and Hartmann’s relation and the well known heat capacities ratio (γ ) is calculated at different frequencies which is well agreed the values for all the substances. 2. Theory: Since sound propagation is an adiabatic process, so the different factors like density ,temperature and frequency of the sound wave may changes the sound speed [11-12].The experimental measured values of sound speed with different frequencies are used to compute the various thermo acoustic parameter like isentropic compressibility(βs ),isothermal compressibility(βT), coefficient of thermal expansion ( α) and the heat capacity ratio (γ ) from the well known thermodynamic relation[13-14 ] Isentropic compressibility ( ) 2 1 C mix S ρ β = Isothermal compressibility ( ) mix mix mixture T C T 3 4 2 9 4 3 10 71 . 1 ρ β − × = Coefficient of thermal expansion ( ) mix mix mix C T 3 1 2 1 9 1 3 10 6 . 75 ρ α − × = Heat capacity ratio ( ) ( ) ( ) mix S mix T mix β β γ = General formulation for the nonlinearity parameter in terms of the acoustical parameters of liquid has been made using the expression for the sound speed. According to the empirical rule of Ballous employed by Hartmann [15], there is a linear relation between the nonlinearity parameter of liquid and reciprocal sound speed as 5 . 0 − = A B + ( ) C 4 10 2 . 1 × 91 | P a g e Hartmann [15] has shown theoretically the physical basis of Ballous equation assuming the intermolecular potential energy is the domain factor in determining the sound speed and derivatives in liquids. The expression for nonlinearity parameter due to Hartmann [15] is given as ( ) C A B 4 10 98 . 0 2 × + = 3. Results and Discussions: Experimental values of ultrasonic speed and calculated values of density of the mixture has been used to determine the different parameters with the help of well known thermodynamic relation. Thermal expansion coefficient and isothermal compressibility are obtained using the relation [13-14 ].The values of the nonlinearity parameter B/A of the binary liquid mixture have been calculated at different frequencies ranging from1MHz to 5MHz and at temperature 303K with the help of two different methods like Ballous empirical relation and Hartmann’s theoretically derived relation .The variation of these thermo acoustic parameter and nonlinearity parameter with frequency are plotted in figure1-7and discussed in the light of molecular interactions. The ultrasonic speed decreases with mole fraction of DIPE followed by an increase at higher mole fraction for all three frequencies. The decrease in ultrasonic speed is attributed to the depolymerisation of polarity in xylene caused by the addition of non polar DIPE.The ultrasonic speed is also increases with the increase of frequency for all concentration as shown in fig.1.Considering the effect of frequency, it is found that in low frequency range like 1MHz the molecules of the two liquid find greater time of interaction for which the ultrasonic speed is low. But when the frequency increases from 3MHz to 5MHz, the interaction between the molecules decreases so that they have small relaxation time [16] and move with high speed as compared to low frequency range. The variation of ultrasonic speed is supported by that of isentropic compressibility, isothermal compressibility and also coefficient of thermal expansion.The values of isentropic and isothermal Fi g.1 Vari ati on of ul trasoni c vel ocity wi th mol e fraction of DIPE 0 500 1000 1500 0 0 . 2 9 0 . 4 1 0 . 6 5 0 . 8 7 1 Mole fracti on of DIPE U l t r a s o n i c v e l o c i t y 1MHz 3MHz 5MHz 92 | P a g e compressibility increases up to ≈ 0.70 mole fraction of DIPE and decreases thereafter for all three frequencies as shown in fig.2 and fig.3.The positive variation of both the profiles suggest that there is association of xylene molecules breaks up progressively with the addition of DIPE leading to expansion in volume and hence isentropic and isothermal compressibility increases. However, in higher mole fraction of DIPE the dipolar association is observed between the DIPE molecules for which both the compressibility decreases. It is observed in low frequency like 1MHz, the interaction between the unlike molecules is very high for which both the compressibility are low. But when the frequency changes from 3MHz – 5MHz the interaction between the unlike molecules is weak due to small relaxation time, which leads to in compressibility at every concentration of DIPE . Considering the variation of coefficient of thermal expansion as shown in fig.4 it is found that the value of α increases with increase of mole fraction of DIPE up to 0.70 mole fraction, then decreases in DIPE rich region. Such variation can be well explained on the basis of the fact that with increase of density, speed of sound decreases which increases the value of α .This increases in α, increases the volume and hence both type of compressibility also increases up to certain mole fraction. Again in higher concentration of DIPE as the density of the mixture decreases, the speed of the sound increases which decreases the value of α. With increase of Fi g.2 Vari ati on of i sentropi c compressi bi l i ty wi th mol e fraction of DIPE 0 1 2 3 0 0 . 2 9 0 . 4 1 0 . 6 5 0 . 8 7 1 Mol e fracti on of DIPE I s e n t r o p i c c o m p r e s s i b i l i t y 1MHz 3MHz 5MHz Fig.3 Variation of isothermal compressibility with mole fraction of DIPE 0 2 4 0 0 . 2 9 0 . 4 1 0 . 6 5 0 . 8 7 1 Mol e fraction of DIPE I s o t h e r m a l c o m p r e s s i b i l i t y 1MHz 3MHz 5MHz Fi g.4 Vari tai on of coeffi ci ent of thermal expansi on wi th mol e fracti on of DIPE 0 0.5 1 1.5 2 0 0 . 2 9 0 . 4 1 0 . 6 5 0 . 8 7 1 Mol e fracti on of DIPE C o e f f i c i e n t o f t h e r m a l e x p a n s i o n 1MHz 3MHz 5MHz Fig.5Vari ation of heat capaci ty rati o wi th mol e fraction of DIPE 1.35 1.4 1.45 1.5 1.55 0 0 .2 9 0 .4 1 0 .6 5 0 .8 7 1 Mol e fracti on of DIPE H e a t c a p a c i t y r a t i o 1MHz 3MHz 5MHz 93 | P a g e frequency from 1MHz-5MHz velocity increases as described on fig.1 which decreases the value of α with increase of frequency. The heat capacity ratio of the binary mixture is found to be increase in a linear trend with the mole fraction of DIPE as shown in fig.5 for all frequencies .Though it increases linearly with mole fraction of DIPE but its value varies from 1.42-1.6 which is well agreed with that of the result for other substances. The authors have also put the interest to calculate the non linearity parameter B/A using Ballou’s and Hartmann’s relation. Many authors have calculated this parameter with variation of pressure but in the present investigation the nonlinearity parameter are calculated with different mole fraction for different frequencies at a constant temperature. With a close perusal of the data shown in fig.6 and fig.7 for Ballou’s and Hartmann’s, it is observed that the nonlinearity parameter are increases with increase of mole fraction of DIPE up to 0.65 mole fraction of DIPE and then deceases for higher concentration of DIPE .This variation of B/A with mole fraction of DIPE in presence of xylene is only due to variation of ultrasonic speed in the binary mixture which is described earlier. Again considering the variation of B/A with frequency it is observed that in low frequency the B/A value has high value in compare to the value obtained in high frequencies like 3MHz and 5MHz.This is due to fact that at low frequency the speed of the ultrasonic sound is small for which the B/.A value is high as the value of B/A varies inversely with speed of sound in both the cases.On the basis of the above discussion it can be concluded that the variation of different thermo acoustic parameter and values of B/A by Ballos and Hartmann is not only affected by the variation of pressure but also with the frequencies. References: 1. R T Beyer, J.Acoust.Soc.Am.32, 719 (1960) 2. R T Beyer and S V Letcher, Physical Ultrasonic, Academic Press, New York, 202, 2043, (1961) 3. K P Thakur, Acustica, 39,270 (19780 4. RPJain, JDPandey and K P Thakur, Z Phys. Chem, (Neue Folge), 94, 211, (1975). 5. P S Westrvet, J.Acoust.Soc Am. 32,8 (1960) Fi g.6 Variation of Hartmann's non l inearity parameter with mole fraction of DIPE 0 5 10 15 20 0 0 . 2 9 0 . 4 1 0 . 6 5 0 . 8 7 1 Mole fraction of DIPE H a r t m a n n ' s n o n l i n e a r p a r a m e t e r 1MHz 3MHz 5MHz Fi g.7 Variation of Ball ou's non l i nearity parameter with mole fraction of DIPE 0 5 10 15 20 0 0 . 2 9 0 . 4 1 0 . 6 5 0 . 8 7 1 Mol e fracti on of DIPE B a l l o u ' s n o n l i n e a r p a r a m e t e r 1MHz 3MHz 5MHz 94 | P a g e 6. J L S Bellin and R T Beyer, J.Acoust Soc.Am.34, 1051(1962) 7. H Endo, J.Acoust, Soc.Am.83, 2043(1986) 8. P Kuchhal, R Kumar and DNarsingh ,Pramana J.Phys.52,321 (1999) 9. G P Dubey, V Sanguri and R Verma Indian J.Pure and Appl. Phys.36, 678 (1998) 10. J Jugan, R Abraham and M A Abdulkhadar, Pramana J.Phys.45,221 (1995) 11. G Nath and R Paikaray, JUSPS, 21, 1, 99, 2009 12. G Nath and R Paikaray, Indian J Phys.83, 9, 1309 (2009) 13. J D Pandey, G P Dubey,N Tripathi and A KSingh J.Int Acad .Phy Sci.,1, 117,(1997) 14. J D Pandey and R Verma Chem. Phys.270, 429 (2001) 15. B Hartmann, J Acoust. Soc. Am. 65, 1392 (1979) 16. M S Chouhan, K C Sharma S Gupta M Sharma ands Chouan, Acost Lett., 18,233 (1995) 95 | P a g e THERMO-ACOUSTIC STUDIES ON TERNARY MIXTURES OF METHYL ISO-BUTYL KETONE, ACETYL ACETONE AND t- BUTANOL WITH CARBON TETRACHLORIDE(CCl4). T. Karunamoy 1* , S. K. Dash 1 , S. K. Nayak 2 and B. B. Swain 3 1 DESM, Regional institute Of Education (NCERT), Bhubaneswar-751022 2 Department of Chemistry, Revenshaw University, Cuttack-753003 3 Plot No. 15, Chintamaniswar Area, Bhubaneswae-751006 ABSTRACT The ultrasonic velocity, density and viscosity of the ternary mixture of MIBK/HAA+t-butanol+ CCl4 were measured at 301.16 K. The thermo acoustic parameters such as isentropic compressibility, inter molecular free length, acoustic impedance, free volume, internal pressure, available volume, relaxation time and relaxation amplitude were computed with the help of measured values of u, and . In an attempt to explore the nature of molecular interaction between the polar-polar, polar-non polar species of the ternary mixture the excess properties were derived. The molecular interactions are dipole-dipole, dipole-induced-dipole and dispersive type in the ternary mixtures containing HAA. However in MIBK there is an indication of complex formation in its the ternary mixture containing t-butanol and CCl4 KEY WORDS MIBK, HAA, t-butanol, ternary mixture, thermo-acoustic parameters. 1. Introduction Methyl-iso-butyl ketone (MIBK) and acetyl acetone (HAA) has been extensively used as extractant in various polar and apolar modifiers/diluents for extraction of actinides and lanthanides in atomic energy industry [1]. Some physico-chemical studies on thermo-acoustic properties of ternary mixtures on MIBK/HAA+t-butanol in the presence of CCl4 have been undertaken. The molecular interaction between the like as well as unlike molecules in the given ternary systems have been studied in the light of several thermodynamic and acoustic parameters. The ultrasonic velocity and dielectric constant of the organic phase changes by blending MIBK/HAA with polar and apolar liquids. To understand the molecular behavior of associating molecules, involving MIBK/HAA, it is necessary to determine various thermo-acoustic parameters which are related to inter and intra molecular association with temperature as well as concentration variation. In an earlier report [2] one of the author (SKD) have been evaluated the Kirkwood- Fröhlich linear correlation factor, g, excess molar polarization ∆P and excess free energy of mixing ∆F for binary mixtures of MIBK in three apolar solvent viz. benzene, CCl4 and p-xylene using dielectric studies. Although several reports are available for studying the molecular interactions in binary liquid mixtures [3, 4] involving polar-polar and polar-apolar systems it is sparse in ternary liquid mixtures involving the nuclear extractant MIBK/HAA. Therefore attempt has been made towards investigations on thermo-acoustic 96 | P a g e behavior in ternary mixtures on MIBK and HAA with t-butanol and CCl4 in the five polar compositional stochiometry for assessment of molecular interactions between the component molecules. 2.Experimental All the chemicals used in the investigations were of AR grade, purified by standard procedures [5] and redistilled before use. The purity of the sample was checked by comparing the measured value of density and viscosity with those reported in the literature [6]. The ultrasonic velocity was measured by single crystal variable path interferometer at 2 MHz with an accuracy of ± 0.5 ms -1 . Circulating water from thermostatic regulated bath around the sample holder with double wall maintained the temperature of the system constant with an accuracy of ± 0.1 o C. The density was measured by a digital microbalance with a pykonometer of 25 ml capacity with an accuracy of ±2x10 -5 g cm -3 . The viscosity was measured by Ostwald viscometer immersed in constant temperature water bath with an accuracy of ±10 -6 Pas. The binary mixtures of MIBK/HAA+t-butanol was prepared by weight for five sets of compositional (mole fraction) stoichiometry viz (0.1+0.9), (0.3+0.7), (0.5+0.5), (0.7+0.3) and (0.9+0.1) separately. For each set of compositional stoichiometry the ternary mixtures of MIBK/HAA + t-butanol + CCl4 was prepared with the decreasing mole fraction of CCl4. 3. Results and Discussion Ultrasonic velocity (u), viscosity() and density () of the ternary mixtures of MIBK/HAA+t-butanol +CCl4 in the polar compositional stoichiometry of (0.1+0.9), (0.3+0.7), (0.5+0.5), (0.7+0.3) and (0.9+0.1) with the function of mole fraction of CCl4 were measured at 303.16 K. Various thermo acoustic parameters such as such as isentropic compressibility(βs), inter molecular free length(Lf) acoustic impedance(Z), free volume(Vf),internal pressure(πi), available volume(Va), relaxation time( τ) and relaxation amplitude (/f 2 ) were measured by using standard relations [7,8].Some of the relevant data are presented in Table-1 and displayed graphically in Fig-1. In perusal with Table-1, it is observed that the values of u and Va increases while that of and Z decreases non linearly with the increase in mole fraction of polar solute i.e. (MIBK/HAA + t-butanol) in all the ternary mixtures containing CCl4. Further, the values of and α/f 2 increases in (0.1+0.9), (0.3+0.7) while decreases in other compositions of polar solute non linearly with mole fraction of CCl4 in the ternary mixtures. However, the non linear variation in the values of βs, Lf, πi, and Vf depends upon the combined effect of the increasing or decreasing trend of u, and which is observed in the present study. This shows molecular interactions as well as interstial accommodations among the polar- polar and polar-non polar components of the MIBK/HAA + t-butanol + CCl4 mixtures. The relaxation time ( τ) which is of the order of 10 -12 s probably due to structural relaxation process [9] and in such situation it is 97 | P a g e expected that molecules get rearranged due to co-operative process. HAA, MIBK and t- butanol are strongly associated polar liquids having dipole moment 2.91 D, 2.70 D and 1.66 D respectively. The dielectric study involving HAA, MIBK and t-butanol reveals that Kirkwood-Fröhlich linear correlation factor, g, in all the three protic liquids viz. gHAA= 1.56, gMIBK = 1.3 gt-butanol =2.18 is greater than one [10, 11]. This indicate that there is re-enforcement of parallel dipolar alignment among the like polar molecules of MIBK, HAA and t-butanol respectively which may be attributed by the presence of 3- dimensional network of H-bondings among themselves and stacked together by head-tail arrangement [12]. HAA/MIBK molecules are equilibrium mixtures of two tautomers such as keto and enol forms and the molecules are arranged in head-tail structure due to C and O linkage resulting intramolecular association. In seemingly non-interacting medium like CCl4, the dipolar alignment of MIBK/HAA is influenced by non- specific interaction due to the solvent effect and dipole-dipole interaction through H-bondings between H and O is also expected among the MIBK/HAA + t-butanol molecules. In perusal with Fig-1, it is observed that the values of βs shows negative in the entire range of concentration in (0.1+0.9) and up to 0.3 mole fraction of CCl4 in (0.3+0.7) compositions. Further, it shows positive in the entire concentration range of concentration in (0.7+0.3) and (0.9+0.1) with a negligible variation in (0.5+0.5) compositions in HAA + t-butanol + CCl4 ternary mixtures. However the magnitude of negative values of βs decreases in the order of composition of (0.1+0.9)> (0.3+0.7)> (0.5+0.5)> (0.7+0.3).The values of Lf E are observed to be negative in the entire range of mole fraction of CCl4 in the composition of (0.1+0.9), while it shows negative up to 0.75 mole fraction of polar solute thereafter shows positive in (0.3+0.7) of the ternary mixtures containing HAA. However in other higher composition the values of Lf E shows positive with the mole fraction of CCl4. On the otherhand Fig -1 shows that the values of Z E and Vf E are positive for all the compositions except (0.9+0.1) in the ternary mixtures containing HAA. The magnitude of Z E , Vf E and Lf E are maximum in (0.9+0.1) compositions. Further the values of Va E are negative in all the compositions while πi E are also negative in all compositions except in the compositions of (0.9+0.1) with a decreasing magnitude (0.1+0.9)> (0.3+0.7) > (0.5+0.5)> (0.7+0.3). This indicates that the degree molecular interaction is relatively higher in the (0.1+0.9) composition in the ternary mixtures containing HAA. In the presence of t-butanol the molecular interactions between HAA and alcohol molecules takes place through the intermolecular H- bondings between O of two carbonyl group of HAA and H of hydroxyl group of alcohol CCl4 molecules are almost spherical in shape and can be easily trapped inside the interstitial voids of the interacting moieties containing HAA and probably favours the stronger molecular interaction in (0.1+0.9) composition in the ternary mixtures of HAA + t-butanol + CCl4. From the close observation of Fig-1, it is observed that the values of βs E and Lf E are negative throughout with the mole fraction of polar solute in compositions of (0.3+0.7) and (0.5+0.5) while it shows partly negative, then positive in other compositions in the ternary mixtures containing MIBK. Further the values of solute mole fraction in all the compositions mole fraction it is observed that the values of ternary mixtures. From such observation it is found that the magnitudes of parameters are not prominent in any of the compositional stochiometry of the ternary mixtures containing MIBK. Although the molecular interaction of t OH groups of alcohol the interstitial accommodation along with the dispersive forces between C and H of alcohols molecules cannot be overruled. As such it is probable that there may be complex formation between the components present in the ternary mixtures of MIBK + t 4.Conclusion The present investigation reveals that the nature of molecular interaction involving MIBK/HAA with t and CCl4 may be dipole-dipole, dipole effective extractant in the presence o (0.1+0.9) in the extraction process. 0 50000 100000 150000 0. 00 2. 00 Z E x 1 0 - 6 ( k g m - 2 s - 1 ) X 2 ( 0. 1+0. 9 ) ( 0. 3+0. 7 ) ( 0. 5+0. 5 ) -5E-11 0 5E-11 0.001.002.00 β s E x 1 0 1 0 ( N - 1 m 2 ) X2 are negative throughout with the mole fraction of polar solute in compositions of (0.3+0.7) and (0.5+0.5) while it shows partly negative, then positive in other compositions in the ternary mixtures containing MIBK. Further the values of Z E are positive while πi E and Va E are negative with the solute mole fraction in all the compositions of this ternary mixture. From the trend of variation mole fraction it is observed that the values of Vf E are positive in all the composition except (0.9+0.1) in the ternary mixtures. From such observation it is found that the magnitudes of the excess thermodynamic parameters are not prominent in any of the compositional stochiometry of the ternary mixtures containing MIBK. Although the molecular interaction of t-butanol and MIBK is possible between O of MIBK with H OH groups of alcohol the interstitial accommodation along with the dispersive forces between C of alcohols molecules cannot be overruled. As such it is probable that there may be complex mponents present in the ternary mixtures of MIBK + t-butanol + CCl The present investigation reveals that the nature of molecular interaction involving MIBK/HAA with t dipole, dipole-induced dipole and dispersive type. As such HAA may be used as an effective extractant in the presence of the modifier t-butanol and diluent CCl4 at compositional stochiometry ( 0. 1+0. 9 ) ( 0. 3+0. 7 ) ( 0. 5+0. 5 ) -50000 0 50000 100000 150000 0.00 1.00 2.00 Z E x 1 0 - 6 ( k g m - 2 s - 1 X 2 (0.1+0.3) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) -6E-11 -4E-11 -2E-11 0 2E-11 4E-11 6E-11 0.00 0.50 1.00 β s E x 1 0 1 0 ( N - 1 m 2 ) X 2 98 | P a g e are negative throughout with the mole fraction of polar solute in compositions of (0.3+0.7) and (0.5+0.5) while it shows partly negative, then positive in other compositions in the ternary are negative with the of this ternary mixture. From the trend of variation Vf E with solute are positive in all the composition except (0.9+0.1) in the the excess thermodynamic parameters are not prominent in any of the compositional stochiometry of the ternary mixtures containing of MIBK with H of OH groups of alcohol the interstitial accommodation along with the dispersive forces between C of CCl4 of alcohols molecules cannot be overruled. As such it is probable that there may be complex butanol + CCl4 system. The present investigation reveals that the nature of molecular interaction involving MIBK/HAA with t-butanol induced dipole and dispersive type. As such HAA may be used as an at compositional stochiometry (0.1+0.9) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) 1.00 1.50 (0.1+0.9) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) 99 | P a g e (a) (b) Fig-1 Variation of Z βs πi E and Va with mole fraction(X2) of (a) HAA+t-butanol+ CCl4 (b) MIBK+t-butanol+ CCl4 with compositions of (0.1+0.9), (0.3+0.7), (0.5+0.5), (0.7+0.3) and (0.9+0.1). Table-1 Variation of density (),ultrasonic velocity (u), viscosity (), adiabatic compressibility (βs), relaxation time (),relaxation amplitude (α/f 2 ) free volume (Vf), available volume (Va) internal pressure (πi) and acoustic impedance (Z) with mole fraction(X2) of polar solute (MIBK/HAA+t-butanols)at(0.1+0.9). X2 ( kg m -3 ) u (m/s) Nm -2 s) βsX10 10 (N - 1 m 2 ) x10 12 (s) α/f 2 ×10 14 (s 2 m -1 ) VfX10 7 (m 3 mol - 1 ) VaX10 5 (m 3 kmol -1 ) πiX10 -6 (pa) Z ×10 -6 (kg m 2 s -1 ) (HAA + t-butanol) + CCl4) 0.00 1588.00 914.33 0.0009 7.53 0.90 1.95 0.815 2.46 853 1.451956 0.10 1479.00 910.00 0.0009 8.16 0.96 2.09 0.766 2.72 859 1.345890 0.19 1408.03 912.40 0.0009 8.53 1.02 2.21 0.700 2.95 886 1.284684 0.30 1328.00 915.00 0.0009 8.99 1.08 2.33 0.642 3.26 911 1.215120 0.39 1273.15 933.20 0.0009 9.02 1.12 2.37 0.577 3.65 954 1.188102 0.49 1185.05 951.20 0.0010 9.33 1.22 2.52 0.502 4.33 993 1.127219 0.60 1108.00 975.00 0.0010 9.49 1.33 2.68 0.420 5.14 1060 1.080300 0.69 1034.74 997.60 0.0011 9.71 1.47 2.91 0.348 6.10 1130 1.032255 0.80 950.00 1037.50 0.0013 9.78 1.67 3.17 0.273 7.82 1220 0.985625 0.90 869.00 1077.00 0.0015 9.92 1.96 3.58 0.204 10.00 1340 0.935913 1.00 801.97 1115.20 0.0017 10.00 2.31 4.08 0.148 12.45 1510 0.894353 (MIBK + t-butanol) + CCl4) 0.00 1588.00 914.33 0.0009 7.53 0.90 1.95 0.815 2.46 853 1.451956 0.10 1455.00 910.00 0.0009 8.30 1.03 2.23 0.713 2.81 872 1.324050 0.18 1382.40 912.80 0.0009 8.68 1.09 2.36 0.655 3.08 891 1.261855 0.25 1330.00 915.00 0.0009 8.98 1.13 2.44 0.618 3.28 910 1.216950 0.37 1238.00 934.00 0.0009 9.26 1.17 2.47 0.572 3.89 933 1.156292 0.47 1164.30 949.00 0.0010 9.54 1.32 2.74 0.465 4.47 1000 1.104921 0.58 1057.00 967.50 0.0011 10.01 1.50 3.05 0.384 5.53 1005 1.022648 0.67 1016.10 984.00 0.0012 10.02 1.66 3.33 0.307 6.09 1016 0.999842 -4E+08 -3E+08 -2E+08 -1E+08 0 10000000 0.001.002.00 π i E x 1 0 - 6 … (X 2 ) (0.1+0.9) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) -3E+08 -2E+08 -1E+08 0 10000000 0.00 1.00 2.00 π i E x 1 0 - 6 … X 2 (0.+0.9) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) -6000 -4000 -2000 0 0.00 2.00 V a E X 1 0 5 ( m 3 k m o l - 1 ) (X 2 ) (0.1+0.9) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) -6000 -4000 -2000 0 0.00 1.00 2.00 V a E X 1 0 5 ( m 3 k m o l - 1 ) X 2 (0.1+0.9) (0.3+0.7) (0.5+0.5) (0.7+0.3) (0.9+0.1) 100 | P a g e 0.80 890.00 1037.50 0.0014 10.04 1.99 3.79 0.225 8.83 1026 0.923375 0.90 845.00 1082.50 0.0017 10.01 2.34 4.27 0.156 10.67 1046 0.914712 1.00 782.60 1132.50 0.0021 9.96 2.78 4.84 0.11 13.53 1067 0.886294 References [1] A.K.Dey,S.M.Khopkar and R.A.Chalmers, Solvent extraction of metals (Van-Nostrand-Reinhold,London, 1970). [2] J.K.Das, S.K.Dash, V.Chakravortty and B.B.Swain, .Indian .J.Chem.Tech 1 230 (1994). [3] J.Conosa, A.Rodrigucz and Z.tozo, Fluid phase equilibrium 156 (1999) 57. [4] M.Dominguez,S.Martin, J.Shantafa, H.Atigas and F.M.Royo, Thermochemica Acta.381(2002) 181. [5] J.A.Riddick, W.B.Bunger and T.K.Sakano, Organic Solvents,4 th Edn.(Wiley- Inter Science, New York)( 1986). [6] CRC Handbook of chemistry and physics edited by DR.Lide,87 th Edn.(CRC Press Boca Raton FL) (2006). [7] T.Sumathi and J.Uma.Maheswari, Indian J.Pure& Appl.phys.47 (2009) 782. [8] D.Sravana Kumar and D.K.Rao, Indian J.Pure& Appl.phys. 45 (2007) 210. [9] M.Selva Kumar and D.K Bhat, Indian J.Pure& Appl.phys. 46 (2008) 712. [10] J.K.Das, S.K.Dash & B.B.Swain. J.Physical Socity of Japan Vol.64 (1995) 2636. [11] S.Acharaya, S.K.Dash,J.N.Mohanty & B.B.Swain,J .Mol Liq. Vol.71 (1997) 73. [12] S.K.Dash,J.K.Das, B.Dalai and B.B.Swain, Indian J. Phys.83(11),1557 (2009). 101 | P a g e GLUECKAUFF’S MODEL FOR LOWERING OF DIELECTRIC CONSTANT OF ELECTROLYTIC SOLUTIONS & ISOENTROPICCOMPRESSIBILITY AND ION ASSOCIATION STUDIES WITH AQUEOUS ELECTROLYTIC SOLUTIONS USING ULTRASONICS ,ION-PAIRS (CHLORIDES) V.Brahmajirao 1** , T. Gunavardhan Naidu 1 , P.Rajendra 3 , T.Srikanth 2 , Shanaz Batul 4 1 Matrix Institute of technology, Cheekatimamidi (V), Bommalaramaram (M), Jawaharlal Nehru Technological University HYDERABAD , Pin Code – 508116 ; 2 Jawaharlal Nehru Technological University (Jagtyal Campus) Jagtyal.A.P.; 3 LNBC Institute of Engineering and Technology,Raigaon, Satara, Maharastra ; 4 Main campus, Jawaharlal Nehru Technological University, HYDERABAD-500072. ; ( 1** E- mail ID for all correspondence:
[email protected] ) Abstract This paper reports the specific evidence of the formation of three types of Ion pairs from the ultrasonic studies in aqueous solutions of six chlorides from our laboratories in J.N.T.U., and the plots of thermodynamic parameters , using equations for partial molal compressibility & apparent molal compressibility, from literature Several correlating arguments cited by, a host of earlier workers , about the findings of Gucker et.al, are incomplete & naïve, since the parameter of the dependence of dielectric constant on concentration is missing in them . Margaret Robson Wright & Robinson and Stokes pointed that the internal field around the central ion of the ionic atmosphere created by the charged solute ions in the solvent of the electrolytic solution, tend to reduce the value of the dielectric constant of the electrolytic solution. The author used the relevant equations modified by him .Using these equations, the mechanism of formation of three types of ion pairs envisaged earlier by Eigen et.al. observed in the plots is explained on firm grounds. The plots clearly show an excellent agreement with many of the recent cited findings. Discrete variation in the slopes of the straight line graphs are explained, correlating them with the prevailing concepts proposed by several scientists, in their respective different types of studies in the very recent literature.An excellent evidence for all of the concepts of all the cited workers is reported .Several unsuccessful attempts made so far to deduce a comprehensive model, and to modify the D-H Theory for an electrolyte solution were cited, and the need to use M.C.Simulations, to incorporate the depression in the dielectric constant of the dielectric continuum , due to solute-solvent interactions was outlined KEYWORDS: Glueckauff’s model, Isentropic compressibility, Monte Carlo Simulations , Ion-pairs in aqueous electrolytes, Debye Huckel theory, Gucker’s equations , Lowering of dielectric constant of dielectric continuum Introduction The departures exhibited in the properties of electrolytic solutions, as the concentration increases, cannot be satisfactorily explained, by the Debye Huckel model even with its several recent modifications that were developed during the last half a century, mainly because of so many shortcomings, in the presumptions of the theory & its later developments, by a host of others. Electrolytic ions entering into the solvent of the dielectric constant “D” creates an internal field around the central ion of the ionic atmosphere & the average effect of all such ions is to reduce the effective value of D to ± ( ) D D − of the solvent of the electrolytic solution.Glueckauff [1] & Von Hippel [2] showed that the dielectric constant in the vicinity of the central ion is modified by the volume fraction of the ions in layer of the solvent around the central ion. Treating the solvent as a continuously non uniform system having spatial distribution of the ions .For a volume fraction φ to (φ +dφ ), where φ = 102 | P a g e 3 8 ( ) 3 Nr π , 2 2 (4 ) d N r dr φ π = and “r” is the distance of the point of calculation from the centre of the reference ion. The integration of this within suitable limits yield [ / log(1 )] [3 ( ) /(2 )] dD d D D D D D φ φ φ − = − + . This equation is used for the estimation of lowering of the dielectric constant. Further the thermodynamic variables that can be estimated from ultrasonic data, are related to the modification to the free energy of the central ion, in the solvent and the details are available in literature Gucker et.al. [3]& [4] established with standard notation the equation for the partial molal compressibility as: 2 0 0 0 2 2 2 2 2 2 2 ( ) ( ) ( ) G G V V K K p p ∂ ∂ − = − = − ∂ ∂ . In this 0 0 0 2 2 2 , , K V G , are parameters corresponding to infinite dilution. Treating the dielectric constant as a variable it can be shown that, the partial molal compressibility Gets modified to: 2 0 2 2 2 2 2 3 5 1 ( ) [ ( ) ( ) ( )] 2 D D D K K D P D P D P β χ ∂ ∂ ∂ − = + + ∂ ∂ ∂ . In this 1 [ ( )] V V P β ∂ = − ∂ 2 1 v ρ = , is the isentropic compressibility, ρ is the density, and “D”, is the dielectric constant, (which is a variable, as per the new revelations ), and, 3 6 1 2 2 ( ) [ ] (1000 ) N e D kT π χ = and N is Avogadro Number .These equations clearly reveal that ( ) 0 2 2 Cversus K K − plot will not be linear Also the apparent molal compressibility is 2 ( ) v k T p φ φ ∂ = ∂ , and 2 0 K K K S C φ φ = + , in which ( / ) ( ) 2 V K V T S S S P β = ∂ ∂ + , leading to 2 3 2 2 6 ( ) [ 2( ) ( ) 6 K i i T T i D S z P D P χ β β ν β ∂ ∂ = + − + ∂ ∂ ∑ 2 2 2 2 15 6 ( ) ( ) ] T T D D D P D P ∂ ∂ − ∂ ∂ Hence ( K vs C φ ) plot cannot be linear in view of the modifications made, to account the solute solvent interactions. SK becomes a function of concentration and dielectric constant. The author opines that: the inherent change of slope of the plot reveals conspicuously the interactions between the ions and the solvent in a discrete way namely the ion-solvent-ion interactions, as detailed in the discussion of the results. Also according to Gucker [3] & Gucker et.al, [4]. 10 (6.3 10 ) K S X δ − = is a constant, where δ is independent of the ion-solvent-ion interactions as per the deductions arrived by the cited workers above. This will be invalid, and needs a total review. Harned & Owen [5], Krishnamurthy [6], B.R.Rao & K.S.Rao [7], Marks [8], Bhimasenachar & Subramanyam [9], Padmini& Rao [10], Mason [11], pointed out the deviations in the Gucker’s equations qualitatively, without rigorous explanation of the same. These shortcomings in the Gucker’s equations are to be attributed mainly to the solvation and the ion-ion & the solvent-ion interactions, consequent of internal field modifications around the central ion inside the ion- atmosphere, as the electrolytic ions enter the solvent, with the increase in concentration. Borukhov et.al. [12] Attempted to arrive at a modified Poisson-Boltzmann Equation but for no complete avail, since several recent findings are not taken care of. The model for viscosity of electrolytic solution by Lencka et.al [13], Wang & Anderko [16]for water as solvent was later improved into a comprehensive model for calculating the viscosity of aqueous or mixed-solvent electrolyte systems ranging from dilute solutions to fused salts, is informative , and several concepts in the approaches are useful to be applied in the M.C.Simulations . The B coefficients data for a large number of aqueous species used by Wang & Anderko was determined by analyzing extensive experimental viscosity data by Marcus [14] for a number of ions in pure organic 103 | P a g e solvents at 25 0 C. For systems for which the B coefficients are not available in literature sources, their values have been determined from experimental viscosity data at low electrolyte concentrations (usually below 0.05 M) in pure solvents using a method described by Lencka et al. The temperature dependence of the B coefficients can be expressed using the equation of Out and Los [15]. Still these models find little use, having failed to incorporate the solute solvent interactions, to make the model applicable to ion pair formation analysis. The Wang & Anderko [16] model incorporates a mixing rule for calculating the viscosity of solvent mixtures and a method for predicting the effect of finite electrolyte concentrations. The effect of electrolyte concentration on viscosity is modeled by combining a long-range electrostatic term obtained from the Onsager-Fuoss theory, a contribution of individual ions, which is quantified by the Jones- Dole B coefficients, and a contribution of specific interactions between ions or neutral species. Formulations have been developed for the contributions of individual ions and species-species interactions. The model reproduces the approach to viscosity of systems such as salts in water, organic or mixed water-organic solvents and aqueous acids or bases up to the pure solute limit. However it is necessary to develop it further in the light of recent findings about solute solvent interactions Experimental and Calculations: This paper reports the data, of our ultrasonic studies using Ultrasonic pulse echo technique similar to that of Mc Clements & Fairley [17] in aqueous solutions of sulphates. Density measurements are made using the bicapillary pyknometer. The conductance data was obtained using the ‘PHILIPS’ Conductivity Bridge Model P.R.-9500 similar to the one used by Power et.al & Singh .et.al. [18] And Bikash Kumar Panda et.al & Mishra et .al. [19]. The bridge used has a cell constant of (1.39). The ionic polarization effecting the Conductivity measurements is balanced the usage of an inbuilt oscillator generating 1 KHz signal, applied to the bridge network as a whole The experimental details for dielectric determinations are given else where [20] The ultrasonic, dielectric and conductance data of the author were used in the calculations, using a programme, in “C- language” and details of analysis of variations in thermodynamic parameters, are presented as graphs with C as abscissa and 2 0 2 2 &( ) K K K φ − , as ordinates separately. Discussion of the results: All the plots record three conspicuous gradient changes per each electrolyte. Each gradient change corresponds to the formation of a type of ion pair. These graphs record distinct changes in slope, at three concentrations, corresponding to, the formation of solvent separated, solvent shared & contact pairs in tune to the expectations of Eigen [21] and is different from the findings reported earlier in literature. As pointed out by Eigen& DeMaeyer [22] the internal field around the central ion of the ionic atmosphere created by the charged solute ions in the solvent of the electrolytic solution, tend to reduce the value of the dielectric constant of the electrolytic solution. Avery exhaustive review on the Ion association & complexation studies is available by Covington & Lilley [23]. Solute solvent interactions of several mixed solvent systems with many electrolytes are studied by Maitra & Bagchi [24]. The Gibbs energy of solvation, as given by log s, where s is the solubility has been found to depend on various modes of solute–solvent interaction and also on the Hildebrand solubility parameter representing the cohesive energy density (solvent–solvent interaction) of solvent. A dimensionless quantity has been defined to represent the deviation of the observed log s values from the mole fraction average. Results have been explained in terms of various modes of solvation interaction. M. J. Blandamer, D.Waddington & J. Burgess et.al. [25] Studied properties of solutions of binary aqueous mixtures from the standpoint of solute-water and solute-solute interactions, using pair wise interaction parameters. With an increase in the amount of solute, strong evidence is obtained for clustering of both aqueous and non-aqueous components. These trends are explained in terms of preferential solvation of initial and transition states using Kirkwood-Buff integral functions. The analysis is applied to kinetic data describing the dependence on the ethanol mole fraction of the first order rate constant for the solvolysis of 104 | P a g e t-butyl chloride in aqueous solution. Kaatze. et.al. (26) discussed the aqueous systems for which measurements of the complex electric permittivity (10 3 Hz ≤ ν ≤ 10 11 Hz) and of the attenuation coefficient of acoustic waves (10 5 Hz ≤ ν ≤ 3·10 9 Hz) had been recently experimented over a broad range of frequencies. The liquids include aqueous solutions of multivalent electrolytes, of transition metal chlorides, of micelles and bilayers, and of small organic molecules. It is shown that, In many cases, the two spectroscopic methods can be favourably used to yield complementary aspects of structural properties and interesting molecular dynamics of liquid mixtures .The qualitative explanation of the mechanism of formation of the three types of ion-pairs, was detailed by Margaret Robson Wright [27] , Robinson and stokes[28] , J.O”M. Bockris & Amulya K.N. Reddy [29], & J.O”M. Bockris et.al. [30] The outlines of the same are available at Brahmajirao, [31].From the plots of [ C versus 2 K φ ] Gucker showed that K c φ 0 lim → represents the reduction in the hydration number. In the reported plots, this intercept is obtained on the 2 K φ axis .This decreasing intercept clearly signifies the reduction in the number of water molecules around the central ion. Also we can write K c φ 0 lim → = β 2 0 1 1 ) ( n v n v f − = - h n 0 1 v 0 β in which n1 is the total number of molecules of water and n2 is the number of moles of electrolytes and h n is the hydration number which is the number of water molecules in the primary hydration sheath round the central ion. Fuoss [32], &Kraus et. al. [33] showed that the solvent with lower dielectric constant favours ion-pair formation to a more marked degree. They showed that at the critical distance defined by 2 1 2 [( ) / 2 ] q z z e DkT = , the potential energy of the ion pair is “2kT”. This fulfils the condition that the energy required to separate the ion pair is comparable to the thermal energy. The decrement in the dielectric constant makes the value of ‘q’ greater than the ionic diameter. An equation for association constant was deduced, applying the method devised by Boltzmann to the equilibrium between ion pairs and free ions. He obtained for the degree of association 2 2 (1 ) A K c f α α − = , where c is concentration, f is Debye-Huckel activity coefficient ,α is the fraction of the (1-1 ) electrolyte present as free ions and A K is the association constant .For 1-1 electrolyte he deduced 3 [4 ]/[3000] b A K Na e π = , in which a is ionic diameter, 2 / b e aDkT = ,since [ z1=z2 ],D is the dielectric constant, k is Boltzmann’s constant , and T is the absolute temperature . 3 2 4 log [log ] 3000 A Na e K aDkT π ⇒ = ⇒ A plot between log A K as ordinate and (1/D) as abscissa, had to be a straight line with constant slope, if D remains constant But the solvent mixture is treated as a dielectric continuum, with no modification attempted for accounting the solvent solute interactions, that would lead to the continuous variation of the dielectric constant as the solute concentration gradually increases .Hence this theory requires modification in the light of the Glueckauff’s model. Consequently Fuoss’ equations fail to predict the behavior of the ion pairs to a better extent the graph between log A K versus (1/D) will not have constant slope and so its analysis reveals valuable information about Ion-pair formation. 105 | P a g e Several workers [34] in addition to Fuoss and Kraus used mixtures of solvents aqueous as well as non aqueous and established the ion pair formation in each of them, exactly in the same lines and hence Fuoss and Kraus theory was applied therein. However the fact that the dielectric constants of the solvent continuum changes once the solute ions enter it is not implanted into their analysis and observations. Hence their observations are incompetent to explain the ion-solvent interactions Stillinger [35] using the dielectric measurements of Hasted, Ritson, and Collie [20] made an attempt to give a mathematical shape to the logical structure of mechanism of ion pair formation for a symmetrical electrolyte, so that the pairing process could be generalized to accommodate unsymmetrical electrolytes in such a way as to divide ions uniquely into uncharged "molecules" with minimal internal distances. KCl was chosen for numerical analysis. Petrucci et .al [36]. Using studies in infrared, Raman spectra, and conductance measurements, supported by dielectric and ultrasound relaxation and related thermodynamic evaluations attempted a systematic analysis of Ionpair mechanism. However their work is to be extended to other sources of data to ensure generalizations. Ohtaki et.al... [37] in their X-ray diffraction & NMR studies in a series of papers 1990’s studied ionic solvation, Rohman [38] in his Ph.D., thesis “Ultrasonic Velocities and Transport Properties of Aqueous and Nonaqueous Electrolytes,” published voluminous data with non -aqueous solvents also. Buchner et.al [39], recently in their dielectric relaxation studies over a wide range of frequencies and concentration ranges similar to those of the author recorded marked evidences of the simultaneous existence of double-solvent-separated, solvent-shared, and contact ion pairs at all the ranges of temperatures studied, with tendency for the formation of contact pairs to be more as the temperature increases. Exactly in the similar lines in our ultrasonic studies, our plots with GKG parameters reported in this paper, record more than two or more gradient changes at places of formation of solvent separated as well as solvent shared ion pairs, with nearly the same stability, since the slopes at these places of formation corresponding to the value of SK is not much different. Buchner et.al [39], used a dielectric relaxation technique that restricts the thermodynamic analysis of the individual ion pairs .They concluded that both the ions influence solvent water molecules beyond the first hydration sphere. They concluded that both the ions influence solvent water molecules beyond the first hydration sphere. Very recently Honggaing Zhao et.al [40], & H.Weingartner [41], attempted the development of an equation of state that considers the statistical conditions to account for association contribution of the solute to the solvent through the reduction of the dielectric constant. We are attempting to use this model, and intend to report our findings shortly. Results for sulphates appear separately at Brahmajirao et.al [42]. 106 | P a g e Rahmat Sadeghi et.al, [43], reported apparent molar volumes and transfer of isentropic compressibility’s of l-alanine from water to aqueous potassium di-hydrogen citrate (KH2Cit) and tri-potassium citrate (K3Cit) from ultrasonic measurements. It was found that the apparent molar isentropic compressibility and the apparent molar volume of alanine in both KH2Cit and K3Cit aqueous solutions is negative and increases by increasing temperatures and salt concentrations. Very recently in the ionic volume measurements Marcus [44], studied the properties of electrolytes in solutions and observed the interactions of the constituent ions with solvent and other ions. The interactions with the solvent alone are manifested at infinite dilution. From the measurement of partial molar volume, & density, additive ionic contributions, for small ions due to the electrostriction of the solvent were obtained from an iterative shell-by-shell calculation from a continuum model of the solvent. The solvation number ‘S ‘ defined by the ratio of the solvent shrinkage per mol of ions to, the molar electrostriction of the solvent is calculated & compared with the experimental values, and good agreement for many univalent ions in both single solvents and in some binary solvent mixtures, is reported. He opines that when no appreciable preferential solvation takes place, ion pairing sets in under certain circumstances of ionic charge and solvent permittivity. In his studies on structural and thermodynamic aspects of the hydrophobic effect. from analysis of the solvation structure around solutes and various water models by the RISM integral equation method, Soda [45] concluded that with increasing solute radius from 0 to 3A, the average orientation of hydrating water varies from an inward to an outward orientation, this shows that some reorganization of water occurs in response to the change in solute size. It is predicted from the scaled particle theory that the solvent exclusion effect caused by the introduction of solute into solvent is an important factor of the hydrophobic effect. Chen. et.al. [46], from a detailed analysis of a series of lengthy molecular dynamics simulations of alkali-halide solutions carried out over a wide range of physiologically relevant concentrations find evidence for pronounced non ideal behavior of ions at all concentrations in the form of ion pairs and clusters which are in rapid equilibrium with dissociated ions. The phenomenology for ion pairing seen in these simulations is congruent with the multistep scheme proposed by Eigen and Tamm based on data from ultrasonic absorption. For a given electrolyte, it was shown that the dependence of cluster populations on concentration can be described through a single set of equilibrium constants. They confirm the conclusions of Fuoss and co-workers, based on conductometric experiments. Ion pairs and clusters form on length scales where thesize of individual water molecules is as important as the hard core radius of ions. Ion pairing results as a balance between the favorable Coulomb interactions and the unfavorable partial desolvation of ions needed to form a pair.Afanasievet.al. [47] and Gardas et.al. [48] With their extensive measurements of the speed of ultrasound, density, and isobaric heat capacity, isentropic compressibility of aqueous solutions, over wide temperature and concentration ranges, evaluated parameters including hydration numbers and osmotic virial coefficients .Several observed deviations were attributed to the change in the dielectric permeability of water in direct proximity to ions, leading to Ionic hydrophobic influence. Gardas et.al compared their results with that of X-ray data analysis in the solid phase. Their interpretations are yet to be confirmed in detail. Jönsson et.al.[49] Worked out Monte Carlo simulations of the hydrophobic effect in aqueous electrolyte solutions which reveal several structural characteristics of the solvent around the central ion during ion pair formation. However the attempts are yet in the primary stage of development, but have a promising scope to understand the solvent behaviour. Pitzer et.al.’s [50] formalism, developed in a series of papers has been put to use and a model was developed by Soto et.al. [51] to correlate the activity coefficient, apparent molar volume and isentropic compressibility of glycine in aqueous solutions of NaCl, based on detailed experimentation with ultrasonic techniques. The results show that the model can accurately correlate the interactions in aqueous solutions of glycine and NaCl. 107 | P a g e 108 | P a g e REFERENCES: (1) GLUECKAUFF, Trans.Faraday.Soc. 60 1637, 572(1964); “Digest of literature on dielectrics” Nat.Acad.Of Sci., National research council Washington .D.C.; (2) VONHIPPEL, “Dielectric materials and applications “, The Technology Press, M.I.T., Massachusetts, U.S.A.; (1954), (3) GUCKER, J.Amer.Chem.Soc 55 2709 (1933) & Chem. Revs 15 111. (4) GUCKER&BACHEM Zeits.F.Physik. 101 541(1936), Z.Electrochem. 41 570(1936), (5) HARNED &OWEN,” The Physical Chemistry of Electrolytic solutions “: Reinhold publishers (1958); (6) KRISHNAMURTY J. Sci. Ind. Res. 9B 215(1951), 10B 149(1952), (7) B.R.RAO& K.S.RAO J.Sci. Ind. Res. 17B 444(1958), (8) MARKS J. Acous.Soc.Amer. 31 936(1960, (9) BHIMASENACHAR & SUBRAMANYAM J. Acous.Soc.Amer. 32 835 (1960), (10) PADMINI& RAO, Ind. 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Phys. 19 (1981) 254; Ibid (1981) “Application of Glueckauff’s model for depression in Dielectric ...Ion pair formation”, Proceedings’ of ‘Ultrasonics International-81’, held at Brighton U.K. 30 th JUNE to 2 nd JULY 1981;Ibid “Analysis of solute- solvent interactions …in relation to ion pair formation”,Procedings of International Symposium on Electro analytical Chemistry Held at Chandigarh, INDIA December1982;Ibid “Study of …in chosen electrolyte solutions “ Proceedings’ of Sir J.C.Ghosh Memorial symposium held at Calcutta, INDIA,Feb1982; Ibid “Electrostatic Potential energies of Ion pairs in nonaqeous media from” Ultrasonic measurements”, Proceedings of Eighth International Conference on Nonaqueous Solutions, Nantes (Cedex) FRANCE, 19 th to 23 rd July 1982 ;Ibid “Ultrasonic studies in solute solvent interactions…..Ionpairs”Procedings of ICNAS-IX Held at Pittsburgh, Pennnsylvania,U.S.A. in August 1984; Ibid “Solute –Solvent interaction and Ion pair formation in the light Of depression in Dielectric constant” Proceedings of VIth International Symposium on Solute–Solvent–Solute…Interactions, Tokyo, JAPAN, July1982.Ibid “Application of Glueckauff’s model of variation of dielectric Constant to association constant – Calculations in relation to Ion pair Formation “Proceedings of 2nd International symposium on Industrial and Oriented Electrochemistry, Held at Karaikudi, INDIA (Dec 1980) (32).FUOSS “Ionic Association.III.The Equilibrium between Ion Pairs and Free Ions”, J. 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Ibid 2000), J.Chem.Phys.113 762; Ibid (2001) Adv.Chem.Phys 116 1; Ibid (1991), Ber.Bunsenges.Phys.Chem. 95 1579; Ibid (1995) J. Stat.Phys.78 169; Ibid (1999) J Phys Chem. B. 103 738; Ibid (1999), J. Solution.Chem. 28 435; Ibid (1989) Ber.Bunsenges.Phys.Chem .93 1058; (42) BRAHMAJIRAO et.al, “Glueckauff’s model for lowering of dielectric const. Isentropic ompressibility Studies ….. With aqueous … using Ultrasonic’s - ‘ION PAIRS ‘- (SULPHATES) “Paperpresented to NSA-2010, Rishikesh, INDIA), Nov 11 th to 13 th , (2010); Ibid “On GLUECKAUFF’S model for variation of dielectric constant of electrolyte Solution, and its Influence on thermodynamic variables, determined by acoustic tools & onfirmation of Eigen Mechanism of ION PAIRS “Paper presented to: I.C.A -2010, Sydney AUSTRALIA, to be held during AUG23 rd TO 27th of (2010);(43) RAHMAT SADEGHI et.al, J. Mol. Liquids, 141, (1-2), Pages 62-68. (2008) ;( 44) MARCUS Biophys.Chem, 124(3), pages 200-7(2006), MARCUS, “Ion Solvation,” Wiley Interscience, New York. (1985) ;( 45) SODA, Adv Biophys. 29 1-54(1993). ;( 46) CHEN et.al., J Phys Chem. B. 111(23): 6469- 78 (2007). ;( 47) AFNASIEV et.al. J Phys Chem. B. 13(1): 212-23 (2009), ;( 48) GARDAS et.al. J Phys Chem. B; 112(11):3380- 89(2008). ;( 49) Jönsson et.al., J Phys Chem.B.110(17): 8782-8(2006). (50)PITZER et.al. J.Phys.Chem. 77, 268 (1973); Ibid J.Am.Chem.Soc, 96, 5701 (1974); Ibid J.Solution Chem., 18, 1007(1989); Ibid (2010) Molecular Structure and statistical Thermodynamics Selected papers of Kenneth S Pitzer’ World Scientific, Singapore Ion interaction approach: Theory and data 110 | P a g e correlation.’ In: “Activity Coefficients in Electrolyte Solutions. 2 “– Editor: Pitzer KS, Boca Raton, Florida, USA: CRC Press; (2010) pp. 75–153; (51) SOTO et. al., Biophys.Chem. 74(3): 165-73 (1998). 111 | P a g e GLUECKAUFF’S MODEL FOR LOWERING OF DIELECTRIC CONSTANT OF ELECTROLYTIC SOLUTIONS : ISOENTROPIC COMPRESSIBILITY AND ION- ASSOCIATION STUDIES WITH AQUEOUS ELEECTROLYTIC SOLUTIONS BY ULTRASONICS -Ion pairs (SULPHATES) V.Brahmajirao 1** , T. Gunavardhan Naidu 1 , T.Srikanth 2 , P.Rajendra 3 Shanaz Batul 4 1 Matrix Institute of technology, Cheekatimamidi (V), Bommalaramaram (M), Jawaharlal Nehru Technological University HYDERABAD , Pin Code – 508116 ; 2 Jawaharlal Nehru Technological University (Jagtyal Campus) Jagtyal.A.P.; 3 LNBC Institute of Engineering and Technology,Raigaon, Satara, Maharastra ; 4 Main campus, Jawaharlal Nehru Technological University, HYDERABAD-500072. ; ( 1** E- mail ID for all correspondence:
[email protected] ) .. ABSTRACT This paper reports the specific evidence of the formation of three types of Ion pairs from the ultrasonic studies in aqueous solutions of sulphates. The data is presented as plots, using equations for partial molal compressibility & apparent molal compressibility. Correlating arguments cited by several earlier workers, are given in support. Also deductions by a host of others in the application of equations of Gucker et.al, [5] & [6] apparently are incomplete, since the dielectric constant dependence on concentration is to be installed into their arguments, to account for the ion-solvent interactions missing in the prevailing theories of electrolytic state. The author modifies the relevant equations and explains on firm grounds ,the mechanism of formation of Three types of ion pairs i.e., (1) solvent separated, (2) solvent shared and (3)contact types, The graphs record an excellent agreement with many of the findings of the very recent work in the field of electrolytic research cited at the appropriate place . Discrete variation in the slopes of the straight line plots are explained, correlating the concepts arrived at in the very recent literature, by a host of workers trying to analyze similar interrelated problems in different angles ,using thermodynamics, molecular dynamics ,and quantum physics . They obtained valuable information with Monte Carlo Simulations and all of us land at concurrent & conspicuous conclusions. KEYWORDS: Glueckauff’s model, Isentropic compressibility, Monte Carlo Simulations , Ion-pairs in aqueous electrolytes, Debye Huckel theory, Gucker’s equations , Lowering of dielectric constant of dielectric continuum Introduction Robinson and stokes [1], point out that Debye- Huckel theory treats the ions of the ionic atmosphere as hard, non deformable spheres of equal radius, and hence crudely neglects the short range interactions between ions and solvent molecules, as well as other possible interactions .which are responsible to create internal field around the central ion of the ionic atmosphere & the average effect of all such ions is to reduce the value of the dielectric constant of the electrolytic solution.. Hasted et.al.,[2] ,showed that the first layer of the solvent molecules of type “B” round the central ion of type “A” of the ionic atmosphere cause short range interaction leading to the reduction in the bulk dielectric constant of the medium around the central ion.Glueckauff & Von Hippel [3], Buckingham [4], used this very important point for correction. and 112 | P a g e developed a model to evaluate the depression in the dielectric constant, of an electrolyte solution as the concentration of the solute increases, starting from Gibbs free energy given by ( ) B A n G G n ∂ = ∂ , at constant temperature and pressure .This model was used earlier by the author to evaluate the dielectric data, that was confirmed to be reasonably accurate, experimentally. This data was used in the present work. Gucker [5] established with standard notation the partial molal compressibility as 2 0 0 0 2 2 2 2 2 2 2 [ ( )] [ ( )] ( ) G G V V K K p p ∂ ∂ − = − = − ∂ ∂ . In this 0 0 0 2 2 2 , , K V G , are parameters corresponding to infinite dilution. Treating the dielectric constant as a variable it can be shown that 2 0 2 2 2 2 2 3 5 1 ( ) [ ( ) ( ) ( )] 2 D D D K K D P D P D P β χ ∂ ∂ ∂ − = + + ∂ ∂ ∂ . In this 1 [ ( )] V V P β ∂ = − ∂ 2 1 v ρ = , is the iso-entropic compressibility, ρ is the density, and “D”, is the dielectric constant, (which is a variable, as per the new expectations ), and, 3 6 1 2 2 ( ) [ ] (1000 ) N e D kT π χ = and N is Avogadro Number .These equations clearly reveal That [ 0 2 2 ( ) Cversus K K − ] plots that were expected to be linear previously, cannot be so. The variations in the slope correspond to the ion-solvent, & solvent -solvent interactions, and other factors that require attention. Also the apparent molal compressibility is [ 2 ( ) v k T p φ φ ∂ = ∂ ,] and [ 2 0 K K K S C φ φ = + ], in which [( / ) ( )] 2 V K V T S S S P β = ∂ ∂ + Leading to 2 3 2 2 6 ( ) [ 2( ) ( ) 6 K i i T T i D S z P D P χ β β ν β ∂ ∂ = + − + ∂ ∂ ∑ 2 2 2 2 15 6 ( ) ( ) ] T T D D D P D P ∂ ∂ − ∂ ∂ Hence ( ) K Cversus φ plot cannot be linear, against the predictions of Gucker et.al. The variations in its slope correspond to the ion-solvent, & solvent -solvent interactions, and other factors, leading to the ion pair formation as detailed in the discussion of the results. According to Gucker et.al, [6]. 10 (6.3 10 ) K S X δ − = is a constant, where δ is independent of the ion-solvent, ion-ion & and other interactions .But the above expression clearly shows that it is not so. Earlier Harned & Owen [7], Krishnamurthy [8], B.R.Rao & K.S.Rao [9], Marks [10], Bhimasenachar & Subramanian et.al. [11], Padmini& Rao [12], Mason [13],Giacomini et.al.[14], Prozorov[15],Barnartt[16] observed that the linearity of the above plots extends into higher concentration regions where the Debye- Huckel theory is not contemplated to be applied .Also the SK value showed irrational variation with the valence of the ion, and no rigorous explanation of these findings is available in the literature.Association constatant is a parameter which gives an insight into the ion-ion and ion-solvent interactions With the notation used by Graham Kell &Gordon[17] ,we can show that A K the association constant can be expressed in terms of conductances η Λ the value corrected for volume effect on viscosity produced by the solute , 0 Λ the value at infinite dilution, and Λ the value at the given concentration ,by the equation 2 0 [ log ] A i i i i i Ec c S c Jc K c f η η Λ = Λ + − + − Λ , and A K is the mass action term,’ E’ is the 113 | P a g e electrophoretic term, ’S’ is the Onsager term, ‘J’is the relaxation term ,and ‘ f ’.is the activity coefficient . It is now established that all these terms are discrete functions of dielectric constant. In addition if ion association comes into existence, the expression for η Λ becomes a cubic equation in γ (to be solved by a method of continued fractions) where 1 [ ] n c γ = , in which 1 n is the free charged ion number, and ‘c’ is the concentration. From this equation γ can be obtained by a process of iteration, to give finally 0 ( ) ( ) F z γ Λ = Λ , where F= 3 2 1 2 4 1 ( ) ( ) cos [( ) cos ( 3 . )] 3 3 2 z F z − = − , in which’s’ is an independent variable given by 1 2 3 2 0 ( )( ) S z c = Λ Λ .This leads to 2 2 2 2 0 0 ( ) [ ] /[ ] A c f K F F Λ = Λ − Λ Λ ,called the GKG equation. We find that these equations do not incorporate the happenings around the reference central ion, consequent of the interactions that generate long range and short range fields in the ion -atmosphere in the continuous dielectric medium of the solvent. Only thermodynamics and statistical tools can help this .Monte Carlo simulations, are finding good utility at hand, since the variety of influencing parameters and the equations to be probed with them is complex .As a preliminary attempt the author used conductance, dielectric constant and activity coefficient data for several aqueous as well as nonaqeous electrolytic systems partly his own and partly from Lobo [46] with the above equations. Several plots, for each electrolyte were drawn. Several findings from recent literature are in consonance with the conclusions from the author’s plots. Paucity of space restricts the discussion about conclusions with this equation by the author here in this paper. Some of the prominent expectations of the recent trends are discussed below. These shortcomings of the respective citations detailed above find a systematic explanation by the author and are to be attributed mainly to the deficiencies in reckoning the electrical interactions, inside the ion- atmosphere, around the central ion as the concentration increases Details are available at ref. Brahmajirao et.al. [39] Experimental and Calculations: This paper reports the data, of our ultrasonic studies using Ultrasonic pulse echo technique similar to that of Mc Clements & Fairley [18] in aqueous solutions of sulphates. Density measurements are made using the bicapillary pyknometer. The conductance data was obtained using the ‘PHILIPS’ Conductivity Bridge Model P.R.-9500 similar to the one used by Power et.al & Singh .et.al. [19] And Bikash Kumar Panda et.al & Mishra et .al. [20]. . . The ionic polarisation effecting the Conductivity measurements is balanced the usage of an inbuilt oscillator generating 1 KHz signal, applied to the bridge network as a whole The experimental details for dielectric determinations are given else where [47] The ultrasonic, dielectric and conductance data of the author were used in the calculations, using a programme, in “C-language” and details of analysis of variations in thermodynamic parameters, are presented as graphs with C as abscissa and 2 0 2 2 &( ) K K K φ − , as ordinates separately. Discussion of the results: All the plots record conspicuous gradient changes corresponding to ,the formation of solvent separated, solvent shared & contact pairs as envisaged by Eigen[21]and worked out by Eigen et.al., [22], entirely different from the cited , previously reported results The qualitative details of the mechanism of formation of ion pairs , is briefed below : In the initial (first) stage an ion pair is formed with no disruption of the individual solvation sheaths of the individual ions, so that in the ion pair these solvation sheaths of the individual ions are in contact and solvent is present between the ions. In this stage the solvent co spheres are in contact , but the ions are 114 | P a g e reasonably distant from one another Hence these are SOLVENT SEPARATED ION PAIRS .In this stage the solvent co spheres are in contact, and the ions are reasonably distant from one another In the intermediate (second) stage an ion pair is formed with partial disruption of the individual solvation sheaths of the individual ions and there is still some solvent present between the ions so that the ions of the ion pair share the solvent sheath between the ions .Hence these are called SOLVENT SHARED ION PAIRS .Ion pairs formed in the first two stages are called outer-sphere ion pairs .In an outer-sphere ion pair one, or at most two, solvent molecules lie between the ions, and the ions yet are not in contact . In the last (third ) stage an ion pair is formed with total disruption of the solvation sheaths of the individual ions so that in the ion pair the bare ions are in contact and there is no solvent between the ions. Hence these pairs are called CONTACT PAIRS or inner sphere ion pairs .In an outer-sphere ion pair one, or at most two, solvent molecules lie between the ions , but for an inner-sphere ion pair bare ions are in contact and all solvent sheaths have been eliminated from between the ions.. However, both inner and outer-sphere ion pairs are still solvated as the composite unit. The ion pairs which can be found are thus not necessarily identical, and there is the possibility that different experimental methods may pick out and detect only one kind of ion pair. In literature, the ultrasonic studies is probably the only tool to detect the formation of all the three types However as pointed by Margaret Robson Wright [23], ion pair formation totally differs from complex formation when a complex is formed an intimate chemical interaction between the ions & electronic rearrangement occurs resulting in covalent interactions, in contrast to the physical columbic electrostatic interactions involved in the formation of an ion pair. Also the Ultrasonic and spectroscopic methods probably allow a distinction to be made with reasonable certainty between outer and inner-sphere ion pairs, while conductance work and scattering of light experiments allow micelle formation to be picked up very easily. These are quite exceptional achievements in the field of ion association. Inferences made from thermodynamic and kinetic experiments have often been used, but they rely very heavily on being able to predict a model for the ideal solution, for which a theory is yet to be conceived. This is being attempted by the author in the lines of. Larsen et al [29] and. Fennell [30] and others. Gucker showed that from the [ C versus 2 K φ ] plots, K c φ 0 lim → represents the reduction in the hydration number. Because we can write K c φ 0 lim → = β 2 0 1 1 ) ( n v n v f − = - h n 0 1 v 0 β in which n1 is the total number of molecules of water and n2 is the number of moles of electrolytes and h n is the hydration number which is the number of water molecules in the primary hydration sheath round the central ion . The slope gradually decreases for each plot, at three places, to reveal the reduction in the number of water molecules in the primary hydration sheath of the ion pair. Very recently Krishnan et.al [24].in his admittance studies of aqueous sodium chloride and NMR relaxation rate of 7 Li + by Mn 2+ or Ni 2+ in aqueous solution , observed measurable difference for two models which are consistent with other magnetic relaxation and thermodynamic data for the solutions. They reported Enthalpy studies in electrolytes in methanol and dimethylformamide leading to similar observations .They pointed out from their admittance studies marked evidences for the ion pair formation, exactly in tune to the authors’ findings Master ton et.al. [25] reported Conductivity data for solutions of [Co (NH3)5NO2] SO4 in water and aqueous dioxan. Ion-pair association constants calculated. A plot of [logK A] vs. [1/D] is found to have a slope considerably greater than that for simple 2:2 salts. A major factor contributing to enhanced association appears to be ion-dipole interaction. However the effect of addition of electrolyte to the solvent is not considered, therein... Fuoss [26] &Kraus et. al. [27] showed that the solvent with lower dielectric constant favours ion-pair formation to a more marked degree. They showed that at the critical distance defined by 2 1 2 [( ) / 2 ] q z z e DkT = , the potential energy of the ion pair is “2kT”. This fulfils the condition that the energy required to separate the ion pair is comparable to the thermal energy. The decrement in the dielectric constant makes the value of ‘q’ greater than the ionic diameter. An equation for association constant was deduced, applying the method devised by Boltzmann to the equilibrium between ion pairs and free ions. He obtained for the degree of association Debye-Huckel activity coefficient ,α the association constant .For 1-1 electrolyte he deduced diameter , 2 / b e aDkT = ,since [ z1=z the absolute temperature . But the solvent mixture is treated as a dielectric continuum, with no modification attempted for accounting the solvent solute interactions, leading to the continuous variation of the dielectric constant as the solute concentration gradually increases .Hence t light of the Glueckauff’s model. Consequently Fuoss’ equations fail to predict the behavior of the ion pairs to a better extent .Several workers aqueous as well as non aqueous and established the ion pair formation in each of them, exactly in the same lines and hence Fuoss and Kraus constants of the solvent continuum changes once the solu observations. Hence their observations are incompetent to explain the ion [29], in the N.M.R.Relaxation studies observed Li and + 2 Mg + in a variety of solvents .For conductance data shows that the addition of a small amount of water causes transformation fr Solvent separated ion pairs Larsen et al [30] of Bjerrum length on several factors from the MC simulations of Yukawa potential for several other models in vogue to establish several lapses in RPM. A corresponding state between that of Yukawa case and unscreened coulomb case was conceived, from which equivalent Bjerrum lengths in the coulomb potential, was correlated usin dynamics simulations, Fennell et.al [31] studied ion-ion interactions in water. and the set of alkali halide ion pairs, and in each case, we test different parameter sets are tested for m both the water and the ions. Several different PMFs were compared. Association equilibrium constants (KA) were calculated and compared with two types of experiments. affinities", about the relative affinity of ions in was applied. From observations on the relative depths of the free energies of the contact ion pair (CIP) and the solvent-shared ion pair (SIP), along with related solvent structure analyses, th correlation with the proposition that small should be more dissociated. Work in the lines of Kaatze et.al. [32] reported ultrasonic absorption spectra at frequencies between 300 kHz and 3 GHz reported for aqueous solutions of MgCl transition metals , of micelles and bilayers, and of small organic molecules. systems for which measurements of the complex electric permittivity (10 attenuation coefficient of acoustic waves (10 broad range of frequencies. It is shown that, in many cases, the two spectroscopic methods can be favorably used to yield complementary aspects of structural properties and of the molecular dynamics of interesting liquid mixtures.All spectra reveal a Debye relaxation time values derived from the spectra display a small range only (0.2 ns corresponding with the τ values for solutions of Mg(NO , the potential energy of the ion pair is “2kT”. This fulfils the condition that the energy required to separate the ion pair is comparable to the thermal energy. The decrement in the nt makes the value of ‘q’ greater than the ionic diameter. An equation for association constant was deduced, applying the method devised by Boltzmann to the equilibrium between ion pairs and free ions. He obtained for the degree of association 2 2 (1 ) A K c f α α − = , where c is concentration, α is the fraction of the (1-1 ) electrolyte present as free ions and 1 electrolyte he deduced 3 [4 ]/[3000] b A K Na e π = , in which =z2 ],D is the dielectric constant , k is Boltzmann’s constant , and T is he solvent mixture is treated as a dielectric continuum, with no modification attempted for accounting the solvent solute interactions, leading to the continuous variation of the dielectric constant as the solute concentration gradually increases .Hence this theory requires modification in the light of the Glueckauff’s model. Consequently Fuoss’ equations fail to predict the behavior of the ion pairs to a better extent .Several workers [27] in addition to Fuoss and Kraus [28] used mixtures of solvents ous as well as non aqueous and established the ion pair formation in each of them, exactly in the and Kraus theory was applied therein. However the fact that the dielectric constants of the solvent continuum changes once the solute ions enter it is yet to be implanted into their observations. Hence their observations are incompetent to explain the ion-solvent interactions [29], in the N.M.R.Relaxation studies observed Contact ion association behaviour of per chlorate in a variety of solvents .For 4 2 ( ) Mg ClO in acetonitrile a combination of N.M.R. and conductance data shows that the addition of a small amount of water causes transformation fr Larsen et al [30] studied the ion solvent interactions in relation to dependence of Bjerrum length on several factors from the Restricted Primitive Model (RPM), and rigorously worked out tential for several other models in vogue to establish several lapses in RPM. A corresponding state between that of Yukawa case and unscreened coulomb case was conceived, from which equivalent Bjerrum lengths in the coulomb potential, was correlated using classical molecular ion interactions in water. and the Potentials of Mean Force (PMF) set of alkali halide ion pairs, and in each case, we test different parameter sets are tested for m both the water and the ions. Several different PMFs were compared. Association equilibrium constants (KA) were calculated and compared with two types of experiments. Collins "law of matching water , about the relative affinity of ions in solution depending on the matching of cation and anion sizes, was applied. From observations on the relative depths of the free energies of the contact ion pair (CIP) and shared ion pair (SIP), along with related solvent structure analyses, th correlation with the proposition that small-small and large-large should associate in water, and small should be more dissociated. Work in the lines of Fennell et.al [27], is in progress with the authors. ultrasonic absorption spectra at frequencies between 300 kHz and 3 GHz reported for aqueous solutions of MgCl2, CaCl2, SrCl2, NiCl2, and CuCl2 , many multivalent electrolytes, of transition metals , of micelles and bilayers, and of small organic molecules.They discussed systems for which measurements of the complex electric permittivity (10 3 Hz ≤ ν ≤ 10 attenuation coefficient of acoustic waves (10 5 Hz ≤ ν ≤ 3·10 9 Hz) had been recently experimented over a cies. It is shown that, in many cases, the two spectroscopic methods can be favorably used to yield complementary aspects of structural properties and of the molecular dynamics of interesting liquid mixtures.All spectra reveal a Debye-type relaxation term with small amplitude. The relaxation time values derived from the spectra display a small range only (0.2 ns corresponding with the τ values for solutions of Mg(NO3)2 and Ca(NO3)2 in water. The relaxation term is 115 | P a g e , the potential energy of the ion pair is “2kT”. This fulfils the condition that the energy required to separate the ion pair is comparable to the thermal energy. The decrement in the nt makes the value of ‘q’ greater than the ionic diameter. An equation for association constant was deduced, applying the method devised by Boltzmann to the equilibrium between ion pairs and , where c is concentration, f is 1 ) electrolyte present as free ions and A K is , in which a is ionic ],D is the dielectric constant , k is Boltzmann’s constant , and T is he solvent mixture is treated as a dielectric continuum, with no modification attempted for accounting the solvent solute interactions, leading to the continuous variation of the dielectric his theory requires modification in the light of the Glueckauff’s model. Consequently Fuoss’ equations fail to predict the behavior of the ion pairs used mixtures of solvents ous as well as non aqueous and established the ion pair formation in each of them, exactly in the theory was applied therein. However the fact that the dielectric te ions enter it is yet to be implanted into their solvent interactions Berman et.al Contact ion association behaviour of per chlorate ion with in acetonitrile a combination of N.M.R. and conductance data shows that the addition of a small amount of water causes transformation from contact to studied the ion solvent interactions in relation to dependence , and rigorously worked out tential for several other models in vogue to establish several lapses in RPM. A corresponding state between that of Yukawa case and unscreened coulomb case was conceived, from g classical molecular Force (PMF) for the full set of alkali halide ion pairs, and in each case, we test different parameter sets are tested for modeling both the water and the ions. Several different PMFs were compared. Association equilibrium constants Collins "law of matching water solution depending on the matching of cation and anion sizes, was applied. From observations on the relative depths of the free energies of the contact ion pair (CIP) and shared ion pair (SIP), along with related solvent structure analyses, they found a good large should associate in water, and small-large , is in progress with the authors. ultrasonic absorption spectra at frequencies between 300 kHz and 3 GHz , many multivalent electrolytes, of discussed such aqueous ν ≤ 10 11 Hz) and of the Hz) had been recently experimented over a cies. It is shown that, in many cases, the two spectroscopic methods can be favorably used to yield complementary aspects of structural properties and of the molecular dynamics of with small amplitude. The relaxation time values derived from the spectra display a small range only (0.2 ns τ 0.6 ns), in water. The relaxation term is suggested to be due to the second step in the Eigen dissociation of ions, namely the equilibrium betw complex. The relaxation amplitudes reflect special properties of the ions. Exactly similar observations are reported in our studies Recent ideas of the mechanism of dielectric relaxation in hydrogen bonded are discussed. Comparison is made with some aspects resulting from computer simulation studies.. Concurring views as the authors of this paper that in many cases, the two spectroscopic methods (dielectric and ultrasonic) can be favorably used to yi molecular dynamics of interesting liquid mixtures were expressed. dielectric response due to the three- suggested. The present model termed the sphere hybrid model, previously used to describe dipolar orientational relaxation The wideband (up to 1000 cm complex permittivity (ω) and absorption α(ω) spectra of NaCl calculated as the sum of the contributions due to cations and anions and to reorientation of polar H molecules. A modification of this model is al Zhao et.al, [34] developed an “ Equation of state for electrolyte solutions by combining statistical associating fluid theory & Mean Spherical Approximation for the non the interactions between different ingredients of the electrolytic solution ,are attempted to be accounted in this . Specifically the Statistically A describes long –range ( ion-ion ),( ion nonprimitive MSA model, in performing the MC simulations . The model yet requires modifications, which are aimed at by the author Wertheim summation over all the possible sites, and species, accommodating for the fraction of the ions that indulges in pair formation, at a given site .However the presumptions many times lead to unrealistic situations, hence demand more in depth pursuance. recently examined the significance of the term ‘activity’ in the context of the properties of aqueous solutions for aqueous solutions containing neutral aqueous mixtures... Properties of aqueous solutions binary aqueous mixtures from the standpoint of solute water and solute-solute interactions, using pair wise interaction parameters are in the amount of solute, strong evidence is obtained for clustering of both aqueous and non components. These trends are explained in terms of preferential solvation of initial and transition states using Kirkwood-Buff integral functions. The analysis is applied to kinetic data describing the dependence on the ethanol mole fraction of the first order rate constant for the solvolysis of solution. Work regarding the application of Kirkwood paper is in progress at the authors end coefficient work.are used by Moggia et.al. [38] However a better alternative with a suitable modification , to develop MC Simulations ,using the formalism with its versatile extensions simulations of ionic solutions is employ single-ion and ion-pair properties simultaneously for five different salt solutions, namely, CsCl, KCl, NaI, KF, and CsI, at finite ion concentration. The force fields of these ions are sy finite-concentration simulations, the pair potential is extracted and the osmotic coefficient is calculated, which is compared to experimental data. They suggest that additional parameters are to be introduced into the modeling, for better results The author is attempting this model for comparisons with parameters obtained with ultrasonic data. Choudhary et.al. [40] and Dougherty et.al. [41] free energy contributions to the hydrophobic interaction between hydrophobic solutes and water using molecular dynamics simulations in the isothermal suggested to be due to the second step in the Eigen–Tamm scheme of stepwise association and dissociation of ions, namely the equilibrium between the complex of encounter and the outer sphere complex. The relaxation amplitudes reflect special properties of the ions. Exactly similar observations are reported in our studies Recent ideas of the mechanism of dielectric relaxation in hydrogen bonded are discussed. Comparison is made with some aspects resulting from computer simulation studies.. Concurring views as the authors of this paper that in many cases, the two spectroscopic methods (dielectric and ultrasonic) can be favorably used to yield complementary aspects of structural properties and of the molecular dynamics of interesting liquid mixtures were expressed. Gaiduk [33] suggested simple model of -dimensional motion of ions inside a spherical ideally suggested. The present model termed the sphere-confined ionic (SCI) model is combined with the so called hybrid model, previously used to describe dipolar orientational relaxation The wideband (up to 1000 cm (ω) and absorption α(ω) spectra of NaCl-water and KCl-water diluted solutions are calculated as the sum of the contributions due to cations and anions and to reorientation of polar H molecules. A modification of this model is also suggested, in which the walls may also vibrate. developed an “ Equation of state for electrolyte solutions by combining statistical associating fluid theory & Mean Spherical Approximation for the non- primitive model” .A m the interactions between different ingredients of the electrolytic solution ,are attempted to be accounted in Associating Fluid Theory for Variable Range potentials ion ),( ion-dipole ), and (dipole-dipole ) interactions ,is combined with the nonprimitive MSA model, in performing the MC simulations . The model yet requires modifications, which are aimed at by the author Wertheim [35], calculated the association contribution, statistically, by a double summation over all the possible sites, and species, accommodating for the fraction of the ions that indulges in pair formation, at a given site .However the presumptions many times lead to unrealistic situations, hence demand more in depth pursuance. M. J. Blandamer, D.Waddington & J. Burgess et.al. [36] recently examined the significance of the term ‘activity’ in the context of the properties of aqueous solutions for aqueous solutions containing neutral solutes, mixtures of neutral solutes and salts, and also binary roperties of aqueous solutions binary aqueous mixtures from the standpoint of solute solute interactions, using pair wise interaction parameters are studied in the amount of solute, strong evidence is obtained for clustering of both aqueous and non components. These trends are explained in terms of preferential solvation of initial and transition states al functions. The analysis is applied to kinetic data describing the dependence on the ethanol mole fraction of the first order rate constant for the solvolysis of t-butyl chloride in aqueous solution. Work regarding the application of Kirkwood-Buff integral functions, to the data reported in this paper is in progress at the authors end Pitzer et.al.’s [37] semi empirical Equations, developed for activity Moggia et.al. [38] in a pseudo lattice approach using Gibbs a better alternative with a suitable modification , to develop MC Simulations ,using the formalism with its versatile extensions for the force field calculations using Molecular dynamics simulations of ionic solutions is employed by Fyta et.al., [39] ,by optimizing ionic force fields based on pair properties simultaneously for five different salt solutions, namely, CsCl, KCl, NaI, KF, and CsI, at finite ion concentration. The force fields of these ions are systematically varied. From the concentration simulations, the pair potential is extracted and the osmotic coefficient is calculated, which is compared to experimental data. They suggest that additional parameters are to be introduced ing, for better results The author is attempting this model for comparisons with parameters Choudhary et.al. [40] and Dougherty et.al. [41]separately Calculated Entropic and enthalpy and excess o the hydrophobic interaction between hydrophobic solutes and water using molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble with free energy perturbation 116 | P a g e Tamm scheme of stepwise association and een the complex of encounter and the outer sphere complex. The relaxation amplitudes reflect special properties of the ions. Exactly similar observations are reported in our studies Recent ideas of the mechanism of dielectric relaxation in hydrogen bonded liquids are discussed. Comparison is made with some aspects resulting from computer simulation studies.. Concurring views as the authors of this paper that in many cases, the two spectroscopic methods (dielectric eld complementary aspects of structural properties and of the suggested simple model of reflecting sheath is confined ionic (SCI) model is combined with the so called hybrid model, previously used to describe dipolar orientational relaxation The wideband (up to 1000 cm −1 ) water diluted solutions are calculated as the sum of the contributions due to cations and anions and to reorientation of polar H2O so suggested, in which the walls may also vibrate. Honggaing developed an “ Equation of state for electrolyte solutions by combining statistical .A major fraction of the interactions between different ingredients of the electrolytic solution ,are attempted to be accounted in ange potentials (SAFT-VR) that dipole ) interactions ,is combined with the nonprimitive MSA model, in performing the MC simulations . The model yet requires modifications, which on contribution, statistically, by a double summation over all the possible sites, and species, accommodating for the fraction of the ions that indulges in pair formation, at a given site .However the presumptions many times lead to unrealistic situations, and M. J. Blandamer, D.Waddington & J. Burgess et.al. [36] Very recently examined the significance of the term ‘activity’ in the context of the properties of aqueous solutions solutes, mixtures of neutral solutes and salts, and also binary roperties of aqueous solutions binary aqueous mixtures from the standpoint of solute- . With an increase in the amount of solute, strong evidence is obtained for clustering of both aqueous and non-aqueous components. These trends are explained in terms of preferential solvation of initial and transition states al functions. The analysis is applied to kinetic data describing the dependence on butyl chloride in aqueous al functions, to the data reported in this Equations, developed for activity Gibbs-Duhem equation. a better alternative with a suitable modification , to develop MC Simulations ,using the Pitzer’s for the force field calculations using Molecular dynamics ,by optimizing ionic force fields based on pair properties simultaneously for five different salt solutions, namely, CsCl, KCl, NaI, stematically varied. From the concentration simulations, the pair potential is extracted and the osmotic coefficient is calculated, which is compared to experimental data. They suggest that additional parameters are to be introduced ing, for better results The author is attempting this model for comparisons with parameters Calculated Entropic and enthalpy and excess o the hydrophobic interaction between hydrophobic solutes and water using isobaric (NPT) ensemble with free energy perturbation 117 | P a g e methodology. The stabilizing contribution to the free energy of association (contact pair formation) was found to be the favorable entropic part, the enthalpy contribution being highly unfavorable. The desolvation barrier is dominated by the unfavorable enthalpy contribution, despite a fairly large favorable entropic compensation. The enthalpy term was decomposed into a direct solute-solute term, the solute-solvent interactions term, and the remainder that contains pressure-volume work as well as contributions due to solvent reorganization. The enthalpy contribution due to changes in water-water interactions arising from solvent reorganization around the solute molecules is shown to have major contribution in the solvent induced enthalpy change. Their observations require in depth application to more data. The data used Dougherty et.al[41] with their model include: molecular orbital-molecular dynamics applied to electrolyte water systems; Raman spectra; infrared spectra; magnetic resonance spectra of ions; the apparent density of water; and the excess free energy of electrolytes in aqueous solutions. Molecular orbital-molecular dynamics calculations of relatively large water clusters containing a molecule of sodium iodide show that the solvent separated ion pair exists in a substantial potential well compared to other possible structures. Raman spectra of univalent electrolyte solutions as a function of concentration can be quantitatively modeled using only the spectra of pure water and electrolyte solution at the concentration of the solvent separated ion pair. This information supplements the author’s observations Buchner et.al [42], recently in his dielectric relaxation studies over a wide range of frequencies and concentration ranges similar to those of the author recorded marked evidences of the simultaneous existence of double-solvent-separated, solvent-shared, and contact ion pairs at all the ranges of temperatures studied, with tendency for the formation of contact pairs to be more as the temperature increases. Even our plots reported in this paper, with GKG parameters record gradient changes at more than two or more places of formation of solvent shared ion pairs, and with nearly the same stability, since the slopes at these formations corresponding to the value of SK is not much different. Buchner et.al, uses a technique that restricts the thermodynamic analysis of the individual ion pair’s .They conclude that both the ions influence solvent water molecules beyond the first hydration sphere. Soto et.al.,[43]developed a model based on the Pitzer et.al’s. [37] formalism developed in a series of papers to correlate the activity coefficient, apparent molar volume and isentropic compressibility of aqueous solutions of electrolytes , based on detailed experimentation wit ultrasonic techniques . The results show that the model can accurately correlate the interactions in aqueous solutions of glycine and NaCl. A positive transfer volume of glycine from a NaCl solution to a more concentrated NaCl solution indicates that the size of a glycine molecule is larger in a solution with higher NaCl concentration. The negative values of apparent isentropic compressibility imply that the water molecules around the glycine molecules are less compressible than the water molecules in the bulk solution. These effects are attributed to the doubly charged behavior of glycine and to the formation of physically bonded ion-pairs between the charged groups of glycine and sodium and chloride ions. The formation of ion-pairs, whose extents of binding reactions depend on the concentrations of both NaCl and glycine, alter the hydration number of glycine. This also explains the reason for the increase in the size of glycine with an increase in the NaCl concentration. Wang et.al. [44] Studied, the thermodynamic properties, like the mean activity coefficient, osmotic coefficient, and water activity,etc. for 129 complex aqueous electrolyte solutions using the modified three-characteristic-parameter correlation model., which considers ion association in a betterway, incorporating solute solvent interactions through thermodynamic parameters . This model is being worked out and the out come will be published soon elsewhere, because the technique is other than ultrasonic in nature. Wang et.al. also calculated the adjustable parameters of the Pitzer model and the Bromley model. and established that their modified model is fairly suitable for predicting the mean activity coefficient, osmotic coefficient, and water activity of these electrolytes, incorporating several interactions. This new model is much better than the Bromley model and shows a better result than the Pitzer model. especially for 3–1 and 3–2 electrolytes. Work on 118 | P a g e chlorides and sulphates and nitrates in aqeous and nonaqeous solvents and observations about thermodynamic and ion association parameters and other related evaluations by the author is available else where at [45] reference REFERENCES: (1)ROBINSON&STOKES“Electrolytic solutions“(second revised edition), DOVER publications NEWYORK, page231, chapter 9,” The limiting law ….Huckel “(2002); (2) HASTED et.al. J.Chem.Phys 16 1(1948). (3) GLUECKAUFF Trans.Faraday.Soc. 60 1637, 572(1964); “Digest of literature on dielectrics “....Nat. Acad, Of Sci., National research council Washington .D.C.; VON HIPPEL “Dielectric materials and applications “, The Technology press, M.I.T., Massachusetts, U.S.A. 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Soc, 96, 5701 (1974); Ibid J.Solution Chem., 18, 1007(1989); Ibid (2010) Molecular Structure and statistical Thermodynamics Selected papers of Kenneth S Pitzer’ (2010) World Scientific, Singapore Ion interaction approach: Theory and data correlation.’ In: Activity Coefficients in Electrolyte Solutions. 2 – Editor: Pitzer KS, Boca Raton, Florida, USA: CRC Press; 1991. pp. 75–153. ;( 38) MOGGIA et.al. J Phys Chem. B. (2008); 112(4):1212-7; Ibid J Phys Chem. B. 111(12): 3183-91(2007).;(39) FYTA & NETZ et.al. J Chem. Phys. 132(2): 024911(2010). ;( 40) CHOUDHURY et.al. J Phys Chem. B. 110(16) 8459-63 (2006).;(41) DOUGHERTY et.al. Biophys. Chem. 105(2-3) pp: 269-78(2003). (42) BUCHNER et.al J Phys Chem. B. 110(30) (2006): 14961-70.; (43) SOTO et. al., Biophys.Chem. 74(3) 165-73(1998); SOTO et. al “Effect of cation …. Of an electrolyte on apparent molar volume, isentropic 119 | P a g e Compressibility…… in aqueous solutions”, Biophys Chem. (1999) 76(1): 73-82. ;( 44) WANG et.al J. Chem. Eng. Data, (2004) 49 (5), pp 1300–1302 ;( 45) BRAHMAJIRAO Ind.J.Pure. Appl .Phys. 14 646(1976) ; Ibid (1979), “Cationic motilities of electrolytic solutions – Ion pairs –EIGEN mechanism” Transactions. Of. Saest, 14 (2) (1979) 53; Ibid (1980), Ind. J. pure & Appl. Phys. 18 12 (1980) 1021; Ibid (1980), “Influence of variation of Dielectric constant.Gucker’s equations…” Proceedings of International Conference on Ultrasonics, ICEU-July 1980, Held at New Delhi. INDIA; Ibid (1980) “Application of ….. Variation of Dielectric.....GKG and Dagget equations “, Proceedings of International Conference on Non Aqueous Solutions, ICNAS-7, held at REGENSBERG, West Germany. (Aug 1980); Ibid (1981), Ind. J.Pure & Appl. Phys. 19 (1981) 254; Ibid “Application of Glueckauff’s model for depression in Dielectric …..Ion pair formation”, Proceedings’ of ‘ULTRASONICS INTERNATIONAL-81’, held at Brighton, U.K 30 th JUNE to 2 nd JULY 1981;Ibid “Analysis of solute- solvent interactions …in relation to ion pair formation”, Proceedings’ of International Symposium on Electro analytical Chemistry Held at Chandigarh, INDIA December1982. ;Ibid “Study of …in chosen electrolyte solutions “, Proceedings’ of Sir J.C.Ghosh memorial Symposium, held at Calcutta, INDIA, Feb1982; Ibid “Electrostatic Potential energies of Ion pairs in nonaqeous media from Ultrasonic measurements”, Proceedings of Eigth International Conference on Nonaqueous Solutions, Nantes (Cedex) FRANCE, 19th to 23 rd July 1982;;Ibid “Ultrasonic studies in solute solvent interactions…..Ionpairs”Procedings of ICNAS-IX, Held at Pittsburgh, Pennsylvania, U.S.A. in August 1984; Ibid “Solute –Solvent interaction and Ion pair formation in the light Of depression in Dielectric Constant” Proceedings of VIth International Symposium on Solute –Solvent – Solute Interactions, Tokyo, JAPAN, July1982.; Ibid “Application of Glueckauff’s model of variation of dielectric Constant to association constant - Calculations in relation to Ion pair Formation “, Proceedings of 2nd International symposium on Industrial and Oriented Electrochemistry, Held at Karaikudi, INDIA (Dec 1980).;(46) V. M. M. Lobo “Handbook of Electrolyte Solutions”, “Elsevier Science Ltd” (1990); (47) Hasted et.al. J.Chem.Phys 16 1. (1948) 1.28 1.285 1.29 1.295 1.3 1.305 1.31 1.315 1.32 0.1320.1370.1420.1470.1520.1570.1620.1670.1720.177 COPPER Solvent shared pairs Contact pairs Solvent separated pairs 1.28 1.285 1.29 1.295 1.3 1.305 1.31 1.35 1.32 0.135 0.14 0.145 0.15 0.155 0.16 0.165 0.17 COBALT Solvent shared pairs Contact pairs Solvent separated pairs 120 | P a g e 121 | P a g e 0.0 2 0.0 0.1 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1 1. 1 1. 2 1. 3 c With ‘C’ in gm moles per litre 0. 0. 0. 0. 0. 0. 0. 0. 0. 1 0. 0. 0. 0. 1. 1. 122 | P a g e TEMPERATURE VARIATION ULTRASONIC VELOCITY IN COW MILK AT DIFFERENT FREQUENCIES Kailash, S. N. Shrivastava* and Poonam Yadav Department of Physics, B N P G College, Rath, Hamirpur, U.P. * Department of Chemistry, Bipin Bihari Post-Graduate College Jhansi, U.P. Email:
[email protected] Milk is considered as an essential food constituent for a foremost segment of population. The present day need is for development of simple reproducible, Sensitive, Cost effective and fast methods for analysis of milk and milk products so that generated information can be effectively utilized for human health. Quality Control may be defined as the operational techniques and activities that are used to fulfill requirement for quality. It revolves around the assessment of specific product and process attributes to confirm standards and specifications Very tiny work has been done to study the quality of milk using ultrasonic techniques. This has motivated us to undertake the present study. In this paper, we have made detailed investigations of ultrasonic wave velocities in pure milk of Cow at different temperatures using multi frequency ultrasonic interferometer. The ultrasonic velocity decreases as temperature increases. INTRODUCTION The major constituents of milk are water, fat, protein, lactose, ash or mineral matter. The colour of milk is due to the scattering of light by the fat globules, casein molecules, colloidal calcium phosphate and to some extent by the pigments caroteine and riboflavin (Walstra and Jenness, 1984). Milk ranger in colour from yellowish creamy white to creamy white to creamy white depending upon type of milk. The intensity of yellow colour of cow milk depends upon size of the fat globules and fat percent, apart from breed and feed (Harper and Hall, 1979). To reduce the fat globules, milk is homogenized. After homogenization, milk creams very slowly, but is alos altered in other aspects. All sterlised milks or, more generally, all long-life liquid milk products, are homogenized in practice. The purpose of homogenization usually is not to make, but to keep a product homogeneous (Jenness and Patton, 1959). The main effect is the disruption of fat globules into smaller ones, which slows down creaming (Burton, 1954). Milk also cantains certain enzymes, which are of different types, and are inactivated by heat. The caroteines, which are present in the milk, impart a yellowish tint. Usually, the extent of colour depends on the ability of the cow to convert caroteine into vitamin A (Paterson, 1950). These colours depend on the amount of caroteine present in the 123 | P a g e milk. The product examines sensory and nutritional quality of cow's milk and addresses quality improvement of a range of other milk-based products. The quality of milk reviews the health aspects of milk and its role in the diet, as well as the essential aspects of milk quality, including microbial spoilage and chemical deterioration, sensory evaluation and factors affecting milk vitamin and mineral content. We discusses various application requirements of milk such as milk quality requirements in yoghurt-maiking, cheese making, infant formulas and applications of milk components in products other than foods. Consumers demand quality milk with a reasonable shelf-life, a requirement that can be met more successfully by the milk industry through use of improved processes and technologies. Guaranteeing the production of safe milk also remains of paramount importance. Improving the safety and quality of milk provides a comprehensive and timely reference to best practice and research advances in these areas. The sensory and nutritional quality of cow’s milk and addresses quality improvement of a range of other milk-based products. The health aspects of milk, its role in the diet and milk-based functional foods. Part two reviews essential aspects of milk quality, including milk microbial spoilage and chemical deterioration, sensory evaluation, factors affecting milk vitamin and mineral content and the impact of packaging on quality. Chapters in Part three look at improving particular products, such as organic milk, goat milk and sheep milk. The impact of milk on the quality of yoghurt and cheese is also covered. (Griffiths, M. 2010). Milk is considered as an important food ingredient for a major sector of population. The present day need is for development of simple reproducible, Sensitive, Cost effective and fast methods for analysis of milk and milk products so that generated information can be effectively utilized for human health. Traditionally, the dairy industry has ensured the quality of its products by employing inspection and test methods managed under the banners of ‘Quality Control’ and ‘Quality Assurance’. In the newer context, the transition in concept and organizational structure has moved from Inspection to Quality Control to Quality Assurance to Continuous improvement and finally to Total Quality Management. Quality Control may be defined as the operational techniques and activities that are used to fulfill requirement for quality. It revolves around the assessment of specific product and process attributes to confirm standards and specifications have been met. In its application Quality Control may become synonymous with the inevitability of product failure, particularly when it is mainly concerned with final product analysis. The technical requirements during dairy product distribution network must be considered by the organization for safe marketing and be included in the quality manual as operational guide. The information on packaging, storage/ warehousing, transportation, retailing, nature of products, marketing conditions etc. must be obtained and recorded for periodical assessment and inducing further improvement in the system. The white colour of milk is an 124 | P a g e expression of good qualities in which etiquette does not alter and thereby colours do not lose their identity in the white. It is the milk in which reside the rhythms and poetry, as well as the colours merge in the white. The molecular assembly in milk which results in whiteness’ ensures not only its purity, but also rejuvenates the hope of good nutrition. Once quality of milk is assured, it will make people pure and free from disease. Therapeutic advances for microbial infections raise expectations that science is on the verge of understanding all manners of pathogenic microbes and their associated illness. MEASUREMENTS The multi frequency ultrasonic interferometer consist of the two parts- the high frequency generator and the measuring cell. The range of multi frequency ultrasonic interferometer is 1-7 MHz. The high frequency generator is designed to excite the quartz plate fixed at the bottom of the measuring cell at its resonant frequency to generate ultrasonic waves in the experimental liquid in the “measuring cell”. A micro ammeter to observe the changes in current and two controls for the purpose of sensitivity regulation and initial adjustment of micro ammeter is provided on the high frequency generator. The measuring cell is a specially designed double walled cell for maintaining the temperature of liquid constant during the experiment. A fine micrometer screw has been provided at the top, which can lower or raise the reflector plate in the cell through a known distance. It has a quartz plate fixed at its bottom the ultrasonic interferometer may be used for determination of ultrasonic velocity in electrolytic and non-electrolytic solutions sound absorption in medium observing liquid, adiabatic compressibility and internal, pressure, a cortical and thermodynamic properties. Reaction rates and formulation of complexes, excess enthalpies of binary and trinary systems, excess properties of binary and ternary systems, latent heat of vaporization of liquids ultrasonic behaviour in liquid crystals molecular relaxation parameters, insolvent interaction, acoustic properties of substances near the critical and freezing temperature sinter molecular interaction, chemical and structural nature of liquid, phase, transition study in liquids, viscous-effects, excess volume and free volume. The measuring cell is connected to the output terminal of the high frequency generator through a shielded cable the cell is filled with the experimental liquid before switching on the generator the ultrasonic waves moves normal from the crystal till they are reflected back from the movable plate and the standing waves are formed in the liquid between the reflector plate and the quartz crystal. The micrometer is slowly moved till the anode current meter on high frequency generator shows a maximum. A number of maximum readings of anode current are passed on and their ‘n’ is counted the total distance (d) thus moved by the micrometer gives the value of wavelength (λ) with the help of the following relation: 125 | P a g e d = n× λ /2 (1) Once the wavelength (λ) is known the velocity (v) in the liquid can be calculated with the help of following relation: V= λ ×f (2) RESULTS AND DISCUSSIONS Earlier we have introduced the significance of milk quality. A review of literature on ultrasonic studies reveals that ultrasonic velocity measurement is used to understand the nature of milk velocity. The Temperature variation of cow milk is effectual its nutrition quality so our aimed is to find at the Temperature in pure milk. For this purpose we have take the pure milk of different animal. On using the measurement techniques presented above, the ultrasonic wave velocities at different Temperature variation are given in Table I using the data of Table 1. The Equation between velocity and temperature are shown in the Table II. We have made detailed investigations of ultrasonic Wave velocities in cow’s milk at different temperatures using multi frequency ultrasonic interferometer (1-7 MHz). The graphs have been plotted between Temperature and velocity shown as in Figs. 1-7. It is clear from Table and Figs. one can state that the ultrasonic velocity is decreases as Temperature variation one may say that the higher velocity is the indication of purity of milk. The present day need is for development of simple reproducible, Sensitive, Cost effective and fast methods for analysis of milk and milk products so that generated information can be effectively utilized for human health. REFERENCES 1. Burton, H. 1954. Colour Chenges in Heated and Unheated Milk I, JI. of Dairy Res. 21:194. 2. Jenness, R. and Patton, S. 1959. ncipal of Dairy Chemictry, Jhon Wiley and Sons. 340- 357. 3. Harper, W. J. and Carl W, Hall. 1979. Dairy Technology and Engineering, Westport, AVI Publishing CO. inc 4. Paterson, W.e. 1950. Dairy Science: Its Principles and Practice, 2 nd Ed., Chicago, J. B. Lippincot Co.: 519-128. 5. Walstra, P. and jenness, R. 1984. Dairy Chemistry and Physics, New York, Wiley and Sons: 160-167. 126 | P a g e 6. Griffiths, M. 2010. Improving the safety and quality of milk improving quality in milk Products. Russian Agricultural Sci.2: 528. 7. Ganguli N.C., An odyssey on milk quality, Indian Dairyman, 54 (2002) 47-50. 8. Sharma R., and Rajput Y.S., Chemical quality of milk its relevance in present situation, Indian Dairyman, 54 (2002) 71. 9. Dhamendra B.V., Kumar C. G., and Kohli R.K., Significance of ultrasonics in food industry-an overview, Indian Dairyman, 52 (2000) 21. 10. Venkatesh P.V., and Singh A., Efficiency of additive and multiplicative correction factors for milk yield in karan fries cattle , Indian journal of dairy science,56 (2003) 320. 11. Singh M., Lodhi R. S., and Nair S., Milk production and reproductive performance of muraha buffaloes hormonally induced in to lactation, Indian journal of dairy science,55 (2002) 30. 12. Ganguli N. C., An odyssey on milk quality, Indian dairyman, 54 (2002) 47. 13. Sharma R., Rajput Y. S., Chemical quality of milk its relevance in present situation, Indian dairyma, 54 (2002) 71. 14. Murthy G. L. N., and Kanawjia S. K., Designer milk nutritional and technological significance, Indian dairyman, 54 (2002) 49. 15. Narang I. K., Our scriptures on cow milk, Indian dairyman 54 (2004) 41. 16. Bhattacharya T.K., Improvement of quality of milk constituents by r DNA technology, Indian dairyman, 54 (2001) 33. 17. Gupta S., Gaudugdh piye sau sal jiye, Kamdhenu Kripa, Lucknow, October (2005) 3. 18. Dube V., Gay ka doodh hi amrat kyon, Kamdhenu Kripa, May (2006) 8. 19. Garg A., Gau vansh poshan avam swasthya, Kamdhenu Kripa, January (2007) 13. Table I. Temperature variation of Ultrasonic velocity in cow milk 1MHz 2MHz 3MHz 4MHz 5MHz 6MHz 7MHz T( 0 C) V(m/s) T( 0 C) V(m/s) T( 0 C) V(m/s) T( 0 C) V(m/s) T( 0 C) V(m/s) T( 0 C) V(m/s) T( 0 C) V(m/s) 28 30 1622.8 1609.7 28 30 1538.0 1510.8 28 30 1479.3 1428.0 28 32 1415.6 1355.2 28 30 1324.5 1299.0 30 32 1250.4 1195.8 28 30 1211.0 1189.3 127 | P a g e 32 34 38 42 47 1599.6 1589.5 1574.4 1562.4 1544.6 32 36 40 46 48 1490.6 1480.4 1472.4 1458.2 1436.0 33 36 40 42 48 1385.7 1370.4 1337.7 1304.1 1282.8 36 40 42 46 48 1302.8 1262.4 1234.4 1194.8 1158.4 34 38 42 46 48 1218.5 1188.0 1127.5 1082.0 1036.5 34 36 40 44 48 1129.2 1075.2 984.0 935.4 886.8 33 37 42 46 48 1062.6 1041.6 978.6 907.9 830.2 Table II. Equations showing relationship between V (m/s) and T ( 0 C) S. No. Freq. (MHz) Equation 1. 2. 3. 4. 5. 6. 7. 1 2 3 4 5 6 7 V = 0.0078*T 3 + 0.96*T 2 - 42*T + 2.2*10 3 V = -0.00036*T 5 + 0.049*T 4 - 3.7*T 3 +1.4*10 2 T 2 - 2.7* 10 3 *T+2.3*10 4 V = 0.001*T 5 - 0.18*T 4 + 12*T 3 - 4*10 2 T 2 + 6.6*10 3 T-4.1*10 4 V = -0.00024*T 5 + 0.045*T 4 - 3.3*T 3 + 1.2*10 2 T 2 - 2.2*10 3 T+1.8*10 4 V = 0.00027*T 5 - 0.053*T 4 + 4.1*T 3 - 1.6*10 2 T 2 + 2.9*10 3 T2*10 4 V = 0.0077*T 4 + 1.2*T 3 - 6.8*T 2 + 1.7*10 3 T - 1.3*10 4 V = 0.0014*T 5 - 0.28*T 4 + 2.1*T 3 - 8*10 2 T 2 + 1.5*10 4 T - 1.1*10 5 28 30 32 34 36 38 40 42 44 46 48 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 Temperature degree centigrate U l t r a s o n i c V e l o c it y in m / s e c Figure1: Frequency Variation of Ultrasonic Velocity in cow milk 1MHz Velocity 28 30 32 34 36 38 40 42 44 46 48 1420 1440 1460 1480 1500 1520 1540 Temperature degree centigrate U l t r a s o n i c V e l o c it y in m / s e c Figure2: Frequency Variation of Ultrasonic Velocity in cow milk 2MHz Velocity 128 | P a g e 28 30 32 34 36 38 40 42 44 46 48 1280 1300 1320 1340 1360 1380 1400 1420 1440 1460 1480 Temperature degree centigrate U l t r a s o n i c V e l o c it y i n m / s e c Figure3: Frequency Variation of Ultrasonic Velocity in cow milk 3MHz Velocity 28 30 32 34 36 38 40 42 44 46 48 1150 1200 1250 1300 1350 1400 1450 Temperature degree centigrate U l t r a s o n i c V e l o c it y in m / s e c Figure4: Frequency Variation of Ultrasonic Velocity in cow milk 4MHz Velocity 28 30 32 34 36 38 40 42 44 46 48 1000 1050 1100 1150 1200 1250 1300 1350 Temperature degree centigrate U l t r a s o n i c V e l o c it y i n m / s e c Figure5: Frequency Variation of Ultrasonic Velocity in cow milk 5MHz Velocity 30 32 34 36 38 40 42 44 46 48 850 900 950 1000 1050 1100 1150 1200 1250 1300 Temperature degree centigrate U l t r a s o n i c V e l o c i t y i n m / s e c Figure6: Frequency Variation of Ultrasonic Velocity in cow milk 6MHz Velocity 28 30 32 34 36 38 40 42 44 46 48 800 850 900 950 1000 1050 1100 1150 1200 1250 Temperature degree centigrate U l t r a s o n i c V e l o c i t y i n m / s e c Figure7: Frequency Variation of Ultrasonic Velocity in cow milk 7MHz Velocity 129 | P a g e ULTRASONIC STUDY OF SOME ORGANIC PATHOLOGICAL COMPOUNDS Kailash 1 , S. K. Shrivastava 2 and Jitendra Kumar 3 1. Department of Physics, BN PG College, Rath, Hamirpur, U.P., 210 431, India 2. Department of Physics, Bundelkhand University, Jhansi, U.P, 284 128, India 3. Department of Physics, Govt. Girls P. G. College, Banda, U.P., 210 001, India Email:
[email protected],
[email protected] ABSTRACT: The use of organic compounds in managing of pathology has increased in recent years, as adjunct therapy and alternative medicine. Extensive ultrasonic study about some organic pathological compounds has been reported in the recent past by some investigators to ensure their characterization and perfect use in medical industry. In this work the measurement of frequency- dependent ultrasonic wave velocity in these organic pathological compounds have been done from 1-8 MHz. One of the characteristic of these organic pathological compounds, ultrasonic wave velocity is measured at room temperature using interferometric technique at different ultrasonic frequencies. Multi frequency ultrasonic interferometer is used for measuring ultrasonic wave velocity in pure Ethyl Acetate, Aniline, Xylene, Acetaldehyde, and Sucrose. The measured data (frequency variation of ultrasonic wave velocity) has been tabulated. The graphical representation of the data has also been given. Interpretation of data shown in graphs is presented through curve fitting and has been discussed widely. KEYWORDS: Pathological, Antibiotics, Ultrasonic interferometer, Herbicides Pigments, Ultrasonic velocity. 1 Introduction: Ultrasonic velocity has become a valuable tool for the study of various physical and chemical properties of the matter [1]. The acoustical properties, compressibility, impedance and viscosity evaluated from ultrasonic velocity and density measurements have been used to elucidate the structure and the nature of molecular interaction in aqueous and non-aqueous solutions [2]. Elastic constants of isotropic solid can be determined ultrasonically when both longitudinal and transverse wave velocities are known [3]. Ethyl acetate is used for the concentration and purification of antibiotics. It is also used as an intermediate in the manufacture of various drugs [4]. Aniline is the simplest and one of the most important aromatic amines, being used as a precursor to more complex chemicals [5]. In addition to its use is as a 130 | P a g e precursor to dyestuffs, such as paracetamol. Xylene is used as a solvent and in the printing, rubber and leather industries and as a cleaning agent for steel and for silicon wafers and chips, a pesticide thinner for paint and in paints as varnishes [6]. Acetaldehyde is a significant constituent of tobacco smoke. It has been demonstrated to have a synergistic effect with nicotine, increasing the onset and tenacity of addiction to cigarette smoking, particularly in adolescents [7]. People who have a genetic deficiency for the conversion of acetaldehyde into acetic acid may have a greater risk of Alzheimer's disease. It is used in medicine as a hypnotic. Sucrose is by far the most important disaccharide which is widely distributed in plants especially in sugar cane sugar beet and sugar maple [8]. The aim of this work is to study the characterization of these organic pathological compounds using ultrasonic techniques. 2 Measurement Technique: The ultrasonic interferometer is simple in construction and operation and gives accurate and reproducible results. From these results, one can readily determine the velocity of sound in a liquid with high accuracy [9-11]. In our experimental work we use multifrequency interferometer which can generate ultrasonic waves of several frequencies from 1 - 12 MHz in the medium. The multi frequency ultrasonic interferometer consists of two parts, the high frequency generator and the measuring cell. The high frequency generator is designed to excite the quartz plate fixed at the bottom of the measuring cell at its resonant frequency to generate ultrasonic waves in the experimental liquid in the measuring cell. A micro ammeter to observe the changes in current is provided on the high frequency generator. A fine micrometer screw has been provided at the top to lower or raise the reflector plate in the cell through a known distance. It has a quartz plate fixed at its bottom the ultrasonic interferometer may be used or determination of ultrasonic velocity. The measuring cell is connected to the output terminal of the high frequency generator and is filled with experimental liquid. On switching on the generator the ultrasonic waves moves normal from the crystal till they are reflected back from the movable plate and the standing waves are formed in the liquid in between the reflector plate and the quartz crystal. The micrometer is slowly moved till the anode current meter on high frequency generator shows a maximum. A number of maximum readings n are taken. The total distance d moved by the micrometer gives the value of wavelength λ with the help of the relation d= n. λ/2. Once the wavelength is known the ultrasonic velocity v of the compound can be calculated with the help of the relation V= λ.f . 3 Evaluation: One of the characterizations of organic compound, velocity is measured at room temperature using interferometric techniques at different ultrasonic frequencies (1-6 MHz and 8-9 MHz). Multi frequency 131 | P a g e ultrasonic interferometer is used for measuring ultrasonic wave velocity in Ethyl Acetate, Aniline, Xylene, Acetaldehyde, and Sucrose. The measured data (frequency variation of ultrasonic wave velocity) are shown in Table 1. The graphical representation of the data is also given in Figs. 1-5. The coefficients of the best fit polynomials of data shown in these figures are presented in Table 2. 4 Results and discussions: The variation of ultrasonic wave velocity with frequency for Ethyl Acetate is presented in Fig 1. It is clear from figure, that with increase in the frequency of ultrasonic wave, the velocity increases. From 3-5 MHz frequency, decrease in velocity is observed and at 6 MHz frequency, there is a highly increase in velocity of ultrasonic wave and for 8-9 MHz an increase in velocity is observed. The variation of ultrasonic wave velocity for Aniline is presented in Fig 2. It is clear from the figure that up to 2 MHz velocity increases with increase in frequency. At 3-4 MHz frequency, there is a slight decrease in velocity. At 5 MHz frequency it increases slightly and at 6 MHz it decreases slightly. At 8 MHz it again decreases and becomes 1412.8m/s which is less than the ultrasonic velocity of water 1509m/s. The variation of ultrasonic wave velocity for Xylene is presented in Fig 3. It is clear from the figure that at 1-2 MHz velocity increases with increase in frequency. At 3-4 MHz frequency, there is a slight decrease in velocity. At 5 MHz frequency there is a slight increase in velocity and for 6 MHz it again decreases. For 8 MHz frequency there is a highly increase in velocity. The variation of ultrasonic wave velocity for Acetaldehyde is presented in Fig 4. It is clear from the figure that for 1-3 MHz velocity increases with increase in frequency. For 4 MHz frequency there is a highly decrease in velocity. At 5 and 6 MHz frequency there is a slight increase in velocity. At frequency 8 MHz the velocity decreases highly to 1382.4m/s. The variation of ultrasonic wave velocity for Sucrose is presented in Fig 5 . It is clear from the figure that at 1-4 MHz velocity slight increases with increase in frequency. At 5-8 MHz frequency increase velocity increases highly. The table shows that as well as on incensement frequency velocity increases. For Sucrose the ultrasonics velocity increases with increasing frequency. The ultrasonic velocity of Sucrose is more than the ultrasonic velocity of water that is 1509 m/s, this is because of density, because the density of Ethyl Acetate is much more than density of water. These studies can also be used to determined the extent of complexation and calculate the stability constants of these compounds [12]. Experimental findings shows that ultrasonic wave velocity is not increasing linearly with frequency, the result shows a slightly deviation from the ideal case but over all these show that with increase in frequency of ultrasonic wave, velocity shows slight variation. 5 References: 132 | P a g e 1. D. G. FRIEND, ‘Speed of sound as a thermodynamic property of fluids’, Exp. Methods Phys. Sc., 39, 237, 2001. 2. K. Y. JHANG, H. H. QUAN et al, ‘Estimation of clamping force in high-tension bolts through ultrasonic velocity measurement’, Ultras., 44, 1339, 2006. 3. G. VARUGHESE, A. S. KUMAR et al, ‘Elastic study of Potassium Sulphamate crystal using ultrasonic Pulse Echo Overlap Technique’, Sol. Stat. Comm., 149, 645, 2009. 4. M. MOLERO, I. SEGURA et al, ‘On the measurement of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials’, Ultras., 50, 824, 2010. 5. V. BHADAURIA, P. MIRAZ et al, ‘Dual trypan-aniline blue fluorescence staining methods for studying fungus-plant interactions’, Biotech. and Histochem., 85, 99, 2010. 6. R. KANDYALA, S. PHANI et al, ‘Xylene: An overview of its health hazards and preventive measure’, J. Oral Maxillofacial Path., 14, 1, 2010. 7. K. NAKAMURA, K. IWAHASHI et al, ‘Acetaldehyde adducts in the brain of alcoholics”, Arch. Toxicol., 2003, 77, 591. 8. Y. HAYASHI and F. T. BIRD, ‘The use of Sucrose gradients in the isolation of cytoplasmic-polyhedrosis virus particles’, J. Invertebrate Path., 11, 40, 1968. 9. O. O. KURAKEVYCH and V. L. SOLOZHENKO, ‘300-K equation of state of rhombohedral boron subnitride’, Sol. State Comm., 149, 2169, 2009. 10. Y. L. GODEC, D. M. GARCIA et al, ‘Compression and thermal expansion of rhombohedral boron nitride at high pressures and temperatures ‘, J. Phys. Chem. Solids, 61, 1935, 2000. 11. H. MAO, B. SUNDMAN et al, ‘Volumetric properties and phase relations of silica-thermodynamic assessment’, J. Alloys Comp., 327, 253, 2001. 12. V. KANNAPPAN and N. I. GANDHI, ‘Ultrasonic studies on charge transfer complexes of certain aldehydes with benzylamine and cyclohexylamine as doners in n-hexane at 303K’, Ind. J. Pure. Appl. Phys., 45, 221, 2007. Table 1. Frequency Variation of Ultrasonic Velocity for Organic Pathological Compounds Frequency (MHz) Velocity (m/sec.) Ethyl Acetate Aniline Xylene Acetaldehyde Sucrose 1 1093.6 1501.2 1204.2 1564.8 1518.2 2 1355.0 1652.2 1359.0 1644.4 1563.4 3 1158.7 1522.2 1269.3 1866.6 1638.9 4 1016.2 1335.2 1041.6 1605.6 1684.0 5 962.5 1558.5 1255.0 1615.0 1935.0 6 1215.6 1460.4 1170.0 1725.0 2097.4 8 1652.8 1411.8 1599.2 1382.4 2217.6 9 1873.8 - - - - Table 2. Coefficient of Best Fit Polynomial for Ultrasonic Velocity Compound A0 A1 A2 A3 A4 A5 Ethyl Acetate -5.20e+02 2.70e+03 -1.34e+03 2.81e+02 -25.93 0.88 Aniline -6.92e+02 4.06e+03 -2.44e+03 6.42e+02 -76.63 3.38 Xylene -7.96e+02 3.66e+03 -2.17e+03 5.67e+02 -67.83 3.03 Acetaldehyde 2.78e+03 -2.69e+03 2.00e+03 -6.22e+02 84.54 -4.14 Sucrose 1.16e+03 6.42e+02 -3.75e+02 0.99e+02 -10.76 0.40 133 | P a g e 1 2 3 4 5 6 7 8 9 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 Frequency (MHz) V e l o c i t y ( i n m / s e c ) Velocity 1 2 3 4 5 6 7 8 1300 1350 1400 1450 1500 1550 1600 1650 1700 Frequency (MHz) V e l o c i t y ( i n m / s e c ) Velocity 1 2 3 4 5 6 7 8 1000 1100 1200 1300 1400 1500 1600 Frequency (MHz) V e l o c i t y ( i n m / s e c ) Velocity 1 2 3 4 5 6 7 8 1300 1400 1500 1600 1700 1800 1900 Frequency (MHz) V e l o c i t y ( i n m / s e c ) Velocity 1 2 3 4 5 6 7 8 1500 1600 1700 1800 1900 2000 2100 2200 2300 Frequency (MHz) V e l o c i t y ( i n m / s e c ) Velocity Fig. 1. Velocity vs. frequency for Ethyl Acetate Fig. 2. Velocity vs. frequency for Aniline Fig. 3. Velocity vs. frequency for Xylene Fig. 4. Velocity vs. frequency for Acetaldehyde 134 | P a g e HIGH TEMPERATURE STUDY OF ANHARMONIC PROPERTIES OF TeO Kailash 1 , Jitendra Kumar 2 and Virendra kumar 1 1. Department of Physics, BN PG College, Rath, Hamirpur, U.P., 210 431, India 2. Department of Physics, Govt. Girls P. G. College, Banda, U.P., 210 001, India Email:
[email protected],
[email protected],
[email protected] ABSTRACT: A proper and systematic evaluation of anharmonic properties of isostructural oxides, and their dependence on temperature provides the fundamental data for determining the characteristics of cation-oxygen bonding interactions which are pertinent to the understanding and theoretical modelling of more complicated oxide compounds. When the values of second and third order elastic constants and density for any material at a particular temperature are known; one may get ultrasonic velocities for longitudinal and shear waves in different crystallographic directions which give important information about its anharmonic properties. In this work, an attempt has been made to evaluate higher order elastic constants for TeO at an elevated temperature from 50K to 600K. The data of SOECs, TOECs and FOECs are used to evaluate the FOPDs of SOECs and TOECs, SOPDs of SOECs and partial contractions. While evaluating these properties it is assumed that the crystal structure does not change during temperature variation. The data of these oxides obtained through different techniques also give important and valuable information about internal structure and inherent properties of materials and can be used in future for different industrial purposes and further investigations of isostructural oxides. KEYWORDS: Anharmonic properties, Higher order elastic constants, Pressure derivatives, Divalent crystals, Partial contractions, Grüneisen numbers. 1 Introduction: Elastic properties of divalent compounds are important because they relate to the various fundamental solid state phenomena such as inter atomic potentials, equation of state and phonon spectra. If the values of second order elastic constants and density at a particular temperature are known for any substance, one may obtain ultrasonic velocities for longitudinal and shear waves which give an important information about its anharmonic properties. Elastic properties are linked thermodynamically with specific heat, thermal expansion, and Debye temperature and Grüneisen parameters. In the last few years studies of anharmonic properties of solids have attracted the attention of the physicists since they provide much valuable information regarding crystal dynamics [1-5]. A number of theoretical and experimental measurements have been made on the anharmonic properties [6]. No 135 | P a g e complete experimental or theoretical efforts have been made so for in obtaining the temperature variation of anharmonic properties of divalent crystals having various crystal structures. The elastic energy density for a deformed crystal can be expanded as a power series of strains using Taylor’s series expansion [7]. The coefficients of quadratic, cubic and quartic terms are known as SOECs, TOECs and FOECs respectively. Several physical properties and crystal anharmonicities such as thermal expansion, specific heat at higher temperature, temperature variation of acoustic velocity and attenuation, and the FOPDs of SOECs and Gruneisen numbers are directly related to SOECs and TOECs. While discussing higher order anharmonicities such as the FOPDs of TOECs, the SOPDs of SOECs, partial contractions and deformation of crystals under large forces, the FOECs are to be considered extensively. The present paper is mainly focussed on the study of temperature variation of higher order elastic constants and their pressure derivatives up to an elevated temperature up to 600 K (near melting point) for Tellurium oxide (TeO) crystals using Born-Mayer and Coulomb potential starting from the nearest neighbour distance and hardness parameter. 2 Formulation: The elastic energy density for a crystal of a cubic symmetry can be expanded up to quartic terms as shown below [8]; U0 = U2 + U3 + U4 = [1/2!] Cijkl αij αkl + [1/3!] Cijklmn αij αkl αmn + [1/4!] Cijklmnpq αij αkl αmn αpq (1) Where Cijkl, Cijklmn and Cijklmnpq are the SOECs, TOECs and FOECs in tensorial form; αij are the Lagrangian strain components; CIJ, CIJK and CIJKL are the SOECs, TOECs and FOECs in Brügger’s definition and Voigt notations. vib IJ IJ IJ C C C + = 0 , vib IJK IJK IJK C C C + = 0 and vib IJKL IJKL IJKL C C C + = 0 (2) 3 Evaluation: The SOECs, TOECs and FOECs for TeO crystal are evaluated from 50-600 K. Selecting a few data obtained in this study, the values of SOECs, TOECs and FOECs at 300 K are given in Tables 1, 2. The FOPDs of SOECs and TOECs, the SOPDs of SOECs and partial contractions are evaluated utilizing data of Tables 1, 2 and the results are shown in Table 3, 4. All these results are discussed widely and some of them are presented graphically in Figs. 1–6. 4 Results and Discussions: It may state that all the SOECs are positive in nature. For TeO crystals the value of C11 and C44 increases and the value of C12 decrease as temperature increases and are represented in Fig 1. For 136 | P a g e Tellurium oxides, the values of C111, C112 and C166 are negative in nature, while C123, C144 and C456 are positive in nature. The values of C111, C123, C144 and C166 increases, the value of C112, decreases as temperature increases, C456 remaining constant. The temperature variation of C111, C112 and C123 are given in Fig 2. The value of C1111, C1112, C1122, C1144,C1155, C1255, C1266, C4444 and C4455 decreases as temperature increases, and the value of C1123 increases as temperature increases. The value of C1456 remains constant. The first three are presented in Fig 3. The value of dC11/dp and dC12/dp decreases and the value of dC44/dp increases as temperature increases. The value of dC111/dp, dC112/dp, dC144/dp, dC166/dp and dC456/dp increases as temperature increases, and the value of dC123/dp decrease as temperature increases. The variation of FOPDs of SOECs are given in Fig 4. The value of d 2 C11/dp 2 and d 2 C44/dp 2 decreases and d 2 C12/dp 2 increases as temperature increases and are presented in Fig 5. The value of all partial contractions W11, W12 and W44decreases as temperature increases but W11 decreases very sharply, which is presented in Fig 6. These elastic constants are used to compute ultrasonic parameters such as ultrasonic velocities, thermal relaxation time etc [9-11]. The variation of elastic constants [12-14] with respect to pressure can reveal many important features of the short range forces at high pressure. The ultrasonic studies [15] can provide interesting information on the specificities of ion-solvent interaction related to the structure of the solute and the reciprocal effects which arises in the solvent and the role of collinear and noncolinear phonons in anharmonic scattering processes and in ultrasonic attenuation for different structured solids [16]. The data obtained in present investigation will be helpful to those workers who are engaged in studying the temperature variation of anharmonic properties [17–21] of solids at higher temperatures. 4 References: 1. M. ZHAO and Q. JIANG, ‘Crystal liquid interface energy and surface stress of alkali halides’, Mate. Chem. Phys., 87, 1, 2004. 2. KAILASH, K. S. KUSHWAHA et al, ‘Internal structure, inherent ananharmonic properties of some mono- and di-valent materials’, J. Pure App. Ultra., 27, 29, 2005. 3. S. E. DOSSO and N. E. COLLISION, ‘Acoustic tracking of a freely drifting sonobuoy field’ J. Acoust. Soc. Am., 111, 2166, 2002. 4. Z. H. FANG, ‘Temperature dependence of interatomic separation for alkali halides’ Phy. Stat. Sol. (b), 241, 2886, 2004. 5. C. KITTEL, ‘Introduction to solid state physics’, John Wiley, Newyork, 1981. 6. Z. P. CHANG and G. R. BARSCH, ‘Nonlinear pressure dependence of elastic constants and fourth- order elastic constants of cesium halides’ Phys. Rev. Letters, 19, 1381, 1967. 7. F. BIRCH, ‘Finite elastic strain of cubic crystals’ Phys. Rev., 71, 809, 1947. 8. P. B. GHATE, ‘Third order elastic constants of alkali halide crystals’ Phys. Rev., 139, A1666, 1965. 137 | P a g e 9. O. N. AWASTHI and V. K. PUNDHIR, ‘Ultrasoniv attenuation in liquid mercury, zinc and gallium metals’ Ind. J. Pure Appl. Phys., 45, 434, 2007. 10. D. SINGH and D. K. PANDEY, ‘Ultrasonic investigation in intermetallics’ Pramana, 32, 389, 2009. 11. D. SINGH, D. K . PANDEY and P. K. YADAWA, ‘Ultrasonic wave propagation in rare earth monochalcogenides’ Cent. J. Phys., 7, 198, 2009. 12. B. S. ARYA, M. AYNYAS and S. P.SANYAL, ‘High pressure behaviour of alkaline earth tellurides’ Ind. J. Phys., 83, 153, 2009. 13. A. RUKMANGAD, M. AYNYAS and S. P. SANYAL, ‘Structural and elastic properties of rare earth nitrides at high pressure’ Ind. J. Pure Appl. Phys., 47, 114, 2009. 14. C. S. RAO and C. E. REDDY, ‘Finite element modeling of nano ndentation to extract load- displacement characteristics of bulk materials and thin films’ Ind. J. Pure Appl. Phys., 47, 54, 2009. 15. P.F. YUAN and Z. J. DING, ‘Ab inito calculation of elastic properties of rock-salt and zinc-blend MgS under pressure’ Physica B, 403, 1996, 2008. 16. I. G. KULEYEV et al, ‘Interaction of collinear and noncollinear phonons in anharmonic scattering processes and their role in ultrasound absorption of fast quasi-transverse modes in cubic crystals’ J. Phys: Condens. Matter., 22, 095403, 2010. 17. KAILASH, K. M. RAJU et al., ‘Anharmonic properties of rock salt structure solids’ Physica B, 399, 270, 2007. 18. K. UDO, E. FRIECTER and L. KARL, ‘Ultrasonic velocity measurement in liquids with high resolution techniques, selected applications and perspectives’ Measur. Sc. Tech., 19, 062001, 2008. 19. S. THIRUMARAN AND K. J. SABU, ‘Ultrasonic investigation of amino acids in aqueous sodium acetate medium’ Ind. J. Pure Appl. Phys., 47, 87, 2009. 20. S. DAHMEN, H. KETATA, M. H. B. GHOZLEN and B. HOSTEN, ‘Elastic constants measurement of anisotropic Olivier wood plates using air-coupled transducers generated Lamb wave and ultrasonic bulk wave’ Ultras., 50 , 502, 2010. 21. A. K. UPADHYAY and B. S. SHARMA, ‘Elastic properties of intermetallic compounds under high pressure and high temperature’ Ind. J. Pure Appl. Phys., 47, 362, 2009. Table 1. The SOECs in 10 10 N/m 2 for TeO crystal at 300 K. Table 2. The FOECs in 10 10 N/m 2 for TeO crystal at 300 K. Table 3. The FOPDs of SOECs and TOECs for TeO crystal at 300 K. Table 4. The SOPDs of SOECs in 10 -9 m 2 /N and partial contractions in 10 12 N/m 2 for TeO crystal at 300 K. M. P. (K) C11 C12 C44 C111 C112 C123 C144 C166 C456 643 20.711 22.109 22.346 -234.110 -102.256 33.826 32.482 -88.531 31.679 C1111 C1112 C1122 C1123 C1144 C1155 C1255 C1266 C1456 C4444 C4455 2392.0 301.0 434.1 -77.23 -74.48 387.4 -79.45 447.1 -74.01 452.6 -74.41 dC11/dp dC12/dpP dC44/dp dC111/dp dC112/dp dC123/dp dC144/dp dC166/dp dC456/dp -5.725 -3.414 0.967 -33.881 -6.652 3.096 1.256 1.596 3.044 d 2 C11/dp2 d 2 C12/dp2 d 2 C44/dp2 W11 W12 W44 138 | P a g e 0 100 200 300 400 500 600 19.5 20 20.5 21 21.5 22 22.5 23 Temperature(K) S O E C s f o r T e O ( i n 1 e 1 0 N / s q . m . ) C11 C12 C44 0 100 200 300 400 500 600 -250 -200 -150 -100 -50 0 50 temperature(K) T O E C s f o r T e O ( i n 1 e 1 0 N / s q . m . ) C111 C112 C123 0 100 200 300 400 500 600 0 500 1000 1500 2000 2500 3000 Temperature(K) F O E C s f o r T e O ( i n 1 e 1 0 N / s q . m . ) C1111 C1112 C1122 0 100 200 300 400 500 600 -7 -6 -5 -4 -3 -2 -1 0 1 2 Temperature(K) F O P D s O F S O E C f o r T e O ( d i m e n s i o n l e s s ) dC11/dp dC12/dp dC44/dp 0 100 200 300 400 500 600 5 10 15 20 25 30 35 40 45 50 Temperature(K) P a r t i a l C o n t r a c t i o n s f o r T e O ( i n 1 e 1 2 N / s q . m . ) W11 W12 W44 0 100 200 300 400 500 600 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Temperature(K) S O P D s O F S O E C f o r T e O ( i n 1 e - 9 s q . m . / N ) ddC11 ddC12 ddC44 Fig. 1. SOECs Vs Temp. For TeO Fig. 2. TOECs Vs Temp. For TeO Fig. 3. FOECs Vs Temp. For TeO Fig. 4. FOPDs of SOECs Vs Temp. For TeO Fig. 5. SOPDs of SOECs Vs Temp. For TeO Fig. 6. Partial Contractions Vs Temp. For TeO 0.380 0.124 0.110 43.101 10.842 12.728 139 | P a g e ORIENTATION DEPENDENCE OF ULTRASONIC ATTENUATION FOR CALCIUM OXIDE IN HIGH TEMPERATURE RANGE Kailash 1 , S. K. Shrivastava 2 and Jitendra Kumar 3 1. Department of Physics, BN PG College, Rath, Hamirpur, U.P., 210 431, India 2. Department of Physics, Bundelkhand University, Jhansi, U.P, 284 128, India 3. Department of Physics, Govt. Girls P. G. College, Banda, U.P., 210 001, India Email:
[email protected],
[email protected] ABSTRACT: Ultrasonic velocity and attenuation parameters are well connected to the micro structural and mechanical properties of the materials. The most important causes of ultrasonic attenuation in solids are electron–phonon, phonon–phonon interaction and that due to thermo elastic relaxation. The two dominant processes that will give rise to appreciable ultrasonic attenuation at higher temperature are the phonon–phonon interaction also known as Akhieser loss and that due to thermo elastic relaxation are observed in calcium oxide crystal. At frequencies of ultrasonic range and at higher temperatures in solids, phonon–phonon interaction mechanism is dominating cause for attenuation. In this work ultrasonic attenuation due to phonon–phonon interaction (α/f 2 )p-p and thermo elastic relaxation (α/f 2 )th are studied in CaO crystal from 100K-1500K along different crystallographic directions. Temperature dependence of ultrasonic absorption in CaO crystal along different crystallographic direction reveals some typical characteristic features. KEYWORDS: Attenuation, Thermo elastic relaxation, Phonon-phonon interaction, Akheiser loss and Gruneisen constants. 1 Introduction: The ultrasonic attenuation study of the materials has gained new dimensions with the progress in the material science [1-4]. The most important causes of ultrasonic attenuation in solids are electron– phonon, phonon–phonon interaction and that due to thermo elastic relaxation. In recent years, the ultrasonic attenuation techniques [5-7] are widely used as versatile tool in studying the inherent properties and internal structure of solids. The two dominant processes that will give rise to appreciable ultrasonic attenuation at higher temperature are the phonon–phonon interaction [8] also known as Akhieser loss [9] and that due to thermo elastic relaxation and are observed in calcium oxide crystal. Oxides and silicates make up the bulk of the Earth’s mantle and crust, and thus it is useful to predict their behaviour. In this work ultrasonic attenuation due to phonon–phonon interaction (α/f 2 )p-p and 140 | P a g e thermo elastic relaxation (α/f 2 )th are studied in calcium oxide at an elevated temperatures (100-1500 K) along <100>, <110> and <111> crystallographic directions. For the evaluation of the ultrasonic coefficients the second and third order elastic constants (SOECs and TOECs) are also calculated using Coulomb and Born Mayer [10] potentials. Several investigators have given different theories; here the one given by Mason has been used. Mason’s theory relates the Gruneisen constants with SOECs and TOECs. The behaviour of ultrasonic absorption and other parameters as a function of higher temperature have been discussed as the characteristic features of calcium oxide. 2 Formulation: The expressions for ultrasonic attenuation coefficient due to phonon-phonon interaction [11] over frequency square (α/f 2 )p-p are as 3 0 2 . 2 2 3 4 ) / ( l l l long Akh V D E f ρ τ π α | ¹ | \ | = , 3 2 3 0 2 4 . ) 2 / ( s V s s D E shear Akh f ρ τ π α | | ¹ | \ | = and 5 2 2 2 2 4 ) / ( V KT f j i th ρ γ π α > < = (1) where the condition ωτth <<1 has already been assumed. Here E0 is thermal energy density, f is frequency of ultrasonic waves, d is the density and Vl, Vs are the ultrasonic velocities for longitudinal and shear waves respectively. D in eqns. (1) is given as 2 0 2 3 ) ( 9 > < | | ¹ | \ | − > < = j i v j i E T C D γ γ (2) Where γi j ,s are the Grüneisen parameters. 3 Evaluation: The SOECs and TOECs for CaO has been evaluated at different temperatures (100 to 1500 K) following Brugger’s approach [12] and are presented in Table 1 at room temperature. Grüneisen parameters have been evaluated using Mason’s Grüneisen parameters tables [13] at different temperatures along different crystallographic directions with the help of SOECs and TOECs. The non- linearity constants are evaluated using the average square Grüneisen parameters <γi j > 2 and square average Grüneisen parameters <γi j2 >. The values of <γi j > and ultrasonic attenuation (α/f 2 )p-p and (α/f 2 )th along with Vl, Vs, τth and D are presented in Table 2 at room temperature along different crystallographic directions. The temperature variations of all these properties are presented graphically in Figs. 1–6. 4 Results and Discussions: It is clear from the Fig. 1 that the value of thermal relaxation time τth is very high at low temperature and decreases as temperature is increased along all crystallographic directions and of the order of 10 -12 141 | P a g e sec, which is also expected. The temperature variation of ultrasonic velocities is presented in Fig. 2 along <100> direction. It is clear from the figure that the ultrasonic velocity for longitudinal wave increases as temperature increases, while for shear wave it decreases. The thermal ultrasonic attenuation along different directions is presented in Fig. 3. It is clear from the figure that thermal attenuation increases with temperature along all these directions and of the order of 10 -18 Nps 2 /m which is expected for the type of crystal under inspection. Figs. 4 -6 represents the ultrasonic attenuation due to phonon-phonon interaction along <100>, <110> and <111> crystallographic directions respectively. Along all these directions the ultrasonic attenuation increases with increase in temperature, the situation is little different for shear wave along <110> direction (pol. <1 1 0>) for which the ultrasonic attenuation decreases with temperature. From the above results one can reach to the conclusion that the thermal relaxation time, ultrasonic wave velocities and attenuation are the properties which depends on the crystallographic directions or one can say that these properties are orientation dependent which strongly supports the results given by other investigators [14] for the same type of crystals that all these properties are strongly dependent on direction of polarization. The results obtained in this study can be used for further investigations [15, 16] and industrial research and development purposes. 5 References: 1. R. P. SINGH and R. K. SINGH, ‘Theoretical study of temperature dependent lattice anharmonicity in TlCl and TlBr’, Current Appl. Phys., 10, 1053, 2010. 2. J. D. PANDEY, A. K. SINGH and R. DEY, ‘Effect of isotopy on thermoacoustical properties’, J. Pure Appl. Ulras., 26, 100, 2004. 3. A. K. UPADHYAY and B. S. SHARMA, ‘Elastic properties of intermetallics compounds under high pressure and high temperature’, Ind. J. Pure Appl. Phys., 47, 362, 2009. 4. R. K. SINGH, ‘Ultrasonic attenuation in alkaline earth metals’, J. Pure Appl. Ultras., 28, 59, 2006. 5. S. K. SRIVASTAVA, KAILASH and K. M. RAJU, ‘Ultrasonic study of highly conducting metals’, Ind. J. Phys., 81, 351, 2007. 6. KAILASH, K. M. RAJU and S. K. SRIVASTAVA, ‘Acoustical investigation of magnesium oxide’, Ind. J. Phys., 44, 230, 2006. 7. T. YANAGISAA, T. GOTO and Y. NEMOTO, ‘Ultrasonic investigation of Quadrupole ordering in HoB2C2’, Phys. Rev. B, 67, 115129, 2003. 8. S. K. KOR, R. R. YADAV and KAILASH, ‘Ultrasonic attenuation in dielectric crystals’, J. Phys. Soc. Jpn., 55, 207, 1986. 9. A. AKHEISER, ‘On the absorption of sound in solids’, J. Phys. (USSR), 1, 277, 1939. 10. M. BORN and J. M. MAYER, ‘Zur Gittertheorie der lonenkristalle’, Z Phys. (Germany), 75, 1, 1932. 11. W. P. MASON, ‘Piezoelectric crystals and their applications to ultrasonics’, D. Van Nortrand Co, Inc, Prinston, New Jersey, 479, 1950. 12. K. BRUGGER, ‘Thermodynamic definition of higher order elastic coefficients’, Phys. Rev., 133, A1611, 1964. 142 | P a g e 0 500 1000 1500 0 1 2 3 4 5 6 7 8 9 10 Temperature(K) T h e r m a l R e l a x a t i o n T i m e ( i n 1 e - 1 2 s e c . ) Along <100> direction Along <110> direction Along <111> direction 0 500 1000 1500 5.5 6 6.5 7 7.5 8 Temperature(K) U l t r a s o n i c W a v e V e l o c i t i e s ( i n 1 e + 3 m / s e c ) Vl Vs Vd 13. W. P. MASON, ‘Effect of impurities and phonon-processes on the ultrasonic attenuation in germanium, crystal quartz and silicon’, Physical Acoustics, Vol. III B, Academic Press, New York, 237, 1965. 14. K. M. RAJU, KAILASH and S. K. SRIVASTAVA, ‘Orientation dependence of ultrasonic attenuation’, Physics Procedia, International Congress on Ultrasonics, Santiago de Chile, 3, 927, 2010. 15. J. A. SCALES and A. E. MALCOLM, ‘Laser characterization of ultrasonic wave propagation in random media’, Phys. Rev E, 67, 046618(1), 2003. 16. T. C. UPADHYAY, ‘Temperature dependence of microwave loss in ADP-type crystals’, Ind. J. Pure Appl. Phys., 47, 66, 2009. Table 1. The SOECs and TOECs in 10 10 N/m 2 at roomtemperature. Table 2. Long. and shear wave velocities in 10 3 m/sec, thermal relaxation time in 10 -12 sec, non linearity constants, thermal attenuation in10 -18 Nps 2 /m and p-p attenuation for long. and shear waves in 10 -16 Nps 2 /m. Direction of propagation <γ γγ γi j > V τ ττ τth D (α αα α/f 2 )th (α αα α/f 2 )p-p <100>long. shear -0.601 -0.015 7.520 6.171 0.836 - 15.414 2.886 0.373 - 0.218 0.037 <110>long. shear(pol.<001>) (pol.<1 1 0>) -0.673 -0.039 -0.512 9.124 6.171 3.375 0.782 - - 12.248 5.777 13.838 0.178 - - 0.091 0.069 6.253 <111>long. shear(pol.< 1 10>) (pol.<11 2 >) -0.665 -0.203 -0.082 9.599 4.504 4.504 1.379 - - 14.115 8.786 13.529 0.135 - - 0.158 0.954 1.469 Fig. 1. Thermal relaxation time Vs Temp Fig. 2. Ultrasonic velocities Vs Temp. along <100> dir Melting Point (K) C12 C44 C111 C112 C123 C144 C166 C456 2843 12.52 12.71 -252.88 -65.10 20.34 19.43 -51.26 4.71 143 | P a g e 0 500 1000 1500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Temperature(K) U l t r a s o n i c A t t e n u a t i o n ( i n 1 e - 1 6 N p s 2 / m ) Akh.long Akh.Shear 0 500 1000 1500 0 1 2 3 4 5 6 7 Temperature(K) U l t r a s o n i c A t t e n u a t i o n ( i n 1 e - 1 6 N p s 2 / m ) Akh.long Akh.Shear1 Akh.Shear2 0 500 1000 1500 0 0.5 1 1.5 2 2.5 3 Temperature(K) U l t r a s o n i c A t t e n u a t i o n ( i n 1 e - 1 6 N p s 2 / m ) Akh.long Akh.Shear1 Akh.Shear2 0 500 1000 1500 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Temperature(K) T h e r m a l U l t r a s o n i c A t t e n u a t i o n ( i n 1 e - 1 8 N p s 2 / m ) Along <100> direction Along <110> direction Along <111> direction Fig. 3. Thermal ultrasonic attenuation Vs Temp. Fig. 4. Ultrasonic attenuation Vs Temp. along <100> dir Fig. 5. Ultrasonic attenuation Vs Temp. Along <110>dir Fig. 6. Ultrasonic attenuation Vs Temp. along <111> dir 144 | P a g e MOLECULAR RADII OF PYRIDINE/QUINOLINE WITH PHENOL IN BENZENE USING ACOUSTICAL METHODS AT DIFFERENT TEMPERATURES Anjali Awasthi a , Bhawana S. Tripathi a , Rajiv K. Tripathi b and Aashees Awasthi a a Material Science Research Laboratory Department of Physics, University of Lucknow, Lucknow-226 007, India b Department of Physics, D. A. V. P. G. College, Lucknow-226 004, India ABSTRACT: The molecular radii of liquid mixtures of heterocyclic compounds viz., pyridine and quinoline with phenol in benzene have been computed at varying physical conditions using various acoustic methods. The results indicate that molecular radii of liquid mixtures evaluated from Rao’s method are in close agreement with the Schaaffs method. The applicability of Schaaffs or Rao’s method for the estimation of the molecular radii in ternary liquid mixtures has been authenticated. A comparative study of the merits and demerits of various acoustic methods are discussed in the light of molecular structure and intermolecular interactions. KEYWORDS: Molecular radii, Molecular interactions, Ternary liquid mixtures 1. Introduction: Acoustic methods are the most powerful tools for the study of structural and physico- chemical behaviour of liquids and liquid mixtures [1-3]. The molecular radius is an important parameter, which reflects the structural features of pure liquids and liquid mixtures. The molecular radius plays an important role in various liquid state theories [4, 5]. Molecular radius has been utilized to compute various important parameters of liquid mixtures to explain the process of molecular association among their components. Bondi [6] provided a qualitative understanding of the nature of Van der Waals radii and proposed their qualitative values. Ernst and Glinski [7] have studied the effects of various physical parameters on molecular radius in pure liquids using several empirical relations, based on acoustic methods, suggested by Schaaffs [4, 8], Rao [9], Eyring [10,11] and Kittel [12]. Besides these acoustic methods, the relation based upon the assumption that liquid system is made up of closely packed molecules with face centered cubic structures, has been used [6]. Recently, Pandey et al. [13] has estimated the molecular radii of pure liquids and binary liquid mixtures using various acoustic methods. The study suggests the superiority of Schaaffs 145 | P a g e method for theoretical estimation of molecular radius over the remaining methods. Ali et al. [14] have evaluated the molecular radii of binary liquid mixtures by employing acoustic and refractive index approaches. Dey et al. [15] has studied the isotopic effects on non-linearity parameter, molecular radius and intermolecular free length of various liquids and their deuterium-substituted compounds. These physico-chemical parameters have been used to study their effects on the intermolecular interactions. In the present study, the various acoustic methods for estimating the molecular radius have been extended to ternary liquid mixtures of pyridine/quinoline with phenol in benzene. The deviations in variation patterns of molecular radii with changing temperature and concentration for ternary liquid mixtures have been studied. Earlier, any worker has made no such attempt as far as our knowledge is concerned. 2. Theory: Various methods can be employed to evaluate the molecular radii of liquid mixtures using ultrasonic velocity, density and other related parameters. Schaaffs and Rao’s methods are based upon the Van der Waals equation of state. Eyring’s and Kittel’s methods are based upon the assumption that the observed velocity of sound results from the propagation of sound waves inside the molecule and in free space between them. These acoustical methods for the computation of molecular radii of liquid mixtures are summarized as under: 2.1 Schaaffs Relation: ( ) ( ) ( ) [ ] 3 2 2 3 1 3 1 . 1 16 3 − + − ⋅ = RT Mu Mu RT N M r γ γ π ρ (1) 2.2 Rao’s Relation: ( ) ( ) 3 3 1 2 1 . 2 1 16 3 | ¹ | \ | ⋅ = − + − RT Mu Mu RT N M r γ γ π ρ (2) 2.3 Eyring’s Relation: ( ) ( )( ) 3 3 2 2 1 3 . 1 1 1 ⋅ | ¹ | \ | ⋅ ⋅ = − − M RT u N M r γ ρ (3) 2.4 Kittel’s Relation: ( ) ( ) ( ) 3 3 2 3 1 1 2 1 ⋅ ⋅ − ⋅ ⋅ = M RT u N M r γ ρ (4) For a system comprising of spheres of mass M/N in a close packed face centered cubic structure (CP- FCC), molecular radius can also be obtained by the relation [7]. 146 | P a g e 2.5 CP-FCC Relation: ( ) 3 2 . 2 1 N M r ρ = (5) where u, ρ, M, N and γ have their usual meanings. 3. Results and Discussion: The molecular radii of both ternary liquid systems of pyridine/ quinoline with phenol in benzene have been computed at various concentrations and temperatures using relations (1-5). Figures 1 (a-f) show the variation of molecular radii for both the ternary liquid systems as a function of mole fraction of phenol. The various acoustic methods for estimating molecular radii have been analyzed graphically at different temperatures. Since the superiority of Schaaffs method has been established by the earlier workers [7, 13, 14], so it is considered as a reference for determining of molecular radii of both the liquid systems in the present study. Theoretical values of molecular radii have also been evaluated. It is observed that the molecular radii data obtained from various acoustic methods are not found to change significantly with concentration at specific temperature for both ternary liquid mixtures. But, a close perusal of the figure reveals that the molecular radii obtained from Schaaffs, Rao’s and CP-FCC method are slightly decreasing with increasing concentration at specific temperature while Kittel’s and Eyring’s relations exhibit a non-linear behaviour for pyridine-phenol system; for quinoline-phenol system molecular radii increasing with the increasing concentration from all acoustic methods except Eyring’s relation showing non-linear trend. Since pyridine has greater pK α value than quinoline and resonating structures of pyridine and quinoline suggests that in pyridine, the availability of the unshared pair of electrons for sharing with acids is more than quinoline. Due to this reason pyridine show strong interaction with phenol showing decreasing trend of molecular radii in pyridine-phenol system while weak interaction in quinoline with phenol provide increasing trend of molecular radii in quinoline-phenol system. It is also seen that at specific concentration and temperature, higher values of molecular radii are obtained in quinoline-phenol system as compared to the pyridine-phenol system. It may be due to bulkier structure of quinoline than pyridine. PYRIDINE QUINOLINE N N . . . . 147 | P a g e A significant inference has been drawn from the molecular radii data, obtained from Eyring’s relation, showing a non-linear behaviour with concentrations at specific temperature. In both liquid mixtures, molecular association process is strongly supported by Eyring’s method, which provide minimum molecular radius at the same concentrations where maximum molecular association was observed [1]. Moreover, for pyridine-phenol system the molecular radii obtained from Eyring and Kittel’s relation shows an opposite trend. Pandey et al. [13] and Ali et al. [14] show similar observations in their studies. It is observed from figure 1 (a-f) that on increasing the temperature values of molecular radii also increases for both the systems (except Kittel’s relation). This is because of thermal energy, which weakens the molecular forces, and hence an increase in molecular radii is expected with temperature [13]. It can also be seen that the values of molecular radii obtained from Rao’s method are in close agreement with Schaaffs method [13, 14]. Both methods are based on the assumptions that liquids behave like real gases. The molecular radii obtained from Kittel’s and Eyring’s methods have not been found to be in agreement with the Schaaffs method. Eyring’s and Kittel’s relation resulted in higher values of molecular radii than obtained by Schaaffs method. These observations show that the assumptions of free space made by these relations have to be modified in the present cases [13]. Therefore, in order to get comparable results with the Schaaffs method, a correction term is needed which will take care of three body effects in the evaluation of molecular radii in these cases. It is seen from the figures that the values of molecular radii obtained from CP-FCC method are always found to be higher than the values obtained from any other method. This may be due to the fact that the CP-FCC method is based upon the assumption that there is no free space between the molecules. The application of this equation for any liquid system should only be limited to compute the maximum possible values of molecular radii [13]. The values of molecular radii obtained theoretically are in close agreement with the values obtained from Schaaffs and Rao’s method. Ernst et al. [7] and Pandey et al. [13] have also emphasized the superiority of Schaaffs and Rao’s method for the estimation of molecular radii over other methods. 4. Conclusions: The variation pattern of molecular radii with the change in various physical parameters seems to be very convincing for both multicomponent liquid mixtures taken under investigation. Eyring’s method may be successfully employed to explain intermolecular interactions in the ternary liquid mixtures. Acknowledgements: 148 | P a g e The authors gratefully acknowledge the University Grants Commission for providing financial assistance as a Major Research Project (F. No. 33-34/2007 (SR)). References: [1] A. Awasthi, M. Rastogi and J. P. Shukla, Fluid Phase Equilib., 215 (2004) 119. [2] M. Rastogi, A. Awasthi and J. P. Shukla, Phys. Chem. Liqs., 42 (2004) 117. [3] A. Awasthi and J. P. Shukla, Ultrasonics, 41 (2003) 477. [4] W. Schaaffs, Z. Phys., 114 (1939) 110. [5] H. Reiss, H.L. Frisch and J.L. Lebowitz, J. Chem. Phys., 31 (1959) 369. [6] A. Bondi, J. Phys. Chem., 68 (3) (1964) 441. [7] E. Ernst and J. Glinski, Acustica, 13 (1981) 109. [8] W. Schaaffs, Acustica, 33 (1975) 272. [9] R.V. Gopala Rao and V. Venkataseshaiah, Z. Phys. Chem., 242 (1969) 193. [10] J.F. Kinkaid and H. Eyring, J. Chem. Phys., 5 (1937) 587. [11] J.F. Kinkaid and H. Eyring, J. Chem. Phys., 6 (1938) 620. [12] C. Kittel, J. Chem. Phys., 14 (1946) 614. [13] J. D. Pandey, R. Dey and B. D. Bhatt, J. Mol. Liq., 111 (2004) 67. [14] A. Ali, M. Tariq, R. Patel, F. Nabi and Shahjahan, 15th National Symposium on Ultrasonics (2006). [15] R.Dey, A.K. Singh, N.K. Soni, B.S. Bisht and J. D. Pandey, Pramana, 67 (2) (2006) 389. Fig.1 Molecular radii versus mole fraction of phenol: Pyridine-phenol in benzene (a, b, c) Quinoline-phenol in benzene (d, e, f) 149 | P a g e (a) (d) (b) (e) (c) (f) At 308.15 K 1.8 2.1 2.4 2.7 3.0 0.00 0.02 0.04 0.06 0.08 mole f rac. (x 2 ) m o l . r a d i u s , r ( 1 0 - 1 0 m ) At 318.15 K 1.8 2.1 2.4 2.7 3.0 0.00 0.02 0.04 0.06 0.08 mole f rac. (x 2 ) m o l . r a d i u s , r ( 1 0 - 1 0 m ) At 328.15 K 1.8 2.1 2.4 2.7 3.0 0.00 0.02 0.04 0.06 0.08 mole f rac. (x 2 ) m o l . r a d i u s , r ( 1 0 - 1 0 m ) At 308.15 K 1.8 2.1 2.4 2.7 3.0 0.00 0.02 0.04 0.06 0.08 mole f rac. (x 2 ) m o l . r a d i u s , r ( 1 0 - 1 0 m ) At 318.15 K 1.8 2.1 2.4 2.7 3.0 0.00 0.02 0.04 0.06 0.08 mole f rac. (x 2 ) m o l . r a d i u s , r ( 1 0 - 1 0 m ) At 328.15 K 1.8 2.1 2.4 2.7 3.0 0.00 0.02 0.04 0.06 0.08 mole f rac. (x 2 ) m o l . r a d i u s , r ( 1 0 - 1 0 m ) 150 | P a g e Ultrasonic and theoretical study of binary mixture of DEHPA (Di-(2- ethyl-hexyl) phosphoric acid) with n-hexane at different temperatures. ***** Sujata Mishra, Rita Paikaray Department of Physics Ravenshaw University, Cuttack E-mail:
[email protected] r_
[email protected] A B S T R A C T Ultrasonic speed and density of binary liquid mixture of di-(2-ethyl hexyl) phosphoric acid ( DEHPA) with n-hexane has been determined at 303K, 308K, 313K, 318K over entire composition range. The acoustical parameters such as adiabatic compressibility ( Ks), Intermolecular free length ( Lf), acoustic impedance ( Z), Relative association (RA), Molar Volume (V), Molecular interaction parameter ( χ) and also excess parameters such as excess velocity ( C E ), excess free length ( L E f), excess compressibility ( K E s), excess molar volume ( V E ) and excess acoustic impedance (Z E ) are computed for the binary mixture at different temperatures. Variation of acoustic parameters with temperatures have been discussed in terms of nature and strength of intermolecular interaction existing in the binary system. The ultrasonic speeds calculated according to Nomoto’s relation, impedance dependence relation, Rao’s specific sound velocity relation and free length theory ( FLT) are compared with those obtained experimentally. The validity of these theoretical relations have been discussed for the present liquid system. Key words:- Binary mixture, Free length of interaction, acoustic parameters, intermolecular interaction. 1. INTRODUCTION Ultrasonic study of liquids, liquid mixtures and solutions is a useful technique for understanding its physico-chemical behaviour and molecular interaction which have demanding applications in many chemical and industrial processes. In order to detect weak and strong molecular interactions in binary liquid mixtures consisting of polar as well as non-polar components, ultrasonic velocity measurement have been employed extensively. Acoustic and thermodynamic parameter have been used to understand different kinds of association, the molecular packing, molecular motion, and various type of intermolecular interactions and their strengths [1,2]. Theoretical evaluation of ultrasonic velocity in binary liquid mixtures and its comparison with the experimental values reflects the molecular interactions in liquid mixtures. Ultrasonic velocities calculated using Nomoto’s relation (NR) [3], impedance dependence relation ( IDR) [4], Rao’s specific sound velocity Relation (R) [5], free length theory [6] and are compared with experimental values. 2. THEORETICAL CONSIDERATIONS The experimentally measured ultrasonic speed (C) and density (ߩ) are used to calculate the derived parameters like isentropic compressibility (ܭ ௦ ), Intermolecular free length ( ܮ ), molar volume (V) acoustic 151 | P a g e impedance (Z), Relative association(ܴ ), Interaction parameter (χ ) and excess parameters by using the following expressions. ܭ ௦ = 1 ………………......... ( 1) ߩC 2 ܮ = k (ܭ ௦ ) 1/2 ………………… (2) V= (x1 M1 + x2 M2 ) / ߩmix ………..…(3) RA= (ρ /ρ o) (Co/C) 1/3 ……………... (4) Z = ߩܿ …………………………… (5) χ = ( C 2 exp/C 2 ideal)-1………………… .(6) Where C ideal = x1C1 + x2C2 is ideal mixing velocity. A E = Aexp – ( x1A1 + x2 A2)……..(7) Where x1 and x2 are mole fractions of DEHPA and n- hexane, ߩ0 = density of DEHPA Co = Ultrasonic velocity in pure DEHPA at particular temperature, ߩmix = density of mixture. M1 and M2 are molecular weight of DEHPA and n-hexane. k (Jacobson’s constant) [ value, 93.875 + 0.375T ) x 10 -8 , T is absolute temperature, A E stands for excess property of parameters ( C E , K E s, L E f, V E , Z E ). The theoretical values of sound speeds are evaluated using the following relationship . Sound Speed by Jacobson’s free length theory is calculated using the following formula [ 6]. C FLT = k________ ܮ (mix) , ρ EXP 1/2 ….(8) The empirical formula for sound speed in binary liquid mixtures given by Nomoto [3] can be written as C NOM = x1R1 +x2R2 3 …..(9) _________ x1V1 + x2 V2 Where X, R = V C 1/3 and V represents mole fraction, molar sound speed and molar volume respectively. The sound speed in mixture is given by Impedance Dependence relation [4] C IDR = Σ xi Zi ………… (10) xiρi Where xi Zi and ρi are the mole fraction, acoustic impedance and density of the ith component respectively. Rao’s specific sound velocity relation is given by C R = Σ ( xi ri ρ) 3 ………(11) Where ri = Ci 1/3 /ρi is the Rao’s specific sound velocity of the i th component of the mixture. 152 | P a g e 3. EXPERIMENTAL The ultrasonic speeds in pure liquids and liquid mixtures have been measured using an ultrasonic interferometer (model Mx-83) supplied by Mittal Enterprises , New Delhi, working at 3 MHz frequency with an accuracy of + 0.1msec -1 . Binary mixtures are prepared by mixing appropriate volumes of the liquid components in the standard flasks with airtight caps and the mass measurements are performed on high precision digital balance with an accuracy of +1mg. Density was determined by using a single capacity Pyknometer of bulb capacity 25 cm 3 at different temperatures. The temperature of the sample was maintained stable by circulating thermo stated water around the interferometer cell that contains the liquid, with a circulating pump to an accuracy of + 0.1 0 C . 4.RESULT AND DISCUSSIONS Measured values of density ( ρ) and ultrasonic speed (C) were used to calculate various thermodynamic parameters and their excess values using equation 1-7 at different temperatures. Representative graphs of ultrasonic velocity (C), excess velocity (C E ), excess isentropic compressibility (K E S), excess free length (L E f), excess molar volume (V E ), excess acoustic impedance (Z E ) as a function of concentration and temperature represented in fig.1-6. Table-1 compares experimental and theoretical values of sound speed and deviations of these theories from experimental sound speeds at temperature 303k. molefraction- velocity V e l o c i t y molefraction of DEHPA Fig-1 Fig-2 DEHPA is an acidic extractant which is polar and its molecules exist as dimmers especially in pure form or in organic diluents due to intermolecular hydrogen bonding.[8] The effect of adding non-polar second component is primarily to disrupt the associated structure of DEHPA and strength of interaction decreases. But breaking up of associated structure of DEHPA releases several dipoles, which induce dipole moments in n-hexane molecules and there exist a dipole- induced dipole interaction between the component molecules, which is supported by slow increase of relative association (RA) values and increase of ultrasonic velocity (fig-1). Further ultrasonic velocity decreases with increase in temperature due to 900 1000 1100 1200 1300 1400 1500 0 0.5 1 1.5 303K 308K 313K 318K -10 0 10 20 30 0 0.5 1 e x c e s s v e l o c i t y molefraction of DEHPA molefraction ~excess velocity 303K 308K 313K 318K 153 | P a g e thermal agitation of molecules. Similar observation made by Syal etal [9] and Subramaniyam Naidu and Ravindra Prasad [10]. The free length ( Lf) and compressibility ( Ks) decreases with increase in concentration of DEHPA and increases with temperature, which shows that dipole-induced dipole interaction becomes stronger and the system is less compressible . Variation of other parameters like acoustic impedance ( Z) and interaction parameter (χ) shows the presence of molecular interaction between component molecules of the system. Fig-3 Fig-4 Excess Thermodynamic parameters give a better insight, into the study of molecular interactions in a liquid mixture than derived parameters. The variation of excess velocity (C E ) [Fig.2] shows negative deviation is low concentration region and positive deviation in high concentration region of DEHPA. The negative deviation is due to breaking up of self association of DEHPA in high concentration of non-polar n- hexane. As the concentration of DEHPA increases, interstitial accommodation of n-hexane molecules increases which results positive excess velocity which increases with increase in temperature. The variation of excess isentropic compressibility ( K E S) with mole fraction of DEHPA at all temperatures are shown in [Fig-3]. Deviation in isentropic compressibility is negative with maxima at about ~ 0.37 mole fraction of DEHPA from 303 to 318K. Mixing of n-hexane with DEHPA will induce breaking up the associated structures which leads to expansion in volume and hence increase in K E S and dipole- induced dipole interaction is responsible for contraction in volume and hence a decrease in K E S. The variation of excess free length ( L E f) [Fig-4] is similar to that of K E S, with negative deviation over entire range of composition at all four temperatures . The less negative magnitude of L E f itself suggests that the interaction between component molecules is not so strong i.e a weak dipole- induced dipole interaction present in the system which dominates over the breaking up of associated structure of DEHPA. Considering the effect of temperature, it is clear that both K E S and L E f become more and more negative with increase in temperature of the system. Increase in temperature promotes the breaking of associates present in pure liquids, releasing more and more dipoles which interact with each other. Hence, strength of interaction increases with rise of temperature [8,9] -4 -2 0 0 0.5 1 e x c e s s i s e n t r o p i c c o m p r e s s i b i l i t y molefraction of DEHPA molefraction~excess compressibility 303K 308K 313K 318K -1 -0.5 0 0 0.5 1 e x c e s s f r e e l e n g t h molefraction of DEHPA molefraction ~excess freelength 303K 308K 313K 318K 154 | P a g e Fig-5 Fig-6 Fig-5 shows variation of excess molar volume ( V E ) with mole fraction of DEHPA from 303 to 318 K. The excess molar volumes are positive for the whole range of composition [7] and at all temperatures with a peak at about ~ .42 mole fraction. The positive values increase with increase in temperature. The curves at all temperatures show that the self association of DEHPA molecules first breaks which results increase of V E and then the interaction between unlike components take place due to increase in mole fraction of DEHPA, which results decrease in V E . It also shows presence of unfavourable interactions between different groups such as –CH3 , -CH2-, -OH of monomeric DEHPA Similar type of result shown by other Researchers [2,7]. The variation of excess acoustic impedance (Z E ) is shown in fig-6 at all four temperatures. The negative Z E values indicate dissociation of self association of DEHPA and more than one type of interaction may be present in the system. The less magnitude of negative (Z E ) values suggest that dipole - induced dipole interaction dominates over dispersion forces which is in close agreement with the variation of L E f and K E S with increasing concentration of DEHPA. Table-1: Application of various theoretical approaches and percentage of deviation for DEHPA +n-hexane system at 303K. ∆C/C % Mole fraction of DEHPA (X1) C EXP ms -1 C NOM ms -1 C IDR ms -1 C R ms -1 C FLT ms -1 C NOM C IDR C R C FLT 0.000 975.0 975.0 975.0 975.0 975.0 0.000 0.000 0.000 0.000 0.1574 1058.0 1109.3 1081.8 1097.8 1058.6 4.840 2.249 3.761 0.056 0.1717 1065.6 1119.3 1090.7 1108.0 1065.6 5.039 2.235 3.978 0.000 0.2036 1074.0 1141.4 1109.9 1135.9 1074.0 6.275 3.342 5.763 0.000 0.3179 1131.8 1211.0 1174.4 1215.7 1142.6 6.997 3.763 7.412 0.954 0.4026 1170.5 1254.4 1217.8 1285.4 1170.9 7.160 4.041 9.816 0.003 0.5785 1253.3 1328.8 1298.5 1359.8 1253.7 6.024 3.606 8.497 0.003 0.7349 1328.0 1381.3 1360.8 1415.4 1328.4 4.013 2.469 6.581 0.003 0.8312 1380.2 1409.0 1395.5 1436.7 1380.5 2.086 1.072 4.093 0.002 1.0000 1468.5 1468.5 1468.5 1468.5 1468.5 0.000 0.000 0.000 0.000 The theoretical values of ultrasonic speeds were calculated using theoretical and empirical relations [8-11]. Table-1 shows that minimum deviations are observed in case of free length theory ( FLT), followed by impedance dependance relation ( IDR) and Nomoto Relation (NR). Rao’s specific sound velocity relation 0 10 20 30 0 0.5 1 e x c e s s m o l a r v o l u m e molefraction of DEHPA molefraction~excess molarvolume 303 K 308 K -0.05 -0.04 -0.03 -0.02 -0.01 0 0 0.5 1 e x c e s s a c o u s t i c i m p e d a n c e molefraction of DEHPA molefraction~excess acoustic impedance 303K 308K 313K 318K 155 | P a g e shows maximum deviation. The order of applicability of the theories for the present system is as follows:- C FLT > C IDR > C NOM > C R . CONCLUSION: The variation of derived parameters and ultrasonic velocity with concentration of DEHPA and temperatures indicate the presence of molecular interaction between component molecules excess values reveal that the interaction mainly of dipole-induced dipole interaction which is weak. The temperature variation indicates that the strength of intermolecular interaction increases with rise of temperature. Among four theoretical models, free length theory ( FLT) shows close agreement with experimental ultrasonic velocity values than IDR, NR and RSSVR, n-hexane acts as a structure breaker for DEHPA. References:- (1) Ali A, Yasmin A & Nain AK, Indian J Pure Appl Phys 40 ( 2002)315 (2) Kannappan V & Jaya Santhi R. Indian J Pure Appl Phys 43 (2005) 750 (3) Nomoto O, J Phys Soc Japan, 13 ( 1958) 1528 (4) Shipra Baluja & parsania PH, Asian J Chem 7 ( 1995) 417 (5) D Sravana Kumar & D Krishna Rao, India J Pure Appl Physics Vol.45 ; PP(210-220)2007 (6) Jacobson B, J Chem Phys, 20 ( 1952) 957 (7) V. Ulagendran, R. Kumar, S. Jayakumar & V. Kannappan proceeding of National Sympossium on Accoustics, 2007 PP. 419-423. (8) S. Mishra & R. Paikaray, J Accoustic Soc India,Vol-37, No-1, PP- (20 -) 2010 (9) Syal VK, Chauhan S & Uma Kumari, Indian J Pure Apply Phys, 43 ( 2005) 844 (10) Subramaniyan Naidu P & Ravindra Prasad K J Pure Appl. Ultrasonics, 27 ( 2005) 15. 156 | P a g e ACOUSTICAL STUDIES OF MOLECULAR INTERACTIONS IN BINARY LIQUID SYSTEM OF CINNAMALDEHYDE AND N-N-DIMETHYLANILINE AT 303 K Padmanabhan G 1 , Kumar R 2 , Jayakumar S 3* & Kannappan V 4 1. Department of Physics, Sri Sankara Arts & Science College, Kanchipuram. 2. Department of Physics, The New College, Chennai – 600 014. 3. Department of Physics RKM Vivekananda College,Chennai-600 004. 4. Department of Chemistry, Loyola College, Chennai – 600 035. E-mail: *
[email protected] Abstract Ultrasonic velocity (u), density (ρ) and Viscosity (η) were measured for binary liquid system of cinnamaldehyde (CA) and aromatic tertiary amine N, N – dimethylaniline (DMA) for the entire composition range, at 303K. From these values, adiabatic compressibility(κ), molecular free length (Lf), internal pressure (πi), free volume (Vf), Lennard – Jones potential (LJP), cohesive energy interaction parameter (χi) and excess thermodynamic parameters such as excess velocity (u E ), excess adiabatic compressibility (κ E ), excess internal pressure (πi E ), excess molar volume (Vm E ), excess impedance (Z E ) were computed using standard relations. The results are interpreted in terms of molecular interactions between the component molecules. It is observed that strong molecular interactions of dipole – dipole and complex formation types exist that depend on the concentration and also the structural aspects of the components in the mixture. 1. INTRODUCTION The acoustical investigation of liquids mixtures reveals the significance of molecular interactions that finds applications in several industrial, technological and biological fields [1 – 3]. The study of molecular interactions in terms of acoustical and excess thermodynamic parameters identifies the specific type of molecular interaction and the structural features of molecules in the solution. These structural dependent molecular interactions are also concentration dependent and this is well reflected by the behavior of the excess parameters [4, 5]. Cinnamaldehyde (CA) is an industrially important compound. It is 157 | P a g e used as flavouring agent in chewing – gum, ice – cream candy and beverages and also as fungicide, insecticide and corrosion inhibitor in steel industries. The interaction between polar groups such as carbonyl group of aldehyde and amino group is significant in practical applications. Carbonyl group is part of several biologically important molecules such as protein, lipids and hormones. It has electron deficient carbon, which can function as electrophile. Amines behave as Lewis bases since they contain nitrogen as the basic centre with a lone pair of electrons. Thus, the formation of donor – acceptor complexes can be expected between amino group of N, N – dimethylaniline (DMA) and carbonyl group of CA. 2. EXPERIMENTAL METHODS AnalaR grade samples are used in the present work. Chemicals are weighed using electronic single pan balance Shimadzu make and the materials are mixed stoichiometrically. The whole range of compositions was studied between components of the binary system. The ultrasonic velocity (u) was measured using Mittal ultrasonic interferometer of fixed frequency of 2 MHz with an accuracy of ± 0.2 m/s, density (ρ) measurements were made using a 10ml specific gravity bottle and viscosity (η) measurements by rate of flow of solutions through Ostwald viscometer and digital stop watch with an accuracy of ± 0.01s. The temperature of solutions was maintained constant by thermostat with an accuracy of ± 0.1K. 3. RESULTS AND DISCUSSION 3.1 Acoustical Parameters: The measured values of ultrasonic velocity (u), density (ρ), viscosity (η) and the computed values of acoustical parameters are tabulated in Table 1. The variation of ultrasonic velocity and adiabatic compressibility with mole fraction of DMA is shown in Figures 1 & 2. The behavior of ultrasonic velocity is non – linear with the mole fraction of DMA as evident from Figure 1. It was reported that the non – linear variation of ‘u’ is an indication of solute – solvent type of interaction which may be of dipole – dipole nature through complex formation between components in the mixture [6, 7]. The values of adiabatic compressibility and free length show similar variation that increase with 158 | P a g e increasing concentration of DMA. The increasing trend in both these parameters may be due to the increase in the void created by the aromatic amine. Though the interaction between the components is stronger, the void makes the system more compressible. Since the effective molecular area of the components decrease with concentration the viscous nature decreases and in turn that decreases the internal pressure of the system [8, 9]. The observed values of cohesive energy are also in the reported range of dipole – dipole and hydrogen bonded types of interactions [10]. (Figure 5) 3.2 Excess Thermodynamic Parameters The computed values of excess thermodynamic parameters are summarized in Table 2. The variation of excess velocity and excess compressibility versus mole fraction of DMA are shown in Figures 3 & 4. The larger negative deviations in u E and Z E from linear dependence on the mole fraction of DMA suggest the presence of complex formation between component molecules [11]. The observed viscosity deviations η E are negative over the entire concentration range investigated. Negative η E from the rectilinear dependence on mole fraction may occur for the systems having components of different molecular size [12]. The excess molar volume Vm E is found to change sign from positive to negative. This again supports our earlier view on the molecular interactions between component molecules and may also due to the difference in the molecular sizes. As CA are much smaller than those of DMA, which might allow the fitting of CA molecules into the voids created by DMA molecules [13, 14]. A perusal of table 2 reveals that the behavior of excess compressibility with concentration is also well reflected with the behavior of excess free length. Both these parameters show almost positive deviations which may be due to the expansion in volume of the system by i) breaking of associated structure of dipolar molecules and ii) increasing concentration of aromatic component that creates void in the liquid mixture. The weakening of unlike molecular interaction than that of strong like molecular association may also the reason for the positive values of these two parameters [11]. CONCLUSIONS The behavior of acoustic parameters shows the existence of strong interaction among the component molecules of dipole-dipole nature through complex formation. The existing strong interaction is weakened by the addition of DMA with CA this is due to the bulky size of the aromatic amine that makes the system more compressible. It is also 159 | P a g e found that there is a possibility of interstitial penetration of the CA into DMA. These conclusion can be drawn by the suggested variation of excess thermodynamic parameters. ACKNOWLEDGEMENT The authors thank the Management of R. K. M. Vivekananda College, Mylapore, Chennai and the Management of Sri Sankara Arts and Science College, Enathoor, Kanchipuram, for their keen interest and support shown towards this work. REFERENCES 1. R. Kumar, S. Jayakumar and V. Kannappan, Ind J Pure & Appl. Phys., 46 (2008) 169. 2. Jayakumar .S Karunanidhi .N and Kannappan V, Ind. J Pure & Appl. Phys., 34 (1996) 761. 3. G. V. Rama Rao, A. V. Sarma and C. Rambabu, Ind. J Pure Appl. Phys., 42 (2004) 820. 4. R. Kumar, P.E. Akilandeswari, M.G. Mohamed Kamil, V. Kannappan and S. Jayakumar, J Mol. Liq., 154 (2010) 69-75. 5. Sivaparasad V, Rajagopal E and Manoharamurthy N, J Mol. Liq., 124 (2006) 1. 6. Subramanyam Naidu P and Ravindra Prasad K, Ind. J Chem., 40 (2002) 264. 7. Isht Vibhu, Avneesh K Singh, Manisha Gupta and Shukla J P, J Mol. Liq., 115 (2004) 1. 8. Nain A K, Chand D, Chandra P and Pandey J D, Phys. Chem. Liq., 47 (2009) 195. 9. Arul G and Palaniappan L, Ind. J Pure Appl. Phys. 43 (2005) 755. 10. Thiyagarajan R, Jaafar M. S and Palaniappan L, J Phys. Sci., 18(2) (2007) 81. 11. Making sense of boiling points and melting points, S. Prahalada Rao et al, Resonance, June (2007) 48 – 57. 12. Ali A,Yasmin A and Nain.A.K, Ind. J Pure Appl. Phys, 40 (2002) 315. 13. Ali A, Hyder S and Nain A. K, Ind. J Phys., 74B (2000) 63. 14. A. Ali and A. K. Nain, Phys. Chem. Liq., 37 (1999) 161.Ali A, Tiwari K, Nain A. K and Chakravorty V, Ind. J Phys.74B (5) (2000) 351. 160 | P a g e Table 1 – Ultrasonic velocity, density, viscosity and other acoustical parameters for cinnamaldehyde + N, N – dimethylaniline system at 303.15K x2 u m/s ρ kg / m 3 η 10 -3 Nsm -1 κ κκ κ 10 -10 N -1 m 2 Lf A 0 Z 10 6 Rayl α αα α π ππ πi 10 5 atm Vf 10 -8 m 3 CE KJ/mol 0 1537.6 1058.9 3.43 3.994 0.3997 1.628 4.924 5.145 67.695 0.0999 1528.8 1043.5 3.24 4.100 0.4050 1.595 -0.0112 4.798 5.155 65.726 0.1998 1546 1032.5 2.96 4.052 0.4026 1.596 0.0115 4.557 6.035 62.124 0.2996 1528.8 1026.6 2.71 4.168 0.4083 1.569 -0.0106 4.388 6.733 59.425 0.3995 1509 1018.3 2.43 4.313 0.4153 1.537 -0.0359 4.182 7.772 56.308 0.4997 1479.4 1019.3 2.33 4.483 0.4234 1.508 -0.0731 4.132 7.941 55.140 0.5996 1512.6 1008.3 2.03 4.335 0.4164 1.525 -0.0307 3.814 10.13 50.634 0.6996 1555.6 1000.2 1.87 4.132 0.4065 1.556 0.0254 3.613 11.90 47.676 0.7995 1510.4 991 1.69 4.423 0.4206 1.497 -0.0331 3.485 13.28 45.716 0.9 1491.2 979.8 1.51 4.590 0.4285 1.461 -0.0572 3.318 15.43 43.305 1 1535.6 969.5 1.50 4.374 0.4183 1.489 3.254 15.65 42.243 Table 2 – The values of excess thermodynamic parameters for cinnamaldehyde + N, N – dimethylaniline system at 303.15K x2 u E m/s η E 10 -4 Nsm -1 κ κκ κ E 10 -11 N -1 m 2 Lf E 10 -13 m Vm E 10 -10 m-3 Z E 10 4 Rayl π ππ π E 10 4 atm 0.0999 -8.6 0.003 0.678 3.402 7.723 -1.894 0.133 0.1998 8.8 -0.904 -0.181 -0.831 10.30 -0.407 -0.801 0.2996 -8.2 -1.433 0.595 3.014 6.680 -1.693 -0.776 0.3995 -27.8 -2.300 1.665 8.198 5.953 -3.586 -1.197 0.4997 -57.2 -1.401 2.984 14.44 -6.254 -5.055 0.346 0.5996 -23.8 -2.468 1.126 5.544 -3.761 -1.943 -1.326 0.6996 19.4 -2.093 -1.285 -6.187 -4.838 2.527 -1.629 0.7995 -25.6 -1.970 1.252 6.063 -4.535 -1.991 -1.176 0.9 -44.6 -1.795 2.536 12.04 -1.753 -4.163 -1.141 161 | P a g e FIGURE 1. FIGURE 2. 0.0 0.2 0.4 0.6 0.8 1.0 1480 1500 1520 1540 1560 B U X2 0.0 0.2 0.4 0.6 0.8 1.0 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 E K X2 162 | P a g e FIGURE 3. FIGURE 4. . 0.0 0.2 0.4 0.6 0.8 1.0 -60 -40 -20 0 20 B E X C E S S U X2 0.0 0.2 0.4 0.6 0.8 1.0 -2 -1 0 1 2 3 D E X C E S S K X2 163 | P a g e FIGURE 5. 0.0 0.2 0.4 0.6 0.8 1.0 40 45 50 55 60 65 70 K C E ( k J / M O L ) X2 164 | P a g e CHARACTERIZATION OF NANOFLUID OF PLATINUM Virendra Kumar, Kailash and Jitendra Kumar 1 Department of Physics, BN PG College, Rath, Hamirpur, U.P., 210 431, Bharat 1. Department of Physics, Govt. Girls P. G. College, Banda, U.P., 210 001, Bharat Email:
[email protected],
[email protected] Abstract: Nanofluids are attracting a great deal of interest with their enormous potential to provide enhanced performance properties, particularly with respect to heat transfer. Nanofluids are stable suspensions of nanoparticles in a liquid. In order to avoid coagulation of the particles, the particles must be coated with a second distance holder phase which in most cases, consist of surfactants that are stable in the liquid. An important application of nanofluid containing nanoparticles is as a coolant, since the addition of only a few volume percent of nanoparticles to a liquid coolant and significantly improves its thermal conductivity. Platinum nanoparticles with narrow size distribution dispersed onto smooth, non-catalytic surfaces are of interest as model systems for the investigation of particle shape and size dependence of the catalytic activity of platinum towards reactions of interest in fuel cell systems. Ultrasonic velocity is the speed in which sound propagates in a certain material. It depends on material density and elasticity. It is related in a simple way to the various coefficients of compressibility, isentropic, isenthalpic and isothermal, hence the importance of its measurement and modeling in temperature and pressure ranges are widely used. Measurement of ultrasonic velocity gives the valuable information about the physicochemical behaviour of the liquid and liquid mixtures. In this work we have measured the ultrasonic velocity at different temperature and frequencies of nanofluid of platinum using Interferometer technique. Key Words: Nanofluids, Ultrasonic velocity, Nanotechnology and Interferometer Technique. 1. Introduction Platinum is used in jewelry, laboratory, equipment, electrical contacts and electrodes; platinum resistance. Platinum occurs naturally in the alluvial sands of various rivers, though there is little evidence of its use by ancient people. The most important application of platinum is in automobiles as a catalytic converter, which allows the complete combustion of low concentrations of unburned hydrocarbon from the exhaust into carbon dioxide and water vapor. Platinum is also used in the petroleum industry as a catalyst. In the laboratory, platinum wire is used for electrodes; platinum pans are used in thermo gravimetric analysis. Nanotechnology is a most important and growing area in science. Nano-science, the science under pinning nanotechnology, is a multidisciplinary subject covering atomic, molecular and solid state physics, as well as much of chemistry. Nanostructures are known to exhibit novel and improved material properties. Nanotechnology is design, fabrication and application of nanostructures or nanomaterials, and fundamental understanding of the relationships between physical properties and material dimensions. 165 | P a g e Application of nanostructures and nano-materials are based on the peculiar physical properties of nanosized materials, the huge surface are the small size that offers extra possibilities for manipulation and room for accommodating multiple functionalities. In future, amazing nanotech-based products are expected, including extraordinarily tiny computers that are very powerful, building materials that withstand earthquakes, advanced systems for drug delivery and custom-tailored pharmaceuticals as well as the elimination of invasive surgery, because repairs can be made from within the body. Future developments and implemention of nanotechnology could certainly change the nature of almost every human made object and activity. Its ultimate societal impact is expected to be as dramatic as first industrial revolution and greater than the combined influences that aerospace, nuclear energy, transistors, computers and polymers have in this century. Nanotechnology development is the need to understand the techniques for atomic and molecular based study of matter in nanoscale [1-3]. Nanofluids are dilute liquid suspensions of nanoparticles with at least one of their principal dimensions smaller than 100nm. There is a growth in the use of colloids which are nanofluids in the biomedical industry for sensing and imaging purposes. This is directly related to the ability to design novel materials at the nanoscale level alongside recent innovations in analytical and imaging technologies for measuring and manipulating nanomaterials. This has led to the fast development of commercial applications which use a wide variety of manufactured nanoparticles. Nanofluids have higher thermal conductivity and single-phase heat transfer coefficients than their base fluids [4]. Nanofluids could be applied to almost any disease treatment technique by reengineering the nanoparticles properties. Several significant gaps in knowledge are evident at this time, including, demonstration of the nanofluid thermal- hydraulic performance at prototypical reactor conditions and the compatibility of the nanofluid chemistry with the reactor materials [5]. Ultrasonic velocity has become a valuable tool for the study of various physical and chemical properties of the matter. Ultrasonic velocity measurement offers a rapid and destructive tool for the characteristics of materials. Various elastic parameters and estimation of grain size has been going on far the past several years. Elastic constants of isotropic solid can be determined ultrasonically when both longitudinal and transverse wave velocities are known [6, 7]. The aim of present work was to study the characterization of copper nanofluid using ultrasonic techniques. 2. Experimental Details Interferometry is the technique of diagnosing the properties of two or more waves by studying the pattern of interference created by their superposition. It is an important investigative technique in the fields 166 | P a g e of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, quantum mechanics, plasma physics and remote sensing. An ultrasonic interferometric sensor has been introduced for the measurement of suitable changes in the physical properties of fluids such as density, viscosity and bulk modulus [8]. The ultrasonic interferometer is simple in construction and operation and gives accurate and reproducible results. From these results, one can readily determine the velocity of sound in a liquid with high accuracy. Formerly, the absorption of sound in the liquid and the coefficient of reflection at the reflector surface have been obtained through a complicated analysis of the electrical and equivalent electrical circuits of the quartz crystal and the associated fluid column. In our experimental work we use multifrequency interferometer. This multifrequency generator can generate ultrasonic waves of several frequencies form 1 MHz to 12 MHz in the medium. The multifrequency ultrasonic interferometer consists of the two parts- the high frequency generator and the measuring cell. The high frequency generator is designed to excite the quartz plate fixed at the bottom of the measuring cell at its resonant frequency to generate ultrasonic waves in the experimental liquid in the measuring cell. A micro ammeter to observe the changes in current and two controls for the purpose of sensitivity regulation and initial adjustment of micro ammeter is provided on the high frequency generator. A fine micrometer screw has been provided at the top, which can lower or raise the reflector plate in the cell through a known distance. It has a quartz plate fixed at its bottom the ultrasonic interferometer may be used for determination of ultrasonic velocity. The measuring cell is connected to the output terminal of the high frequency generator through a shielded cable the cell is filled with the experimental liquid before switching on the generator the ultrasonic waves moves normal from the crystal till they are reflected back from the movable plate and the standing waves are formed in the liquid in between the reflector plate and the quartz crystal. The micrometer is slowly moved till the anode current meter on high frequency generator shows a maximum. A number of maximum readings of anode current are passed on and their n is counted the total distance x thus moved by the micrometer gives the value of wavelength λ with the help of the following relation; x = n× λ /2 (1) Once the wavelength is known the ultrasonic velocity V of copper nanofluid can be calculated with the help of following relation; V= λ ×f (2) 167 | P a g e 3. Evaluation Ultrasonic velocity measurements have been successfully employed to detect and assess weak and strong molecular interactions present in nanofluids. These studies can also be used to determine the extent of complexation and calculate the stability constants of such complexes [9]. Nanofluids are suspensions of nanoparticles in fluids that show significant enhancement of their properties at modest nanoparticle concentrations. Nanofluids are considered to offer important advantages over conventional heat transfer fluids. Nanofluids contain suspended metallic nanoparticles, which increases the thermal conductivity of the base fluid by a substantial amount [10, 11]. Measurement of ultrasonic velocity gives the valuable information about the physicochemical behaviour of the liquid and liquid mixtures. Several relations, semi-empirical formula and theories are available for the theoretical computation of ultrasonic velocity in liquid and liquid mixtures. Temperature variation of ultrasonic velocity for nanofluid of platinum is given in Table 1 and frequency variation of ultrasonic velocity for this fluid is shown in Table 2. 4. Results and Discussions Ultrasonic velocity measurements are helpful to study the ion-solvent interactions in aqueous and non-aqueous solutions in recent years. Ultrasound has been extensively used to determine the ion solvent interactions in aqueous containing electrolytes. The measured data of ultrasonic velocity for nanofluid of platinum at different temperature and frequencies are given in Table 1 - 2. Graphical representation of data is given in Figures 1 - 2. From Figure 1(i), at 1Frquency(F) in MHz; it is observed that at increasing temperature from 311K to 317K, the ultrasonic wave velocity is increase and when temperature again increase up to 320K, there is a slightly decreases, when temperature is reached slightly at 323K, velocity is increase but at 326K velocity again decrease. Temperature variation of ultrasonic velocity at 2 MHz frequency is shown in Figure 1(ii), one can say from this figure velocity is increase from temperature 312K to 315K but when we increase temperature at 318K, velocity decreases. Again increasing temperature till 327K, ultrasonic velocity is increase. This shows proportionality relation between temperature and velocity. It is clear from Figure 1(iii), on increasing temperature from 312K up to 318K, the velocity of ultrasonic wave is increase and up to 321K the velocity is slightly decrease and at 324K the velocity of ultrasonic wave is slightly increase and again at 327K the ultrasonic wave velocity is slightly decrease. This shows linear and inverse relation separately between temperature and velocity. Ultrasonic wave velocity for nanofluid of platinum is measured at different frequencies ranging form 1 - 5 MHz, at room temperature, the result is given in table 2. Frequency variation of ultrasonic velocity for this 168 | P a g e fluid is shown in Figure 2. It is observed that with increase in frequency from 1 MHz to 3 MHz, velocity is increase; velocity is decreases on increasing frequency to 5MHz. 5. Acknowledgement The authors are thankful to the University Grants Commission, New Delhi for financial support. 6. References [1] G. Cao, ‘Nanostructures and nanomaterials’, Imperial College Press, London, 391-412, 2007. [2] G.A. Mansoori, ‘Principles of nanotechnology’, World Scientific Publishing Co., Singapore, 1-28, 2006. [3] C.W. Shong, S.C. Haur and A.T. Wee, ‘Science at the nanoscale’, Pan Stanford Publishing, Singapore, 1- 17, 2010 [4] J. Buongiorno, ‘Convective Transport in Nanofluids’, J. Heat Transfer, 128, 240-250, 2006. [5] K.V. Wong and O.D. Leon, ‘Applications of Nanofluids: Current and Future’, Advances in Mechanical Engineering, 2010, 519659-519669, 2010. [6] V. Kannappan and S.C. Vinayagam, ‘Ultrasonic investigation of ion-solvent interactions in aqueous and non- aqueous solutions of transition and inner transition metal ions’, Ind. J. of pure and Appl. Phys., 45, 143-150, 2007. [7] A. Kumar and Y. Kumar, ‘Ultrasonic velocity measurement in cylindrical rod material’ J. Pure Appl. Ultras., 20, 15-19, 1998. [8] K. Balasubramaniama and S. Sethuraman, ‘Ultrasonic Interferometer Technique’ Centre for NDE and Department of Mechanical Engineering, IIT Madras, 2006. [9] V. Kannappan and N.I. Gandhi, ‘Ultrasonic studies on charge transfer complexes of certain aldehydes with benzylamine and cyclohexylamine as doners in n-hexane ay 303K’, Ind. J. of pure and Appl. Phys., 45, 221- 225, 2007. [10] S. Kakaç and A. Pramuanjaroenkij, ‘Review of convective heat transfer enhancement with Nanofluids’, Inter. J. of Heat and Mass Tran., 52, 3187-3196, 2009. [11] D.P. Kulkarni, D.K. Das and R.S. Vajjha, ‘Application of nanofluids in heating buildings and reducing pollution’, Applied Energy, 86, 2566-2573, 2009. Table 1 - Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Temperature (K) Frequency (F) 311 312 314 315 317 318 320 321 323 324 326 327 1 MHz 1343 1330 1363 1380 1398 1400 1390 1390 1394 1400 1364 1300 2 MHz 1530 1534 1540 1541 1530 1531 1530 1533 1550 1567 1590 1589 3 MHz 1520 1534 1510 1548 1590 1586 1530 1507 1520 1552 1600 1542 4 MHz 1510 1531 1520 1512 1500 1506 1540 1556 1580 1571 1460 1330 Table 2- Frequency Variation of Ultrasonic Velocity in Nanofluid of Platinum Frequency [MHz] 1 2 3 4 5 Velocity [m/sec] 1329 1513 1570 1430 1414 169 | P a g e Figure 1(i). Temperature Variation of Ultrasonic Figure 1(ii). Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Velocity in Nanofluid of Platinum Figure 1(iii). Temperature Variation of Ultrasonic Figure 2. Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Velocity in Nanofluid of Platinum 170 | P a g e ULTRASONIC BEHAVIOUR OF MIXED CRYSTALS Virendra Kumar, Kailash and Bharat Singh Department of physics, B.N.P.G. College, Rath, Hamirpur, U.P., 210 431, Bharat Email-
[email protected],
[email protected] Abstract: In the mixed crystal systems, the anions are substituted by other anions of nearly equal size without breaking the crystal symmetry and so any ratio of two components yields the mixed crystal. A mixed crystal has physical properties analogous to those of the pure crystals. The mixed crystals of alkali halides are found to be harder than the crystals of end members and so they become more useful. The mixed alkali halides find their applications in optical, optoelectronic, and electronic devices. In addition, mixed crystals with multiple phases have been found to be more interesting. Further, it is interesting to prepare multiphase mixed crystals with new composition from miscible alkali halides. The behaviour of the ultrasonic properties plays an important role in providing valuable information about the mechanical and dynamical properties, such as inter atomic potentials, equation of state, and phonon spectra. Elastic properties are also thermodynamically related to the specific heat, thermal expansion, Debye temperature, melting point and Grüneisen parameter. The aim of this work is to give a detailed description of the behaviour of non-linear properties such as second, third and fourth order elastic constants of mixed potassium and rubidium fluoride and mixed lead selenide and telluride crystals at different temperature by using Coulomb and Börn - Mayer potentials. The evaluation of other ultrasonic properties such FOPDs of second and third order elastic constants, SOPDs of SOECs and partial contractions are computed using higher order elastic constants using this theory. Key Words: Ultrasonic Properties, Elastic Constants, Coulomb and Börn-Mayer Potentials, Mixed Crystals and Partial Contractions. 1. Introduction In recent years considerable interest has been paid to the study of mixed crystal properties as they are useful in many technological applications such as mixed crystals of alkali halides are used for laser windows. Lead selenide nano-crystals embedded into various materials can be used as quantum dots. Lead Telluride is used in a number of industrial applications including infrared detection and imaging. PbTe single crystals doped with VII A Periodic system group elements will continue to attract a widespread attention both for their fundamental electronic properties and for the applications in infrared optoelectronic [1-3]. Studies on mixed crystals are quite useful as they are of considerable technological importance in the field of storage cells. Ultrasonic characterization of materials is a versatile tool for the inspection of their micro-structure and their mechanical properties. This is possible because of the close 171 | P a g e association of the ultrasound wave with the elastic and the inelastic properties of the materials; also this technique offers the possibility of using different frequency ranges and many modes of vibration of the ultrasound waves to probe into structural level [4]. To study the ultrasonic behaviour of a deformed crystal, the elastic energy density is expanded by Taylor’s series expansions. One gets a series with higher order coefficients. These coefficients are known as higher order elastic constants. In this expansion, the second, third and fourth order elastic constants are the coefficients of second, third and fourth order terms. In last and present decade considerable interest has been taken in investigation of ultrasonic properties of materials [5-8]. Elastic and dielectric properties of mixed ionic solids have been carried out by number of workers using different phenomenological models. In present investigation, some efforts have been made for obtaining SOECs, TOECs and FOECs at an elevated temperature, the FOPDs of SOECs and TOECs, the SOPDs of SOECs and partial contractions of mixed (KF)X - (RbF)1-X and mixed (PbSe)X - (PbTe)1-X crystals. In this paper we represent mixed (KF)X - (RbF)1-X as A and (KF)100 - (RbF)0, (KF)80 - (RbF)20, (KF)60 - (RbF)40, (KF)40 - (RbF)60, (KF)20 - (RbF)80, and (KF)0 - (RbF)100 as A1----A6. Similarly B for mixed (PbSe)X - (PbTe)1-X and B1----B6 for its fractions. 2. Formulation As we presented earlier the elastic energy density for a crystal of a cubic symmetry can be expanded up to quartic terms as shown below [9]; 4 3 2 0 U U U U + + = [ ] [ ] [ ] pq mn kl ij ijklmnpq mn kl ij ijklmn kl ij l ijk X X X X C X X X C X X C ! 4 1 ! 3 1 ! 2 1 + + = (1) These elastic constants have two parts as given below. vib IJ IJ IJ C C C + = 0 , vib IJK IJK IJK C C C + = 0 , vib IJKL IJKL IJKL C C C + = 0 (2) 3. Evaluation With the help of nearest-neighbour distance and hardness parameter; the second, third and fourth order elastic constants for A and B crystals are evaluated at different temperature. The values of SOECs at room temperature for A and B are given in Table 1 and third and fourth order elastic constants at 300K are given in Tables 2(i)-3(ii) for these crystals. The FOPDs of SOECs and TOECs, the SOPDs of SOECs and partial contractions for mixed crystals are evaluated utilizing room temperature data, and the results are shown in Tables 4 – 5. 172 | P a g e 4. Results and Discussions The temperature dependence of elastic constants has been a subject of study in a number of investigations. The temperature variation of various ultrasonic are represented graphically for A and B. There are three SOECs for face centered cubic crystals. The values of C11 and C44 are increasing and the value of C12 is decreasing as temperature increases for A and B. From Figure 1, the value of C11and C44 increases and the value of C12 decreases as temperature increases for A1. For all crystals the values of C111, C112 and C166 are negative in nature while C123, C144 and C456 are positive in nature shown in Table 2(i)-(ii). Figure 2(i)-(ii) shows that the values of C111, C123, C144 and C166 are increasing; the value of C112 is decreasing as temperature increases and C456 remains constant for A2. There are three FOPDs of SOECs for mixed crystals. Figure 3 present the temperature variation of FOPDs of SOECs for B3. From this figure, it is clear that the value of dC11/dp and dC12/dp decreases and the value of dC44/dp first increases than decrease as temperature increases. It may be stated that all the second order pressure derivatives of second order elastic constants are positive. Figure 4 present the value of d 2 C11/dp, and d 2 C44/dp decreases as temperature increases and d 2 C12/dp decreases first and increases last for B4. From Figure 5, one can say that the value of 11 Ψ , 12 Ψ decreases as temperature increases and 44 Ψ somewhere increases or decreases as temperature increases for B5 crystals. 5. Acknowledgement The authors are thankful to the University Grants Commission, New Delhi for financial support. Table 1. SOECs in 10 11 dyne/cm 2 at room temperature for A and B Fraction A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C11 9.97 8.97 9.20 9.45 9.70 5.29 14.57 14.66 15.02 15.38 15.76 13.04 C12 1.67 1.39 1.47 1.52 1.59 1.54 5.418 4.109 4.375 4.664 4.976 3.938 C44 1.88 1.59 1.66 1.73 1.80 1.67 5.545 4.233 4.502 4.794 5.109 4.052 Table 2(i) TOECs in 10 11 dyne/cm 2 at room temperature for A Fraction A1 A2 A3 A4 A5 A6 C111 -106.902 -96.147 -100.034 -101.340 -105.861 -4.933 C112 -26.916 -24.256 -24.831 -25.463 -26.148 -15.302 C123 3.806 3.215 3.352 3.496 3.647 3.455 C144 3.535 3.022 3.141 3.266 3.397 2.952 C166 -7.343 -6.183 -6.450 -6.733 -7.028 -6.591 C456 3.141 2.679 2.786 2.899 3.016 2.578 Table 2(ii) TOECs in 10 11 dyne/cm 2 at room temperature for B 173 | P a g e Fraction B1 B2 B3 B4 B5 B6 C111 -220.85 -206.11 -209.79 -213.49 -217.18 -202.42 C112 -31.76 -26.53 -27.68 -28.93 -30.29 -25.47 C123 9.42 7.45 7.90 8.37 8.88 7.04 C144 9.04 7.20 7.61 8.50 8.53 6.81 C166 -22.08 -17.08 18.19 -19.39 -20.68 -16.05 C456 8.72 6.93 7.33 7.76 8.22 6.56 Table 3(i) FOECs in 10 11 dyne/cm 2 at room temperature for A Fraction A1 A2 A3 A4 A5 A6 C1111 286.74 183.52 207.91 233.31 260.07 169.01 C1112 -206.88 -203.77 -204.60 -205.39 -206.39 -69.936 C1122 -84.00 -89.07 -87.95 -86.72 -85.43 -2.68 C1123 -5.76 -4.60 -4.86 -5.14 -5.43 -6.15 C1144 -7.72 -6.60 -6.86 -7.13 -7.42 -6.31 C1155 27.73 22.97 24.06 25.22 26.43 2.51 C1255 -10.63 -9.16 -9.50 -9.86 -10.23 -8.81 C1266 37.09 31.10 32.48 33.94 35.47 32.56 C1456 -7.33 -6.26 -6.51 -6.77 -7.04 -6.02 C4444 40.80 34.40 35.88 37.44 39..07 35.58 C4455 -7.41 -6.32 -6.57 -6.84 -7.12 -6.41 Table 3(ii) FOECs in 10 11 dyne/cm 2 at room temperature for B Fraction B1 B2 B3 B4 B5 B6 C1111 2457.17 2304.64 2343.89 2382.56 2420.38 2264.77 C1112 -10.12 -38.22 -31.75 -24.98 -17.78 -44.16 C1122 71.12 37.80 45.39 53.47 62.03 30.59 C1123 -20.02 -15.53 -16.53 -17.61 -18.77 -14.59 C1144 -20.67 -16.44 -17.39 -18.40 -19.49 -15.56 C1155 101.05 78.11 83.22 88.73 94.66 73.34 C1255 -22.90 -18.33 -19.36 -20.46 -21.64 -17.37 C1266 119.03 92.63 98.52 104.87 111.69 87.13 C1456 -20.38 -16.20 -17.14 -18.14 -19.22 -15.33 C4444 121.83 95.03 101.02 107.47 114.39 89.44 C4455 -20.47 -16.27 -17.20 -18.22 -19.30 -15.39 Table 4. First Order Pressure Derivatives of the SOECs and TOECs for A and B Fraction A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 dp dC / 11 -14.40 -14.98 -14.83 -14.68 -14.54 -10.72 -9.86 -10.69 -10.48 -10.28 -10.07 -10.89 dp dC / 12 -6.12 -6.34 -6.29 -6.23 -6.17 -5.18 -3.02 -3.03 -3.02 -3.02 -3.02 -3.04 dp dC / 44 -0.05 -0.08 -0.07 -0.07 -0.06 -0.34 0.20 0.09 0.11 0.14 0.17 0.06 dp dC / 111 48.74 63.35 59.58 55.87 52.28 21.49 -68.85 -73.96 -72.78 -71.53 -70.22 -75.07 dp dC / 112 37.56 42.60 41.31 40.03 38.79 18.49 1.20 3.56 2.95 2.34 1.76 4.20 dp dC / 123 1.60 1.49 1.51 1.54 1.57 2.27 2.29 2.16 2.19 2.22 2.25 2.13 dp dC / 144 1.233 1.232 1.233 1.234 1.234 1.789 0.69 0.61 0.63 0.65 0.67 0.59 174 | P a g e dp dC / 166 2.59 2.63 2.62 2.61 2.60 2.93 1.45 1.47 1.46 1.46 1.45 1.48 dp dC / 456 2.28 2.26 2.271 2.276 2.282 2.623 2.42 2.33 2.35 2.37 2.39 2.31 Table 5. SOPDs of SOECs in 10 -10 (dyne/cm 2 ) -1 and Partial Contraction ( Ψin 10 13 dyne/cm 2 ) for A and B Fraction A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 2 11 2 / dp C d 3.48 3.99 3.85 3.72 3.59 3.68 1.57 2.01 1.89 1.78 1.67 2.13 2 12 2 / dp C d 0.90 1.04 1.00 0.96 0.93 1.07 0.22 0.25 0.25 0.24 0.23 0.26 2 44 2 / dp C d 0.28 3.04 2.97 2.91 2.85 5.38 0.18 0.19 0.19 0.19 0.18 0.19 11 Ψ -7.20 -8.12 -7.96 -7.72 -7.47 -1.26 25.19 21.97 22.75 23.54 24.36 21.20 12 Ψ -6.10 -6.08 -6.09 -6.10 -6.11 -1.75 0.22 -0.74 -0.55 -0.31 -0.05 -1.00 44 Ψ 0.75 0.61 0.65 0.68 0.72 0.71 3.25 2.49 2.66 2.85 3.04 2.34 6. References [1] S. Prabahar, K. Rajasekar and S. Srikanth, ‘Lead selenide thin films from vacuum evaporation Method- structural and optical properties’, Chalcogenides Letters, 6, 203–211, 2009. [2] F. Ren, E. D. Case, J. E. Ni, E. J. Timm, E.L. Curzio, R. M. Trejo, C. H. Lin and M.G. Kanatzidis, ‘Temperature-dependent elastic moduli of lead telluride-based thermoelectric materials’, Philosophical Magazine, 89, 143–167, 2009. [3] Y. Zhang, X. Ke, C. Chen, J. Yang, and P. R. C. Kent, ‘Thermodynamic properties of PbTe, PbSe, and PbS: First-principles study’, Phys. Rev. B, 80, 024304–024316, 2009. [4] M.S. Gaafar, H.A. Afifi, M.M. Mekawy, ‘Structural studies of some phospho-borate glasses using ultrasonic pulse echo technique DSC and IR spectroscopy’, Physica B, 404, 1668–1673, 2009. [5] P. F. Yuan and Z. J. Ding, ‘Ab inito calculation of elastic properties of rock-salt and zinc-blend MgS under pressure’, Physica B, 403, 1996, 2008. [6] K. M. Raju, R. K. Srivastava and Kailash, ‘Temperature Variation of Higher Order Elastic Constants of MgO’, Pramana, 69, 445-450, 2007. [7] D. Varsney, N. Kaurav, U. Sharma and R.K. Singh, ‘Phase transformation and elastic behaviour of MgX ( X= S, Se Te ) alkaline earth chalcogenides’, J. Phys. and Chem. of Solids 69, 60, 2008. [8] J. Sinova, A.S. Nunez, J. Schliamann and A.H. Mcdonald, ‘Electron- Phonon Interaction in Polyacene Organic Transistors’, Phys. Stat. Sol. (b), 230, 309-312, 2002. [9] Kailash, K.M. Raju, S.K. Srivastava and K.S. Kushwaha, ‘Anharmonic properties of rock-salt structure solids’, Physica B, 390, 270, 2007. 175 | P a g e Figure 1 Temperature Variation of SOECs for A1 Figure 2(i) Temperature Variation of TOECs for A2 Figure 2(ii) Temperature Variation of TOECs for A2 Figure 3 Temperature Variation of FOPDs for B3 Figure 4 Temperature Variation of SOPDs for B4 Figure 5 Temperature Variation of Partial Contractions for B5 176 | P a g e TEMPERATURE DEPENDENDE OF ULTRASONIC ATTENUATION IN STRONTIUM OXIDE CRYSTAL Kailash, Virendra Kumar and D.D. Gupta 1 Department of Physics, BN PG College, Rath, Hamirpur, U.P., 210 431, Bharat 1. Department of Physics, Bipin Bihari College, Jhansi, U.P., 284128, Bharat Email:
[email protected],
[email protected] Abstract: The ultrasonic attenuation is a measure of the relative amplitudes of a wave at two locations in space. Attenuation, itself, is not relative, however. Attenuation is a definite quantity for a particular mode of wave motion at a certain frequency in a given material under specific conditions. Ultrasonic absorption coefficients can be used for non-destructive techniques to characterize the materials. The temperature dependent part of ultrasonic attenuation has been explained in terms of model where the acoustic phonon interacts with a number of thermal phonons in the lattice. In sewage treatment facilities, ultrasonic attenuation is used as a sensing mechanism to control pumps and maintain sludge levels in setting basins. The strontium oxide crystal possesses face centred cubic crystal structure. In this work ultrasonic attenuation due to phonon–phonon interaction (α/f 2 )p-p and thermo elastic relaxation (α/f 2 )th are studied in strontium oxide at an elevated temperatures along <100> direction. For the evaluation of the ultrasonic coefficients the second and third order coefficients are also calculated using Coulomb and Born Mayer potentials utilizing nearest neighbour distance and hardness parameter data. Key Words: Attenuation, Thermo elastic relaxation, Phonon-phonon interaction, Akeiser loss and Gruneisen Numbers. 1. Introduction Attenuation is the term used to account for loss of wave amplitude or signal due to all mechanism, including absorption, scattering and mode conversion. The ultrasonic attenuation gained very wide acceptance in scientific experiment. The most important causes of ultrasonic attenuation in solids are electron–phonon, phonon–phonon interaction and that due to thermo elastic relaxation. At room temperature, electron mean free path is not comparable to phonon mean path and no coupling will take place. Thus the attenuation due to electron–phonon interaction will be absent. The two dominant processes that will give rise to appreciable ultrasonic attenuation at higher temperature are the phonon–phonon interaction also known as Akeiser loss and that due to thermo elastic relaxation [1, 2]. Both these type of attenuation are observed in calcium oxide crystal. It has been established that at frequencies of ultrasonic 177 | P a g e range and at higher temperatures in solids, phonon–phonon interaction mechanism is dominating cause for attenuation. The ultrasonic attenuation study of the materials has gained new dimensions with the progress in the material science [3-10]. The temperature dependent part of ultrasonic attenuation has been explained in terms of model where the acoustic phonon interacts with a number of thermal phonons in the lattice. In present work ultrasonic attenuation due to phonon–phonon interaction (α/f 2 )p-p and thermo elastic relaxation (α/f 2 )th are studied in strontium oxide at an elevated temperatures along <100> direction. For the evaluation of the ultrasonic coefficients the second and third order coefficients are also calculated using Coulomb and Born Mayer [11] potentials. 2. Formulation Here we use phonon-phonon interaction [12] for evaluating ultrasonic attenuation coefficient over frequency square (α/f 2 )p-p, the expressions are given as: (α/f 2 )l = 4π 2 E0( Dl/3) τl / 2dVl 3 (1) and (α/f 2 )s = 4π 2 E0( Ds/3) τs / 2dVs 3 (2) where the condition ωτth <<1has already been assumed. Here E0 is thermal energy density, ω is the angular frequency (=2πf), f is frequency of ultrasonic waves, d is the density and Vl, Vs are the ultrasonic velocities for longitudinal and shear waves respectively. The Vl, Vs and D V are given as Vl = (C11/d) 1/2 , Vs = (C44/d) 1/2 and 3/ 3 D V = 1/ 3 l V +2/ 3 s V (3) Two relaxation times are related as (1/2)τl = τs = τth = 3K/Cv 2 D V (4) Where τth is the thermal relaxation time for the exchange of acoustic and thermal energy, K is the thermal conductivity, Cv is specific heat and D V is the Debye average velocity. The acoustic coupling constant D in eqns. (1) and (2) is obtained from the values of the SOEC and TOEC data using theoretical formulae for <(γi j ) 2 > and <γi j > 2 and given as D = 9 <(γi j ) 2 > – (3Cv T/ E0) <γi j > 2 (5) Where γi j are the Grüneisen parameters corresponding to particular direction of propagation and polarization. The thermoelastic attenuation is obtained as (α/f 2 )th = 4π 2 <γi j > 2 KT/2dV 5 (6) We have calculated the SOEC and TOEC for the evaluations of acoustic coupling constants D, thermal relaxation time τth and ultrasonic absorption coefficients over frequency square of the ultrasonic wave. 3. Evaluation 178 | P a g e The temperature dependence of second and third order elastic constants for Strontium Oxide has been evaluated at different temperatures following Brügger’s approach [13] and the method given by Mori and are presented in Table 1 along with melting point. The theoretical [14] values of SOECs and TOECs in 10 11 dyne/cm 2 at room temperature are also given in this Table for comparison. Using the formulation, the room temperature data of longitudinal and shear wave velocities, debye average velocity, thermal relaxation time and non-linearity constants for Strontium Oxide along <100> direction are presented in Table 2. Grüneisen parameters have been evaluated using Mason’s Grüneisen [15] parameters tables at different temperatures along <100> direction with the help of second and third order elastic constants. The non-linearity constants D are evaluated using the average Grüneisen parameters <γi j > and average square Grüneisen parameters <γi j2 > and are presented in Table 3 along with attenuation (α/f 2 )l, (α/f 2 )s and (α/f 2 )th. 4. Results and Discussion The elastic constants of an isotropic solid specimen can be accurately determined by measuring the velocities of transverse and longitudinal ultrasonic waves in the specimen. The variation of the wave velocities with pressure can be used to determine the pressure derivatives of the elastic constants. In the present study all the SOECs are positive, while among TOECs three are positive and three are negative in nature. The magnitude of second and third order elastic constants and their temperature variation plays a crucial role in the investigation of ultrasonic attenuation in Strontium Oxide; their temperature variation is presented in Figure 1, 2. It is clear from the Figure 3 that the value of thermal relaxation time τth is very low at low temperature and increases as temperature is increased. The temperature variation of ultrasonic velocities is presented in Figure 4. It is clear from this Fig. that the ultrasonic velocity for longitudinal wave and shear wave increases as temperature increases along <100> direction. From Figure 5 one can see that non-linearity constants decrease as increase temperature. It is clear from Figure 6 that the value of (α/f 2 )l and (α/f 2 )s increases with temperature, the values of (α/f 2 )l are found greater than those of (α/f 2 )s along <100> direction, similar behavior has been observed by other researchers in solids. 5. Acknowledgement The authors are thankful to the University Grants Commission, New Delhi for financial support. 6. References [1] S. K. Kor, R. R. Yadav and Kailash, ‘Ultrasonic attenuatio in dielectric crystals’, J. Phys. Soc. Jpn., 55, 207, 1986. [2] A. Alkeizer, ‘On the absorption of sound in solids’, J. Phys. (USSR), 1, 277, 1939. [3] D. Singh, D. K.Pandey, P. K. Yadawa and A. K. Yadav, ‘Attenuation of ultrasonic waves in V, Nb and Ta at low temperatures’, Cryogenics, 49, 12, 2009. [4] E. S. R. Gopal and B. J. Thangaraju, ‘Physical ultrasonics: current scenario and future prospects’, Pure Appl. Ultrasonics, 22, 29, 2000. 179 | P a g e [5] S. K. Kor, R. R. Yadav and D. Singh, ‘Ultrasonic studies of CTAB in glycol’, Mol.Cryst. Liq. Cryst., 392, 75, 2003. [6] A. K. Upadhyay and B. S. Sharma, ‘Elastic properties of intermetallics compounds under high pressure and high temperature’, Ind. J. Pure Appl. Phys., 47, 362, 2009. [7] O. N. Awasthi and V. K. Pundhir, ‘Ultrasonic attenuation in liquid mecury, zinc and gallium metals’, Ind. J. Pure Appl. Phys., 45, 434, 2007. [8] R. K. Singh, ‘Ultrasonic attenuation in alkaline earth metals’, J. Pure Appl. Ulrason., 28, 59, 2006. [9] J. D. Pandey, A. K. Singh and R. Dey, ‘Effect of isotopy on thermoacoustical properties’, J. Pure Appl. Ulrason., 26, 100, 2004. [10] K. Foster, R.G. Leisure, J. B. Shaklee, J. Y. Kim and K. F. Kelto, ‘Ultrasonic study of hydrogen motion in a Ti-Zr-Niicosahedral quasicrystal and a 1/1 bcc crystal approximant’, Phys. Rev. B, 61, 241, 2000. [11] M. Born and J. M. Mayer, Zur Gittertheorie der lonenkristalle, Z Phys. (Germany), 75, 1, 1932. [12] W. P. Mason, ‘Piezoelectric crystals and their applications to ultrasonics’, D. Van Nortrand Co, Inc, Prinston, New Jersey, 479, 1950. [13] K. Brugger, ‘Thermodynamic definition of higher order elastic coefficients’, Phys. Rev., 133, A1612, 1964. [14] J. Shanker and J. P. Singh, third and fourth order elastic constants for silver halides, alkaline earth oxides, and chalcogenides of Pb and Sn, phys. stat. sol. (a) 70, 677, 1982. [15] W. P. Mason, ‘Effect of impurities and phonon-processes on the ultrasonic attenuation in germanium, crystal quartz and silicon’, Physical Acoustics, Vol. III B, Academic Press New York, 237, 1965. Table 1. Room Temperature data of Second and Third Order Elastic Constants in 10 11 dyne/cm 2 for SrO Mel. Point C11 C12 C44 C111 C112 C123 C144 C166 C456 Reference 2430 0 C 18.18 17.35 10.327 4.175 10.495 5.587 -249.62 -22.50 -54.85 -2.21 16.94 1.310 16.18 1.410 -41.99 -2.72 15.66 1.46 This Work [14] Table 2. Room Temperature data of Longitudinal and Shear Wave Velocities, Debye Average Velocity in 10 5 cm/sec 2 , Thermal Relaxation Time in 10 -12 sec and non linearity constants for SrO along <100> direction l V S V D V th τ l D S D 6.218 4.693 5.038 7.174 14.195 2.149 Table 3. Room Temperature data of Grüneisen Parameter, Square Average Grüneisen Parameter, p-p Attenuation for Longitudinal and Shear Waves in Nps 2 /cm and Thermal Attenuation in 10 -20 Nps 2 /cm for SrO along <100> direction < j i γ > <( j i γ ) 2 > (α/f 2 )L (α/f 2 )S (α/f 2 )th -0.561 1.764 1.083 0.190 1.399 180 | P a g e Figure 1. Temperature Variation of SOECs Figure 2. Temperature Variation of TOECs 181 | P a g e Figure 3. Temperature Variation of Thermal Relaxation Time Figure 4. Temperature Variation of Ultrasonic Velocities Figure 5. Temperature Variation of non-linearity constants Figure 6. Temperature Variation of Ultrasonic attenuation 182 | P a g e ULTRASONIC WAVE PROPAGATION IN REFRACTORY MATERIALS Devraj Singh 1* , P. K. Yadawa 1 , Ravi S. Singh 2 and S. K. Sahu 2 1 Department of Applied Physics, Amity School of Engineering and Technology Bijwasan, New Delhi- 110 061, India 2 Department of Physics, D. D. U. Gorakhpur University, Gorakhpur- 207 009(U.P.) *
[email protected] ABSTRACT: The ultrasonic attenuation of TiC and TiN are investigated at room temperature along <100>, <110> and <111> orientations using Mason’s theory. For these materials, Second and Third Order Elastic Constants (SOEC and TOEC), bulk modulus, elastic anisotropy, acoustic impedance, adiabatic compressibility, molar volume, intermolecular free path length, Rao’s constant, Wada’s constant, van der Waals constant, ultrasonic velocities, thermal relaxation time, acoustic coupling constants are computed. Ultrasonic attenuation due to phonon-phonon interaction mechanism is predominant over thermoelastic relaxation mechanism. All calculated results have been discussed and comparision with available experimental results are drawn. KEYWORDS: Ultrasonic attenuation, elastic constants, thermal conductivity INTRODUCTION: The ultrasonic properties can be used as nondestructive techniques for the detection and characterization of materials properties not only after the production but during processing as well [1- 3]. The refractory titanium compounds like TiC and TiN is known for its extreme hardness (> 2500 VDH), high melting temperature and chemical inertness. The usual and interesting properties have attracted a large number of experimental, theoretical and industrial investigations [4-6], and make it attractive as a structural material or as a coating for cutting tools. In present paper some characteristic microstructural thermophysical parameters those make considerable contribution to orientation and temperature dependence of ultrasonic attenuation in TiC and 183 | P a g e TiN along <100>, <110> and <111> orientations are discussed. For this analysis, we have also evaluated second and third order elastic constants, acoustic impedance, adiabatic compressibility, molar volume, intermolecular free path length, Rao’s constant, Wada’s constant, van der Waals constant, ultrasonic velocities, thermal relaxation time, acoustic coupling constants. THEORY For the evaluation of ultrasonic attenuation, second and third order elastic constant play a vital role. We calculated SOEC and TOEC following Brugger’s definition of elastic constants at absolute zero o IJ C ( and o IJK C ) [7,8]. The SOEC (C11, C12 and C44) and TOEC (C111, C112, C123, C144, C166 and C456) at room temperature (300K) are achieved by method developed by Leibfried, Ludwig, Mori, Ghate and Yadav [9-13] for NaCl-type crystal. Since the crystalline form of stoichiometric titanium carbide and titanium nitride adopt the simple rocksalt structure. These titanium compounds have ionic metallic bonding. Here it is assumed that Φµv(r) is the interaction potential equal to the sum of the electrostatic potential ( Coulomb potential) and the Born-Mayer short range repulsive potential, i.e. Φµv(r) = ± (e 2 /r) + A exp (-r/b) Where, e is the electronic charge, r the nearest neighbor distance, the ± sign apply like and unlike charge, A is the strength parameter and b is the hardness parameter. We further assume A and b are the same for interaction between like (positive and negative) and unlike ions [11-13]. All the formulations used in the computation of SOEC and TOEC of TiC and TiN are the same as those for previous paper [13]. With the help of second and third order elastic constant (SOEC and TOEC) , the other physical parameters like zero pressure bulk modulus, elastic anisotropy, acoustic impedance, adiabatic compressibility, molar volume, intermolecular free path length, Rao’s constant, Wada’s constant and van der Waal constant [14]. The main causes of ultrasonic attenuation for perfect antiferroelectric and antiferromagnetic crystals are due to phonon-viscosity, the thermal relaxation time and electron-phonon interaction. However at room temperature these remain only two types of losses, which are due to phonon-viscosity and thermoelastic relaxation mechanism. The loss due to electron-phonon interaction is only appreciable below 80K and hence it could be ignored safely at room temperature. Akhieser [15] has assumed that the equilibrium distribution phonons in a crystal can be distributed by the propagation of an acoustic phonon and the reestablishment of the equilibrium is the relaxation phenomenon. Theory to evaluate ultrasonic attenuation has been discussed in our previous paper [12-13]. 184 | P a g e RESULTS AND DISCUSSION Evaluated Second order elastic constants (C11, C12, and C44) are presented in Table 1 with available comparative experimental and theoretical values. The third order elastic constants are presented in Table 2. Other physical parameter like bulk modulus, elastic anisotropy, acoustic impedance, adiabatic compressibility, molar volume, intermolecular free path length, Rao’s constant, Wada’s constant, van der Waal’s constant were also evaluated by means of second order elastic constants and are presented in Table 3. Results of various investigators are different because of they used different theoretical approach. For example Tan et al. [4] used tight binding model, Nguyen Manh used ab-initio calculation method [4] and Weber used phenomenological model theory. Our results for C11 is very similar as Tan et al. [4], while approximately half as ab-initio calculation [4] and experimental [16]. The value of C12 is approximately 10 times less while value of C44 is approximately 5 times less than those obtained by others [4, 16-20]. The obtained values of C11, C12 and C44 are less because we have taken approximation upto second nearest neighbor. The order of achieved SOEC is same as obtained by other investigators [16-20]. From Table 1, it is known that agreement between theoretical/experimental data of TiC and TiN for C11, C12 and C44 are good. Table 1 depicts that the higher value of C11 for TiN, shows that the TiN has better mechanical strength than TiC. The obtained values of wave velocities are in good agreement with other refractory materials and are comparable with literature [12-13]. The thermal relaxation time is of the order of the picosecond as expected for other NaCl-type materials []. The physical constants like bulk modulus, elastic anisotropy, acoustic impedance, adiabatic compressibility, molar volume, intermolecular free path length, Rao’s constant, Wada’s constant, van der Waal’s constant are of the same order as obtained for solids. The ultrasonic attenuation due to phonon-phonon interaction is predominant over total attenuation. The obtained results are summary of various parameters involved during computing approaches. Ultrasonic attenuation values of TiN are less than those of TiC. Hence TiN is more ductile than TiC. TiN is more appropriate for general purpose. CONCLUSION On the basis of above discussion, we conclude the following points: 185 | P a g e 1. Although several potentials are available to evaluate elastic constants like Pseudo potential, Morse-potential and Lenard-Jones potential, but Coulomb and Born-Mayer potential is more appropriate to find out elastic constant of NaCl-type, TiC and TiN as we found satisfactory results of SOEC and TOEC in present investigation. 2. The natures of ultrasonic velocities are found satisfactory. The order of thermal relaxation time is found the order of the picoseconds. 3. On the basis of ultrasonic attenuation values of these materials, we can say TiN is more ductile, appropriate and useful for its characterization and industrial applications. Obtained results of present investigation correlated with other physical parameters are applicable for further investigation. REFERENCES 1. R. R. Yadav, A. K. Tiwari and D. Singh, “Effect of pressure on ultrasonic attenuation in Ce monopnictides at low temperature”, J. Mat. Sc. 40(2005) 5319-5321. 2. D. Singh and P. K. Yadawa, “Effect of platinum addition in coinage metals on its ultrasonic properties”, Platinum Metals Rev. 54 (2010) 169–176. 3. A. Keith, “A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone”, J. Acoust. Soc. Am. 109(3) (2001) 1213. 4. K. E. Tan, A. M. Bretkovsky, R. M. Harris, A. P. Horsfield, D. Nguyen Manh, D. G. Pettifort and A. P. Sutton, “Carbon vacancies in titanium carbide”, Modelling Simul. Mat. Sc. Eng. 5(1997) 187- 198. 5. V. A. Gubanov, A. L. Ivanovsky and V. P. Zhukov, “Electronic Structure of Refractory Carbides and Nitrides”, Cambridge University Press, Cambridge, 1994. 6. L. Pintschovius, W Reichardt and B. Scheerer, “Lattice dynamics of TiC”, J. Phys. C: Solid State Physics., 11(1978) 1557-1562. 7. M. Born and J. E. Mayer, “Zur Gittertheorie der Ionen Kristalle”, Z-Phys. 75 (1931) 1. 8. K. Brugger, “Thermodynamic definition of higher order elastic coefficients”, Phys. Rev. 133 (1964) 41611. 9. G. Leibfried and H. Haln, “Zur temperaturabhangigkeit der elastischen konstantaaen von alhalihalogenidkristallen”, Z. Phys. 150 (1958) 497. 186 | P a g e 10. G. Leibfried and W. Ludwig, “Theory of Anharmonic effect in cryatal”, Solid State Physics, 12 (1964) 275. 11. S. Mori and Y. Hiki, “Calculation of the third and fourth order elastic constant of alkali-halides”, J. Phys. Soc. Jpn., 45 (1978) 1449-1456. 12. D. Singh, “Behaviour of acoustic attenuation in rare earth chalcogenides”, Mat. Chem. Phys. 115 (2009) 65-68. 13. D. Singh and D. K. Pandey, “An investigation of ultrasonic properties of NpX (X: S,Se and Te)”, Braz. J. Phys. (Communicated). 14. S. K. Sahu, M. Phil Thesis submitted to Bundelkhand University, Jhansi, 2009. 15. A.Akhieser, On the absorption of ultrasound, J.Phys.(Moscow)1 (1939) 277-287. 16. R. Chang, L. J. Grahm, J. Appl. Phys. 37 (1996) 3778. 17. W. Weber, Phys. Rev. B, 8(11) (1973) 5082-92. 18. D. Chen, J. Chen, Y. Zhao, B. Yu, C. Wang and D. Shi, “Theoretical study of the elastic properties of titanium nitride”, Acta. Metall. Sci (Engl. Lett.) 22(2) (2009). 19. Z. Ming, Z. Maosheng and H. E. Jiawen, Chin. J. Mat. Res. 15(5) (2001) 577-582. 20. W. Kress, P. Roedhammer, H. Bilz, W. Tenchent and A. N. Christensen, “Phonon anomalies in transition- metal nitrides: TiN”, Phys. Rev. B 17 (1978) 111. TABLE 1. Compared results of Second order elastic constants (SOEC) of TiC and TiN, Elastic Constants Present work ab initio [4] Experiment [16] [4] [19] TiC C11 (x 10 11 N m -2 ) 3.144 6.14 5.15 3.13 5.1 TiC C12 (x 10 11 N m -2 ) 0.26 0.77 1.06 2.07 1.0 TiC C44 (x 10 11 N m -2 ) 0.383 1.83 1.79 1.19 1.8 Elastic Constants Present work [18] [19] [20] TiN C11 (x 10 11 N m -2 ) 6.044 5.594 4.978 4.978 TiN C12 (x 10 11 N m -2 ) 0.1 1.125 1.056 1.287 187 | P a g e TiN C44 (x 10 11 N m -2 ) 0.392 1.572 1.681 1.681 TABLE 2. Third order elastic constants (TOEC) are given below, Material C111 C112 C123 C144 C166 C456 TiC (x 10 10 Nm -2 ) -614.23 -7.74 -3.53 7.19 -14.5 7.12 TiN (x 10 10 Nm -2 ) -152.99 9.279 -30.46 7.62 -13.83 7.6 TABLE 3. Calculated ultrasonic parameters at room temperature Parameters TiC TiN Bulk modulus (x 10 10 Nm -2 ) 12.213 20.813 Elastic anisotropy 0.266 0.132 Acoustic impedance (x 10 7 Kg m -2 s -1 ) 1.544 2.206 Adiabatic compressibility (x 10 -11 m Kg -1 s 2 ) 2.069 1.496 Molar volume (x10 -5 m3 mol -1 ) 1.214 0.849 Intermolecular free path length (x 10 -14 m) 2.876 2.834 Rao’s constant (x 10 2 ) 8.474 7.65 Wada’s constant (x 10 2 ) 5.676 5.349 Van der Waal constant (x 10 -6 m3 mol -1 ) 11.741 11.007 TABLE 4. Longitudinal and Shear velocities (Vl and Vs), Debye average velocity (V) and thermal relaxation time (τth) of TiC and TiN at room temperature. Material TiC TiN <100> Vl (x 10 5 cm/sec) 7.99 10.54 Vs (x 10 5 cm/sec) 2.79 2.67 V (x 10 5 cm/sec) 3.131 3.028 τth(x 10 -12 cm) 5.440 4.760 <110> Vl (x 10 5 cm/sec) 6.51 7.99 188 | P a g e Vs1 (x 10 5 cm/sec) 2.79 2.67 Vs2 (x 10 5 cm/sec) 7.65 10.46 <111> Vl (x 10 5 cm/sec) 5.93 6.92 Vs (x 10 5 cm/sec) 4.7 6.24 TABLE 5: Ultrasonic attenuation {(α/f 2 )long., (α/f 2 )shear and (α/f 2 )th} of TiC and TiN at room temperature. Material TiC TiN <100> (α/f 2 )l (10 -17 Nps 2 /cm) 0.2809 0.2179 ♣ (α/f 2 )s1 (10 -17 Nps 2 /cm) 0.1376 0.1441 (α/f 2 )th (10 -17 Nps 2 /cm) 0.0134 0.0113 Total 0.9319 0.3733 <110> (α/f 2 )l (10 -17 Nps 2 /cm) 0.5918 0.5830 # (α/f 2 )s2 (10 -17 Nps 2 /cm) 0.0716 0.0520 $ (α/f 2 )s3 (10 -17 Nps 2 /cm) 0.2839 0.2252 (α/f 2 )th (10 -17 Nps 2 /cm) 0.0516 0.0632 Total 0.9989 0.9234 <111> (α/f 2 )l (10 -17 Nps 2 /cm) 0.4706 0.4743 * (α/f 2 )s4 (10 -17 Nps 2 /cm) 0.8250 0.6941 (α/f 2 )th (10 -17 Nps 2 /cm) 0.0779 0.0406 Total 1.3735 1.2090 ♣=shear wave polarized along <100>, # = shear wave polarized along <001>, $= shear wave polarized along ൏ 11 ത 0 and *= shear wave polarized along ൏ 1 ത 10 189 | P a g e Ultrasonic wave propagation in II-VI hexagonal semiconductor compounds Pramod Kumar Yadawa* and Devraj Singh Department of Applied Physics, AMITY School of Engineering and Technology, Bijwasan, New Delhi-110 061, India *Tel: +91-11-2806-2106/1487, Fax: +91-11-28061821 *E-mail:
[email protected] ABSTRACT The paper presents a comprehensive computation of second- and third- order elastic constants and then velocities and attenuation of ultrasonic waves along unique direction in hexagonal II-VI group semiconducting materials like ZnS, ZnSe, ZnTe and CdTe at room temperature. We have developed a computer program to compute the elastic constants, ultrasonic velocities and ultrasonic attenuation in C ++ language. The comparison of our computed results has been made with available theoretical and experiment results. The value of ultrasonic attenuation of ZnS is smallest in comparison to other chosen materials. So ZnS is more ductile and more pure than the others. Obtained results, together with other well known physical properties, may expand future prospects for the applications and study of these materials. Keywords: Semiconductors, Elastic properties, Thermal conductivity, Ultrasonic properties. 1. Introduction It is well known that II-VI semiconductor compounds have a large optical gap, but the feasibility of green-blue opto-electronic devices based on these materials has been demonstrated by Hasse et al. [1]. Due to their wide direct band gap, the electronic properties of II-VI semiconductors, such as ZnS, ZnSe, ZnTe and CdTe, appear to be rather promising for applications in optical devices. Technological and theoretical interest in II-VI compound and their alloys is due to its appealing properties in electro-optical and electron acoustic devices [2-4]. Actually, their technological potential is very great. In addition to their use in optical devices operating in the short- wavelength radiation range from red to ultra-violet [5], in recent years, these materials have been used as catalysts when studying photochemical reactions [6]. Due to the possibility of intense photoexcitation, especially between the top of the valence band and the bottom of the conduction band at the Γ point, they are used in solar cells [7]. Ultrasonic attenuation is very important physical parameter to characterize the material, which is well related to several physical quantities like thermal conductivity, specific heat, thermal energy density and higher order elastic constants [8]. The 190 | P a g e elastic constants provide valuable information about the bonding characteristic between adjacent atomic planes and the anisotropic character of the bonding and structural stability [9, 10]. Therefore, in this work we predict the ultrasonic properties of hexagonal structured semiconductor compounds at room temperature. The ultrasonic attenuation coefficient, acoustic coupling constants, higher order elastic constants, thermal relaxation time and ultrasonic wave velocities for these semiconductors for unique direction of propagation of wave are calculated at 300K. The calculated ultrasonic parameters are discussed with related thermophysical properties for the characterization of the chosen semiconductors. The obtained results are analyzed in comparison to other hexagonal structured materials. 10. 2. THEORY In the present investigation, the theory is divided into two parts: 2.1 Second-and third order Elastic constants The second (CIJ) and third (CIJK) order elastic constants of material are defined by following expressions. 1,......6 J or I ; e e U C J I 2 IJ = ∂ ∂ ∂ = (1) 1,......6 K or J or I ; e e e U C K J I 3 IJK = ∂ ∂ ∂ ∂ = (2) where, U is elastic energy density , eI=eij (i or j = x, y, z, I=1, …6) is component of strain tensor. Eqs (1) and (2) leads six second and ten third order elastic constants (SOEC and TOEC) for the hexagonal close packed structure materials [8, 11]. ¦ ¦ ) ¦ ¦ ` ¹ ′ = ′ = ′ = ′ = ′ = ′ = C p 851 . 9 C C p 309 . 2 C C p 464 . 3 C C p 925 . 1 C C p 918 . 5 C C p 1 . 24 C 4 66 4 44 8 33 6 13 4 12 4 11 (3a) ¦ ¦ ¦ ) ¦ ¦ ¦ ` ¹ = ′ + = = = = = ′ − = ′ + = ′ − = ′ + = B p 196 . 5 C C p 007 . 9 B p 039 . 101 C B p 464 . 3 C B p 309 . 2 C B p 539 . 1 C B p 695 . 3 C C p 155 . 1 B p 617 . 1 C C p 155 . 1 B p 924 . 1 C C p 61 . 1 B p 168 . 19 C C p 853 . 8 B p 9 . 126 C 8 333 4 2 222 6 344 4 144 4 155 6 133 6 4 123 6 4 113 4 2 112 4 2 111 (3b) 191 | P a g e where p = c/a: axial ratio; 5 p / a χ = ′ C ; 3 3 p / a B ψ = ; }] a /{ )} m n ( nb )[{ 8 / 1 ( 4 n 0 + − = χ )} 6 n m ( a /{6 2 + + χ − = ψ ; m, n=integer quantity; b0=Lennard Jones parameter. 2.2 Ultrasonic attenuation and allied Parameters The predominant causes for the ultrasonic attenuation in a solid at room temperature are phonon- phonon interaction (Akhieser loss) and thermoelastic relaxation mechanisms. The ultrasonic attenuation coefficient (A)Akh due to phonon-phonon interaction and thermoelastic relaxation mechanisms is given by the following expression [11, 12]. (A /f 2 )Akh ( ) V 2 / T C ) ( E 3 4 3 V 2 j i 2 j i 0 2 ρ τ > γ < − > γ < π = (4) (A /f 2 )Th 5 L 2 j i 2 V 2 / kT 4 ρ > γ < π = (5) where, f: frequency of the ultrasonic wave; V: ultrasonic velocity for longitudinal and shear wave; VL: longitudinal ultrasonic velocity; E0: thermal energy density; j i γ : Grüneisen number (i, j are the mode and direction of propagation). The Grüneisen number for hexagonal structured crystal along <001> orientation or θ=0 0 is direct consequence of second and third order elastic constants. ( ) 0 V 2 j i 2 j i 0 E / T C ) ( E 3 3 D > γ < − > γ < = is known as acoustic coupling constant, which is the measure of acoustic energy converted to thermal energy. When the ultrasonic wave propagates through crystalline material, the equilibrium of phonon distribution is disturbed. The time for re-establishment of equilibrium of the thermal phonon distribution is called thermal relaxation time (τ) and is given by following expression: 2 D V L S V C / k 3 2 / = τ = τ = τ (6) Here τL and τS are the thermal relaxation time for longitudinal and shear wave. k and CV are the thermal conductivity and specific heat per unit volume of the material respectively. The Debye average velocity (VD) is well related to longitudinal (VL) and shear wave (VS1, VS2) velocities. The expressions for ultrasonic velocities are given in our previous papers [11, 12]: where ρ and θ are the density of the material and angle with the unique axis of the crystal respectively. The ultrasonic velocities have been used for the calculation of ultrasonic attenuation and allied parameters in the chosen materials. 3. Results and discussion 3.1 Higher order elastic constants 192 | P a g e The unit cell parameters ‘a’ (basal plane parameter) and ‘p’ (axial ratio) for ZnS, ZnSe, ZnTe and CdTe are 3.83Å, 4.02Å, 4.28Å, 4.58Å and 1.639, 1.631, 1.637, 1.635 [13] respectively. The value of m and n for chosen materials are 6 and 7. The values of b0 for these materials are 7.2x10 -64 erg cm 7 , 9.2x10 -64 erg cm 7 , 14.0x10 -64 erg cm 7 and 20.0x10 -64 erg cm 7 respectively. The SOEC and TOEC have been calculated for these materials using Eq. (3) and are presented in Table 1. Table1. Second and third order elastic constants (SOEC and TOEC) & bulk modulus (B) in the unit of 10 10 Nm -2 of materials at room temperature. C11 C12 C13 C33 C44 C66 B ZnS 13.643 3.351 2.927 14.151 3.511 5.350 6.650 ZnSe 10.830 2.659 2.301 11.015 2.760 4.247 5.244 ZnTe 8.731 2.144 1.869 9.013 2.242 3.424 4.249 CdTe 6.396 1.571 1.366 6.570 1.638 2.508 3.107 ZnS[12] 13.59 3.33 2.91 14.00 3.49 5.13 ZnSe[14] 10.72 4.46 3.53 11.65 2.50 3.13 ZnTe[15] 8.56 3.70 3.00 9.26 2.02 2.43 CdTe[15] 6.22 3.59 2.91 6.89 1.16 1.31 C111 C112 C113 C123 C133 C344 C144 C155 C222 C333 ZnS -222.47 -35.27 -7.509 -9.54 -47.78 -44.81 -11.12 -7.41 -176.03 -180.56 ZnSe -176.60 -27.99 -5.90 -7.50 -37.21 -34.88 -8.74 -5.83 -139.73 -139.18 ZnTe -142.37 -22.57 -4.79 -6.09 -30.44 -28.54 -7.10 -4.73 -112.65 -114.71 CdTe -104.30 -16.54 -3.50 -4.45 -22.19 -20.80 -5.19 -3.46 -82.53 -83.42 The elastic constants of the material are important, since they are related to hardness and therefore of interest in applications where mechanical strength and durability are important. Also, the second order elastic constants are used for the determination of the ultrasonic attenuation and related parameters. It is obvious from Table 1 that, there is good agreement between the present and reported theoretical and experimental second order elastic constants of these semiconducting materials [12, 14, 15]. Also, the comparison can be made with the value of Debye temperature of ZnSe and ZnTe. The present value of Debye temperature for ZnSe and ZnTe are 269.9 0 K and 218.4 0 K respectively, calculated using second order elastic constants. The Debye temperature experimentally determined by Lee [14] are 278.5 0 K and 225.3 0 K respectively. Thus our theoretical approach for the calculation of second order elastic 193 | P a g e constants for hexagonal structured materials at room temperature is well justified. However, third order elastic constants are not compared due to lack of data in the literature but the negative third order elastic constants are found our previous papers for hcp structure materials [8, 11, 12, 16-18]. Hence applied theory for the evaluation of higher order elastic constants at room temperature is justified. The bulk modulus (B) for these alloys can be calculated with the formula B= 2(C11+ C12+ 2C13 + C33/2)/9. The evaluated B for these alloys is presented in Table 1. 3.2. Ultrasonic velocity and allied parameters The density and thermal conductivity at room temperature have been taken from the literature. The value of CV and E0 are evaluated using tables of physical constants and Debye temperature. The thermal conductivity k and calculated acoustic coupling constants (DL & DS) are presented in Table 2. Table 2: Density (ρ: in 10 3 kg m -3 ), specific heat per unit volume (CV: in 10 6 Jm -3 K -1 ), thermal energy density (E0: in 10 8 Jm -3 ), thermal conductivity (k: in Wm -1 K -1 ) and acoustic coupling constant (DL, DS) of hcp semiconductor materials. ρ CV E0 k DL DS ZnS 4.09 0.977 1.91 27.0 53.76 1.27 ZnSe 5.262 0.876 1.92 19.0 54.72 1.17 ZnTe 5.636 0.710 1.65 11.0 54.31 1.24 CdTe 5.849 0.600 1.46 6.0 54.58 1.21 The computed orientation dependent ultrasonic wave velocities and Debye average velocities at 300 K are shown in Figs 1–4. Figs 1–3 show that the velocities VL and VS1 have minima and maxima respectively at 45° with the unique axis of the crystal while VS2 increases with the angle from the unique axis. The combined effect of SOEC and density is reason for abnormal behaviour of angle dependent velocities. The nature of the angle dependent velocity curves in the present work is found similar as that for heavy rare-earth metals, laves-phase compounds and other hexagonal wurtzite structured materials [8, 11, 12, 16-18]. The chosen semiconductors have shown similar properties with their crystal structure. The comparative study of ultrasonic velocities is presented in Table. 3. Table 3: Comparative velocities (in 10 3 m/s) of hcp semiconductor materials. 194 | P a g e Velocity Present work theoretical Carl et al.[19] experimental Kim et al.[20] experimental Bijalwan et al.[21] theoretical ZnS long. 5.88 5.51 5.45 6.49 shear 2.93 2.65 2.92 3.78 ZnSe long. 4.57 4.25 shear 2.29 2.83 ZnTe long. 3.99 3.58 shear 2.00 2.74 CdTe long. 3.35 3.47 shear 1.67 2.93 Hence values of velocities are in good agreement with experimental/theoretical values. Thus the angle dependencies of the velocities in these materials are justified. VD of these materials are increasing with the angle and have maxima at 55° at 300 K (Fig. 4). Since VD is calculated using VL, VS1 and VS2 [8, 12], therefore the angle variation of VD is influenced by the constituent ultrasonic velocities. The maximum VD at 55° is due to a significant increase in longitudinal and pure shear (VS2) wave velocities and a decrease in quasi-shear (VS1) wave velocity. Thus it can be concluded that when a sound wave travels at 55° with the unique axis of these crystals then the average sound wave velocity is maximum. The calculated thermal relaxation time is visualised in Fig. 5. The angle dependent thermal relaxation time curves follow the reciprocal nature of VD as 2 D V V C / K 3 ∝ τ . This implies that τ for chosen materials are mainly affected by the thermal conductivity. The τ for hexagonal structured materials is the order of pico second [18]. Hence the calculated τ justifies the hcp structure of chosen materials at room temperature. The minimum τ for wave propagation along θ = 55 0 implies that the re-establishment time for the equilibrium distribution of thermal phonons will be minimum for propagation of wave along this direction. Thus the present average sound velocity directly correlates with the Debye temperature, specific heat and thermal energy density of theses materials. 3.3. Ultrasonic attenuation due to phonon-phonon interaction and thermal relaxation phenomena In the evaluation of ultrasonic attenuation, it is supposed that wave is propagating along the unique axis [<001> direction] of these materials. The attenuation coefficient over frequency square (A/f 2 )Akh for longitudinal (A/f 2 )L and shear wave (A/f 2 )S are calculated using Eq. (4) under the condition ωτ<<1 at room 195 | P a g e temperature. The thermoelastic loss over frequency square (A/f 2 )Th is calculated with the Eq. (5). The values of (A/f 2 )L, (A/f 2 )S, (A/f 2 )Th and total attenuation (A/f 2 )Total are presented in Table 4. Table 4: Ultrasonic attenuation coefficient (in 10 -17 Np s 2 m -1 ) of hcp semiconductor materials. Alloys ZnS ZnSe ZnTe CdTe (A/f 2 )Th 0.266 0.513 0.543 0.691 (A/f 2 )L 254.138 554.962 621.738 832.617 (A/f 2 )s 24.259 42.223 57.180 74.288 (A/f 2 )Total 278.663 597.698 678.918 907.596 Table 4 indicates that the thermoelastic loss is very small in comparison to Akhieser loss and ultrasonic attenuation for longitudinal wave (A/f 2 )L is greater than that of shear wave (A/f 2 )S. This reveals that ultrasonic attenuation due to phonon-phonon interaction along longitudinal wave is governing factor for total attenuation ((A/f 2 )Total =(A/f 2 )Th+(A/f 2 )L+(A/f 2 )S). The total attenuation is mainly affected by thermal energy density and thermal conductivity. Thus it may predict that at 300K the ZnS behaves as its purest form and is more ductile as evinced by minimum attenuation while CdTe is least ductile. Therefore impurity will be least in the ZnS at room temperature. Since A 3 V − ∝ and velocity is the largest for ZnS among CdTe thus the attenuation A should be smallest and material should be most ductile. The minimum ultrasonic attenuation for ZnS justifies its quite stable hcp structure state. The total attenuation of these compounds are much larger than third group nitrides (AlN: 4.441x10 -17 Nps 2 m -1 ; GaN: 14.930x10 -17 Nps 2 m -1 and InN: 20.539x10 -17 Nps 2 m -1 ) due to their large thermal conductivity and acoustic coupling constants [18, 22]. This implies that the interaction between acoustical phonon and quanta of lattice vibration for these alloys is large in comparison to third group nitrides. 4. Conclusions On the basis of above discussion, we conclude following points: 196 | P a g e • Our theory of higher order elastic constants is justified for the hexagonal structured materials. • The order of thermal relaxation time for these materials is found in picoseconds, which justifies their hcp structure at 300K. The re-establishment time for the equilibrium distribution of thermal phonons will be minimum for the wave propagation along θ = 55 0 due to being smallest value of τ along this direction. • The acoustic coupling constant of these materials for longitudinal wave are found five times larger than third group nitrides. Hence the conversion of acoustic energy into thermal energy will be large for these materials. This shows general suitability of chosen materials. • The ultrasonic attenuation due to phonon-phonon interaction mechanism is predominant over total attenuation as a governing factor thermal conductivity. • The mechanical properties of ZnS are better than those of CdTe, because CdTe has low elastic constants and ultrasonic velocities. Thus obtained results in the present work can be used for further investigations, general and industrial applications. Our theoretical approach is valid for ultrasonic characterization of these alloys at room temperature. The ultrasonic behavior in these semiconductor materials as discussed above shows important microstructural characteristic feature, which are well connected to thermoelectric properties of the materials. These results, together with other well-known physical properties, may expand future prospects for the application and study of these materials. References [1] M. A. Hasse, J. Qiu, J. M. DePuydt, H. Cheng, Appl. Phys. Lett. 59 (1991) 1272. [2] M. Matsuoka, K. Ono, J. Vac. Sci. Technol. A 7 (1989) 2975. [3] M. A. Haase, H. Cheng, D. K. Misemer, T. A. Strand, J. M. DePuydt, Appl. Phys. Lett. 59 (1991) 3228 [4] M. J. Weber (Ed), Handbook of Laser Science and Technology, Vol.III, CRC Press, Cleveland, 1986. [5] D. M. Bagnall, Y. F. Chen, T. Yao, Appl. Phys. Lett. 70 (1997) 2230. [6] L. Chen, W. Gu, X. Zhu, J. Photochem. Photobiol. A 74 (1993) 85. [7] H. W. Shock, Sol. Energy Mater. Soc. Cells 34 (1994) 19. [8] P. K. Yadawa, D. Singh, D. K. Pandey, R. R. Yadav, The Open Acoustic Journal 2 (2009) 80. [9] P. Ravindran, L. Fast, P.A. Korzhavyi, B. Johansson, J. M. Wills, O. Eriksson, J. Appl. Phys. 84 (1998) 4891. [10] L. Louail, D. Maouche, A. Roumili, F. Ali Sahraoui, Mater. Lett. 58 (2004) 2975. 197 | P a g e [11] A. K. Yadav, R. R. Yadav, D. K. Pandey, D. Singh, Mat. Lett. 62 (2008) 3258. [12] D. K. Pandey, P. K. Yadawa, R. R. Yadav, Mat. Lett. 61 (2007) 5194. [13] T. V. Gorkavenko, S. M. Zubkova, V. A. Makara, L. N. Rusina, Semiconductors, 41 (2007) 886. [14] B. H. Lee, J. Appl. Phys. 41 (1970) 2984. [15] R. M. Martin, Phys. Rev. B 6 (1972) 4546. [16] D. K. Pandey, P. K. Yadawa, R. R. Yadav, Mat. Lett. 61 (2007) 4747. [17] D. K. Pandey, D. Singh, P. K. Yadawa, P.K., Plat. Met. Rev. 53 (2009) 91. [18] D. K. Pandey, D. Singh, R. R. Yadav, Appl. Acoust. 68 (2007) 766. [19] F. C. Carl, L. D. Harold, W. H. Glenn, J. Appl. Phys. 38 (4) (1967) 1944. [20] E. K. Kim, S. I. Kwun, S. M. Lee, H. Seo, J. G. Yoon, Phys. Rev. B 61 (9) (2000) 6036. [21] R. D. Bijalwan, P. N. Ram, M. D. Tiwari, J. Phys. C: Solid State Phys., 16 (1983) 2537. [22] Landolt-Bornstein, Numerical Data and Function Relationship in Science and Technology, Group III Vol. 11, Bellin Springer 1979. Figure Captions: Fig.1: VL vs angle with unique axis of crystal Fig.2: VS1 vs angle with unique axis of crystal Fig.3: VS2 vs angle with unique axis of crystal Fig.4: VD vs angle with unique axis of crystal Fig.5: Relaxation time vs angle with unique axis of crystal 198 | P a g e Fig.1. Fig.2. 3 3.5 4 4.5 5 5.5 6 0 10 20 30 40 50 60 70 80 90 angle V L ( 1 0 3 m / s e c ) ZnS ZnSe ZnTe CdTe 1 2 3 4 0 10 20 30 40 50 60 70 80 90 angle V S 1 ( 1 0 3 m / s e c ) ZnS ZnSe ZnTe CdTe 199 | P a g e Fig.3. Fig.4. 1.5 2.5 3.5 0 10 20 30 40 50 60 70 80 90 angle V S 2 ( 1 0 3 m / s e c ) ZnS ZnSe ZnTe CdTe 1.5 2 2.5 3 3.5 4 0 10 20 30 40 50 60 70 80 90 angle V D ( 1 0 3 m / s e c ) ZnS ZnSe ZnTe CdTe 200 | P a g e Fig.5. 5 6 7 8 9 10 11 0 10 20 30 40 50 60 70 80 90 angle R e l a x t i m e ( 1 0 - 1 2 s ) ZnS ZnSe ZnTe CdTe 201 | P a g e SOUND VELOCITY AND DENSITY STUDIES TO FIND THE EFFECT OF PEG ON AQUEOUS ANIONIC SURFACTANT (SDS) S. CHAUHAN, R.S. THAKUR and DEEPIKA KAUSHAL Department of Chemistry, Himachal Pradesh University, Shimla-171005. And V.K.SYAL, KIIT College of Engineering, Maruti Kunj, Gurgaon-122018 ABSTRACT Polymer- surfactant formulations are used extensively in industrial, pharmaceutical and cosmetic applications. The versatility in such systems is achieved owing to the reason that polymer– surfactant interactions influence the behaviour of solution significantly and also these interactions can be modified to get the enhanced desired benefits, e.g. polymers are often added to control the rheology of the solution whereas surfactants can cause alterations in wettability, emulsification or solublization properties of the system under investigation. In the present work, therefore, the effect of Polyethylene glycol (PEG-6000), a synthetic polymer, on anionic surfactant i.e. sodiumdodecyl sulfate (SDS) in aqueous solutions has been investigated with the help of density and sound velocity measurements at different temperatures (15, 20, 25, 30 and 35 o C). From the measured values of density and sound velocity, the acoustical parameters namely, Specific acoustic impedance (Z), Intermolecular free length (Lf), Molar sound velocity (Rm) and Relative association (R.A.) have been calculated and their variations with different concentrations of PEG and SDS have been discussed. Interactions of surfactant with polymer have been found to indicate the binding of surfactant with the polymer molecule at lower concentration followed by the usual micellization at higher concentration of surfactant. KEYWORDS: PEG, SDS, Interaction, Sound Velocity and Density. INTRODUCTION Ultrasonic velocity offers a rapid and nondestructive method for characterisation of materials and serves as a powerful, effective and reliable tool to investigate properties of polymer solutions.In continuation with our 202 | P a g e previous work on polymers [1-3], in this paper,we report various acoustical parameters for PEG-SDS system in order to explore polymer- surfactant interactions. EXPERIMENTAL Sodium dodecyl sulfate (Biochemical grade from BDH) was further purified as suggested in literature [4]. Polyethylene Glycol (PEG) molecular weight 6000 (L.R grade) from s.d. fine- Chem private limited was used for this study. Densities and sound velocities were measured from Density and Sound Velocity Analyzer (DSA-5000) supplied by Anton Paar Gmbh, Graz, Austria which measures the speed and density of the solution simultaneously with a resolution of 1×10 −1 ms −1 and 1×10 −6 gcm −3 respectively and was thermostated with in ±0.002°C with Peltier heating device. However, doubly distilled water of conductivity in the range <1-2 X10 -7 Scm -1 was used in all sample preparation. RESULTS AND DISCUSSIONS Density (d) and sound velocity (v) for surfactant SDS in the concentration range (1-15 mmol dm -3 ) have been measured in aqueous solutions of 1, 5, 10 % w/v PEG over wide range (15-35 o C) at interval of 5 o C. The Density (d) and sound velocity (v) data has been reported in Table 1-2. The variation of Rm is non-linear at all concentrations of PEG, however, the marked difference in the of plots reflect that the PEG concentration is also playing important role. At 1% PEG, there is decrease in Rm values up to 5mmol [SDS] and then occurs a significant hump in 6-10 mmol [SDS], after which the Rm value remains almost constant. At 5% PEG solution with [SDS], the Rm value increases initially up to 4mmol [SDS] after which no effect of [SDS] is observed, however, at 10% PEG, the nature of graph shows no regular trend.The variation of Rm plots remains same at different temperatures studied.This difference in behaviour of Rm clearly shows that at lower concentration of PEG, PEG- surfactant interactions dominate and at higher concentration of PEG, polymer-polymer interactions prevail. The variation of R.A with SDS concentration as well as temperature is shown in [Fig 3]. The values of R.A. remain close to unity and show slight increase with the increase of [SDS] content in mixtures. This increase is again due to the fact that the polymer-SDS interactions dominate over polymer- polymer interactions. In case of carbohydrates (fructose and maltose) also,in binary mixtures of DMSO-H2O system at 25 o C, the R.A. values show a regular increase indicating considerable solute-solvent interactions [5]. 203 | P a g e However,on comparing the behaviour of R.A. at different PEG concentrations, a marked non-linear behaviour seems to be quite significant at 6-10mmol [SDS] at 1% PEG. This may be taken as a region of maximum structural changes which may involve micellization to greatest extent. In fact, PEG offers hydrophobic carbon moiety on which micellization of SDS seems to be facilitated and it seems true also as maximum such structural changes are significant in [SDS] range of 6-10 mmol as reflected by Rm and R.A. values at 1% PEG. At higher PEG concentration polymer-polymer interactions dominate. The variation of Lf with SDS concentration as well as temperature is shown in [Fig2]. From these plots, it is observed that Lf decreases regularly with concentration of surfactant but varies in magnitude with temperature. This kind of trend is similar to the behaviour of polymers PEG in AN- H2O mixtures [1] and polyvinylpyrrolidone in DMSO-H2O system at 25 o C [2]. The variation of Z with SDS concentration as well as temperature is shown in [Fig4]. In the plots of Specific acoustic impedance (Z) w.r.t SDS concentration, it is observed that Z is also almost independent of concentration of surfactant but its magnitude increases with increase in temperature and also with concentration of PEG solution. All these parameters collectively show extent of solute- solvent interaction. REFERENCES 1. V.K. SYAL, A. CHAUHAN and S. CHAUHAN ‘Ultrasonic velocity and density studies of poly (ethyleneglycols)(PEG-8,000, PEG-20,000) in acetonitrile (AN) and water (H2O) mixtures at 25 o C.’ J. Pure Appl. Ultrason. 27, 2-3 (2005). 2. V.K. SYAL, A. CHAUHAN and S. CHAUHAN ‘A study on solutions of poly (vinylpyrrolidone) in binary mixtures of DMSO+H2O at different temperatures by ultrasonic velocity measurements.’ Indian J. Phys. 80 (4), 379-385 (2006). 3. V.K. SYAL, A. CHAUHAN, POONAM SHARMA and S. CHAUHAN ‘Ultrasonic velocity and density studies on solutions of Poly(vinylalcohol) (PVA) in binary mixtures of dimethylesulphoxide (DMSO) + water (H2O) mixtures at 25 o C.’ J. Polym. Mater. 22 363-368 (2005). 4. S. CHAUHAN, M.S. CHAUHAN, J.JYOTI and RAJNI ‘Acoustic and viscosity studies of sodium dodecyl sulfate in aqueous solutions of gelatin’ Journal of molecular liquids 148, 24-28 (2009). 5. V.K. SYAL, S. CHAUHAN and R.GAUTAM ‘Ultrasonic velocity measurements of carbohydrates in binary mixtures of DMSO + H2O) mixtures at 25 o C’Ultrasonics 36, 619-623(1998). 204 | P a g e Table 1 Density d (g cm -3 ) for SDS in various aqueous PEG solutions at different temperatures. (T o C) [SDS] ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- (mmol dm -3 ) 15 20 25 30 35 15 20 25 30 35 15 20 25 30 35 1% (w/v) PEG 5% (w/v) PEG 10% (w/v) PEG ----------------------------------------------------------------------- ----------------------------------------------------------------------- ---------------------------------------------------------------------------- 1 1.00089 0.99994 0.99874 0.99730 0.99564 1.00746 1.00636 1.00502 1.00345 1.00168 1.015006 1.013726 1.012219 1.010503 1.008597 2 1.00094 0.99999 0.99879 0.99734 0.99569 1.00750 1.00640 1.00506 1.00349 1.00172 1.015105 1.013828 1.012317 1.010595 1.008685 3 1.00100 1.00005 0.99884 0.99740 0.99574 1.00754 1.00644 1.00510 1.00353 1.00176 1.015171 1.013884 1.012372 1.010652 1.008733 4 1.00105 1.00010 0.99889 0.99744 0.99579 1.00750 1.00640 1.00506 1.00349 1.00172 1.015172 1.013883 1.012369 1.010648 1.008735 5 1.00110 1.00015 0.99894 0.99749 0.99583 1.00762 1.00651 1.00516 1.00360 1.00182 1.015280 1.013989 1.012472 1.010749 1.008832 6 1.00117 1.00021 0.99899 0.99755 0.99589 1.00767 1.00656 1.00521 1.00364 1.00187 1.015230 1.013941 1.012424 1.010702 1.008788 7 1.00116 1.00019 0.99898 0.99753 0.99587 1.00771 1.00661 1.00525 1.00368 1.00191 1.015319 1.014028 1.012511 1.010786 1.008870 8 1.00120 1.00024 0.99902 0.99757 0.99590 1.00780 1.00669 1.00533 1.00376 1.00198 1.015348 1.014055 1.012536 1.010811 1.008895 9 1.00126 1.00030 0.99908 0.99763 0.99596 1.00781 1.00669 1.00534 1.00377 1.00199 1.015457 1.014162 1.012640 1.010913 1.008993 10 1.00139 1.00043 0.99921 0.99776 0.99610 1.00781 1.00670 1.00535 1.00378 1.00200 1.015453 1.014152 1.012637 1.010908 1.008990 11 1.00144 1.00048 0.99925 0.99780 0.99614 1.00787 1.00675 1.00540 1.00382 1.00204 1.015503 1.014205 1.012684 1.010905 1.009034 12 1.00149 1.00052 0.99930 0.99785 0.99618 1.00790 1.00679 1.00543 1.00385 1.00207 1.015438 1.014140 1.012620 1.010892 1.008973 13 1.00154 1.00057 0.99935 0.99789 0.99623 1.00793 1.00682 1.00546 1.00388 1.00210 1.015522 1.014222 1.012698 1.010969 1.009049 14 1.00158 1.00061 0.99938 0.99793 0.99626 1.00802 1.00690 1.00554 1.00397 1.00218 1.015594 1.014295 1.012769 1.011038 1.009116 15 1.00162 1.00066 0.99943 0.99797 0.99630 1.00802 1.00690 1.00554 1.00396 1.00215 1.015613 1.014313 1.012788 1.011056 1.009133 Table 2 Sound velocity v (ms -1 ) for SDS in various aqueous solutions of PEG at different temperatures. 1 1472.85 1488.45 1502.22 1514.21 1524.48 1497.21 1510.97 1523.00 1533.33 1542.04 1526.33 1537.80 1547.69 1555.98 1562.82 2 1473.06 1488.70 1502.48 1514.40 1524.66 1497.23 1511.03 1523.06 1533.36 1542.07 1526.70 1538.03 1547.87 1556.14 1562.95 3 1473.30 1488.66 1502.48 1514.40 1524.66 1497.44 1511.10 1523.10 1533.37 1542.07 1526.74 1538.15 1547.97 1556.22 1563.00 4 1473.38 1488.91 1502.63 1514.52 1524.71 1497.23 1511.03 1523.06 1533.36 1542.07 1526.69 1538.08 1547.89 1556.13 1562.90 5 1473.44 1488.95 1502.65 1514.52 1524.72 1497.51 1511.22 1523.20 1533.45 1542.14 1526.97 1538.34 1548.15 1556.36 1563.13 6 1473.54 1489.06 1502.74 1514.64 1524.82 1497.52 1511.23 1523.19 1533.47 1542.13 1526.76 1538.11 1547.88 1556.09 1562.84 7 1473.72 1489.16 1502.79 1514.59 1524.76 1497.53 1511.25 1523.20 1533.47 1542.13 1526.87 1538.23 1548.00 1556.21 1562.96 8 1473.73 1489.15 1502.76 1514.57 1524.70 1497.76 1511.33 1523.28 1533.55 1542.20 1526.78 1538.11 1547.88 1556.08 1562.83 9 1473.66 1489.07 1502.64 1514.42 1524.55 1497.55 1511.20 1523.11 1533.33 1541.97 1526.93 1538.28 1548.06 1556.25 1562.97 10 1473.79 1489.28 1502.94 1514.78 1524.95 1497.55 1511.19 1523.10 1533.31 1541.96 1526.81 1538.04 1547.78 1555.98 1562.70 11 1473.73 1489.24 1502.90 1514.74 1524.88 1497.58 1511.22 1523.15 1533.35 1542.00 1526.86 1538.17 1547.90 1555.86 1562.78 12 1473.82 1489.21 1502.85 1514.70 1524.84 1497.48 1511.14 1523.06 1533.27 1541.90 1526.55 1537.86 1547.61 1555.79 1562.49 13 1473.78 1489.26 1502.89 1514.70 1524.85 1497.46 1511.06 1522.96 1533.15 1541.77 1526.59 1537.90 1547.63 1555.78 1562.51 14 1473.76 1489.22 1502.86 1514.66 1524.78 1497.52 1511.05 1522.95 1533.18 1541.77 1526.61 1537.91 1547.64 1555.80 1562.51 15 1473.71 1489.18 1502.81 1514.62 1524.51 1497.38 1511.01 1522.90 1533.09 1541.69 1526.61 1537.91 1547.64 1555.79 1562.49 205 | P a g e 0 2 4 6 8 10 12 14 16 -0.70 -0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 R m ( m s -1 ) [SDS] (mol dm -3 ) 1% w/v PEG 15 o C 20 o C 25 o C 30 o C 35 o C 0 2 4 6 8 10 12 14 16 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 [SDS] (mol dm -3 ) R m ( m s -1 ) 15 o C 20 o C 25 o C 30 o C 35 o C 5 %w/v PEG 0 2 4 6 8 10 12 14 16 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 [SDS] (mol dm -3 ) R m ( m s -1 ) 15 o C 20 o C 25 o C 30 o C 35 o C 10 % w/v PEG Fig 1. Molar sound velocity (Rm) (m s -1 ) for SDS in various aqueous PEG solutions at different temperatures. 206 | P a g e 0 2 4 6 8 10 12 14 16 1.0000 1.0001 1.0002 1.0003 1.0004 1.0005 1.0006 1.0007 1.0008 R A [SDS] (mol dm -3 ) 15 o C 20 o C 25 o C 30 o C 35 o C 1%w/vPEG 0 2 4 6 8 10 12 14 16 1.0000 1.0001 1.0002 1.0003 1.0004 1.0005 1.0006 1.0007 R A [SDS] (mol dm -3 ) 15 o C 20 o C 25 o C 30 o C 35 o C 5 %w/v PEG 0 2 4 6 8 10 12 14 16 1.0000 1.0001 1.0002 1.0003 1.0004 1.0005 1.0006 1.0007 R A [SDS] (mol dm -3 ) 15 o C 20 o C 25 o C 30 o C 35 o C 10 %w/v PEG Fig 2. Relative association (R.A.) for SDS in various aqueous PEG solutions at different temperatures. 207 | P a g e 0 2 4 6 8 10 12 14 16 147000 148000 149000 150000 151000 152000 Z ( k g m -2 s -1 ) [SDS] (mol dm -3 ) 15 o C 20 o C 25 o C 30 o C 35 o C 1%w/vPEG 0 2 4 6 8 10 12 14 16 150800 151200 151600 152000 152400 152800 153200 153600 154000 154400 Z ( k g m -2 s - 1 ) [SDS] (mol dm -3 ) 5%w/vPEG 15 o C 20 o C 25 o C 30 o C 35 o C 0 2 4 6 8 10 12 14 16 154800 155200 155600 156000 156400 156800 157200 157600 [SDS] (mol dm -3 ) Z ( k g m -2 s -1 ) 15 o C 20 o C 25 o C 30 o C 35 o C 10 %w/v PEG Fig 3. Specific acoustic impedance (Z) (kg m -2 s -1 ) for SDS in various aqueous PEG solutions at different temperatures 208 | P a g e 0 2 4 6 8 10 12 14 16 4.32E-011 4.33E-011 4.34E-011 4.34E-011 4.35E-011 4.35E-011 4.36E-011 [SDS] (mol dm -3 ) L f ( m ) 1 %w/v PEG 15 o C 20 o C 25 o C 30 o C 35 o C 0 2 4 6 8 10 12 14 16 4.25E-011 4.26E-011 4.27E-011 4.28E-011 4.29E-011 L f ( m ) [SDS] (mol dm -3 ) 5 %w/vPEG 15 o C 20 o C 25 o C 30 o C 35 o C 0 2 4 6 8 10 12 14 16 4.15E-011 4.16E-011 4.17E-011 4.18E-011 4.19E-011 4.20E-011 4.21E-011 4.22E-011 [SDS] (mol dm -3 ) L f ( m ) 10 %w/vPEG 15 o C 20 o C 25 o C 30 o C 35 o C Fig 4. Intermolecular free length (Lf) (m) for SDS in various aqueous PEG solutions at different temperatures. Journal of Acoustical Society of India The Refereed Journal of the Acoustical Society of India (JASI) CHIEF EDITOR CHIEF EDITOR Mahavir Singh Mahavir Singh Acoustics Section Acoustics Section National Physical Laboratory National Physical Laboratory Dr. KS Krishnan Road New KS Krishnan Road Dr. Delhi 110 012 Tel +91-11-45609319 New Delhi 110 012 Fax +91-11-45609319 Tel +91-11-45609319 E-mail:
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[email protected] The journal and all articles and illustrations published herein are protected by copyright. No part of this journal may be translated reproduced stored in a retrieval system or transmitted in any form or by any means electronic ,mechanical, photocopying, microfilming recording or otherwise, without written permission of the publisher. Copyright @2007, Acoustical Society of India ISSN 0973-330 Printed at Alpha Printers BG-2/38C Paschim Vihar, New Delhi-110063 Tel:9811848335, JASI is sent to ASI members free of charge. 2|Page MAHAVIR SINGH Chief Editor OMKAR SHARMA Managing Editor TRINATH KAR Associate Scientific Editor Youdhishter kumar Anil Kumar Nain Assistant Editor Naveen Garg Assistant Editor EDITORIAL BOARD M L Munjal IIsc Banglore India S Narayanan IIT Chennai India V Rajendran KSRCT Erode India R J M Craik HWU Edinburg. UK Trevor RT Nightingle NRC Ottawa, Canada B V A Rao VIT Vellore, India P Narang NMI Lindfield, Australia E S R Rajagopal IISc Banglore, India V Bhujanga Rao NSTL Vizag, India AL Vyas IIT Delhi, India V Bhujanga Rao NSTL Vizag, India Yukio Kagawa NU Chiba Japan S Datta LU Loughborough UK Sonoko Kuwano OU Osaka Japan KK Pujara IIT Delhi (Ex) India AR Mohanty IIT Kharagpur India Ashok Kumar NPL New Delhi India V mOhanan NPL New Delhi ,India 3|Page Sound Transmission through Building Enclosures The article deals with sound transmission through building enclosures including different forms of predominantly lightweight wall construction. It gives guidance on how walls comprising a number of separate element can be assessed. Sound transmission from outside to inside the reader should also see BS EN 12345-4:2000 if they are concerned with containment of sound within a building. The performance of a wall or roof has to be considered in terms of the internal spaces. The aim is to provide a building envelope that gives the required sound pressure levels within a room or other internal space. The noise level within a room will depend on the amount of sound energy transmitted through the wall and interreflection of sound inside the room. The room effect is usually determined by the amount of sound absorbing material in the room. Sound transmission of an assembly of components can be calculated provided the wall can be analysed as discrete areas for each of which the Sound Reduction Index is known. This applies to windows in walls and collections of windows but note that sound transmission through interface components such a joining mullions between windows may not be known. Sound transmission through a whole wall Is established by calculating an apparent sound reduction index (SRI) for the wall. This is used to determined the difference in sound between the outside and inside. The procedure is to calculate the sound power reduction for each element of the wall. The total sound power reduction can then be calculated and converted to an apparent reduction index. When sound of intensity 1W/m2 falls on a wall the sound power (in watts) transmitted by an element is given by: Wi =Si 10 Where Si is the area of an element (m2 ) Ri is the sound reduction Index of that element (dB) (Mahavir Singh) 4|Page Mathavan.S.R. Samathab Study of Solvation number and related parameters of Ammonium bifluoride in non-aqueous medium A. Megala & T.K. X.E. & Lavanya. M. R Thermo .Vivekanandam Ultrasonic investigations of n-methylpyrrolidone in 1-propanol T.A. 8-13 14-19 20-22 23-27 28-33 34-38 39-44 45-50 51-56 57-62 63-69 70-76 77-82 83-88 5|Page . J.Gokila.S. J. V Apparaoa. S. Ravidhas Ultrasonic studies of nn'-methylene bis-acrylamide in water T.A.Vivekanandam Determination of ultrasonic interaction parameter for Poly (acrylic acid) in water T. V.Valarmathi & T. S. E.Mathavan.Jothi Rajan.S. G.Abirami. Ethanol with Ethylacetoactate P.N Ultrasonic investigations of peg (400) in toluene-clay mixture T. G. Bharathi & K.V Ramaraob. Beulah Mary. Bharathi & K. A.Umapathy. Padmavathi.acoustic and spectroscopic study of polymer salt in nonaqueous medium using ultrasonic velocity Jasmine Vasantha Rani. Beulah Mary.Johnson A comprehensive analysis of solvation number of some organic acid salts in non. Paul Divakara. I.A. M. Radha. Armstrong Arasu & Dr.Umapathy.M.Stephen Raja & T.A. Nagarjuna. R.Hemalatha & T.H.aqueous medium Jasmine Vasantha Rani E & Suhashini Ernest Ultrasonic study on binary mixtures of ethyl benzoate with benzene and substituted benzenes at different temperatures B. C.Rakini Chandrasekaran. A.Jothi Rajan.Jothi Rajan. Alfred Nobel Antony. M.Johnson Study of Thermo Acoustical Parameters of Some Binary Mixtures from volume Expansivity Data M. G. Seethalakshmi.S. M. Jasmine Vasantha Rani.Vivekanandam A study of solvation effect of some sodium salts in non-aqueous medium using ultrasonic velocity Padmavathy.V. M.Dravida Selvi.Hakkim. S.V Sarmaa & C. R. Mathavan.Umapathy.Ganthimathi Effect of electronegativity on free volume and vanderwaals constant of binary and ternary liquid mixtures K.H. Armstrong Arasu & Dr. S.N.Vivekanandam Acoustical Study on Thermo dynamical and Excess parameters of binary and ternary mixtures M.1 2 3 4 5 US-1 US-2 US-3 US-4 US-5 6 US-6 7 US-7 8 US-8 9 10 11 12 13 14 US-9 US-10 US-11 US-12 US-13 US-14 Velocity and Thermodynamic properties of Binary liquid mixtures of Methanol. Kannagi. K.Umapathy. M. Y.Mathavan.Dolour Selvarajan. K & Rahmathunnisa.Jothi Rajan.Rakini Chandrasekaran. I. B.Ganthimathi Study of Internal pressure and Equivalent conductance of solutions of calcium fluoride in non-aqueous medium A. J. S. VIJAYALAKSHMI. Madhusudhanacharyulua & Mrs. A.M. S. Gunavardhan Naidu. Bhawana S.Rajendra . T. Acetyl acetone and butanols with carbon tetrachloride (CCl4) T. T. Nath & R. Jayakumar S & Kannappan V Characterization of Nanofluid of Platinum Virendra Kumar. K. and D. Singh and S. Kailash and Bharat Singh Temperature Dependence of Ultrasonic Attenuation in Strontium Oxide Crystal Kailash. Tripathi. Kumar R. K.15 16 17 US-15 US-16 US-17 18 US-18 19 20 21 22 23 24 25 26 27 28 29 30 US-19 US-20 US-21 US-22 US-23 US-24 US-25 US-26 US-27 US-28 US-29 US-30 Rambabuc Study of non linear parameter (b/a) and thermo acoustic parameter of binary mixture at different frequencies G.D. S.Karunamoy. Shrivastava & Jitendra Kumar Molecular radii of Pyridine/quinoline with phenol in benzene using acoustical methods at different temperatures Anjali Awasthi. Gupta Ultrasonic Wave Propagation in Refractory Materials Devraj Singh . K. Shrivastava & Jitendra Kumar High Temperature Study of Anharmonic Properties of TeO Kailash. P. K Dash.Brahmajirao . Kailash and Jitendra Kumar Ultrasonic Behaviour of Mixed Crystals Virendra Kumar. T. P.Nayak & B B Swain Glueckauff’s model for lowering of dielectric constant of electrolytic solutions & Isentropic Compressiblity Studies with aqueous electrolytic solutions using Ultrasonics –IONS PAIRS (CHLORIDES) V. N.Brahmajirao . Tripathi & Aashees Awasthi Ultrasonic and theoretical study of binary mixture of DEHPA(Di-(2ethyl-hexyl) phosphoric acid) with n-hexane at different temperatures Sujata Mishra & Rita Paikaray Acoustical Studies of Molecular Interactions in Binary Liquid System of Cinnamaldehyde and N-N Dimethylaniline at 303 K Padmanabhan G. Ravi S.K. S. Virendra Kumar.Srikanth . S.Srikanth & Shanaz Batul Glueckauff’s model for lowering of dielectric constant of electrolytic solutions & Isentropic Compressiblity Studies with aqueous electrolytic solutions using Ultrasonics –IONS PAIRS (SULPHATES) V. Jitendra Kumar & Virendra kumar Orientation Dependence of Ultrasonic Attenuation for Calcium Oxide in High Temperature Range Kailash. Gunavardhan Naidu . Sahu Ultrasonic Wave Propagation in II-VI Hexagonal Semiconductor 89-94 95-100 101-110 111-121 122-128 129-133 134-138 139-143 144-149 150-155 156-163 164-169 170-175 176-181 182-188 189-200 6|Page . Yadawa. Rajiv K. K. S. T. Shrivastava & Poonam Yadav Ultrasonic Study of some Organic Pathological Compounds Kailash. S.Rajendra & Shanaz Batul Tempareture variation of velocity in cow milk at different Ultrasonic frequencies Kailash. Paikaray Thermo-acoustic Studies on Ternary Mixtures of Methyl Iso-butyl Ketone. P. THAKUR 201-208 7|Page . CHAUHAN & R. M.S.S.31 US-31 Compounds Pramod Kumar Yadawa & Devraj Singh Sound Velocity And Density Studies To Find The Effect of PEG on Aqueous Anionic Surfactant (SDS) S. CHAUHAN. Visakhapatnam – 530 003 Professor. Samatha # # * Research Scholars. INTRODUCTION: The ultrasonic velocity measurements are very important and playing vital role not only in characterizing the behaviour of liquid mixtures but also in the study of molecular interactions. free length etc. Andhra University. KEYWORDS: Adiabatic compressibility. Department of Physics. ETHANOL WITH ETHYLACETOACTATE AS COMMON SOLVENT P. Department of Physics. Paul Divakar *. and their excess values so as to relate them towards explaining the molecular interactions and hydrogen bonding taking place between the components of the binary liquid mixtures [1-5]. free volume. Visakhapatnam – 530 003 email: putla_paul@yahoo. Free volume. inter molecular free length. density(ρ) and viscosity(η) measurements were made in two binary liquid mixtures for methanol and ethanol with ethylacetoacetate as a common solvent at 303. molar volume and enthalpy. Madhusudanacharyulu* and Mrs. Most of the work on binary mixtures is channelized towards the estimation of thermodynamic parameters like adiabatic compressibility. 308. Andhra University. 8|Page .co. Internal pressure.. In recent times ultrasonic velocity has been adequately employed in understanding the nature of molecular interaction in pure liquids and binary mixtures. 313 and 318 K with increasing mole fraction of ethylacetoacetate using single crystal variable path ultrasonic interferometer at 2 MHz frequency. K. A. The excess values of the above parameters have been evaluated and discussed in the light of molecular interactions.S. The experimental data have been used to calculate adiabatic compressibility. Inter molecular free length.VELOCITY AND THERMODYNAMIC PROPERTIES OF BINARY LIQUID MIXTURES OF METHONOL. Molar volume and Enthalpy. internal pressure.in ABSTRACT: Ultrasonic velocity(U). R is a gas constant and T absolute temperature K is the temperature dependent constant is equal to 4. Mittal enterprises) at 2 MHz frequency with an accuracy of ±0. 636×10 and 640.28 X109 for all liquids.01kg/m. An Oswald viscometer (5ml) was used for the viscosity measurements and efflux time was determined using a conventional stop-watch. intramolecular interactions and also hydrogen bonding. 308. THEORY AND CALCULATIONS Various Physical and thermo dynamical parameters are calculated. The excess values are made to use for the explanation of the intermolecular interactions.e. ultrasonic velocity. (1) Adiabatic Compressibility βad = 1/(ρU2) cm2 / dyne (2) Intermolecular free length Lf = k( βad )1/2 A0 where k is a temperature dependent constant.The present study involves the binary mixtures of methanol and ethanol with ethylacetoacetate of various mole fractions at four different temperatures 303. η is the viscosity. 313 and 318K.1K.01%. density and viscosity of the mixtures. 318 K. The densities and viscosities were measured and compared at the working temperature with the corresponding literature values. 631. A constant temperature bath has been used to circulate water through the measuring cell made-up of steel containing the experimental liquid at the desired temperature with an accuracy of ±0. The weight of the samples were measured using a single pan balance (electronic. (4) Internal Pressure Πi = bRT (Kη/U)1/2 [ (ρ)2/3 / (Meff)7/6] dynes / cm2 where b is the cubic packing which is assumed to be 2 for all liquids and solutions. EXPERIMENTAL DETAILS: The chemicals used in the present work are AR grade of purity 99% from EMerck. The densities were measured using specific gravity bottles by relative measurement method with accuracy of ±0. Keroy).. Speeds of sound measurement were made with a single crystal variable path ultrasonic interferometer (Model F-81. (3) Molar volume V = Meff /ρeff cm3 / mole where Meff is the molecular weight of the mixture in which Meff = ∑ mi xi where mi and xi are the molecular weight and the mole fraction of the individual constituents respectively.5×10 respectively at 303.5×10 . 308. The excess values of some acoustical and thermo dynamical parameters have been calculated from the experimentally measured values i. 313. Its values are 627×10 . 9|Page –6 –6 –6 –6 . 9 1164.0381 0.0189 1.0 1144.7239 0.9273 0.8 1169.6692 0. RESULTS AND DISCUSSIONS The experimental values of ultrasonic velocity.8978 0.98 1303.7806 0.8610 0.6 1092.9297 0.8299 0.9138 0.9416 1.7676 0.6681 0.8 1247.8932 0.7668 0.9499 0.2546 0.2 1195.3482 0.9 1107.0692 1.5481 0.1 1184.9769 1.8567 0.43 1168.1131 1.85 1048.0000 0.8650 0.4345 0.5571 0.8911 0.00 System II : Ethanol + Ethylacetoactate 303K 308K 313K 318K 1132.4756 0.8208 0.0 1245.24 1204.8587 0.0157 1.7 1153.5940 0.8 1159.9900 1.8929 0.7726 0.8072 0.0281 1.00 1253.63 1135.9870 318K 0.0 1238.8540 0.4236 0.6 1199.0 1209.9373 0.8083 0.8964 0.9 1142.9685 0.69 1251.8643 0.5275 0.7718 0.Aid Where Aid = ∑ Ai xi where Ai is any acoustical parameter and xi is the mole fraction of the liquid component.1 1135.0540 1. 313 and 318K are given in Table 1.7951 0.9629 0.8443 318K 0.0914 1.7998 0.5110 0.4 1255.9373 0.8704 0.1 1231.9719 0.1230 1.2626 0.0936 1.6073 0.8583 0.8418 0.7656 0.8653 0.(5) Free volume Vf = ( Meff U / Kη )3/2 cm3 / mole (6) Enthalpy H = ΠiV cal / mole Excess values of the above parameters can be evaluated using AE = Aexp .7200 0.6181 0.3 1055.0 1160.1298 ρ x 103 gr/cm3 308K 0.9 1093.4747 0.1324 0. Density (ρ ) and viscosity(η ) for mole fraction X of ethylacetoacetate X System I : Methanol +Ethylacetoacetate U x 104 cm/sec 303K 308K 313K 318K 1088.8334 0.0366 1.7420 0.7 1274.0 1286.3 1211.9630 0.26 1108.9819 0.8073 0.8276 0.9250 313K 0.2 1152.9531 0.9843 0.0816 1.8251 0.8373 0.0058 1.0 1260.4478 0.6 1132.9 1105.0000 10 | P a g e .0192 313K 0.4 1181.7 1221.9670 0.0192 308K 0.9960 308K 0.9750 303K 0.9360 0.20 1097.9192 0.7796 0.8994 0.0 1270.4 1193.1919 0.8471 0.7809 0.2 1098.6 1067.6 1123.20 1151.1298 303K 0.7839 0.53 1089.1076 1.7605 0.34 1188.0000 X 0.7976 0.1135 0.8871 0.6940 0.7709 0.4889 0.0 1172.9704 1.0 1152.0 1220.4548 0.32 1074.7 1186.0 1250.8218 1.8826 0.7931 0.01 1215.8243 0.9870 313K 0.1 1116.5876 0.9761 0.9075 0.0522 1.0621 1.8650 0.8530 0.9075 0.0828 1.8127 0.1 1270.9 1210.6617 0.6411 0.9250 318K 0.9222 0.8783 0.8181 0.0000 0.9960 313K 0.0 1252.8389 0.1180 0.8970 0.8228 0.4 1080.9 1172.0 1236.9543 0.3 1303.9562 0.5 1080.9156 0.0 1253.3387 0.6720 0.8443 0.4539 0.30 1034. Table 1 : Values of Ultrasonic Velocity(U).0 1225.68 1123.9067 0.75 1143.0480 1.8224 0.5 1070.9424 0.8870 0.9090 0.9340 0.0 1194.8791 0.7622 1.6 1235.9019 0.0025 1.0 1229.8 1141.8383 0.17 1120.15 1169.7750 0.9124 0.9856 1.8199 0. The excess values of acoustical and thermo dynamical parameters are presented in tables 2-3.52 1061.0 1178.1391 303K 0.7670 0.7763 0.9502 0.3 1119. 308.5709 0.1082 1.9577 0.9720 0.13 1105.4968 0.5124 0.6140 0.9949 1.9020 0.8795 0.0539 0.8037 0.9750 318K 0.1391 η centi poise 308K 0.8 1197.7881 0.6 1267.9184 0.9785 0.5445 0.9902 0.2 1139.0 303K 0.9750 0.4 1235.9366 0.8313 0.0 1286.8285 0.5548 0.7190 0.9083 0.0 1212.8370 0.9470 0.0818 0.8358 0.7928 0.8 1081. density and viscosity for the two binary liquid systems at 303. 6720 0.0000 318K 0.882 -2.0000 -0.446 -15.011 -0.636 -5.0000 0.0000 -0.874 -19.528 -1.330 -0.185 -1.642 -1.583 -11.650 0.119 -1.88 -13.048 -0.0000 303K 0.0000 308K 0.023 -0. Table 2: Excess values of adiabatic compressibility (βad E ) .09 -12.531 -9.030 -0.343 -1.033 -0.0381 0.638 -2.0000 with mole fraction concentration of ethylacetoacetate confirmed the increase of cohesive forces because of strong 0.024 -0.0000 -0.999 -2.406 -1. The linear increase in molecular interactions.4969 -5.1180 0.042 -0.1324 0.568 -1.328 -6. excess free length.0000 313K 0.862 -2.887 -20.469 -8.0000 -0.0000 -0.359 -2.014 -0.359 -8.688 -1.0000 0.517 -2.746 -1.880 -15.900 0.0000 -0.0539 0.665 -1.056 -10.350 -0.091 -6.038 -6.741 -2.0000 -0.039 -0.039 -0.048 -3.120 -2.718 -2.0000 318K 0.19 -10.2626 0. In order to substantiate the presence of interaction it is essential to study the excess parameters such as internal pressure.4345 0.909 -2.027 -0.4539 0.311 -8.493 -2.107 -2.The ultrasonic velocity values increases with increase in concentration of ethylacetoacetate in both the systems.605 -2.031 -0.036 -0.063 -0.117 -5.0000 313K 0.400 -2.039 -0.052 -0.020 -0.05 -8.026 -0.073 -0.465 -1.985 -15.384 -8.066 -0. Moreover it has been decreasing with increase in temperature for both the binary systems.985 -10.464 -4.0000 0.0000 0.260 0.430 -2.998 -11.5445 0.035 -0.973 -2.15 -10.0000 0.260 -15.605 -14.250 0.631 -2.8218 1.0000 -0.025 0.121 -17.046 -1.654 -2.0000 -0.620 -1.036 -0.0000 313K 0.325 -11.0000 0.0000 318K 0.50 -10.3387 0.63 -10.0000 318K 0.0000 0.041 -0.710 0.038 -0.454 -7.821 -2.221 -15.16 -12.062 -0.184 -1.056 -1.0000 -0.95 -12.855 -6.063 0.059 -0.047 -0. and excess molar volume.033 -0.017 0.040 -0.023 -1.326 -1.243 -20.0000 0.030 -0. An increase in the ultrasonic velocity with increase in concentration appears to be associated with an overall increase in the cohesion in both the systems.011 -0.86 -12.701 -2.892 -2.463 -11.051 -0.024 -0.052 -0.028 -0.785 -2.036 -0.022 0.575 -22.104 -4.0000 0.271 -9.511 -1.962 -4.023 -0.111 -9.0000 -0.014 -0.052 -0.0000 313K 0.08 -11.45 -8.750 -19.418 -16.241 -1.2546 0.010 -8.562 -11.016 0.017 0.018 -0.427 -3.036 -0.0000 System II: Ethanol +Ethylacetoacetate 303K 308K 313K 318K 0.067 -0.0000 303K 0.682 -1.034 -0.039 -0.466 -13.249 -2.759 -16.720 -2.873 -1.071 -0.0000 303K 0.710 -1.028 -0.035 -0.662 -1.024 -0.0000 -5.58 -13.053 -0.661 -2.1919 0.14 -13.026 -0.891 -2.7622 1.0000 VE cm3 / mole 308K 0.030 -0.212 -23.031 -0.891 -2.0000 -0.580 -21. free volume and enthalpy apart from excess adiabatic compressibility.025 0.680 -2.032 -0. The viscosity values from observations are regularly increasing without having any maxima with the increase of mole concentration of ethylacetoacetate at all the temperatures..907 -2.815 -13.0000 X 0.1135 0.0000 -3.730 -1.510 -1.128 -9.849 -2. Free length ( LfE ) and Molar volume (VE) for mole fraction X of ethylacetoacetate X System I : Methanol +Ethylacetoacetate βadE cm2/ dyne 303K 308K 313K 318K 0.343 -2.0000 0.404 -6.639 -1.610 -12.0000 0.0000 LfE x10-8 cm 308K 0.521 -7.0000 0.0000 0.035 -0.037 -0.516 -12.028 -0.0000 308K 0.760 -2.4241 0.590 0.3482 0.675 -2.0000 -0.5876 0.033 -0.0000 -1.249 -11.0000 0.0000 303K 0.042 -0.992 -11.013 -0.980 0.038 -0.684 -2.019 0.674 -2.83 -11.106 -2.929 -8.689 -7.030 -0.020 -0.0000 -0.030 -0.146 0.0000 -0.040 -0.018 0.0000 11 | P a g e .0818 0. 638 -2.3286 -1.9 -922.0469 -0.0000 318K 0.4828 -0.7 -593.6 -1090. -1508 -1402.0000 X 0.0000 0.0000 -528.7622 1.20 0. it reaches negative maximum till the mole concentration reaches 0.The excess adiabatic compressibilities (βadE) are negative as observed for both the systems.5135 -1.4539 0. i..1653 -1.0000 318K 0.5900 0.5 0.0000 -0. -1334.8202 -1.0000 0.4 -813.4331 -0.6 -1073.980 -0.5736 0.520 -2.637 -3.0000 -1200 -3189 -6017 -9643 -13791 -17789 -20200 -18506 -9867 0.0 -1204. It indicates strong molecular interactions in liquid mixtures. -1163.0000 303K 0.2186 -0. free volume (VfE ) and Enthalpy( HE) for mole fraction X of ethylacetoacetate System I : Methanol +Ethylacetoacetate X ΠiE dyne / cm2 303K 308K 313K 318K 0.0000 318K 0. In the present case the mutual breaking of hydrogen bonds in alcohols with ester leading to decrease in free lengths in the mixture contributing to negative deviation in the adiabatic compressibility for both the systems.8 -1360.823 -1.0000 12 | P a g e .0000 313K 0. -997.0000 303K 0.8218 1.3 -409.2759 -0.0000 -11165 -19182 -24007 -25761 -24886 -22211 -18919 -16055 -12673 0.0000 318K 0.761 -2.0648 -0.5 -1277.0000 -16409 -27899 -34394 -36088 -33692 -28563 -22713 -18179 -14427 0. -1558 -1529.0000 313K 0.0539 0.0000 0.0000 0.0818 0.08 0.836 -2.17 -1119.015 -2.1 -1264.287 -1.0000 -0.4345 0.2115 -0.40 -1202.0000 -520.08 -932.0000 VfE cm3 / mole 308K 0.3697 -1.5510 -0.1255 -1.543 0.e.0000 -7157 -12313 -15046 -15011 -12126 -6940 -1275 -1131 -36470 0.0000 -7674 -14182 -19365 -23031 -25010 -25165 -23357 -19350 -12394 0.366 -0.5 (approx) then again begins to increase as the mole fraction increases.9 -932.2134 -0.636 -1.941 0.5876 0. -1378 -1259.4459 -0.0381 0.734 -1.5177 -1.150 -0.5 0.070 -0.3387 0.7 -895.335 -1.0522 -1. -1487 -1498.0000 -0.7 -841.5 1289.3 -946.1884 -0.9 -1031.7 -1101.81 -874.83 -640.0000 0.0000 313K 0.1 -337.7548 0.7032 -0.al [6] suggested that the negative excess values have been due to closely packed molecules which account for strong molecular interactions Table 3: Excess values of Internal pressure (ΠiE ).al [2] found that the negative values of excess compressibilities indicates greater interaction between the components of the mixtures.10 -526.1324 0.0000 -0.444 -0.462 -2.4 -393.765 -1.0000 308K 0.6720 0.0000 0.2 -1166.0494 -1.67 -1206.0 -652.0000 0. -1294 -1311.6 -875.6 -1122.9 -887.0000 -0.2 -586.8 -1347.394 -0.90 -924.0000 -0.162 -1.1925 -1.0000 303K 0.7403 -1.5445 0.6715 0.0000 -2712 -6128 -10205 -14765 -19322 -22911 -23743 -19096 -7077 0.2546 0.0000 -0.470 -3.306 -1.4285 -1.0000 308K 0.0000 313K 0. Sridevi et.0000 System II: Ethanol +Ethylacetoacetate 303K 0.0000 -0.6 0.0 -781.9787 -1.0000 -784 -2022 -3731 -5870 -8246 -10421 -11507 -10017 -4546 0.0000 -17579 -29612 -36064 -37230 -34024 -28108 -21903 -17808 -15102 0.1135 0.0000 -453.6 -633.074 -2. The excess adiabatic compressibilities are not only negative but also vary non-linearly with increase in temperature. -834.870 0.905 0. -1509 -1437.048 -1.0000 0.8166 -1.0000 308K 0. -1392 -1420.9 -1375.261 -1.5 -357.1180 0.0 -905.1942 -0.1 -897.116 -1.1919 0. So the βadE is associated with a structure forming tendency.0000 -181. -1350 -1252.7 -1092.0000 318K 0.3716 -1.0000 -346.2495 -0.0000 0.26 -596.208 -1.3 -1275.9 -1351.4883 -1.18 -1037.2626 0.8 -1122.113 -3.0000 HE cal / mole 308K 0.379 -1.8 -738.283 -0.0000 313K 0.3482 0.0000 303K 0. Fort et.0632 -0.2530 -1.716 -2.521 -1. weakening of intermolecular forces between the components. The excess molar volumes also exhibit a similar trend as that of VfE and are in good agreement with the aforesaid observations. Hence it represents the existence of greater interactions. NY (1977) U. 2102 (1965) S..Kasare and B. Also the LfE decreases with increase in the mole fraction of ethylacetoacetate.Pal and Anil Kumar J. 1 (2004) J N Spencer.32 (2005) 13 | P a g e . 2.Eng.al 2 noticed that the negative VfE trend is due to decrease in the strength of the interaction between the unlike molecules. 2950 (1929) R. Pure & Appl. Samatha. The excess free volume (VfE) values are found to be negative for both the systems studied over the entire mole fraction range and at all the temperatures.Patadi. This ascribes dominant nature of hydrogen bond interaction between unlike molecules. In the present study the excess internal pressure (ΠiE )for both the systems shows negative values and reaches a maximum at middle concentration as mole fraction of ethylacetoacetate goes on increasing . Pure & Appl. Phys 25. Chem. of Phys.. The negative deviation of high magnitude of VfE and negative values of ΠE and HE indicate the existence of strong interaction such as hydrogen bond formation between hetero molecules in both the systems.al [7] have also reported a similar observation on the basis of excess values of free length.chem. 8. Chem. Indian J.e. Kinocid. K.R.Moore. 760 (2000) Y Marcus. Data 50. Fort et. CONCLUSION The excess parameters of non-ideal binary mixtures have been satisfactorily used in explaining the extent of interactions between mixing components [8. Chem. 4.J. i. A Viswanadha Sarma.Faraday soc. 61. Ultras 26. Moreover the ΠiE values increases with increase in temperature.Soc. The excess values of enthalpy( HE) are negative for both the systems over the entire mole fraction range is observed. Sridevi. Wiley-inter science. Indian Coun.A. pure & Appl.Forte and W. References: 1. This trend shows a pre-dominance of repulsive forces. E Jeffery & C Robert J. 7. 5. 180 (1987) Mehra. 9. 83. This negative trend of HE indicates that strong interaction between the unlike molecules besides dipole-dipole interactions are predominant.B. 1249 (1979) A. These conclusions are good in agreement with those parameters derived from ultrasonic measurements. Spencer et. J.K Sanjami. Indian J. 3.The excess intermolecular free length (LfE) is negative at all temperatures over the entire composition range for both the systems. 9]. 856 (2005) Rita Mehra and Pancholi J. Am. S1. 6. 22 . Trans. Phys 38. J. Introduction to Liquid state Chemistry. Pudukottai. density and ultrasonic velocity through the non-aqueous solutions of various concentrations are measured at different temperatures ranging from 35°c to 55°c. Holy Cross College. Department of Physics. disturb the equilibrium between the solute and solvent molecules. 14 | P a g e . For such study. Bharathi2. Govt. 2.From Adiabatic compressibility. Department of Physics. Beulah Mary1. molar solvated volume.H. INTRODUCTION Study of non-aqueous solutions of electrolytes is interesting for the physical understanding of the ion-solvent interactions. A primary solvation number can be defined as the number of solvent molecules. and Apparent solvated volume are calculated. 1. It can also be defined as the number of solvent molecules. These parameters provide the sufficient information about the interaction between the ions and molecules of solvent. Ultrasonic velocity measurement is used to throw light on various aspects of solvation chemistry including ion-ion and ion-solvent interactions. which are aligned in the force field of the ion. Tiruchirappalli. solvation number and its related parameters namely Apparent molal compressibility.STUDY OF SOLVATION NUMBER AND RELATED PARAMETERS OF AMMONIUM BIFLUORIDE IN NON-AQUEOUS MEDIUM A. Arts College. In the present study. The forces will cause some of the solvent molecules to break away from the solvent network and attach themselves to the ion [1]. Bishop Heber College. ABSTRACT The passage of ultrasonic waves through liquids. computation of solvation number for Ammonium bifluoride in Dimethyl sulfoxide is undertaken for highlighting the existing interactions. Department of Physics. Apparent molal volume. which have surrendered their own translational freedom and remain with the ion when it moves relative to the surrounding solvent. KEY WORDS: Adiabatic compressibility. apparent molal compressibility. Apparent molal volume.Ganthimathi2 and J. molar solvation number. G.Hence the variation of all these parameters with respect to temperature and concentration are analyzed. K. Tiruchirappalli. All these parameters are temperature and concentration sensitive . 3. Rakini Chandrasekaran3 1. the solvent molecules can break out of the solvent network and enter interstitial space due to the close packing. EXPERIMENTAL STUDY Dimethyl sulfoxide solutions of various concentrations upto saturation of Ammonium bifluoride are prepared with AnalaR grade substances. solvent molecules are wrenched out of the solvent framework so as to envelop themselves with solvent sheaths. on the introduction of ions into the solvent. The origin of the influence of the ion is the electric field of the ion. Thus the electric field causes compression of the material upon which they exert their influence.Solvent has been described as having an open framework structure with many holes in it. the solvent is more packed in primary solvation sheath as compared to the packing if the ion were not there. It is calculated using the relation (4) φv = V1 [N n'h / n1 . Ultrasonic velocity of the solution is measured with a Mittal type ultrasonic interferometer with an accuracy of ±2m/s. From the adiabatic compressibility (β). When pressure is applied. 2. Because the molecules are oriented in ionic field.(3) where n₂ʹ is the total molal concentration of the solution and N´ is the number of moles of solvent in 1000 g It is also computed by the traditional method using the equation. The temperature is maintained from 35˚C to 55˚C with an accurate thermostat.βN/ βo ] / n2 -----(2) where βo is the compressibility of solvent.(4) -------------------. The density of the solution is measured with 10 ml specific gravity bottle. due to the phenomenon known as electostriction [2]. 15 | P a g e . The adiabatic compressibility can be computed using standard relation as given below: β = 1/ (u 2 ρ) ---------------------. CALCULATIONS The simplest but accurate method of determining the adiabatic compressibility is through ultrasonic study [3].β/βo] N' / n2' of the solvent. In addition to this. the volume decreases. The molal solvation number nh' has been computed through Passynsky’s [6] equation nh '= [1 . 3.nh] -------. The apparent molal volume of the solution (φv) is defined as the volume of the solution containing one mole of the solute minus the volume of the solvent. the solvation number (nh) can be found [4]. n1 is the number of moles of the solvent present in 1000 cc of solution of molar concentration n2 and N is the number of moles of the solvent in 1000 cc of the solvent.(1) The molar solvation number is calculated using Barnartt’s [5] relation nh = [ n1 . 6827 4.6268 4.The value of solvation number decreases with temperature upto 50⁰C and then increases to a higher value at 55⁰C.716 -67.5 0.V1 βo nh -------.6014 5. apparent molal compressibility.2352 4.(6) and the traditional equation. It is calculated from the following equations φs = φv + nh V1 φs = V (β – β0) / n2 β0 4.9958 4.Positive Solvation number suggests that compressibility of the solution will be less than that of the solvent.5055 9.731 -48.2 0.202 -59. apparent molal volume and molar solvated volume of Dimethyl sulfoxide solutions of Ammonium bifluoride are given in Tables 1-2.(7) The molar solvated volume (φs) is defined as the volume of the solvated part that comprises the solute and bound solvent.032 -62.2993 .3 0.716 -67.202 -59.1655 9.032 -62.4001 3. Table No. φk = [1000 (ρo β – βo ρ ) / n2 ρo ] + M2 βo / ρo ---------.4167 6.239 -48.1 Molar solvation number and Apparent molal volume of NH₄HF₂+DMSO System Temparature ⁰c Molality n₂' nh nh' Фv*10^6 m³/Mole By Equation(4) -63.(5) The apparent molal compressibility is the compressibility of an amount of solution containing one mole of the solute minus the compressibility of the solvent. RESULTS AND DISCUSSION: The computed values of solvation numbers. A gradual decrease of Solvation number from lower to higher concentrations is observed standing in agreement with the statement ‘the more dilute the solution the greater the solvation of the ion’ [7].9281 3.885 16 | P a g e --------.1 0.239 -48.2182 10.4 0. The values of apparent molal compressibility.(9) 35 40 0. apparent molal volume and molar solvated volume calculated using solvation number and traditional formula are found to be in agreement.731 -48.1 10.(8) ------.φv = [1000 (ρo -ρ ) / n2 ρo] + M2 / ρo -----. Solvation number is found to decrease with concentration.885 Фv*10^6 m³/Mole By Traditional method -63. It has been calculated using the relation (6) φk = . 999 -34.681 -63.5 0.0664 9.51 402.171 -61.281 -1.92 386.475 -1.1 0.3735 3.1041 4.4 0.2 0.4261 4.253 -56.5 0.9907 4.5187 4.5 0.727 -59.22 276. The decrease in the apparent molal volume suggests that there is strong ion-ion interaction and increase in apparent molal volume with respect to concentration supports the solute-solvent interactions.3 0.037 -61.253 -56.2 Apparent molal compressibility and Molar solvated volume of NH₄HF₂+DMSO System Temparature ⁰c Molality n₂' Фk*E7 m³ By Equation(6) 35 0.001 -59.41 245.8497 3.329 -3.1 0.477 -60.7246 5.4337 4.9032 4.8912 4.8899 4.8257 3.0015 5.4 0.1 0.577 Фs*10^6 m³/Mole By Equation(8) 689.001 -59.1116 8.281 -1.964 -1.6692 3.924 -59.999 -34.2 0.956 -59.1033 4.4 0.3 0.681 -63.2 0.4 0.6505 4.2455 5.7731 10.4563 5.1 0.475 -1.4451 3.8186 6.31 670.321 -46.5417 -42.965 Apparent molal volume values are found to change with concentration as well as with temperature.3 0.2 0.259 -48.477 -60. Apparent molal compressibility increases with concentration at all temperatures and it decreases upto 50⁰C and then decreases at 55⁰C for all concentrations.727 -59. Table No.964 -1.89 305.577 Фk E7m³ By Traditional method -3.142 -49.079 -50.1 0. It is found to be maximam at 0.89 305.2 0.2469 5.956 -59.71 17 | P a g e 40 .423 -60.924 -59.573 -1.5 5.0651 5.037 -61.22 276.142 -49.41 245.7441 4.2 molality and at all temperatures.0571 10.51 402.63 313.8694 3.079 -50.3 0.278 -1.5 0.573 -1.2748 3.495 -61.041 -28.904 -1.759 -37.321 -46.495 -61.3721 4.92 386.041 -28.759 -37.6095 4.278 -1.45 50 55 0.423 -60.2 0.63 313.171 -61.3 0.1762 3.4 0.3 -3.31 670.9941 4.259 -48.965 -42.904 -1.3952 7.329 -3.71 Фs*10^6 m³/Mole By Traditional method 689.0331 3.5949 4.3361 8. 649 -1.65 288.36 245.65 288.4 0.2 0.482 -1.51 734.85 239.56 216.655 -1.266 -3.953 -1.1 0.066 -1.774 -1.51 612.402 -1.713 -1.363 -2.5 0.713 -1.655 -1.04 277.476 -1.56 251.774 -1.2 0.82 392.488 -1.476 270.488 -1.649 -1.91 274.45 234.4 0.2 0.311 -3.69 313.04 277.4 0.72 Molal Solvation number of NH HF +DMSO System Molar Solvation number of numb NH HF +DMSO System Fig :1 Apparent Molal Volume of NH HF +DMSO System NH₄HF₂+DMSO Apparent Molal Volume E+6 m³/Mole Apparent Molal Compressibility M³ 0 -20 0 -40 -60 -80 0.5 1 35⁰C 40⁰C 45⁰C Fig : 2 Apparent Molal Compressibility of NH HF +DMSO System NH₄HF₂+DMSO -10 -20 -30 -40 0.2 339.19 339.51 734.3 0.82 392.69 581.72 270.69 581.5 -1.928 -1.33 326.19 412.6 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C Fig : 3 Molality Fig :4 50⁰C 0 0.4 Molar55⁰C Solvated Volume of Molality NH HF +DMSO System NH₄HF₂+DMSO 900 700 500 300 100 0 0.363 -2.5 0.482 -1.4 0.528 -1.266 -3.45 50 55 0.528 -1.928 -1.69 313.3 0.36 245.1 0.066 -1.91 274.33 326.56 251.2 0.45 234.3 0.2 0.85 239.6 Molar Solvated Volume E+6 M³/Mole 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C 18 | P a g e Molality .087 -1.087 -1.1 0.761 -2.761 -2.19 412.5 0.311 -3.56 216.402 -1.953 -1.4 0.51 612. J. Chem. (1999) pp 331–333.. Scand.. The above results show that there is strong solvent-solute interaction.. 6.. Pia Thomas and Ganthimathi K. Modern Electrochemistry A Plenum/Rosetta Edition Vol. 27 No. 385 (1930). REFERENCES 1.. 4. 8. Jacobson B. Chem. 1–4. N. Suhashini Ernest Ph.J. 278 (1952). 5. 7. M. Phys. John O. 2. (1977). 20. Acta Physiochem. 3. Ind. Bokris and Amulya K. 6. Reddy... Christian Riechardt “Solvent and Solvent effects in organic chemistry”Wiley VCH Third Edition 2003.D.Fig : 5 The molar solvated volume is found to decrease in concentration as in the case of salvation number.Acoust. Hydration Number and Apparent Molal Compressibility From Ultrasonic Measurements.Soc. Passynsky A. 19 | P a g e . Vol.1. 1485 (1952). Barnartt S. Thesis submitted to Bharathidasan University 2010. Acta. This shows that solvation number plays an important role in deciding the value of molar solvated volume. V. Internal pressure is due to coulumbic interaction between ions with net charges leading to long range interaction. KEY WORDS: Ultrasonic velocity.7&µ=1. ABSTRACT Thermodynamic and electrochemical properties of electrolytes find extensive application in characterizing physico-chemical properties. Bharathi3 and K.Ganthimathi3 1. Internal pressure is a measure of cohesive force in a solution and is considered as a rational basis to understand thermodynamics of electrolytic solutions [2]. G. 1. INTRODUCTION Dimethyl formamide is a protic solvent and it has very high dielectric constant and dipole moment (=3. viscosity and ultrasonic velocity leads to the determination of internal pressure which tells about the interaction between molecules and ions. Suryanarayana found the relation [4]. 2. in all the electrolyte solutions Λc decreases with increase in concentration potential [3]. πi V=Λc exp (m₁Cp+k₁) -------------. When we examine values of the equivalent conductance Λc with the variation of concentration potential Cp. concentration remaining constant. The relation between equivalent conductance and internal pressure of the solutions are studied.STUDY OF INTERNAL PRESSURE AND EQUIVALENT CONDUCTANCE OF SOLUTIONS OF CALCIUM FLUORIDE IN NON-AQUEOUS MEDIUM A.4305) compared to other protic solvents.The internal pressure is found to decrease with concentration for some electrolytes and to increase for some other solutions.H. Tiruchirappalli. The ionic behaviour of the solutions is explained by the equivalent conductance of the solutions.V. Rakini Chandrasekaran2. Holy Cross College.(1) to hold good in the case of electrolyte solutions at constant temperature where m1 and k1 are constants. Internal Pressure. Bishop Heber College. Tiruchirappalli. C. Cohesive energy barrier which is the product of internal pressure and molar volume also depends on the equivalent conductance. Specific conductance values are also measured for studying ionic behaviour of the solutions. Department of Physics.Department of Physics. J. Beulah Mary1. EXPERIMENTAL PROCEDURE AND COMPUTATIONS 20 | P a g e . Concentration potential. 2. Measurement of density. All the measurements are carried out for various concentrations of the solutions in the temperature range from 35˚C to 55˚C. (i. ε=36. Department of Physics.86D. This paper deals with the thermodynamic and electrochemical behaviour of solutions of calcium fluoride in dimethyl formamide. Arts College. Pudukotta 3.e) πi V=Λc exp (m₂T+k₂) --------------.(2) The validity of these equations is checked for dimethyl formamide solutions of calcium fluoride. Suryanarayana formulated a similar equation for the variation of (πiV/Λc) with temperature. The high values indicate the existence of appreciable non specific coulombic interactions and specific forces like hydrogen bonding resulting in dimers [1]. Govt. Equivalent Conductance. Based on this theory C. 60 4988. It proves the validity of the equations (1&2). Internal pressure and equivalent conductance values are computed using the following formulae.87 4648.75 4544.2359 16. Thus.45 4881.4338 27.1298 55⁰C 43. The equivalent conductance is found to decrease with concentration and increase with temperature. The temperature is maintained from 35˚C to 55˚C with an accurate thermostat.94 4884.They are linear.00 4364.18 4160.15 4526.39 4247.67 4890.36 0.61 5223.2 Cp 0.89 0.31 0.75 5133.4581 25.4955 28.91 4776. RESULTS AND DISCUSSION The computed values of internal pressure and equivalent conductance of the electrolyte solutions are given in table (1&2.65 4405.Solutions of various concentrations of calcium fluoride in dimethyl formamide are prepared with AnalaR grade substances.0.45 0.6699 32.2826 25.15 0.60 0.8562 30.75 5011.3225 21 | P a g e .75 4669. Viscosity is measured with the help of Oswald viscometer.3905 20.0249 21.9684 14.5429 21.29 4407.47 0.). the equivalent conductance depends directly on cohesive energy barrier and inversely on the exponential function of concentration potential or temperature [5&6].7329 21.42 0.37 4393.99 4183.(3) ----------.47 4548.13 4977.46 4284.71 4893.94 0.88 5097.9453 16.32 0. The density of the solution is measured with 10 ml specific gravity bottle.89 4375.09 4539.5792 20. This shows that calcium fluoride has structure making nature in dimethyl formamide. the terms carry the usual meaning.00 Table No.55 1.81 5135.1 Internal Pressure of CaF₂+DMF System in Atmos 35⁰C 40⁰C 45⁰C 50⁰C 55⁰C Cp 4285.9031 18.4906 23.99 5090.9589 14. 1 2 2 3 ----------.1376 17.88 4547.75 Equivalent Conductance of CaF₂+DMF System in cm²/ohm 35⁰C 40⁰C 45⁰C 50⁰C 23.(4) 3.4849 36. Specific conductance values are also measured using conductivity meter with a cell constant 1.52 4682. The variation of internal pressure and equivalent conductance with concentration of the solutions is shown in Figs (1&2). In this solution the internal pressure values increase with concentration and decrease with temperature. Ultrasonic velocity of the solution is measured with a Mittal type ultrasonic interferometer with an accuracy of ±2m/s.54 5140. kη ρ Internal Pressure Π i =bRT atmos 7 u 6 M eff k ×1000 Equivalent conductance ∧ c = c N Where.91 5169.90 5256.8283 33. Table No.0374 19.30 0.41 4985.45 5104.75 4227.7584 23. Variation of Ln(πiv/Λ) with Cp and Temperature of solutions are shown in Figs (3&4).8382 21.27 4854.62 5054.30 4715. 5 Variation of Ln(πiv/Λ)1 Λ) with Cp 55⁰C of Concentration Potential Fig 2 Variation of Ln(πiv/Λ with 50⁰C iv/Λ) 10 55⁰C Temperature of CaF +DMF System 0 0.3378 20.7657 Internal Pressure of CaF +DMF System Equivalent Conductance cm²/ohm Equivalent Conductance of CaF +DMF System m 50 40 30 20 CaF₂+DMF Internal Pressure Atmos 5500 5000 4500 4000 35⁰C 40⁰C 45⁰C CaF₂+DMF 35⁰C 40⁰C 45⁰C Fig :1 50⁰C 0 0.and Mingos D. 228.D.New York.4907 12.V. Ph. Glasstone S.00 12.IndianchemSoc (1982)562 3.6085 14. Introduction to Electrochemistry’ Litton educational Publishing Inc. Dhanalakshmi A. and Natarajan.Chem.and Ganthimathi K. ‘Proton Relaxation Rate. una. C.Vol. Ind. Free Volume and Equivalent Conductance as functions of Internal Pressure in Aqueous Electrolytes’ . J. (1942) 4. 6 0 . Ganthimathi k. 327 333 (1991). 327-333 5. 2 (1995). CV.Voi. Soc.5 1 Concentration Potential CaF₂+DMF 10.2358 15. 82.5 30 Fig 4 REFERENCES 0 .6493 13.0501 18.: Ind.Aruna. 3 0 . Suryanarayana.5 Fig 3 Ln(πiv/Λ) 10 9.P. John E. Mc Grady.4618 17.90 1. 219 kshmi 219-222 22 | P a g e . 9 40 50 Temperature ⁰c 60 1. P. Perkin Trans.5 9 8.29.0. 1993.J. Bharathidasan University (1992) 6.. s.J.Lalitha V. Suryanarayana.Thesis. Michael. Acoust.4907 18. Tech.. Soc.XXI. 2.9104 16. J. One of two fundamental types of solute–solvent intermolecular interactions are the specific interactions. formation of Hydrogen bonding etc. Vf decreases throughout the entire concentration and the Vander waals constant curves are non linear It was observed that the depolymerisation increases the free volume and electrostatic attraction and association reduces the free volume. Moreover an increase in the value of b due to increase in the hydro carbon chain shows a reduction in the free volume. From the measured values of density.the free volume increases with percentage of alcohol due to mutual destruction of association between Lactic acid and alcohol molecules. In the present case. Keywords: Thermodynamic parameters. liquids and gases .Ultrasonic velocities and derived thermodynamic parameters are of considerable interest in understanding the nature and strength of various intermolecular interaction.EFFECT OF ELECTRONEGATIVITY ON FREE VOLUME AND VANDERWAALS CONSTANT OF BINARY AND TERNARY LIQUID MIXTURES K. Hydrogen bonding. Lactic acid and n-alcohols have been carried out at 250C temperature using Interferometer technique. India Abstract Ultrasonics is an interesting field of study which makes an effective contribution to many areas of human endeavor. [1]. liquids and gases . In the recent years many attempts have been made in the field of physical acoustics and ultrasound on solids. Tiruchirappalli. In Lactic acid – Alcohol systems . The free volume is an important quantity that determines the nature and strength of various inter molecular interaction in binary and ternary liquid mixtures. 1 Introduction Ultrasonics is an interesting field of study which makes an effective contribution to many areas of human endeavor.In the present work. These parameters were successfully employed to understand the nature of molecular interaction between the interacting components in the mixtures. In all the other ternary systems. work undertaken is to study the thermo- 23 | P a g e .the ultrasonic velocity measurements of binary and ternary liquid mixtures of Dioxane. Vijayalakshmi and C. viscosity and ultrasonic velocity. such as hydrogen bonding complexation between solute and solvent. the thermodynamic and acoustic parameters such as free volume Vf and Vander waals constant b have been evaluated. Bbishop Heber College. In the recent years many attempts have been made in the field of physical acoustics and ultrasound on solids. molecular interaction. Tamil nadu.Ravidhas Department of physics. R the universal gas constant and T the absolute temperature.acoustical behavior of binary and ternary liquid mixtures of n-alcohols with Lactic acid and Dioxane from the variation of Vanderwaal’s constant b and Free volume Vf. A constant temperature bath with a compressor unit is used for maintaining the temperature constant at 25°C. 4. Free Volume Vf = Mu Kη 3 2 Vander Waals constant b = M RT 1 − ρ Mu 2 2 1 + Mu − 1 3RT where M is the effective molecular weight of the mixtures. the Free volume and Vander waals constant are computed [3]. 2. viscosity η and ultrasonic velocity u. Ultrasonic velocity of the mixtures are measured using Mittal type Ultrasonic Interferometer of fixed frequency 2MHZ [2]. during the mixing of liquids [4]. The change in the size and shape of the molecules results in structural rearrangement of the molecules in the mixture. Using Specific Gravity bottle and Kenon-Fenske Viscometer. Due to overall increase in size of the molecules. their 24 | P a g e . These structural changes feature in different types of interaction between like and unlike molecules. The free volume of Lactic acid is less and Dioxane is more. k a constant = 4. density and viscosity of the mixtures are measured.Theory From the measured values of density ρ. The free volume is the effective volume in which the molecules in the liquid can move and obey perfect gas law. Materials and Methods Binary liquid mixtures of n-alcohols (from Methanol to Hexanol) with Dioxane and Lactic acid and ternary mixtures of Lactic acid.28 x 109 independent of temperature and nature of the system. Dioxane and n-alcohols of various proportions are prepared by volume. 3. Results and Discussion Free volume is the free space available for the molecule to move. However the free volume of n-alcohols decreases as the hydrocarbon chain increases. 01 0 0 10 20 30 40 50 60 70 80 90 100 0 0 10 20 30 40 50 60 70 80 90 100 25 | P a g e .06 60 0. FIG. indicates the specific interaction between alcohol and Dioxane molecules.03 20 0.07 80 2. since b may be even 4 times greater than the molar volume [6]. the free volume increases with percentage of alcohol due to mutual destruction of association between Lactic acid and alcohol molecules [7]. The variation of Vanderwaals constant b (Fig. In Lactic acid – Alcohol systems [Fig.Brownian motion may be affected [5].This is reflected in the values of Vander waals constant b. Since the molecules are large. they occupy more volume and hence the free space for their movement is reduced.Alcohol Systems [Fig 4].1). As the free volume of alcohols is in the order Methanol > Ethenol > Propanol > Butanol > Pentanol > Hexanol.09 0. FREE 0. 2 Vander Waal’s Constant of Alcohol – Dioxane system 140 0. 1. So an increase in the value of b suggests a reduction in the free volume Vf of the alcohols.02 0.1 120 0. the Vf curve goes low as we go from Methanol to Hexanol.08 Vander Waal’s Constant (b) 100 M : D E : D 0. 2).04 40 0. 1 FREE VOLUME OF Fig. Alcohol-Dioxane system shows an exponential increase in the value of free volume (Fig.05 0. 3]. So the free volume available for their movement is decreased as the chain length increases from Methanol to Hexanol .The variation of Vanderwaals constant b is non-linear in Lactic acid . 04 0.09 0.05 0.03 0.02 0. FIG.01 0 0 10 20 30 40 50 60 65 60 55 50 45 40 0 10 20 30 40 50 60 % of Alcohol by volume % of Alcohol by volume 26 | P a g e .02 0.07 90 9.06 L:D:M L: D:E L: D:P L: D:B L:D:P e L: D:H 85 80 75 70 6.07 0. FREE 0. FIG.05 0.04 0. FREE 0.1 0. 6 VANDER WAAL’S Vander Waal’s Constant (b) 85 80 L: D 10. FIG . FIG.03 0.08 0.09 0. 5 FREE VOLUME 0.01 0 0 10 20 30 40 50 60 70 80 90 100 75 70 65 60 0 10 20 30 40 50 60 70 80 90 100 % of Dioxane by volume % of Dioxane by volume 8. 7 FREE VOLUME Vander Waal’s Constant (b) 7. 8 VANDER WAAL’S 90 0.06 0.08 0.11. 12. indicates the possible breaking of hydrogen bonds at higher Dioxane contents[8]. Rahmat Sadeghi. J Acoust Soc Ind. From the above observation. 3. Kelkar. Fluid Phase Equilibria. J Pure and Appl Ultrasonics. (1969). V. 4. Ilja Siepmann. Academic Press. Ind. Acoust. 260 (2007) 335.. Roushan Khoshnavazi and Hana Parhizkar. Beyer R T and Letcher S V. 122-129. Vijayalakshmi K. J. 28.(1998). Moreover an increase in the value of b due to increase in the hydro carbon chain shows a reduction in the free volume.277-374.That is the variation of Vf and b with % of solvent shows an exponential behavior. 39. (2001). 6]. Fluid Phase Equilibria 260 ( 2007) 218. In all the other ternary systems. Jake L. Soc.The variation of free volume and Vander waals constant in Lactic acid – Dioxane system [Fig 5. Ind J Pure and Appl phys. 133-138. Academic Press New York. and J..Physical Ultrasonics. indicating the possible breaking of hydrogen bonds at higher Dioxane contents. 5. Maginn. Rafferty. Edward J. 365 9. Neena Jaggi and Jaiswal R M P. (1998).65. 7.Alcohol systems the free volume rise initially at 10% o Methonal and thereafter Vf decreases. Papadakis E P. J Acoust Soc Ind. In Lactic acid – Dioxane . 2. 29. Lalitha. No. 324.. References 1. it is found that the depolymerisation increases the free volume and electrostatic attraction and association reduces the free volume [9].. Vol. 6. Thakare J B. Dongre D T and Deogaonkar. and the Vander waals constant curves are non linear (Fig 8). 136 27 | P a g e . XXVI. 20 . 39 8. Vf decreases throughout the entire concentration (Fig 7). Physical Acoustics:Principles and Methods. 5.(2000).(1976). pp. Manish S.. Baral K K and Mandal R K.(2001). India. M. 313 K. India. adiabatic modulus(B). Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions.Mathavan 1*. NMSSVN College.Dolour Selvarajan 1. Madurai Kamaraj University. Gibbs energy(G). acoustic impedance(Z). 1. absorption coefficient(α/f2).Stephen Raja 1 1 Department 2 of Physics. Arul Anandar College. internal pressure(πi). Karumathur – 625 514. Madurai – 625 021.ULTRASONIC STUDIES OF NN'-METHYLENE BIS-ACRYLAMIDE IN WATER T.Jothi Rajan 3. Corresponding author. The sound velocity is one of those physical properties that help in understanding the nature of liquid state. School of Physics. Madurai . Nagamalai.co. 318 K and 323 K. relaxation time(τ). of Physics. S. KEYWORDS: Thermodynamics. 28 | P a g e . V.Hakkim 1. A. 1. J. molar volume(V). E-mail address:
[email protected] 3 Department ABSTRACT: NN'-Methylene bis-acrylamide (NN'MBA) is dissolved in water and its physical parameters such as isentropic compressibility(Ks). Alfred Nobel Antony 1. Hence an attempt is made to study the interaction of NN'MBA in water. free volume(Vf). intermolecular free length(Lf). The acoustic measurements were carried out for four different concentrations at temperatures 308 K. India. INTRODUCTION The ultrasonic studies are extensively used to estimate the thermodynamic properties and predict the intermolecular interactions of binary mixtures [1-3].A. Rao’s number(R) and Wada’s constant(W) were determined and studied. ultrasonic velocity and viscosity. X.Umapathy 2. attenuation constant(α).625 019. WHICH WERE CLEANED AND DRIED BEFORE USE.0ML-1) WERE PREPARED AND THE MEASUREMENTS WERE TAKEN FOR 308 K. Adiabatic bulk modulus B = 1/ Ks 3.17G/MOLE AND CHEMICAL FORMULA (CH2:CH.(4) ----. 3. DELHI. Intermolecular Free length Lf = k/( U2) k is the temperature dependent constant. 1. In this work the following parameters were determined. 318 K AND 323 K OBTAINED BY WEIGHING THE SOLUTE BY A DIGITAL BALANCE (ACCURACY 0. INDIA. Densities of the solutions were measured by specific gravity bottle of capacity 5ml to an accuracy of 0.. (BOISAR 401501) HAVING MOLECULAR WEIGHT 154. viscosity( and density( measurements are extensively used to study the physical. WATER.0.FINE-CHEM. Molar volume (V) V= Meff/ Meff = X1M1+X2M2 ----. THE REQUIRED CONCENTRATIONS OF THE SOLUTION (0. EXPERIMENTAL ANALAR GRADE (AR) SAMPLE OF NN'MBA SUPPLIED BY S. INDIA) TO AN ACCURACY OF 0. DOUBLY DISTILLED OVER ALKALINE PERMANGANATE IN ALL GLASS APPARATUS WAS USED AS THE SOLVENT FOR PREPARING THE SOLUTION.1 kgm-3. SINGLE FREQUENCY ULTRASONIC INTERFEROMETER (M/S. Absorption co-efficient /f2 = 82/3U3 6. 2. 1. chemical behavior of liquid solutions.(2) ----. Viscosities of the solutions were measured by pyknometer to an accuracy of 0. 1.(6) ----.NH)2CH2 WAS USED AS SUCH WITHOUT FURTHER PURIFICATION.01C WERE USED FOR ULTRASONIC VELOCITY MEASUREMENTS. Relaxation time = 4 / 3 U2 5. TOSHNIWAL BROTHERS. MITTAL ENTERPRISES.2. 4.(3) 29 | P a g e . Isentropic compressibility Ks = (U2)-1 2.(7) ----.CO. Attenuation co-efficient = 82 f2/3U3 7. MODEL F81. 2 MHZ) AND CONSTANT TEMPERATURE WATER BATH (M/S.05%.(1) ----.D.001G) AND MIXING WITH THE ALREADY PURIFIED WATER IN GLASS BEAKERS.5.(5) ----. ACOUSTICAL PARAMETERS The ultrasonic velocity (U).5. LTD. 313 K. M1 is the molecular weight of water.5% is shifted to the concentration 1% when the temperature is increased to 323 K. Therefore Lf decreases with increase in the volume of water in the solution [6.(13) where R is the universal gas constant and b=1. which is generally considerably larger than the shear modulus. Gibbs free energy G = RT ln (V/hNa) where h is the Planck’s constant and Na is the Avogadro number. Relaxation occurs in liquids and can be either thermal relaxation type as found in gases or of the type due to structural rearrangement of the molecules which are usually associated with longer chain molecules. 2 that Ks varies linearly for 308 K and 318 K for all concentrations.(12) ----. and then increases as concentration increases. RESULTS AND DISCUSSION Ultrasonic velocity (U) in the solution varies according to the molecular interactions in it. whereas Ks varies non-linearly for temperatures 313 K and 323 K for all concentrations.1). It is observed from the fig.78 (fcc). The classical absorption of ultrasound arises because the propagating wave loses energy in overcoming the shear viscosity and thermal conductivity of liquids. Rao’s number R = Meff U1/3/ 13. 7]. Specific Acoustic Impedance Z= U 11. indicating breaking up of hydrogen bonds as temperature rises. Meff is the effective mass of the binary liquid. Wada’s constant W = Meff K-1/7/ 4. X1 is the mole fraction of the water. it has been observed that intermolecular free-length decreases as concentration increases for all temperatures (308 K. 5]. 10. The difference in free length of 0. 12. X2 is the mole fraction of NN'MBA.01A between these two temperatures indicates significant interactions between the components unlike molecules.(10) ----. 8. Ultrasonic velocity in water of NN'MBA shows a general increase in temperature (Fig. Internal pressure i = Μ 7/6 bRT(k/U)1/2 2 / 3/ eff ----.where is the density of the solution. The non-linear increase and decrease in Ks values with concentration indicates significant molecular interactions (association) between the component unlike molecules [4.5% concentrations respectively. 1. 318 K) except for the temperatures 313 K and 323 K where the free length decreases up to 1%. In the present investigation as shown in figure 3.(8) ----. Free volume (Vf) Vf = (Meff U/k)3/2 9.(11) ----. and M2 is the molecular weight of NN'MBA. However the attenuation due to shear 30 | P a g e . Longitudinal propagation of waves involves the compressional modulus.(9) ----. The minimum observed at 313 K in the concentration 1. The same trend is observed when the temperature is increased except for 323K where there is a maximum at 1% concentration. 8.5% there is a minimum and at 323 k at 1. In the present study the absorption coefficient α/f2 decreases with increase in concentration of the solution in general.5% to 1% with the corresponding shift in absorption coefficient of 0. 7. which appears to vary due to all the internal interactions [9].75% of the solution and thereafter decreases abruptly as shown in Fig. 6. Specific acoustic impedance is similar to the index of refraction in optics. In the present investigation the relaxation time fluctuates in between 9. Wada’s 31 | P a g e . Even when the temperature is increased there is a very small increase in the molar volume for various concentrations. This indicates that the strength of the bond is slowly shifting from higher strength to lower strength. The variation of the attenuation coefficient with respect to the variation of concentration and temperature is as shown in fig. There is a shift of 1.5 x 10-5s for 323 K.. the hydrogen bonds are weakened or broken during compression. Internal pressure is a single factor.viscosity will be a significant contribution. Internal pressure shows a general decrease with increase in temperature. But it is observed for the temperatures 313 K at 1. 11 it is observed that the Gibbs free energy increases slightly with increase in concentration. There is appreciable increase in the Gibbs free energy with the increase in temperature for a constant concentration of the solution. for low and high concentrations respectively as shown in fig 4. These suggest that cohesive forces decrease with increase in temperatures [10]. An analysis of the experimental data shows that Rao’s constant is almost constant up to 1. Free volume of NN'MBA solution shows a general increase in raise of temperature but the free volume almost remains constant for all the concentration range as shown in fig. from weak to strong and vice-versa). 5.4 x 10-5s for 313 K and 8. Variations of internal pressure of aqueous solutions of NN’MBA at various concentrations and at different temperatures were shown in fig. Rao’s number gives an idea of how the molecular interactions change (i. 10. In the present investigation the specific acoustic impedance increases with increase in concentration almost linearly as shown in fig. From the fig.e. 9.0% there is a minimum respectively. This agrees very well with the theory. As the ultrasonic waves pass through the experimental solution.12. When free volume is minimum it is inferred that close packing of molecules inside the shell which may be brought about by the formation of associated complexes due to hydrogen bonding [8]. The molar volume almost remains constant with increase in the concentration of the solution as in fig. The decreasing trend after 1% of concentration may be due to the change of dielectric constant of the medium (solute-solvent).01x10-10 Nms-2 as shown in fig. 34 3.M Mole concentration.6 0.4 1..110 0.6 1.0 1.38 3.0 2.8 1.M Mole concentration.6 1.404 0.0 1.4 0.8 Free volume Vs Mole concentration .0 2.210 0.8 1.422 0.204 0.212 0.8 1.M Mole concentration.4 0.209 0. 1575 1570 1565 1560 4.4 1.106 48 47 46 45 44 43 0.4 1. 6.108 0.0181 0.M Figure 1 Acoustic velocity Vs Mole concentration .8 308K 313K 318K 323K 5.M Mole concentration.2 6.5 0 0 .0 2.6 0.9 8.5 2 1 . The various parameters calculated in this work are the premises of the study of interactions and complex formation in solutions.6 0.8 2.ms -1 -10 2 -1 Free length.216 0. 5.203 1 .1 9.36 3.8 2.2 1.6 0 .48 3.211 0. Figure.8 2.0 1.6 8.44 1 .116 0.2 Mole concentration.72 6.5 Absorption coefficient Vs Mole concentration.8 1.0 2.408 0.0 1.52 6.418 0.218 0.0183 0.2 1.54 6.0 1.8 2.4 9.6 1.4 0.6 0.2 0.9 9.0 0.0178 0.50 6.6 0.414 0.2 70 0.4 0.4 1.4 0.205 0.2 0.219 0.2 1.0 1.4 1 .6 0 0.2 Absorption coefficientx10 -10 9.0 1.0 2 .5 6 4 -1 6.217 0.64 Gibb's energyX10 RTunits -2 -1 Accoustical impedancex10 kgm s -6 6.213 0.0182 0.0 2.2 Mole concentration.7 Molar Volume Vs Mole concentration.2 3 1 .128 0.e.420 B C D E 1550 1545 1540 1535 1530 1525 1520 0.48 6.58 6.6 0.112 0.8 1.6 0.0 2. 308K 313K 318K 323K 308K 313K 318K 323K 0.42 0.2 1.0 2.5 ms 9.0 2.2 1.66 6. CONCLUSION For NN'MBA in water for different concentrations the velocities of ultrasonic waves were determined at a fixed frequency 2MHz.32 -10 2.426 0.6 0.8 1 . 2.42 3.424 0.8 2.412 0.8 2.0 1.215 0. 0.124 0.6 1 .6 1. Figure.5 0.0 1.2 M o le co n ce n tra tio n .8 2.6 1.40 3.0 2.2 1 .2 0.416 0.118 0.114 0.8 1.4 1.4 1.8 2 .4 1.8 1.4 4.6 1.207 0.214 0.410 4.0184 0.5 4 1 .6 1.120 0. Figure.428 0.208 0.0185 0.206 0.6 0.M Figure.M 32 | P a g e .4 0.8 9.0176 0. Figure.56 6. 13).4 0 .4 1.8 8.2 4.6 1.8 2.68 6.4 0.6 0 30 8K 31 3K 31 8K 32 3K 6.0 308K 313K 318K 323K 88 86 84 308K 313K 318K 323K 3.2 Adiabatic compressibilityx10 m N 1555 Velocity.7 0. Figure 2 Adiabatic compressibility Vs Mole concentration.7 8.0179 0.4 Relaxation time Vs Mole concentration.2 1.6 1.62 0.46 308K 313K 318K 323K Free volume x10 ml/mol Molar volume ml/mol 82 80 78 76 74 72 Internal pressurex10 amu 3.122 Attenuation constant 0.2 1.6 0.0 2.3 9.0 1 .406 0.4 1.6 0.8 2.2 1.4 0.8 1.4 0.46 6.M 7 Mole concentration.2 1.9 Internal pressure Vs Mole concentration.70 Figure.0 1.6 1.constant also gives an idea of the changing nature of the molecular interaction i.2 9.6 0. they are weak or strong interactions (fig. for four different temperatures.60 Rao's contantx m mol ms -1 1 .6 Attenuation constant Vs Mole concentration.2 1.4 0.8 1.M Figure.2 Mole concentration.0177 0.8 1.4 1.6 1.126 308K 313K 318K 323K 51 50 49 308K 313K 318K 323K S -10 Relaxation timex10 9.8 2.5 8 6.M Mole concentration.3 Free length Vs Mole concentration . A 4.0 308K 313k 318K 323K 0.4 1.2 1.0 1.220 0.M Mole concentration. 308k 313K 318k 323K -2 9.8 2.M Mole concentration.8 1.0180 0.44 3.0 8.4 0. 1993. December 1986.406 0. 9. A Dhanalakshmi and A R Rankuna. S M Gaour.386 0.1:pp 213-220. Figure. p 400. 15. Faraday Trans. 7. ‘ultrasonic velocities and Rao formalism in Solutions of Poly (ester .imides)’. “Analysis of Thermodynamical and Electrochemical Properties of Potassium Bromide in Formamide”. 2-4:270-274. 2000.Figure.4 1.6 0. Asian Journal of Chemistry. 29.0 2. 1-4. Kch Rao. J M Leal and J S Matos. p 3347. E Jasmine Vasnatha Rani and R Padmavathy. Trans. 5.0 1. 3. 2001. Vol 24.390 0. Polymer Bulletin. 4. pp 329-332. D Muraliji.10 Acoustical impedance Vs Mole concentration. 92.384 0. References 1. Vol 40.8 1. Journal of Acoustical Society of India. Journal of Chemical Society. p 582. p 743. J S Tomav and R P Varma. 2. Subba Rao and R Gopal Krishnan. Vol 5. S Sekar. Acta Polymer. p 602.12 Rrao’s constant Vs Mole concentration.404 0. ‘Acoustical parameters of poly (trinyl pyrrolidone)’. p 2102. R J Fort and W R Moore. A V Rajulu and S V Naidy.M Figure.398 0. p 5. Indian Journal of Pure and Applied Physics.2 3 -1 Mole concentration. 1965. “Internal Pressure and free Volume in Phenols”. 1989. R P Singh and S Math.392 0.394 0.2 1.396 0. 8. 1987. 0. 33 | P a g e .13 Wadd’s constant Vs Mole concentration.388 0. 61. 1980. “Ultrasonics Investigations of Organic Liquid Mixtures”. Journal of Acoustic Society of India.6 1. B Garcia. 10. Journal of Acoustical Society of India.402 Wadd's constantxm mol Nm -2 0. 6. 1979. 28.11 Gibb’s energy Vs Mole concentration .4 0. 1996. K Ganapathy and D Anbanathan. 308K 313K 318K 323K Figure. R Alcalde. Vol 7. Journal of Acoustical Society of India.400 0. A V Rao. ‘Acoustical parameters of polystyrene in Binary mixture’.8 2. S Das. Vol 2. 6. G K Raman and A V Rajulu. Faraday Society. 36.A. We report here the interaction 34 | P a g e . Madurai – 625 021. NMSSVN College. In this report.60 and 0. Karumathur – 625 514.Valarmathi 2 1 Department 2 of Physics. The measurements have been discussed about the interaction of molecules indirectly [1-4]. B. 1. remarkable similarities exist between the interaction parameters obtained from viscometric and relaxation time values. We report the results for weight concentrations 0.DETERMINATION OF ULTRASONIC INTERACTION PARAMETER FOR POLY (ACRYLIC ACID) IN WATER T.Mathavan 1*. the study of interaction parameter using the change in Gibb’s free energy employing the viscosity and relaxation.co. India. water. Madurai Kamaraj University.Jothi Rajan 3.12. 4MHz and 5MHz. INTRODUCTON Ultrasonic absorption measurements for Poly (acrylic acid) (PAA) in water can be attributed to shear viscosity and possibly. to structural relaxation.time values is reported [5]. which serve to vary the interaction parameter. 400C.625 019. which relates to the complex molecular formation [1-4]. Neverthless. India. 0. PAA in a high polar solvent. The decreasing interaction parameter values have shown the effects of increasing temperatures. India. M. 0. S. For a high polar polymer. School of Physics. * E-mail: tjmathavan@yahoo. 450C and 500C. Nagamalai. Madurai . the ultrasonic investigations have shown the interesting result of strengthening in association and the interaction effects and the influence of a macromolecule on the other molecules. 3 Department of Physics. In this work it has been found that the effect of interchain forces strengthened interaction between polymersolvent molecules.in ABSTRACT: Ultrasonic interaction parameter measurements have been made for poly (acrylic acid) in water solutions at 1MHz. Arul Anandar College.Umapathy 2.84 g/100ml at various temperatures 350C. 9483 0. which can be expressed as ∆G-G1Φ1 χ = -----------------n1Φ2 where ∆G is the free energy per unit mole of the solution.IV.0 1. 1.0409 0.74781 0. Table I.0 1.0492 0. Φ1 and Φ2 are the respective volume fractions of the solvent and the polymer [6].0130 0.5694 1. Calculated interaction parameter values of PAA in water at 35°C.0129 Frequency ΜΗz 1 Concentration Weight % 0.6968 1. The thermodynamic property Gibb’s free energy is used to estimate the interaction parameter.2928 1.4 0. n1 is the number of solvent molecules. Flory-Huggins proposed the method of estimation of the interaction parameter from relative vapour pressure and by osmotic pressure of solution [5]. G1 is the free energy of the solvent.0077 0.0093 0.75493 0.parameter values for PAA in water which exist the structure changes for increasing concentration and also present the effects of varying the temperature of the system.6 Viscosity η * 103 Nsm-2 0.41638 0.7194 1.90667 0.1 Theory The properties of polymer solution depend both on the nature and size of the polymer chains and also on the interaction between polymer and solvent molecules.0157 0.0157 from τ 0. The interaction parameter χ measures the extent with which the polymer interacts with the solvent.5694 Relaxation time τ * 1012sec 0.2 3.2928 1.97847 1.91702 4 35 | P a g e .0412 0.4178 0.6 6.0 8. The literature values of viscosity and relaxation time and the estimated values of χ were shown in tables I .0064 0.7194 1.0053 0.1267 0.2 3. ° χ From η 0.0492 0. 6 6.0076 0.65702 0.2 3.6 6.0058 from τ 0.0075 0.0113 0.4138 0.0116 0.0172 0.0 1.0068 - 4 0.4 0.0 36 | P a g e .0377 0.0 8.0064 0. Calculated interaction parameter values of PAA in water at 45°C.91010 0.6968 1.0066 0.0142 0.0416 0.80928 0.0093 0.0075 0.9514 1.3771 1.9483 0.0455 0.6529 1.0052 Table II.99431 1.0083 0.7194 1.92001 0.0 8.0058 0.75255 0.0 1.2 1.0058 0.0186 4 0.0380 0. ° χ From η 0.4 1.4 5 0.0051 from τ 0.6.0068 0.5960 Relaxation time τ * 1012sec 0.0772 0.9483 0.97285 1. Calculated interaction parameter values of PAA in water at 40°C.0142 0.0455 0.0 1.1574 1.0083 0.2 3.0 8.0099 0.37711 0.82147 6.0 8.6 6.6529 0.6 1.41290 0.61573 0.0116 0.1355 0.0128 0.2928 1.0772 1.0455 0.2 3.88655 8.4 Viscosity η * 103 Nsm-2 0.0404 0.6968 1.61701 0.0142 0.6 6.6529 1.0047 0.61460 3.4138 1.0093 0.0132 0.0 0.02730 Table III.7606 1.89423 1.5526 1.0535 0.5960 0.0052 0.34181 χ From η 0.0 1.7606 0.37047 1.198 0.0370 0.4 1.0045 Frequency ΜΗz 1 Concentration Weight % 0. ° 5 Frequency ΜΗz Concentration Weight % 0.0068 0.4 Viscosity η * 103 Nsm-2 0.7606 Relaxation time τ * 1012sec 0.88609 1.5526 1.82472 0.0157 0.2 3.0 8.0046 0.6120 0.5694 1.4138 1.0772 1.0492 0.0064 0.54348 0.0094 0.5526 0.37524 0.0 1.78369 0.33877 0.0083 0. 5217 0.0075 0.0301 0.3771 1.30873 0.3209 1.78635 0.0104 0.0051 0.86244 0.75545 0.2 3.2 3.5960 0.0 1.0117 0.3209 1.0 8.0045 0.0369 0.0416 0.9514 1.0107 0.0369 0.2 3.0369 0.63429 0.0344 0. Calculated interaction parameter values of PAA in water at 50°C.5217 0.0117 0.66451 0. As both PAA and water are strong polar molecules.0 1. DISCUSSION An important finding in this investigation was giving the result in numerical scale of inter/intra molecular interactions as a single parameter χ although the other parameters were there.1003 1.33667 0.0092 0.4 0.9263 1.1003 1.6 6.86558 4 5 2.1003 1.0061 0.9514 1.9263 1.0036 0.91666 0.0051 0.0035 0.0052 0.3771 1.62236 0.51812 0.0 1.5217 Relaxation time τ * 1012sec 0.1574 1.92216 0.4 Viscosity η * 103 Nsm-2 0.0 8.0 8.0035 Frequency ΜΗz 1 Concentration Weight % 0.1. 6.0066 0.74206 0.0092 0.85489 0. it might be expected to show decreasing values of χ for increasing 37 | P a g e .0132 0.4 0.0040 Table IV.6120 0.5468 0.75880 0.2 3.77943 0.0132 0.6 6.0416 0.31207 0.0052 0.0041 0.6120 0.4 0.54094 0.0045 0.4 5 0.0 8.0091 0.5468 0.0075 0.0045 from τ 0.0 1. The negative values of χ reveal explicitly the strong attractive interaction between interchain molecules [6].0066 0. ° χ From η 0.3209 1.1574 1.9263 1.0295 0.52500 0.54052 0.0295 0.0051 0.0059 0.52527 0.0066 0.66599 0.2 3.5468 0.6 6.30825 0.0 8.0335 0.62414 0.0117 0.6 6. 7. B.Hassun. India. R.Plym.B. Newyork.Kalyanasudaram and J. S. J. 32(1951).10.Hemalatha.Jeik. 75. This interaction χ is a measure of the polymer-solvent interaction [7].A. 4.Vigoureuse. 2. direct segment-segment interactions may exist 3.” AIP Press.J.Phys.14.S. Similar behaviour is seen with the χ values of increasing temperatures.Arnold. REFERENCES 1.H.Faraday Trans 11.Bell. School of Physics. 8. New York. 51(1942).So.Esquivel-Sirvent.B.Flory. A. 3. 12(9). R.Phil Dissertation.A. M. S. John Wiley & Sons. 98 (1).A. “Ultrasonic Investigations of Poly (acrylic acid) in water ”. Am. 1115(1979).Yun and F.Stumpf.Orwoll and P. Madurai Kamaraj University. W. 4.North. P. “Thermodynamics of High Polymer Solutions.” J.Soc. Soc. “Ultrasonic studies on PVC in Chlorobenzene. (1997).Mater. 161-165(1989).K. 170(1996). 6. In more concentrated solutions. J. Ultrasonic. Acoustics Letters.Valarmathi. CONCLUSION The interaction parameter values obtained from thermodynamic property Gibbs free energy for poly (acrylic acid) in water which exhibits structure changes for increasing concentration. “Ultrasonic velocity and Absorption Measurements for Poly (acrylic acid) and Water Solutions”. J Acoust.concentrations. 285-289(1997).Chem. The effects of varying the temperature of the system are also reported.” J. 5. 659-660 (1995). P. S.Hand Book.Chem. R. Here the interaction may be between (monomer) units or groups of (monomer) units.Pethrick and P.M. 38 | P a g e . “Phys Prop Poly. R. S. Excess parameters. of Physics. Abstract: LOW POWER ULTRASONIC TECHNIQUE IS ONE OF THE MOST POWERFUL AND USEFUL NONDESTRUCTIVE TESTING TOOLS TO INVESTIGATE PROPERTIES OF SOLUTIONS. low power ultrasound.A.Dravida Selvi 1 1 Department of Physics. S. VE AND ПIE ARE FOUND OUT AND THESE GIVE INSIGHT ABOUT THE NATURE OF THE INTERMOLECULAR ASSOCIATION BETWEEN THE NMP AND 1PROPANOL.Umapathy 2. 2 School of Physics. FROM THESE VALUES THE EXCESS PROPERTIES SUCH AS ηE. N. 39 | P a g e . ARE THE ACOUSTICAL ON THE BASIS AND OF PARAMETERS COMPUTED EXPERIMENTALLY DETERMINED VALUES OF ULTRASONIC VELOCITY. THE LOW POWER ULTRASONIC MEASUREMENTS ARE CARRIED OUT AT FIVE DIFFERENT CONCENTRATIONS AND AT TWO DIFFERENT TEMPERATURES FOR N-METHYLPYRROLIDONE THERMODYNAMICAL IN 1-PROPANOL. M. Madurai . DENSITY AND VISCOSITY. S. N-METHYLPYRROLIDONE (NMP) IS MIXED WITH 1-PROPANOL AND ITS PHYSICAL PARAMETERS SUCH AS DENSITY.Mathavan 1*. βAE.S.Abirami 1. author.S.Hemalatha 1. Arul Anandar College.co. Madurai – 625 021. India.in * Corresponding 3 Department 3. VISCOSITY AND VELOCITY WERE MEASURED EXPERIMENTALLY.K. Thermodynamical parameters.625 019.M. E-mail : tjmathavan@yahoo. India. KEYWORDS: NMP.Gokila 1. LFE. 1-Propanol.Vellaichamy Nadar College.ULTRASONIC INVESTIGATIONS OF N-METHYLPYRROLIDONE IN 1-PROPANOL T. Nagamalai. M. Karumathur – 625 514.Jothi Rajan 3. India. Madurai Kamaraj University. The required amount of the solution was placed in the cell and maintained at a predetermined temperature using a constant temperature water bath (M/S. Delhi. 2.5W/cm2. 2.4. 1-Propanol. Thus. 0..001g) and mixed with the already purified 1-propanol in cleaned and dried glass beakers. doubly distilled over alkaline permanganate was used as the solvent for preparing the solution.8 and 1.CO. velocity measurements were made for five different concentrations (0. Experimental 2. excess adiabatic compressibility. Densities of the solutions were measured by specific gravity bottle of capacity 5ml to an accuracy of ±0. Mittel Enterprises. The solutions of different concentrations were prepared by weighing the solute by a digital balance (accuracy ±0.13g/mole and chemical formula (CH2: CH. Theory The ultrasonic velocity. INTRODUCTION N-Methylpyrrolidone (NMP) is a dipolar aprotic solvent. In this work an attempt is made to study the interaction of NMP in 1-propanol for five different concentrations and two different temperatures by measuring the various thermodynamics parameters. This works on the principle of piezo-electric effect and imparts ultrasonic waves into the solution in a 12 ml thermostatic cell. Ultrasonic velocity studies on NMP in 1-propanol may reveal its suitability of being used as coating agent in aircrafts under high pressure and various atmospheric conditions. India.d.NH)2CH2 is used as such without further purification. Studies of excess thermodynamic functions such as excess viscosity. (BOISAR 401501) having molecular weight 99. excess molar volume and excess 40 | P a g e . Model F81) was used for ultrasonic velocity measurements and the measured intensity was 5. Viscosities of the solutions were measured by Oswald viscometer to an accuracy of ±0. 1. For each concentration of the solution velocity measurements were made for two different (constant) temperatures (308 K and 313 K).2. Apparatus Analar grade sample of NMP supplied by s.fine-chem.6. Large amounts of NMP are consumed in the polymer industry as a medium for polymerization and as a solvent for finished polymers.01°C. The study of propagation of ultrasonic waves in liquids and liquid mixtures is well established for examining the nature of molecular interactions [1-7].2. Single frequency (2 MHz) ultrasonic interferometer (M/S. 0. Ltd.05%.0 ML-1) of the experimental solution.1.4. India) to an accuracy of ±0. viscosity and density measurements are extensively used to study the physical and chemical behavior of liquid solutions. Toshniwal Brothers. 0. excess free length.1 Kgm-3. . X2 is the mole fraction of 1-propanol. X1 is the mole fraction of NMP. Excess internal pressure (ПiE) The excess internal pressure is given by ПiE = Пiexp – [X1Пi1 + X2Пi2] ----. 3. The non-zero values confirm the presence of interaction i. β1 is the adiabatic compressibility of pure NMP and β2 is the adiabatic compressibility of pure 1-propanol. Excess free length (LfE) The excess free length is given by LfE = Lfexp – [X1Lf1 + X2Lf2] ----.(3) where βexp is the adiabatic compressibility of the solution.e. X2 is the mole fraction of 1propanol. V1 is the molar volume of pure NMP and V2 is the molar volume of pure 1-propanol.(2) where Lfexp is the free volume of the solution. Excess Molar volume (VE) The excess molar volume is given by VE = Vexp – [X1V1 + X2V2] ----.(1) where ηexp is the viscosity of the solution. Results and discussion 41 | P a g e . Πi1 is the internal pressure of pure NMP and Πi2 is the internal pressure of pure 1-propanol. Excess adiabatic compressibility (βE) The excess adiabatic compressibility is given by βE = βexp – [X1β1 + X2β2] ----. X1 is the mole fraction of NMP. X1 is the mole fraction of NMP. X2 is the mole fraction of 1propanol.internal pressure are useful in understanding the nature of intermolecular interactions in liquid mixtures [14]. In this work the following parameters were determined: Excess viscosity (ηE) The excess viscosity is given by ηE = ηexp – [X1η1 + X2η2] ----. η1 is the viscosity of pure NMP and η2 is the viscosity of pure 1-propanol. The excess value of the above parameters provides the nature and strength of the interactions [5-7].(4) where Vexp is the molar volume of the solution. X2 is the mole fraction of 1-propanol. X1 is the mole fraction of NMP. excess values are the indicators of magnitude of the relative strength of interaction. X2 is the mole fraction of 1propanol. X1 is the mole fraction of NMP.(5) where Πiexp is the internal pressure of the solution. Lf1 is the free length of pure NMP and Lf2 is the free length of pure 1-propanol. The partial molar volume as a function of X1 suggests that these values are positive in the NMP+1propanol system. When the concentration of the solution is increased. 3). In the present work the positive values of LfE signify decreasing dipoledipole interactions due to decreasing proton donating abilities. 1. This factor contributes to positive value of VE. Similar changes in physical parameters are also observed when the temperature of the solution is varied. In this case the tendency of change from positive values to negative values indicating the strong interaction between the unlike molecules [10]. 4). Positive values in excess properties correspond mainly to the existence of dispersion forces and a positive βE tending towards a negative one shows that the strength of interaction increases. The positive LfE values decrease with increase of temperature suggesting a decrease in hetero-association of molecules at elevated temperatures (Fig. The increase in negative values of ΠiE suggests the predominance of hydrogen bonded interactions over the interstitial accommodation of component molecules at higher concentration of 1-propanol (Fig. 9]. correspondingly its various physical parameters change considerably. namely the mutual disruption of associates present in the pure liquid (Fig. and also suggests that this effect is due to break up of dipolar association of NMP+1-propanol predominates over that of hydrogen bonding between unlike molecules making VE values positive (Fig.4). 2) [8. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions. The βE decreases as temperature increases. which influences this excess function. The positive VE values can also be attributed to the weak dipole-dipole interaction leading to weak complex formation between unlike molecules [8].The excess viscosity ηE calculated shows the reverse trend of βE as shown in the Fig. The excess free length of NMP with 1-propanol at two different temperatures 308K and 313K are found out. In this system there may be a strong interaction between the 1-propanol molecules due to hydrogen bond and the addition of NMP may weaken the interactions. 42 | P a g e . The excess adiabatic compressibility of NMP with 1-propanol for two different temperatures 308K and 313K are studied (Fig. The variation of ultrasonic velocity in a solution depends upon the increase or decrease of intermolecular free length after mixing the components. 5) [11]. The observed value of VE can be qualitatively explained by considering the factor. 4. Conclusion Acoustic investigations were carried out for five different mole concentrations of NMP+1-propanol system. 2 0.8 1.6 β .2 0.005 0.005 -0.0 0.002 0.030 -0.4 0.8 1.2 0.020 -0.000 0.008 0.005 0.000 π .4 0. 0.2 0.4 0. A o 0.010 0.018 0. 10 M -10 E E -4 -1 2 Mole concentration Mole concentration Fig. 10 m N -1 0.6 0.020 0.030 0.010 -0. 2 Mole concentration vs Excess freelength. 3 Mole concentration vs βE Fig.308 K 313 K 0.006 0.015 0.6 0.8 1.6 0.004 308 K 313 K 0.4 0. 1 Mole concentration vs Excess viscosity.016 0.020 308 K 313 K v i s c o s i t y.0 0. 4 Mole concentration vs VE 0.012 0.035 -0. 10 atm Ε 10 -0.010 0.8 1.0 Excess Mole concentration Mole concentration Fig.6 0.8 308 K 313 K 0.025 -0.0 V .0 Mole concentration. M 43 | P a g e .2 0.005 308 K 313 K 0.035 0.0 Lf .040 -0.4 0.015 -0. Nsm -2 -0.015 E -0.045 -0.050 0. Fig.010 -0.000 -0.4 0.025 0.010 0.014 0.2 0.6 0.8 1. 7. 8. A. Polymer Bulletin. Singh and S. 11. Pethnik and D. Raman and A. Acous. Molecular Physics. J. 113-120. Indian Journal of Physics. 6. (2003).Fig. G. Math. 27. A.X. ‘Acoustic studies of Polymer solutions’. Narashimham and A. (1973). ‘ultrasonic velocities and Rao formalism in Solutions of Poly (ester – imides)’.K. Acta Polymer. Rajulu and S. ‘Acoustic Absorption of dilute solution of polystyrene in Toluene and cyclohexane’. Rajulu.V. B. 400. Chemistry. 15. (1980).. 91. (2002). 312-318. Sheng. Amalendu Pal. Journal of Macromolecule Science Review. (1977). ‘Acoustical parameters of polystyrene in Binary mixture’. 263. Rekha Israni.R. of Pure and Applied physics.P.V. 72. 582. Seshadri. Tekale. (1974). Journal of Polymer Science.B. (1998). Steinhauer. India.V. 4. Pethrick.V. 675. Narashimham. Asian Journal of Chemistry. R. 9. T. 743. Arbad and A. (1992). J. J. 65B (4).P. Macromolecule. 44-48. Indian Journal of Physics. Li and O. Harsh Kumar. Kch Rao. 44 | P a g e . ‘Statistical Thermodynamics of Molecules’.A. ‘Acoustical parameters of poly (trinyl pyrrolidone)’. Das.T.V. 5. 699(4). C9. 41. S. A. Huang. (1991). 65B (3).V. 40. REFERENCES 1. I. S. Dunbar. Indian J. (1989). Boubbik. Physics Edition. 10. J. 30. 5 Mole concentration vs П E 5. Guo. 2. 2. A. (1993). A. Journal of Applied Polymer Science. 1415-1477. Rita Mehra. Rao. R.M. 3. ‘Phase Behavior and Properties of PMMAPolyvinyl acetate’. 5.Y.B. Soc. Naidy. Keywords: solvation number. Ultrasonic velocity measurement is used to throw light on various aspects of solvation chemistry including ion-ion and ion-solvent interaction. Govt.R1. Tamilnadu 5. Arts College.A STUDY OF SOLVATION EFFECT OF SOME SODIUM SALTS IN NON-AQUEOUS MEDIUM USING ULTRASONIC VELOCITY Padmavathy. In the present case. By measuring the fundamental quantities such as density and ultrasonic velocity of sodium citrate. thus various interactions taking place between the solute and solvent are interpreted.R4 123Department of Physics. Seethalakshmi Ramasami College. ABSTRACT Ultrasonic studies of solutions yield valuable information about the ionic interactions. Trichy-2. These changes have been determined quantitatively as solvation number. The velocity of such a wave is a thermodynamic quantity and it is related to the physio-chemical properties of the medium. Tamil Nadu 4Department of Physics. sodium 45 | P a g e . the nature and strength of the interactions.solvent interaction. Seethalakshmi. Jasmine Vasantha Rani.K3. sodium molybdate. structure maker/breaker 1. solute . Velocity of sound waves in a medium is fundamentally related to the binding forces between the molecules. Rahmathunnisa. When an electrolyte is added to a solvent the volume of the solvent changes and hence there is a change in compressibility. The ultrasonic velocity data combined with density constitute the standard means of determining the compressibility of the system. the effect of temperature and concentration on solvation is analyzed for some sodium salts in non acqueous medium. E2. Pudukkottai.Introduction The passage of ultrasonic waves through solutions and liquids disturb the equilibrium between the solute and solvent molecules. in which the normal bulk structure of the solvent is broken down in various degrees. Therefore no change in compressibility. From the analysis of solvation. sodium salicylate and sodium calcium edetate of various concentrations are prepared in formamide with (AR/BDH) salt. it is negative at low temperature and no abrupt change in solvation number is found at higher molalities. Solvation number is decided by relative values of compressibility of solution and solvent.001gm/cc. Negative values of solvation number at lower molalities. The in-between solvent molecules. This may be due to ion solvent interaction energy equal to intermolecular interaction energy. 1. Constant values of solvation number only indicates that no change occurs in the compressibility value of the solvent when the solution is formed. At lower molalities.2. do not partake of the translational motion of the ion.salicylate and sodium calcium edetate in formamide from 5oc to 55oc at different concentration. Then there is a secondary or structure broken region. The solvation number was calculated using the formula: nh = (ns / ni )[1 − ( β / β o )] 1. however. Mittal’s interferometer of frequency to 2MHz. In the primary or structure enhanced region next to the ion. emphasizes that solutions are more compressible than solvent. The structural changes in the primary and secondary regions are generally referred to as the solvation.4).3. the solvent molecules are immobilized and oriented by the ionic field. The solvation numbers reflect the dynamic situation of the ion as it moves around in the solution. with an accuracy of ±2m/s is used for the measurement of ultrasonic velocity.(1. the solvation number were computed.1(a)Results and Discussions Solvation is the attraction and the association of the molecules of a solvent with molecules or ions of the solute.[1] The general observations made on solvation number of the system studied in relation to temperature and molality are as shown in figs. sodium molybdate.1 Experimental technique Solutions of sodium citrate. The solvation number is positive at a high temperature. Density of the solutions is measured using 25ml specific gravity bottle with an accuracy of . the solvation number changes from negative values to the positive values. The structure of the solvent near an ion will be having three regions. hence the negative sign for the solvation 46 | P a g e . the sodium salts in formamide reveals the structural interaction taking place in the solutions. 7.6].e.number. sodium citrate& sodium molybdate in formamide acts as structure makers and sodium salicylate & sodium calcium edetate in the solvent acts as structure breakers fig(5.solvent interaction energy of the solutions. the solvation number of the sodium salts reveal very high solvation number in formamide. The solvation number of an ion depends on the solvent.1(b)Conclusion: In the present investigation.solvent interaction[3]. The concept of solvation is a measure of the ionic force field and ion . 1. The negative solvation number for various molalities is reported in literature[4. Positive solvation number of the solution suggests that the compressibility of the solution at high temperature and at low molalities will be less than that of the solvent. The decrease in solvation number with increasing molality is due to either not enough solvent molecules available for ions or preferentially ion pairing occurred[7]. 47 | P a g e .8).5. But however a fall in the solvation number at high temperature or rise in solvation number from negative maximum towards zero at low temperature may be attributed to decreasing ion-solvent interactions[2]. Structural elucidation of the solute in the solvent.6. i. The solvation approach is used to interpret ion . 63 5.43 25°C 745.82 8.16 3.53 15°C -436.54 96.51 44.59 -2.17 5.83 3.61 -191.001 0.75 63.94 30.26 -190.44 -189.32 -1.66 -232.22 9.36 3.30 5.98 -148.22 2.58 25°C -1236.33 12.06 -9.50 85.10 19.75 -9.58 -21.17 Molaity(m) 0.005 0.58 112.005 0.30 -1. Figures and Tables Solvation Number Table –1 Sodium citrate Molality(m) 0.77 3.51 -186.050 0.83 174.100 0.30 55°C 266.11 -65.92 79.67 4.72 48 | P a g e .19 59.03 11.55 -0.01 -4.56 6.58 77.07 6.01 9.92 108.18 35°C -784.40 25°C -198.34 0.001 0.06 -1.53 -4.12 1.44 -31.38 83.33 192.050 0.005 0.010 0.2.87 18.71 45°C 318.86 60.25 45°C 235.53 45°C 1438.020 0.19 -26.01 9.41 18.85 Table – 4 Sodium calcium edetate Molality(m) 0.75 7.10 -43.97 7.44 9.37 20.010 0.73 5.17 -5.200 5°C -592.75 -4.09 16.13 5.72 55°C 1355.27 2.59 -13.70 -22.050 5°C -137.48 55°C 419.85 2.10 Table – 3 Sodium salicylate Molality(m) 0.53 45.93 33.030 5°C 485.100 0.27 -65.84 8.23 15°C -17.010 0.48 11.025 0.40 5.46 33.001 0.97 55°C 329.30 6.47 12.30 -107.56 -24.80 10.77 10.22 27.010 0.005 0.71 8.63 7.82 35°C 1457.37 33.24 -21.16 -0.12 59.02 57.25 5.41 1.95 -6.64 33.42 -1.56 3.00 87.16 -1.92 6.51 73.96 0.95 10.74 35°C 70.70 -4.94 4.45 45°C -146.18 12.94 15°C 752.54 57.150 Table – 2 Sodium molybdate 5°C 15°C 25°C 35°C -300.84 -22.78 6.67 5.64 23.001 0.58 13. SOLVATION NUMBER Fig – 1 SODIUM CITRATE Fig – 2 SODIUM MOLYBDATE Molality Vs Solvation number 300 Molality Vs Solvation number 400 Solvation number 200 100 0 -100 -200 -300 0.5 Fig .05 0.01 0.005 0.01 0.01 0.05 0.2 5° C 15° C 25° C 35° C 45° C 55° C 1600 1400 Molality Vs Solvation number Solvation number Solvation number 1200 1000 800 600 400 200 0 -200 -400 0. 4 SODIUM CALCIUM EDETATE IG – 3 SODIUM SALICYLATE FIG – Molality Vs Solvation number 600 400 200 0 -200 -400 -600 -800 -1000 -1200 -1400 0 0.6.005 0.05 5° C 15° C 25° C 35° C 45° C 55° C Solva tion num be r 300 200 100 0 -100 -200 -300 -400 0 0.001 0.03 5° C 15° C 25° C 35° C 45° C 55° C Molality(m) Molality(m) Fig .01 0.02 0.001 0.1 0.15 5° C 15° C 25° C 35° C 45° C 55° C Molality(m) Molality (m) 7.1 0.6 49 | P a g e .01 0.01 0.025 0. (1963) IA – 823.Lakshmanan A. Chem.. Energy Comm.73(1991)292.Fig . Isr At.S...Bull.k.N.R.V.M. Khim. Japan . Soc. Bockris and Amulya K.Pure and Appl.Acoustica.Bakshi. M. KuppuswamiJ.Pure and applied Phys.K. Reddy.8 3.al. 38.C. and Suryanarayana C. Jasbir.1(10) (1963) 362. (16PP).M. and Rao B.. et. J. Rajkotia. Bhullar.4(1963) 830 5. Lakshminarayanan R. (1965) 1610. Rajaram N.S. 6. 3. A Plenum / rosetta Edition.. Bhavneet. 50 | P a g e . John O..G.. Padova J. Ultrasonics. Vol 1.Strukt. References: 1. Zh. Vol. (1997) 2.S. and Joshi I. 21(1999)132-135 7.. A-830(23PP) 4..J. Sharma S. Lit vinenko. Rao M.S. “Modern Electrochemistry”.7 Fig . In electrostatic dissipation.[1] PANI is one of the most widely studied materials. INDIA
[email protected]. polyaniline salts are used.N. ultrasonic velocity. Lalgudi. 1. #RADHA. This results are also confirmed by FTIR and UV spectra.[2] A wide range of technological applications have been associated with polyaniline. @KANNAGI.1. PANI is an organic metal.in&jasstephen@yahoo. FTIR. It has unlimited worldwide commercial availability.N *Department of Physics. anticorrosion coatings in various optoelectronic devices and as an antistatic material. UV. Using the above values. Seethlakshmi Ramaswami College. Its thermo power has been classified as metallic. Kalaignar arts and science college. In this present investigation acoustic and thermodynamic properties are studied for poly aniline perchlorate in Formamide from 5°C to 55°C at different molalities using ultrasonic velocity. &LAVANYA.co. its specific conductivity are semi-metallic. 1.com ABSTRACT Polyaniline (PANI) is an organic metal. Keywords: Thermodynamic properties. Various molecular interactions have been analyzed and these interactions indicate the structural enhancement of this material in formamide. internal pressure . Density.Experimental technique and computation: 51 | P a g e .THERMO .[3][4] The present work dealt with the acoustic and spectroscopic study of polyaniline perchlorate in formamide. Introduction: Polymers conduct electric current without the addition of inorganic dopants. *PADMAVATHY. Polyaniline salts have been synthesized by chemical oxidative polymerization of aniline in the presence of phenoxy acetic acid. Its thermo power has been classified as metallic. viscosity and ultrasonic velocity are determined at various molality from 5°C to55°C.R. Tamil Nadu.K. free volume and acoustic parameters at different concentrations and at different temperatures are evaluated. #Department of Chemistry @ Dr. Trichirapalli-2.ACOUSTIC AND SPECTROSCOPIC STUDY OF POLYMER SALT IN NON -AQUEOUS MEDIUM USING ULTRASONIC VELOCITY *JASMINE VASANTHA RANI. 001m.04.015m. Internal pressure is the measure of cohesive energy. The experiment has been carried out at various temperatures and at different molalities (0.[7] These non-linear variations emphasize that there is an association between molecules of the solution. 0. Rao’s (R) Wada’s (W). Hildebrand and others. the internal pressure increases with concentration.The irregular behaviour of Rao’s constant. Significance of thermodynamics such as internal pressure and free volume in liquids had been emphasized by Richards. 0. The variations are shown in Figure-1. Results and discussion: 1.2 (a) Thermodynamic study: Internal pressure is the single factor which varies due to all the internal interactions. This increase in internal pressure suggests that there is a strong solute and solvent interaction. Wada’s constant and van der Waal’s constant supports that there is a strong ion-solvent interaction occurring in the solution.Formamide is taken as the solvent for preparing polyaniline perchlorate solution.02m). and 0. It is unusual in its properties. In the present investigation. at higher temperatures. hence there is a reduction in internal pressure[6]. 0. This result is also confirmed from the study of free volume. when the temperature is increased there is a tendency for the ions to move away from each other.[5] But. It is shown in Figure-2. Internal pressure (πi) and the free volume (Vf) and various acoustic parameters.01m.van der Waal’s (b) constants and adiabatic compressibility (βad) are computed using the following formulae πi Vf R W b βad = bRT(kη/u) 1/2 *(P2/3 / Meff7/6 ) atms = (Meff * u/kη) 3/2 cc = Meff (u) 1/3/ ρ = Meff (βad) -1/7/ ρ = (Meff/ρ) ((1-RT)/ Meff u2) (1+( Meff u2/3RT-1))1/2 = 1/u2ρ dynes/cm2 The values are given in the Tables 1-6 1. The variations of adiabatic compressibility with respect to concentration and temperature are given in Figure3.2.(Figures 4-6) 52 | P a g e . It has high dielectric constant 109 with low molecular weight 45.005m. between the C=O and N=H groups in formamide and confirm the cage structure[6] . Tamil center]. the spectrum there is also an N-H out of plane bending .82 cm-1. The molecular structures of formamide and polyaniline are given below (I& II).98cm-1. This confirms that structure making nature of the solutes in the solvent[7] The same results are reported from the thermodynamic study[8]. the structure making nature of the PAPC is confirmed from the spectr spectroscopic and thermodynamic studies.e. Nadu. The deviations in the peaks support the tightening of hydrogen bonds in the caged structure of n formamide. non-aqueous solvent.Joseph’s college [ACIC center]. PAPC exhibits peak at aqueous λmax=349.82 nm. (i.99 cm-1.35 cm-1.) towards higher frequency side by 1 cm-1. I.89 cm-1. C=O stretching is shifted to 1688. It is found to be in good agreement with the result reported in literature. when PANI is dissolved in polar hat. These two peaks in PAPC are the characteristics of the benzenoid and quinoid moieties. When PAPC is added to formamide(figure -8) the N-H stretching absorption is H shifted to 3417. C=O stretching absorption known as amide I band is observed at 1686. 1308. No shift is observed in N out of plane N-H bending. Tiruchirapalli. Well defined peaks are observed at 1390. (figure-7 and Table-7) a strong N-H stretching absorption H occurs at 3416. (i.36. These slight deviations in the absorption peaks are due to the tightening of hydrogen bonds in the caged structure. Also these shifts indicate the presence of hydrogen bonding.94 nm and another peak at 677.(figure -9).) towards higher frequency side by 1. It promotes a thermodynamically more stable chain[9]. 2.2 53 | P a g e .1. Structure of Formamide II II-structure of polyaniline From the IR spectrum of formamide.77 cm-1 this confirms the presence of C-H presenc group.45 cm -1.At 2886. The ratio of the intensities of the quininoid to benzenoid peak is 0.2 (b) Spectroscopic study: Infrared spectroscopy is the subset of spectroscopy that deals with the infrared region of the y electromagnetic spectrum. In the present study. This indicates PAPC has more benzenoid forms than that quinoid forms.In H absorption at 601. The low frequency absorption of amide I band is due to the resonance in the amide functional group.e.5. Solution of Polyaniline perchlorate (PAPC) in formamide is prepared using AR grade salts and IR spectra have been taken at St.34 shi cm -1. It is already confirmed that. Figures and Tables: Figure – 1 Figure . 0 .00 4.0.0 3000 2000 cm-1 1500 1000 400.sp 100.9 55°C ° 54 | P a g e .35 0.26 1311.55 0.40 A 3 49 .53 600 3417.95 1052.97 IR Spectrum Figure – 7 Molality(m) Figure – 8 Table -1 Internal Pressure (atms) 5°C 15°C 25°C 35°C 45°C ° ° ° ° ° UV Spectrum Figure .43 2366. 94 2774.52 33 2 60 1 054. 45 7.44 1605.59 1308.86 47.52 94 .0 Sam = Formamide.05 .45 1688. 47 1688.27 2771.89 21.52 2197 .Joseph's College ( Autonomous ) T richy-2 ACIC St.26 23.0 100 .51 1686.82 .0 5.pk SAM_FO~1.50 0.73 2889.87 72.34 0.98 7.58 71.31 70 2771.77 1390.3 5 8.60 601.00 %T 5 0.00 6.220 60 20 1390.82 23.25 67 7.94 100.97 82.Figure – 3 Figure – 4 Figure – 5 Figure – 6 ACIC St.15 0.Joseph's Colleg e ( Autonomo us ) Trichy-2 ACIC St.03 92.000 250. 0 0 .93 Instrument Model: Lambda 35 2691.60 80 2 691.00 % T 5 1.50 REF 4000 99.20 0.75 Spectrum Name: SRC-P APC.0 4000.61 2000 98. 96 601.94 2886.77 18.SP 0.0 4000.0.sp 2395.42 2000 98.35 1308.555 16 0.82 33.62 1311.0 3000 2000 cm-1 1500 1000 40 0.63 93.03 90 2191.31 81.36 601.0 Date: 1/8 /2010 UV sp ectru m Spe ctrum Name: PAPC.05 0.04 SRC-PAPC.94 .00 7.63 0.70 25 4.pk SRC-PAPC.27 23.0 300 400 500 600 nm 700 800 900 1000 1100.90 2197.82 30 0.S P 3601 4000.13 60 %T 50 %T 50 0.00 4.37 1054.30 30 2886.10 10 34 16.77 10 1605.58 70 1052.0 .97 80 2774.36 22.34 16.44 90 2366.42 2395.86 40 40 0.44 97.13 61 .27 601.87 0.65 0. 44 100.0 0. 69 1390.45 2 57 .34 3417.00 400.800 0.82 0.98 1686. 34 6.00 REF 4000 99.36 2191.00 400 .Jo seph's Colle ge( Auton omo us) Trich y-2 FT IR SPECT RUM Date: 07-1-2010 FTIR S PECTRUM Date: 08-1-2010 Spectrum Name: Sam = Formamide.83 600 3416.s p 3601 4000.89 20 1390.27 98 5 2889. 2 Free Volume (cc) Molality(m) 5°C 15°C 25°C 35°C ° ° ° ° 0.5 .4 110.01 120.001 118.03 1.21 0.005 377 360 347 378 398 379 .5 Wada’s Constant Molality(m) 5°C 15°C 25°C 35°C ° ° ° ° .9 115.56 2 1.6 105 .59 1.39 1.48 0.07 2.001 .7 119.01 .19 0.28 0.21 0.4 Rao’s Constant 5°C 15°C 25°C 35°C ° ° ° ° 2116 2143.015 1230 1232.01 0.001 .015 .5 114.0 118 119.46 0.48 0.005 .5 136.5 118.02 0.5 2166 2165 2132 2136.2 132.2 119.8 2149 2185 2134 2139.87 1.34 0.67 0.01 354 353 362 344 384 334 .78 Table .32 0.5 1.9 110.6 2221 2161 45°C ° 2213 2160 2171 2247 2193 45°C ° 1269 1243 1248 1285 1259 55°C ° 2243 2196 2237 2156 2200 55°C ° 1283 1260 1281 1241 1262 Table .02 1215 1231.02 115.1 1273 1243 Table-6 van der Waal’s constant Molality(m) 5°C 15°C 25°C 35°C 45°C 55°C ° ° ° ° ° ° .5 119.3 .8 1.001 1221 1234.5 119.015 0.3 116.49 0.4 1282 1247 .5 1245 1245 .015 119.1 1237 1255 .02 Table .01 .21 45°C 55°C ° ° 2.3 Adiabatic Compressibility (10^-13) Molality(m) 5°C 15°C 25°C 35°C 45°C 55°C ° ° ° ° ° ° .02 377 359 293 370 363 378 Molality(m) .005 0.22 0.87 1.1 118.4 2240 2169 2104 2136.82 1.6 1.001 0.9 118.8 2162 2154 2127 2140.5 115.42 0.001 361 353 344 360 344 334 .005 118..69 2.015 367 358 281 361 315 401 .1 112 107.5 113.7 110.3 125.8 .005 1229 1231.9 119.74 1.1 118.015 .01 1226 1233.02 19178 19453 19933 19987 20458 16357 16542 16848 16953 17084 13412 13664 13945 13312 13592 12678 13178 12931 13282 13387 11396 11862 11951 11434 11913 10450 11056 10823 11502 11238 Table.53 1.005 .1 1244 1240 .8 Table-7 Polyaniline perchlorate (PAPC) Wave number in cm -1 Possible functional groups 55 | P a g e . V..Acoustic Soc.Sadananda and A.R.K.N .M. 2) Li-MingHuanga.Srinivasa Rao.44 1688.Polymer Engineering Science.C. Radha.Ramamurthy. 8) Jasmine Vasantha Rani . 5) Ravichandran.Study of molecular interactions of calcium pantothenate in non-aqueous medium through ultrasonic speed measurement and spectroscopic analysis . Electrochemical and Thermodynamical properities of Calcium lactate solution using ultrasonic velocity –(2005).Harrell. Cheng-Hou Chena and Ten-Chin Wen Electrochimica Acta.R. 7) Analysis of internal pressure. B.. 4376-4378. Leena Bhoumik. Samuelson Althea Angnostopoulos. W. 2002. E.G. Jayant Kumar and Sutant. 1994.G.(2005).87 601.Rao.Maya Dutta Gupta.Suhashini Ernest. References: N-H Stretching Intermolecular hydrogen bond O-H Stretching C-H Stretching N+H2 and N+H Stretching C=O Stretching Inplane O-H bending C=O Symmetric Stretching C-O Stretching N-H out of plane bending 1) Lynne.Roy.31 2395.3417.(26)58585863.A and Nambinarayanan.28. 9) Bidhan C. 56 | P a g e . Free volume and also some acoustical parameters of sorbiton monosterate – J. Pure and Applied Chemistry. Spectroscopic investigation of water-soluble polyaniline copolymers – Synthetic Metals 130(2002) 27-32.44. T. 857.Gregory. Macromolecules 1998. K. Padmavathy. 3) P. 2006.867. R.34 1390. India vol xxx pp23-25 NSA 2002.A. 32. 31.An investigation of solvation number.27 1052.51.82 3.26 1311. 6) Jasmine Vasantha Rani. K.45 2889..Indian Journal of Pure and Applied Physics.Shridhara Alva.2004 4) Gilbert R. vol. 74. E. Tripathy.Suhashini Ernest.86 2774. It is important to select favorable reaction media for use of enzymes in organic synthesis. 3 Department of Physics. Specially. 57 | P a g e . mostly because of their use in two-phase aqueous systems for separation of biomolecule mixtures. Madurai – 625 021. Arul Anandar College. School of Physics. Ultrasonic studies in polymer solutions have drawn the attention of several investigators in the recent years [1-5]. proteins. adiabatic bulk modulus. intermolecular free length. The acoustical and thermodynamic parameters are computed based on experimentally determined values of ultrasonic velocity. NMSSVN College. M. if any in association with the formation of mixture of a polymer solute and clay-solvent mixture due to molecular interaction between them. E-mail address:
[email protected]. solutions of polyethylene glycol (PEG) in water have attracted much attention.Mathavan 1. Rao’s number.625 019. Toluene is chosen because it is a good solvent. The present study is undertaken on the ultrasonic study of PEG (400) in Toluene-Bentonite (Clay) mixture at several concentrations for four different temperatures (300C. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions. Poly(ethylene glycol)-400 (PEG-400) in toluene-bentonite clay mixture solution and its physical parameters such as adiabatic compressibility. correspondingly its various physical parameters change considerably.ULTRASONIC INVESTIGATIONS OF PEG (400) IN TOLUENE-CLAY MIXTURE T. Similar changes in physical parameters are also observed when the temperature of the solution is varied. aqueous polymer solutions have found widespread applications. India. Madurai . India. Madurai Kamaraj University. INTRODUCTION The main aim of this study is to bring out the structural changes. India.Jothi Rajan 3. Karumathur – 625 514. 400C and 450C). if any between the solute and solvent-clay mixed molecules. Corresponding author. These solutions have been used in bio-chemistry and biochemical engineering to separate and purify biological products. acoustic impedance. surface tension and refractive index are determined. Bentonite is a lightly absorbent clay-like substance that helps to lift impacted waste matter which has accumulated on the walls of the gastrointestinal tract. density and viscosity. enzymes from the complex mixtures in which they are produced. relaxation time.A. S. 350C. In this report ultrasonic method is used to study the physical parameters and investigate the associative nature. 1. Megala 1 1 Department 2 of Physics. absorption coefficient.Umapathy 2. M. In recent years.in ABSTRACT: Low power ultrasonic technique is one of the most powerful and useful non-destructive testing tools to investigate properties of polymer/clay composite solutions. When the concentration of the solution is increased. biomaterials. Nagamalai. 1. 3.5.(3) ----. Isentropic compressibility βd = (C2)-1 2. Model F81.2.(7) ----.0 ML-1) were prepared and the measurements were taken for 308 K.3×10-4) X ----. Rao’s Number (R) is given by solution. Surface tension (C3/2) X (6.5.(1) ----. EXPERIMENTAL Analar grade (AR) sample of PEG (400). In this work the following parameters were determined: 1.0. viscosity ( and density ( measurements are extensively used to study the physical and chemical behavior of liquid solutions. India and clay (Aldrich) were used as such in the sample preparation. 313 K. Mittal Enterprises. 3. ACOUSTICAL PARAMETERS The ultrasonic velocity (C).05%. which were cleaned and dried before use. Water. 7.(6) ----. Single frequency ultrasonic interferometer (M/S. Toshniwal Brothers. Intermolecular Free length Lf = k/( C2) k is the temperature dependent constant. Densities of the solutions were measured by specific gravity bottle of capacity 5ml to an accuracy of ±0. toluene supplied by Merck.(5) ----. 2 MHz) and constant temperature water bath (M/S.01° K were used for ultrasonic velocity measurements. The required concentrations of the solution (0.001g) and mixing with the already purified water in glass beakers. India. Viscosities of the solutions were measured by pyknometer to an accuracy of ±0. doubly distilled over alkaline permanganate in all glass apparatus was used as the solvent for preparing the solution. India) to an accuracy of ±0. Specific Acoustic Impedance Z= C 4. Absorption co-efficient /f2 = 82/3C3 8. Adiabatic bulk modulus K = 1/ βd 5.(4) ----. 1. 2. 318 K and 323 K obtained by weighing the solute by a digital balance (accuracy ±0.1 Kgm-3.(8) R = C1/3 V ----. Relaxation time = 4 / 3 C2 6. Delhi.(2) Where V is the molar volume which is equal to molecular weight/density of the 58 | P a g e . 0. Variation of ultrasonic velocity in any solution generally indicates nature of the interaction existing in between molecules in them [1].4. It indicates that weak polymer solvent interactions between PEG in Toluene-clay mixture. 1M) of polyethylene glycol (400) in toluene-bentonite clay mixture at for different temperatures (300C. 0. It indicates that. One of the important properties of a liquid is the free length (Lf) between the surfaces of the neighboring molecules and is the distance covered by the propagating acoustic waves between two neighboring molecules. 2) [3]. The experimental solution shows an increase in acoustical impedance with increasing concentration and also it shows a decreasing value of acoustical impedance with increasing temperature (fig. The adiabatic compressibility decreases with increasing concentration and increases with increase in temperature (fig. It directly gives information about complex formation between solute and solvent (fig.6M.7M. The isentropic compressibility (βd) values of the solutions of different concentrations were calculated from the density and the ultrasonic velocity. The velocity deviation depends upon the increase or decrease in the freelength in the solution after mixing [5]. 0. 0.3M. This is due to formation of more hydrophobic character with increase in concentration as result of solute-solvent-clay interaction. And also it shows non-linear behavior. The value of isentropic compressibility decreases in all system which indicates the presence of molecular interaction in these systems (fig. 4). This is due to strong molecular interaction of PEG (400) in toluene-clay mixture. In this work. there is complex formation between the unlike molecules [2]. 350C. 400C. The variation of the acoustic velocity is given by graph in figure 1. RESULTS AND DISCUSSION The variation of the measured and derived parameters for various concentration(0. 0.2M. 0. The ultrasonic velocity increases with increasing concentration. 3) [4]. The ultrasonic velocity decreases with increasing temperature. The experimental solution shows a decrease in intermolecular free length with increase in concentration and it increases with temperature. In this. The βd value decreases with increase of concentration and increases with increase of temperature.5M. and hence an increase in ultrasonic velocity is observed.4M. 450C) were studied and shown graphically in figures 1-10. It indicates significant interaction between solute and solvent-clay molecules due to which to structural arrangement [6] in the neighborhood of constituent ions are considerably affected. 59 | P a g e .1M. This is in agreement with requirement both ultrasonic velocity and density increase with increase in concentration and also due to effective solute solvent-clay interaction [7]. 5). non-linear increase in velocity may be due to the molecule-clay association. it indicates that there is a complex formation between the solute and solvent-clay mixture. 7).4 0.0 6.1 0.0 8.6 0. The variation of refractive index with concentration has been plotted in fig. the structure of the solution changes by forming association of molecules and clay layers (fig. It may be understood that this relaxation is a structural relaxation.4 0. 9].5 9. 8).5 0.0 0. Poly(ethylene glycol)-400 (PEG-400) in toluene-bentonite clay mixture solution and its physical parameters such as adiabatic compressibility. Isotropic compressibility Vs Mole concentration.0 0. Fig 3.0 0 -1 30 C 0 35 C 0 40 C 0 45 C 9. adiabatic bulk modulus. 10. CONCLUSION Acoustic investigations were carried out for different mole concentrations of polymer/clay mixture in toluene.8 1. Free Length Vs Mole concentration.0 10.0 8.5 12.0 0. absorption coefficient.0 11. 60 | P a g e .5 8. acoustic impedance. surface tension and refractive index were determined. The classical absorption factor of experimental polymer-toluene-clay mixture shows increase of concentration and decreases with increase of temperature and it is characteristic of polymer solvent-clay interaction (fig. This result in high viscous nature and hence the time taken for the flow of ultrasonic wave in the viscous medium increases [8. Similar changes in physical parameters are also observed when the temperature of the solution is varied.2 0. acoustic velocity Vs Mole concentration. intermolecular free length.6 0. When the concentration of the solution is increased. The value of surface tension is plotted against concentration for four different temperatures (300C.5 7. 5.0 6. For increase in concentration. 400C. relaxation time.5 10. This variation confirms the changes in molecular interactions.2 0. Surface tension value increases with increase of concentration and decreases with increase of temperature. Ultrasonic parameters provide information about various intra and intermolecular interactions in solutions.0 7.0 30 C 0 35 C 0 40 C 0 45 C βdX10 N m 2 0 12.6 0.2 0. increases while increasing the concentration and decreases while increasing the temperature.4 0.Relaxation time gives the orientation of the molecules in a particular direction. Fig 2.0 Mole concentration 0. The value of Rao's constant shows decrease with increase in temperature and also increases with increase in concentration (fig.0 9. 350C. 1380 1360 1340 1320 1300 1280 1260 1240 1220 0. correspondingly its various physical parameters change considerably.5 11.5 9.7 MOLE CONCENTRAT IO N MOLE CONCENTRATION Fig 1. The value of the refractive index decreases with increase of concentration and increases with increase of temperature. 450C). It shows the value of classical absorption factor of the experimental solution. 6).3 0. Rao’s number. From the figure.5 10. it is clearly evident that the variation is non-linear. The variation of surface tension is shown in figure 9.8 1.5 30 C 0 35 C 0 40 C 0 45 C 0 -10 LfX10 m -11 C (m/s) 8. 0 -14 10 2 4 5 6.0 9.470 1.0 2 MOLE CONCENTRATION 0.0 0 0.2 7.0 0.4 0.495 1.4 0.2 0.6 6.2 6.4 0.4 7.125 0.0 30 C 0 35 C 0 40 C 0 45 C 0 n Mole concentration Figure 10.66 0.88 0. Fig 9.0 0.82 0. Fig 5.8 1.2 0.5 9.8 1. 1. Refractive index Vs mole concentration.4 6.460 1.0 8.6 0.8 1.0 7.0 0.6 0. Adiabatic bulk modulus Vs Mole concentration. Fig 6.70 0.72 0.0 0.0 0.4 0.6 0.2 0.80 0.8 1.105 0.8 3 30 C 0 35 C 0 40 C 0 45 C 0 25 30 C 0 35 C 0 40 C 0 45 C 0 10.090 6 4 0. Relaxation time Vs Mole concentration.0 0.465 1. Rao’s Number Vs Mole concentration.4 0.0 MOLE CONCENTRATION MOLE CONCENTRATION Fig 4.78 0.5 7.8 1.2 0.74 0.0 0.0 MOLE CONCENTRATION MOLE CONCENTRATION MOLE CONCENTRATION Fig 7.90 0.110 0. Acoustic impedance Vs Mole concentration.0 0.4 0.4 0.0 6.0 5.8 6. Classical Absorption Factor Vs Mole concentration. 7.6 0.120 30 C 0 35 C 0 40 C 0 45 C 0 18 16 14 12 10 8 6 30 C 0 35 C 0 40 C 0 45 C 0 ZX10 Kg/m s 2 KX1010Nm-2 0.0 0.5 30 C 0 35 C 0 40 C 0 45 C 0 20 RX10 2 α/f X10 m/s -1 15 γX10 Nm 8.8 1.2 0.085 0. Fig 8.6 0. 61 | P a g e .455 0.5 6.76 0.68 0.84 0.0.485 1.095 0.500 1.490 1.86 -12 0.480 1.Surface tension Vs Mole concentration.8 1.0 0.115 τX10 sec 30 C 0 35 C 0 40 C 0 45 C 0 0.2 0.6 0.2 0.100 0.6 0.475 1.080 0. Phys. Phys. Nomoto O. 9. Phys. 177... Pure and Appl.. 8.. Vol 65 B. Vijayalakshmi T. Indian J. 6. Indian J Pure and Appl.V and Seshadri A. (1975). 2. Singh R.. Acad sci. Phys. Srinivastar B and Prakash O.V. 312-318. Soc. 57(A). J Polym. 215.3. 62 | P a g e . Sheo Prakash S.T. Phys. 61B. 285-291.A. Narashimham A. (1987). 44-48. (1995). REFERENCES 1. Indian J. Indian J.M. Nambinarayanan T. 553.N.65 B.R. (1987). India. August (1991). Nambinarayanan T. No.K and Srinivasa Rao A. 8. 13. 5. Net. Materials. Phys.K. Sosamma S. Proc. 7. 28..4. 31.P. J. 62B. and Srivastava T. Manuel Stephen A and Gopalan. 105. No. Srinivasa Rao A and Krishnan B. Indian J.6. Japan. 12. 191.S & Naidu P. (1953). (1992). (1988). 3. Vol. Indian J. Narashimham A. 4. Velmurugan S. Phys. Kalyana Sundram S. (1990). given as VM = (x1M1+x2M2) /ρm .01K was used. by mixing the calculated volumes of liquid components in airtight glass bottles.15K.0001g) were made using an electronic balance. St. of Physics. free length. Trichy – 620 002. 63 | P a g e . 3. viscosity and speed of sound is measured for binary mixture of Propanol + Ethyl acetate for temperatures 308. INSREF thermostat with a constant digital temperature display accurate to ±0. INTRODUCTION In this paper density. Armstrong Arasu and Dr. The excess volume. The density.M. I. Viscosity is measured by calibrated Ostwald’s Viscometer. Wada constant. Johnson Centre for Nano Science and Applied Thermodynamics. For all the mixtures and pure solvent. acoustic impedance. free volume& Gibb’s free energy were calculated for binary mixture at the constant temperature of 308.15K. In all the measurements. The accuracy of density measurements was 0. 2. ultrasonic relaxation time.s-1. These data are required in the development of process design and efficiency and in the evaluation of possible environmental impacts. i (4) where the φi is the volume fraction of the ith liquid. The speed of sound was determined using a constant frequency (2MHz) ultrasonic interferometer with an accuracy of ± 2 m. The adiabatic compressibility βa was obtained from sound velocity and density measurements as (3) βa= 1/(u2ρ) The excess adiabatic compressibility was calculated as βa = βam –Σφi βai . A set of 18 and 11 compositions were prepared for ternary and binary mixtures respectively and also their physical properties were measured. ultrasonic velocity. Dept. THEORY The excess molar volume VE was calculated from the density data by the relationship VE = VM –Σ xiVi . The mass measurements (±0. Joseph’s College. (2) where ρm is the density of the liquid mixture. for ternary mixture at the constant temperature of 303. viscosity and speed of sound for ternary mixture of Propanol + Ethyl acetate + water were measured at 303. triplicate measurements were performed and the averages of all values were considered in the calculation.cm-3.15K.0001g. xi the mole fraction of the ith component and VM is the molar volume of the mixture. 1. internal pressure. adiabatic compressibility viscosity. deviations enthalpy. ABSTRACT: Industry demands reliable and accessible reference data on the physical and chemical properties of a wide variety of compounds.15K. India. (1) i where Vi represents the molar volume. EXPERIMENTAL The binary and ternary mixtures were prepared by mass.ACOUSTICAL STUDY ON THERMO DYNAMICAL AND EXCESS PARAMETERS OF BINARY AND TERNARY MIXTURES M. KJ is the temperature dependent parameter which varies directly with the square root of the absolute temperature i.Σ xiVfi i=1 (15) The excess internal pressure of the mixture is obtained using the relation 3 Pi = (Pi)mix –Σ xiPi i=1 (16) The dispersion of the ultrasonic velocity in this system should contain information about the characteristic time τ of the relaxation process that causes the dispersion. K J α √T (9) The excess free length is given as (10) Lf = Lf mix – (ΣxiLfi) i where xi and Lfi.e. The relaxation time τ is estimated from the following relation 64 | P a g e ..Rg . On the basis of the dimensional analysis using the free volume concept. are the mole fractions and inter-molecular free lengths of the respective components. u. Equations (13) and (14) are used for mixtures for which parameters such as M. Ka is the constant having value of 4. Lfmix is the free length of the ternary mixture.28x109. ρ and η corresponds to those mixtures.Σxizi (12) i The free volume of a liquid and liquid mixture can be calculated using the formula Vf = [Mu/Kaη]3/2 . The Wada’s constant was calculated using the formula W = (Meffβa -1/7)/ρ (7) The inter molecular free length was calculated using the formula given by Jacobson et al.is the gas constant and T is the temperature in degree Kelvin . (11) where u is the ultrasonic velocity and ρ the density. independent of the temperature and nature of the liquids and η is the viscosity. Suryanarayana suggested the expression for the internal pressure as Pi = bRgT [Kaη/u] 1/2ρ2/3/Meff7/6. i (5) (6) The excess viscosity is obtained as η = ηm – Σxiηi . i where ηm and ηi refer to the viscosity of the mixture and pure components respectively . (8) where KJ is Jacobson’s constant. u is the ultrasonic velocity. (14) where b is the space packing factor (equal to 2 in the present case) . (13) Where M is the molar mass of the liquids. The acoustic impedance is given as Z = ρu. The excess free volume of the mixture is given as 3 Vf = Vfmix . The excess acoustic impedance is given as Z = Zmix . Lf = KJ √ βa .φi = xiVi/ΣxiVi . The excess enthalpy of a binary mixture is obtained from the fundamental relation 3 H= Σ (xiPij Vj . The excess adiabatic compressibility values are also positive which confirms 65 | P a g e . ultrasonic velocity. Wada for 35 constant.(Pi)mixVm. The negative values suggest that there is a decrease in free length and compressibility.15. Z = uρ adiabatic compressibility.The excess internal pressure is negative which shows that the presence of cluster formation. When the mole fraction of any one of the three liquids kept constant and the mole fraction of the other three liquids have been varied Wada’s constant variation is nonlinear. The relaxation amplitude and Gibbs free energy also positive in most of the mixture. It has been found that the free volume of liquid molecules depends on the particular temperature of the liquid at which it is measured. The excess internal pressure is negative which shows the presence of cluster formation. βa = 1/ (u2ρ) shows that the behaviour is opposite. adiabatic compressibility. viscosity and speed of sound 0 C for the system of binary mixtures of Ethyl acetate + Propanol and the excess volume. LEf are positive which shows that there is increase in free length and compressibility. ultrasonic relaxation time. internal pressure. The relaxation amplitude and Gibbs free energy also negative in most of the mixture. the negative value suggest that the force between pairs of unlike molecules are less than the forces between the forces of like molecules while positive value suggest that the force between pairs of unlike molecules are greater than the forces between pairs of like molecules . When the mole fraction of any one of the three liquids kept constant and the mole fraction of the other three liquids have been varied Wada’s constant variation is linear. The free volume plays a important role in ultrasonic wave propagation in liquids found that the free volume of liquid molecules depends on the particular temperature of the liquid at which is measured. The trend of variation of Vf is opposite to the change in the Pi. free length. The free volume plays an important role in ultrasonic wave propagation in liquids. For the system of ternary mixtures (Ethyl acetate+ Propanol + Water) at 303. LEf are negative and positive. The Vf values are positive while VEf are negative. viscosity. V another. For the system of binary mixtures Ethyl acetate + Propanol the excess adiabatic compressibility and excess volumes values are also positive which indicates that influence of -OH bonding interaction or E. deviations in enthalpy. RESULTS AND DISCUSSION In reference with table 1and 2 gives experimental results density. Excess volumes are positive which proves the influence of – OH bond interactions over dispersion type interactions. the Gibb’s free energy of activation for the relaxation process ∆G was obtained as 1/τ = KT/h) exp (-∆G/kT). The positive values suggest that there is a increase in free length and compressibility .K (Table 3&4). ηE are negative and positive. free volume & Gibb’s free energy are calculated at the constant temperature of 308 K. (18) where k is the Boltzmann’s constant and h is the Planck’s constant. βaE are negative indicate interstitial accommodation of one liquid molecule into chemical forces. acoustic impedance.τ = 4η/3ρu2 (17) From the Eyring’s rate process theory. the ηE values are positive in most of the combinations of the ternary system studied. According to Fort and Moore ηE values are negative in system of unequal molecular size which is very much evident. Specific acoustic impedance is the complex ratio of the effective sound pressure at a point to the effect particle velocity at that point. The mathematical relations for specific acoustic impedance. i=1 (19) (20) The classical absorption or relaxation amplitude is given by (α/f2)cl= (8∏2η/3ρu2 ) 4. 0012 .3002 0.6002 0.0174 -0.0011 0.7991 0. The free volume plays an important role in ultrasonic wave propagation in liquids found that the free volume of liquid molecules depends on the particular temperature of the liquid at which is measured.6958 0.4004 0.1247 0.8055 8.1514 -7.1186 0.00056 0.00081 0.1002 7. The relaxation amplitude and excess Gibbs free energy also positive in most of the mixture.665 0.7866 0. βa = 1/ (u2ρ) shows that the behavior is positive .00048 0.0010 0.8085 0.0008 0.Specific acoustic impedance is the complex ratio of the effective sound pressure at a point to the effect particle velocity at that point.0000 Table -2 Ethyl Acetate + Propanol 66 | P a g e .1055 0. The VE and βaE are negative indicate interstitial accommodation of one liquid molecule into another.7470 8.0371 -6. Table -1 Ethyl Acetate +Propanol S.1348 -7.4862 1.7403 0.1462 0.0000 P i x106 pa 0.8612 8.4394 0.sm-2 U ms-1 W τD x102 pa G KJ/mole Z x105 Kgm-2s-1 Z x105 Kgm-2s-1 0.1003 0.1980 0.0000 0.1393 0.3501 1.0000 0.0007 0.00088 1085 1090 1096 1100 1107 1112 1118 1123 1129 1134 1140 2855 2778 2726 2659 2574 2517 2458 2376 2320 2240 2166 0.1863 0.00063 0.8460 8.9447 8.0066 0.1660 0.0176 -0.0008 0.0846 -7.6611 8.0007 0.7534 1.1317 0.the above fact.1246 -7.9352 1.332 5.9396 5.7999 0.7001 0.0051 -0..0099 -0.6505 8.1101 0.0009 0.000 5.7747 0.0063 -0.9756 -6.00067 0.2026 Pi x106 Pa 1 2 3 4 5 6 7 8 9 10 11 1.0000 -0.1570 0.00054 0.0007 0.0008 0.0147 -0.0165 -0. When the mole fraction of any one of the three liquids kept constant and the mole fraction of the other two liquids have been varied.9478 8. NO X(i) ρ x10-3 kgm-3 η N.00049 0.9002 0.9397 8.7549 0.5001 0.0009 0.00058 0.7.2305 10.2012 -7.8209 0.0126 -0.7493 0.00070 0.7703 0.00061 0.4971 8.5228 8.8244 0.8005 0.0598 -7.1946 -7. S. NO X(i) VE x106 cm3/mol βa x10-10 m2n-1 0.0000 -0.0578 -0.0216 -0.0019 -0.1224 -0.0618 -0.0247 -0.0676 0.0207 -0.0044 0.0000 U ms-1 0.0000 -0.4890 -0.0055 -1.4945 0.0110 -0.4945 0.0221 -0.4890 -0.1100 -0.4835 0.0000 H KJmol-1 0.0000 0.0031 0.0024 0.0046 0.0062 0.0076 0.0101 0.0094 0.0111 0.0033 0.0000 G Kg mol-1 0.0000 -0.9407 0.0567 -0.5124 -1.1328 -1.3814 -2.1084 -2.1129 -2.6259 -0.4720 0.0000 α/f2 x10 -15 M-1s-2 0.0000 -0.4890 -0.0055 -1.4945 0.0110 -0.4945 0.0221 -0.4890 -0.1100 -0.4835 0.0000 Vf x 106 m3/mol 0.1055 0.1101 0.1186 0.1247 0.1317 0.1393 0.1462 0.1570 0.1660 0.1863 0.2026 Vf x 10 m3/mol 0.0000 -0.0051 -0.0063 -0.0099 -0.0126 -0.0147 -0.0176 -0.0165 -0.0174 -0.0066 0.0000 Lf x106 m3/mol 64.6100 64.4506 64.5874 64.6733 64.3206 64.5382 64.6829 64.5786 64.8873 64.8422 64.8918 Lf x 106 m3/mol 0.0000 -0.1875 -0.0790 -0.0212 -0.4020 -0.2127 -0.0960 -0.2286 0.0513 - 0.021 0.0000 1 2 3 4 5 6 7 8 9 10 11 1.0000 0.9002 0.7999 0.7001 0.6002 0.5001 0.4004 0.3002 0.1980 0.1003 0.0000 0.0000 -0.3853 0.3108 0.4028 -0.357 0.1794 0.5836 0.0405 0.6888 0.1970 0.0000 Table: 3. Ethyl Acetate + Propanol + Water at 303.15 K S. No βa X (i) Y (i) x10-10 m 2n-0.849 -0.843 -0.056 0.1923 -1.272 -0.208 -1.954 -1.669 -1.409 -0.375 -0.645 -0.359 -0.110 0.1595 0.8763 1.1157 0.5194 0.4136 V x106 m3 -7.751 -7.129 -3.654 1.0247 0.3595 0.9844 1.7183 0.8048 0.8051 0.9399 1.0809 0.9648 0.8286 0.9700 1.0948 1.8614 1.7196 1.2972 H Kg mol-1 G Kg mol-1 η x10-3 m2s-2 U ms-1 Lf x103 A0 Pi x 106 Pa -0.1029 -0.1526 -0.2233 -0.2642 -0.2905 -0.2142 -0.2749 -0.2456 -0.2505 -0.2161 -0.1926 -0.1391 -0.0855 -0.0484 -0.0552 -0.0619 -0.0653 -0.0706 Z x105 Kgm-2s-1 -45.0507 -23.8818 -67.1043 -130.728 -54.6449 -137.012 -7.1016 -26.0531 -41.4531 -96.7512 -63.2401 -52.2058 -42.9605 -35.9857 -68.4114 -81.2803 -54.2248 -47.9292 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.7214 0.6277 0.5056 0.4206 0.3195 0.2129 0.1005 0.0992 0.1010 0.1001 0.0988 0.0971 0.0962 0.0994 0.1890 0.3051 0.3998 0.5156 0.1005 0.1013 0.0978 0.0977 0.0988 0.0963 0.0982 0.2048 0.3084 0.4105 0.5128 0.6374 0.7296 0.8116 0.7254 0.6114 0.5166 0.3973 -0.0094 -0.0115 -0.0058 -0.0026 -0.0048 -0.0418 -0.0011 -0.0154 -0.0081 -0.0115 -0.0037 -0.0025 -0.0083 -0.0027 0.0021 0.0068 0.0087 0.0110 5.0567 7.4368 7.9435 10.540 13.331 22.368 12.979 15.910 13.140 11.996 9.1613 6.6955 6.6639 3.1532 0.901 -0.436 -0.407 -1.320 0.0000 0.0000 0.0000 0.0001 0.0001 0.0005 0.0002 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 -0.0001 -0.0001 -0.0001 -0.0001 -19.367 -28.411 -65.872 -46.903 46.183 -23.433 164.332 115.777 92.543 12.969 38.350 20.018 4.2955 -10.096 -55.817 -65.827 -34.074 -31.199 -1.206 -0.451 3.0749 4.4056 -0.188 3.6783 -3.398 -2.201 -1.431 1.8625 0.4016 0.6575 0.9078 1.2242 3.5664 4.3443 2.4920 2.1951 67 | P a g e Table: 4. Ethyl Acetate + Propanol + Water at 303.15 K S. N o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 X (i) 0.7214 0.6277 0.5056 0.4206 0.3195 0.2129 0.1005 0.0992 0.1010 0.1001 0.0988 0.0971 0.0962 0.0994 0.1890 0.3051 0 3998 0.5156 Y (i) 0.1005 0.1013 0.0978 0.0977 0.0988 0.0963 0.0982 0.2048 0.3084 0.4105 0.5128 0.6374 0.7296 0.8116 0.7254 0.6114 0.5166 0.3973 ρ x10-3 kgm-3 0.9063 0.9113 0.8831 0.8277 0.8438 0.8433 0.8393 0.8311 0.8093 0.7911 0.7767 0.7661 0.7602 0.7533 0.7613 0.7656 0.7757 0.7898 η N.sm-2 0.00067 0.00071 0.00070 0.00077 0.00087 0.00130 0.00099 0.00110 0.00100 0.00099 0.00093 0.00091 0.00097 0.00090 0.00079 0.00071 0.00068 0.00062 U ms-1 1129 1131 1108 1137 1242 1185 1386 1336 1311 1230 1254 1234 1217 1201 1146 1124 1146 1137 βa x10-10 m 2n 0.0483 0.0342 W 2200 1994 1769 1689 1471 1205 999 1147 1323 1472 1653 1849 1991 2131 2177 2271 2350 2414 τD x102 ps 0.0008 0.0008 0.0009 0.0010 0.0009 0.0015 0.0008 0.0010 0.0010 0.0011 0.0010 0.0010 0.0011 0.0011 0.0011 0.0010 0.0009 0.0008 G Kg mol-7.0109 -6.9904 -6.9660 -6.9206 -6.9515 -6.7438 -6.9870 -6.9080 -6.9210 -6.8623 -6.8970 -6.8868 -6.8453 -6.8617 -6.8815 -6.9123 -6.9521 -6.9917 Z x105 Kgm-2s-1 10.2321 10.3068 9.7847 9.4109 10.4800 9.9931 11.6327 11.1035 10.6099 9.7305 9.7398 9.4537 9.2516 9.0471 8.7245 8.6053 8.8895 8.9800 Pi x 106 Pa 0.1599 0.1842 0.2133 0.2403 0.2937 0.4567 0.4842 0.4385 0.3582 0.3205 0.2720 0.2379 0.2264 0.2025 0.1858 0.1679 0.1567 0.1443 Lf x103 A0 58.7083 58.4435 60.6017 61.0004 55.3080 57.9856 49.6944 51.8079 53.5022 57.6778 57.0959 58.4213 59.4668 60.5344 63.1054 64.1597 62.5170 62.4468 0.0082 -0.0098 -0.0314 -0.0580 -0.0641 0.0265 0.0713 0.0935 0.1042 0.1089 0.1094 0.1122 0.1784 0.2238 0.2325 0.2134 68 | P a g e 5. REFERENCES Periodicals [1] I. Johnson, M.Kalidoss and R.Srinivasamoorthy, 2001, Acoustical investigation of some binary and ternary liquid mixtures – Proceedings of the 17th international congress on Acoustics (ROME), ,Vol.I,Physical Acoustics – Part B,(12). [2] Pandey,J.D. and Ashok kumar, 1994,Ultrasonic velocity in pure liquids, J. Pure and Applied Ultrasonic, 16(63). [3] J.P.E.Grolier, and A.Viallard, 1971, J.chem.phy. 68(1442) [4] J.ortaga, J.A.Pena, M.I. Paz-Andrade, and E. Jimnez, 1985 J. Chem. Thermodyn.17(1127). [5] V.D.Gokhale and N.N.Bhagavat, 1989, Evaluation of Ultrasonic Velocities in some Binary Liquid Mixtures by Rao Specific Sound Velocity. J.Pure and Appl.Ultrasonic., 11(21). [6] C.V Sorianarayan , 1976 ,J Acoustics Soc. Of India ,4 ( 76). [7]Senanayake,P.C., Gee,N. and Freeman,R.G.1987Can. J.Chem.Eng.Data,65(2441). [8] Kalidoss.M and Srinivasamoorthy .R, 1997 J.Pure and Appl.Ultrasonic 19,(9). [9] Viswanatan ,S, and Anand rao,M, 1999.J.Chem. Eng.Data 45,(764). [10] Ambinabhavi ,M and Virupakashagouda , 1998,J.Chem.Eng.Data 43,(497) Books [1]Riddick,J.A., Bunger,W.B., Sanako,T.K., 1986, Physical properties and methods of purification , John Willy & Sons ,New York, [2] Hirschfelder, J.O, Curtio, and Byron bird .R., 1950,Molecular theory of gases and liquids.John Willy & Sons, New Yark. Others [1] R.N.Fort and W.R.Moore – 1965Trans.Faraday Society 61,(2102) [2] Handbook of Chemistry and Physics, 1984, The Chemical Rubber Company, USA, [3] Zorebski,E Zak, A Z.1999 Physikalis che Cheie. 210,(223). [4] Chauhan , M.S. Sharma, K.C et al .1995 Acoustics letters 18,12,(223) [5] Mukhrejee,A.Kamila ,S et al ,1999, Acoustics letters 23,1,(17) [6] Belsae, N.s. Akhare, V.P and Deogaonkar, V.S, 1990, Acoustic letters 14,2,(37) 69 | P a g e STUDY ON THERMO-ACOUSTICAL PARAMETERS OF SOME BINARY MIXTURES FROM VOLUME EXPANSIVITY DATA M.M. Armstrong Arasu and Dr. I. Johnson Centre for Nano Science and Applied Thermodynamics, Dept. of Physics, St. Joseph’s College, Trichy – 620 002, India. ABSTRACT: Researches have previously shown that the contribution of internal pressure and the temperature coefficient of volume to the sound velocity in the condensed phase is significant and that volume expansivity is the controlling factor for satisfactory description of the various parameter which describe the thermo-acoustic properties of polycrystalline solid, metal, alkali halide salt, polyatomic ionic liquid and organic liquid mixtures. Such a description employs only volume expansivity data. From the volume expansivity data the isothermal, isobaric and isochoric acoustical parameters, Moelwyn-Hughes parameter, fractional free volume, Huggin’s parameter, sharma’s parameters and repulsive exponent in Mie’s potential have been evaluated. Keywords: volume expansivity , Gruneisen parameter, Moelwyn-Hughes parameter, fractional free volume, Huggin’s parameter and Sharma’s parameters. 1. INTRODUCTION The volume expansivity data is highly useful for evaluating Gruneisen parameter which is a useful quantity in studying the internal structure, molecular order and thermo acoustical properties of liquids and polymers. The important of volume expansivity in evaluating various thermo acoustical properties has been amply demonstrated earlier. In this paper an attempt is made to analyze the relationship between different parameters that are used for system description like Moelwyn-Hughes parameter, fractional free volume, Huggin’s parameter, Sharma’s parameters and repulsive exponent in Mie’s potential have been evaluated in the mixtures Ethyl acetate + n-propanol and Methyl acetate + n-propanol at 308.15K. It is interesting to note that all these thermo acoustical properties are linked to a single experimentally determinable quantity, volume expansivity. 2. EXPERIMENTAL The binary mixtures were prepared by mass, by mixing the calculated volumes of liquid components in airtight glass bottles. In all the measurements, INSREF thermostat with a constant digital temperature display accurate to ±0.01K was used. For all the mixtures and pure solvent, triplicate measurements were performed and the average of all values was considered in the calculation. The mass measurements (±0.0001g) were made using an electronic balance. The accuracy of density measurements was 0.0001g.cm-3. A set of 11 compositions was prepared for binary mixtures and their physical properties were measured. Viscosity is measured by calibrated Ostwald’s Viscometer. The speed of sound was determined using a constant frequency (2MHz) ultrasonic interferometer with an accuracy of ± 2 m.s-1. 3. THEORY The volume expansivity is given by α= 1 dV 1 dρ = V dT ρ dT (1) 70 | P a g e 1 + 2αT (3 + 4αT ) S0 = ~ V C1 4 S * = 1 + αT 3 * S0 = (5) (6) (1 + 2αT ) 4 1 + α T 3 * S 0 S1 . S. (9) k’ = k = k’’ In which 1 ∂lnu ∂lnu k = - = . β ∂P T ∂V T 1 ∂ ln u 1 ∂lnu k" = k' = k = − α ∂T P β ∂P T 5 1 2αT + + 3 2αT 3 (10) (11) (12) Alternatively. F = 2− S *+ ( ) (8) Eqns. C1. Carnevale and Litovitz. While examining the relationship between sound velocity u and density in liquids and determining the difference between k and k’ in liquids. and respectively molar volume. α ∂T P ∂ ln V P 1 ∂lnu ∂lnu k' = - = . since all the parameters involved therein may be determined from the knowledge of alone.Let V. S0. β = ~ ~ β = V C1 β* 3 ~ αT V V = 1+ V * 3(1 + αT ) (2) (3) The Moelwyn-Hughes parameter is C 1 = dlnβ dlnV = 13 + αT 3 ( ) −1 4 + αT 3 (4) The Sharma’s parameters are expressed as. and Sharma have shown that the isochoric acoustical parameter k’’ is given by. due to Rao.1 αT (7) Huggin’s parameter F is given in terms of Sharma’s parameters given above as. (1)-(8) demonstrate the importance of in the evaluation of the parameters V. Volume expansivity and isothermal compressibility. S0* and F. the their reduced values are given by. The volume dependence of sound speed in liquids at constant pressure and at constant temperature is represented by isobaric and isothermal acoustical parameters k and k’ respectively. Aziz. If * and V* are the characteristic compressibility and volume (at absolute zero temperature and zero pressure). the isobaric and isochoric acoustical parameters may be expressed in terms of α as k= (13) 71 | P a g e . liquids. They are characterized by high values of ’. V f k' f B* = 1+ k A* = 1+ (17) (18) The pseudo-Gruneisen parameter used for structural study of liquids is usually expressed as Γ= αV Mu 2α (γ − 1) = = β s Cv Cp αT (19) The Gruneisen parameter is an important quantity of current interest because of its usefulness in studying the internal structure. Cp and Cv are respectively the isobaric and isochoric heat capacity of the liquid. For organic molecules. this fact can be explained by noting that not all the normal mode contributions to heat capacity Cp also contribute to the volume change of the sound speed (molecular rotation. including intermolecular and intra molecular vibrations which employ thermodynamic parameters such as the isochoric Cv and isobaric Cp heat the intermolecular vibrations on the heat capacity Cp in quasi spherical molecular liquids and fluorocarbon fluids. The ratio of the Gruneisen parameters (/’) is utilized to measure the intermolecular isobaric heat capacity and the adiabatic bulk modulus due to the molecular vibrations in these liquids. f = Va/V = (k’+1)-1 (15) The repulsive exponent n in the Mie’s potential is given by. It may be clearly pointed out that the concept of ’ and is appropriate to all the solids. The low frequencies of these modes are determined almost entirely by the weak intermolecular forces.k" = - (2αT ) −1 − C1 −V +1 − C1 (14) Using these calculated values of k and k’’. and arise from the strong intra molecular forces which are altered little by pulling the molecules apart. where = Cp/Cv. n = 3 (2k’ -3) (16) The equation (13) can be rearranged to give the dimensionless thermo acoustic parameters A* and B* as. while is an average over all modes of vibration. Swamy overlooked the basic conceptual aspect that and ’ may not have the same values for different substances. the isothermal acoustical parameter k’ can then be calculated for the binary liquid mixtures. should be used in eqn. 72 | P a g e . for example).M. the analysis of the theoretical foundations of the relationship between ’ and t is essential for this class of liquids. The fractional free volume f which is a measure of disorder due to the increased mobility of molecules in a liquid and can be expressed as. using eqn(9). As relatively little is known about the influence of the intermolecular vibration. liquefied gases and polymers which show anharmonicity of molecular vibrations. It was shown that ’ and in case of organic liquids differ from one another. including intermolecular and intra molecular vibrations which employ capacities of the liquid. The analogous situation in the case of polymeric materials has already been noted. There are two distinct modes are of low frequency and are anharmonic. only a fraction Cp’ of the total cp that is taken up by the molecular vibrations which interact with volume. experimentally it is observed that ’> which implies that a certain fraction of the molecules in a molecular liquid has a finite and common fractional frequency dependence on the volume at a constant temperature and the remaining modes are unaffected by volume changes. The sound speed can be expressed as u2 = s. K. molecular order and other thermo acoustic properties of polymers and liquids. We have a distinct relationship between the microscopic isothermal Gruneisen parameter ’ (as a measure of anharmonicity of the normal mode frequency v of the molecular vibrations). and the conventional thermodynamic Gruneisen parameter ’ (used for the structural study of liquids). However. They are characterized by low values of .(15). The anharmonic (microscopic isothermal) Gruneisen parameter ’ is determined primarily by the intermolecular vibration. Following Hart-mann. molten metals. The intra molecular optical modes of vibration are of high frequency and are harmonic. In order for to be as large as ’. Much confusion has existed in literature to recognize the difference between ’ and for liquids. while r is an average over all modes of vibration. S*.1 to 1.07 respectively in the case of fluorocarbon fluids. in other nonassociated of the liquids. It may be absorbed from table 1 and 2 that C values vary from 6. liquid alkali metals and ionic liquids.It may be interesting to note that So* is equal to 1.Thus (20) ’u α/Cp’ From eqns (19) and (20) it follows that X-1 = /’ = Cp’/Cp (21) Eqn(21) shows that the quantity X = /’ is of some interest since it gives a simple method to measure the ration C’p / Cp for a complex liquid and hence Cp which refers to that part of the isobaric heat capacity taken up by molecular vibrations which interact with volume. So.2 to 4.1 as compared to the range from about 5 to 14 for the molen alkali halides and 4 to 6 for polymers. The Value of the Huggin’s parameter ranges from about 0. which is the same order as reported by Sockiewies. for liquid. The estimated values of So are on the average.8 for the liquid mixture studied in agreement with the value of C.05 for fluorocarbon fluids.49.(26) lead to a way to determine the Beyer’s nonlinear parameter theoretically.( -1) (-1) (24) (25) (26) (23) Eqns (23) .3 to 18.5 for polymers . A*. This signifies the non –linear variation of volume expansivity of the liquids with mole fraction. for binary liquid mixture of Propanol + Ethyl acetate and Methyl Acetate + n-proponol using only the experimental data of density at three different temperatures.S. The Calculated acoustical parameter k range from 0.4 to 1. 4. The value of reduced compressibility s ranges from 5. N.05 for holds for these liquids mixtures as compared to A* =B* =1.8 with different mole fraction.2 similar to that of poly crystalline solids. s.2 for the binary mixture as compared to 1. k”. B* and k/ k’.~ . crystalline and molten alkali halides.2 to 1. The value of n is found to 13. This means that on the average the approximate relationship A* = B* = 1. The calculated values of S* are around 1.3 which is of the same order as observed for polymers.03 to 1. 73 | P a g e .1 to 1. k. The Sharma’s parameter So may be termed a molecular constant which varies its constancy for a wide verity of binary mixtures for investigating thermo acoustic and an harmonic properties. The Andeson-Gruneisen parameters has been expressed as ∆= 1 ∂inβ s = 2k + 1 α ∂T P (22) Beyer’s nonlinearity parameter B/A of liquids can be obtained from the distortion of the finite amplitude waves. the value of the ratio k/k’ is close to about unity. F.8 to 9. C. and from the variation with pressure and temperature of the sound velocity.2 to 13.4 in the mixtures. RESULTS AND DISCUSSION In the table 1to 4 give the calculated values of . f. The B/A is a particular combination of the temperature and pressure derivation of the sound of speed is a given by B ∂u 2uαT ∂u = 2 ρ u + A ∂T T C P ∂T P which can be rewritten as Where B/A = (B/A)’ + (B/A)” (B/A)’ = (C1-1) (B/A)” = . lie the range 1. The average values of the dimensionless parameters A* and B* for the liquid mixtures examined have the value 1. The value of So remains fairly constant within the experimental error. 0020 1.58901 1.2874 7.68684 7.7083 3.7486 1.6 0.1380 0.2145 0.0 1.19984 1.2036 14.0630 0.345 1.2986 7.48480 1.5594 1.600 1.5 0.61914 10.0 7.0 1.43861 1.14892 -4.2749 1.3921 1.6355 1.51888 1.56194 -2.1769 0.59940 1.4734 1.6766 3.9915 0.1064 6.0476 3.0601 0.0724 1.8537 X(i) V~ 1 C ~ V~ S C So S* F k k” k’ f n A* B* k/k’ Table -2 Nonlinear parameter of Ethyl Acetate + proponol (Temp=30.6697 3.5068 1.8940 1.8691 0.7096 3.461 1.0075 3.31869 1.0520 1.4280 1.9 1.0 1.05019 9.41481 1.0629 0.4252 1.6918 1.7178 1.5904 14.7880 1.5438 1.9135 3.1791 7.4644 1.31574 7.2003 14.9102 0.1609 1.1077 6.9093 1.1930 0.6713 3.1681 0.62270 1.4573 1.1577 1.4964 1.17239 -2.2009 14.4901 1.0501 1.3713 1.Table -1 Nonlinear parameter of Ethyl Acetate + proponol (Temp=30.531 1.55469 1.2521 0.38637 1.5435 1.8 1.74042 6.45090 1.9318 3.2746 7.5 1.1664 0.037 0.0 1.3683 6.1111 6.2718 0 6613 3.6867 1.2 1.68674 6.0619 0.460561 9.0978 0.9294 3.8562 0.1230 1.49644 6.1125 7.3022 7.425764 9.9195 0.2 0.1985 15.4098 1.472 1.8270 0.72356 -3.4510 1.2032 14.1554 1.46449 7.6 1.89407 Table -3 Nonlinear parameter of Methyl Acetate and n-proponol (Temp=30.225 1.1685 0.2059 14.7 1.9336 0.1118 6.5459 1.0533 1.8292 0.0531 1.1793 0.50033 10.4 0.2414 6.6149 1.9 1.3203 7.3 1.4708 2.2189 0.3434 0.3286 0.9121 0.31563 6.4903 7.2795 7.2322 0.1 0.6213 3.0515 1.137 1.8287 0.3030 1.2373 0.3216 1.0518 1.1075 6.4 1.7460 7.89416 1.6321 3.7 0.50428 7.74051 7.3328 0.0 0.4579 1.9954 3.2760 2.8409 0.8441 1.0530 1.0594 0.27615 7.35and 40 0 C) Note: x(i) is Mole fraction of Methyl Acetate 74 | P a g e .8318 0.47084 6.9730 1.5042 1.853 1.1146 7.0518 1.6506 1.1116 7.0652 81376 0.2053 14.215 1.715938 9.4 1.0613 3.0349 0.7373 1.9218 0.2936 7.517 1.0972 3.1153 7.3156 2.8 1.46456 10.3268 1.1219 0.0649 0.77381 -2.0650 0.0991 6.3 0.5 1.3488 1.04519 10.46439 6.1608 0.9756 0.35and 40 0 C) Note: x(i) is Mole fraction of Ethyl Acetate X(i) 1.2618 7.3014 7.1785 1.1 1.1644 1.6780 3.3702 0.0520 1.8266 0.0784 7.272562 (B/A)” -4.2702 1.58580 -3.35and 40 0 C) Note: x(i) is Mole fraction of Ethyl Acetate X(i)1 1 1.302373 9.8169 0.3 1.38008 1.0575 0.54363 7.2335 0.32162 6.4990 1.2020 14.27603 6.1168 7.8165 0.4609 1.7 1.37495 -3.2035 14.63815 1.12354 1.8443 0.2978 7.8674 0.8565 7.3616 1.0491 1.9930 3.9848 3.2031 14.949 1.64924 1.879134 9.1491 1.4434 1.08175 (B/A)’ 10.6 1.7404 1.6201 6.02948 -3.37848 (B/A) 6.2671 1.5083 1.5008 1.9 0.692 1.34309 -4.9747 7.3256 7.8 0.92932 -2.54354 6.45479 1.50418 6.2482 0.1578 0.7181 3.2354 0.4470 0.47094 7.0926 1.3195 7.32172 7.1110 6.20045 1.204 1.0625 0.2054 14.9827 3.0624 0.5476 1.7766 1.1668 0.1 1.2 1.0505 1.49654 7.65691 1.1765 0. 2116 13.0744 0.328334 9.691925 6.882 1.2037 14.1339 0.267194 7.717821 5.1799 0.9095 3.5 0.5499 1.8504 3.6123 1.0943 1.9837708 .4516 1.9546 0.518882 1.748702 6.460 1.717931 6.9817998 .9695939 .748593 5.8539 1.8377 3.884011 8.2077 13.1555 1.355 1.909399 7.8372 1.414816 1.938812 -3.630624 9.7755 10.5100 1.7318 0.8422 3.2060 14.0656 1.0631 0.8720 3.0678 0.7043 2.0736 0.9082 0.0544 1.1109 1.0 6.8027 7.0594 0.8113 1.909846 -2.737373 1.409254 -3.7203 0.599735 -2.0569 1.787998 5.8038 3.0873 1.909297 6.0615 0.1998 0.2118 13.6219 3.450904 1.57974 -3.35and 40 0 C) Note: x(i) is Mole fraction of Methyl Acetate X(i) 1.061678 (B/A)” -3.943 1.8099 1.911823 8.5622 1.656918 1.322 1.691812 5.7522 3.018563 (B/A)’ 9.0740 0.1689 0.0502 1.1899 0.4210 2.1257 1.9710738 .554692 1.0711 0.756214 -3.7247 0.001978 6.8441 Table-4 Nonlinear parameter of Methyl Acetate and n-proponol (Temp=30.7 0.8131 7.7627 1.844169 6.2362 0.7861 9.348 1.5835 2.692 1.964404 .7434 0.197252 9.2101 13.2119 3.9398 1.0553 1.6656 1.904 1.551 1.0559 1.122 1.622704 1.0657 0.457373 6.1152 1.0563 1.2303 0.6 0.1007 1.0806 1.390 1.380082 1.8459 0.911737 9.8537 0.5292 2.0521 1.975575 8.2671 6.7684 11.8138 0.4769 2.9804 3.8953 1.449 1.9935296 1.3 0.0721 0.9817346 .0606 3.7817 0.123152 7.8589 0.0728 1.2422 0.866835 8.1 0.457465 7.2287 0.8 0.7805 9.6794 3.8614 3.58901 1.690 1.7723 3.788105 6.241714 -3.0696 0.3085 1.228 1.1979 1.2 0.4303 1.9 0.2091 13.2003 14.484806 1.7716 11.9679546 .0010 0.2239 0.7201 3.9722448 .8745 0.8940 0.4 0.1061 1.7654 12.760957 -2.7806 3.454365 -2.0730 0.085779 8.474034 9.0568 1.8261 6.0 0.2113 13.002077 7.7935 8.737284 75 | P a g e .7585 0.123055 6.066279 -2.9782763 .9220 0.0499 1.7179 0.0570 1.588 1.7173 1.0583 1.~ S So S* F k k” k’ f n A* B* k/k’ 13.493 1.2163 0.6459 2.345 .2108 13.0534 1.0566 1.2088 0.3686 0.9906 0.844065 5.8214 3.324394 (B/A) 5. 1997 J. and A. 210. N.ortaga. V.D.O. Evaluation of Ultrasonic Velocities in some Binary Liquid Mixtures by Rao Specific Sound Velocity.I. REFERENCES: Periodicals [1] I. and Byron bird.1995 Acoustics letters 18.M.S et al . M. J.Ultrasonic. Swamy. M. 2001.(37) 76 | P a g e ..17 (1127).(2102) [2] Handbook of Chemistry and Physics. USA.(12). Eng.Physical Acoustics – Part B.2.Eng.5. 1986. J.Kalidoss and R. 1989.J Acoustics Soc. 11(21).Bhagavat.G. Others [1] R.1987 Can.C et al . Molecular theory of gases and liquids.Data. 16(63).T.Gokhale and N.Ultrasonic 19. New Yark.J.1999. chem. [3] Zorebski.A.N.N. Physical properties and methods of purification . Chem.B. Of India. [8] Kalidoss..Ultrasonic velocity in pure liquids.R. 68(1442) [4] J. Sharma. Thermodyn. Acoustics letters 23.(223) [5] Mukhrejee.P. J.1999 Physikalis che Cheie. J.Grolier.Srinivasamoorthy. (764). A Z. Sanako.P and Deogaonkar.Pure and Appl. Chem. The Chemical Rubber Company.(9). Bunger.Jimnez. 1985 J. J. R. 1971. Pure and Applied Ultrasonic. . 1994. and Freeman.Data 45. M.65(2441). 1950. phys.Chem. [4] Chauhan .Data 43.John Willy & Sons... [9] Viswanatan. [10] Ambinabhavi. M and Virupakashagouda. Paz-Andrade. 4 (76). Acoustic letters 14.D.197(1973) Books [1]Riddick.(497) [11]K. S.New York. Curtio.Moore – 1965Trans.P.J.K. Gee. K.N.M.E Zak.Chem. J.Fort and W. 1998. [2] Pandey. Eng.Vol.Viallard. [2] Hirschfelder. and E. John Willy & Sons . and Ashok kumar. [3] J.I.Faraday Society 61.S. Acoustical investigation of some binary and ternary liquid mixtures – Proceedings of the 17th international congress on Acoustics (ROME).A. 1976 . [7]Senanayake.Pure and Appl.E. [5] V.(17) [6] Belsae.A.W.S. Acoustic (Germany) 29.Kamila ..J. [6] C.M and Srinivasamoorthy . R..12. 1999. Akhare. V. and Anand rao.R.Pena.C. 1990. 1984.V Sorianarayan .s.(223). J. Johnson.1. com Ultrasonic measurement can be used as a powerful probe to study the structural. E mail: suha_ernest@yahoo. The density (ρ) measurements are made with accuracies of ±0.ion and ion-solvent interactions.co. Trichy-620019. liquid mixtures. aqueous and non-aqueous electrolytes solutions.AQUEOUS MEDIUM Jasmine Vasantha Rani E^ and Suhashini Ernest * ^ Dept. The study of molecular interactions existing in the non-aqueous solutions of calcium salts has been made through ultrasonic velocity measurements. formamide. Trichy-620002. calcium salts of some organic acids INTRODUCTION Ultrasonic measurements have gained momentum in recent years for the study of liquids. measurements of ultrasound velocities. The compressibility of the system throws light on the ion. Solvation number (ns) is computed using the following formula Solvation number ns = (nf /ni) (1-(β / β0)) 77 | P a g e . Keywords: Solvation number. of Physics. In the present study. *Dept. The ultrasonic velocity data combined with density constitute the standard means for determining the compressibility of the system under consideration. India. India. of Physics.001gm/cc.A COMPREHENSIVE ANALYSIS OF SOLVATION NUMBER OF SOME ORGANIC ACID SALTS IN NON. physical and chemical properties of matter. The result obtained from compressibility method is seen to agree well with the results from different theoretical and experimental methods. Urumu Dhanalakshmi College. The samples chosen are calcium salts of carboxylic acids and its derivatives. and densities for various concentrations of non-aqueous formamide solutions of calcium salts of some organic acids for different temperatures have been made in order to investigate the compressibility behaviour in the solutions.in jasstephen@yahoo. Calculation of solvation number of the solutions is undertaken to highlight the interactions existing in the solutions. EXPERIMENTAL PROCEDURE AND COMPUTAION Ultrasonic velocity (u) of AR grade Calcium salts in Formamide is measured at the frequency of 2 MHz with a Mittal Interferometer with an accuracy of ± 2 m/s. Seethalakshmi Ramaswamy College. • The sign of the solvation number indicates the relative values of compressibility of solution and the solvent. ρ the density .1m and 0.where u the ultrasonic velocity.The general observations on solvation number of the system studied in relation to temperature and molality may be summarized as follows. which remain attached to a given ion long enough to experience its translational movements. ni is the number of moles of solvent formamide and number of ions solvated. 8. • The solvation number is positive above room temperature and is negative below room temperature. The solvation number is defined as the number of solvent molecules per ion. This may be due to the dominant effect of intermolecular attraction of solutes over ion. β . The solvation number values are approximately found to be zero near higher concentration of 0. • • Gradual increase of solvation number from lower to higher concentrations is observed. The study of solvation number is used to interpret ion-solvent interactions. The positive solvation number for the solutions suggests that the compressibility of the solution at high temperatures may be less than that of solvent. the fall in solvation number at high temperatures and the rise in solvation number from negative maximum towards zero at low temperatures may be attributed to the decreasing ion-solvent interactions but with further increase in concentration. it remains constant. β0 the adiabatic compressibility of the solutions and the solvent and nf . RESULT AND DISCUSSION Passynski has taken consideration of the adiabatic compressibility of the solute and solvent for deriving solvation number[1]. The values of solvation number for various values of temperatures and molalities are presented in Table 1 The decrease in the solvation number with increasing concentration reveals that either there is not enough solvent for all the ions or preferably ion pairing has occurred.15m mostly at lower temperature.solvent interactions. 78 | P a g e . However. The rise in solvation number from negative value towards zero at low temperatures and fall in solvation number at higher temperature with increasing concentration may be attributed to decreasing solute-solvent interaction. Zero value of solvation number indicates that no change occurs in the compressibility value of the solvent when the solution is formed [2]. Positive solvation number suggests that compressibility of the solution at high temperatures at all molalities will be less than that of the solvent supporting the fact that ions gain high mobility and have more probability of contacting solvent molecules. Therefore solution is more compressible than the solvent and hence the negative sign for the solvation number. 79 | P a g e . which agree with the values calculated in the present measurements. Therefore an increase in interaction between ion and solvent molecules is expected.The negative values of solvation number at temperatures emphasize that the solutions are more compressible than the solvent.Table. The constant values of solvation number at higher concentrations and higher temperatures may be due to the strong ion-ion attractions between the electrolyte molecules than the ion-solvent interactions[3]. The perusal of Table 2 shows that the number of solvent molecules in the coordination sphere varies with anions [4].3 presents the solvation number computed from different methods. CONCLUSION The solvation number of calcium ion calculated from the compressibility study for sample solutions agree well with the values reported from other methods. An inspection of Table. This may be attributed to the mobility of the ion being low at the low temperatures.the greater the solvation of a given ion’[5].1 stands in agreement with the fact that ‘the more dilute the solution . . and Surayanarayana C..pp 611-612..N. Yasutiro Umebayashi.. Chem. (Can .)1930. Azzam A.K. Vol.118.. 7.) 2002.Y. 8. 993-1002. no.. 6. 45-49. chem. Bhavneet K. 3. (Consultants Bureau New York... chem.)1927. Jabir S.S.)1965.(Proceedings of National Symposium on acoustics. Chem. Passynski .V.( vol.S.. 80 | P a g e .. 38. Bernd Michal Rode. Taiga Tsukamoto Yue Zhang.Chem. Bakshi M. 1610. Rajaram N. chem.. Kritsana Sagarik. 12.)2007.REFERENCES 1.’Solvent and solvent effects in organic chemistry. 2. 168.. Yutaka Mune.108..J. Samoilov O.158.. 4.)2003.) 1965.Ya.( A..) 1927.4.) 2007.. of Raman spectroscopy vol. Lakshminarayanan R.( Trans Faraday Soc 23.) 2005. 11. 14.. C and Joshi I. 5. R.35. Ishiguro. 12.. 15.(Wiley VCH Third Edition.K.. E..M. Kanzaki. 73. Gapon.(Allg. Phys. Meyes Jünde Grosz Tamas Radnai Tamas Bako Imrl Palinkas Gabor.. Anan Tongraar. Ulich H. 9.. Number 7. 10.R..) 1960.(J. 125. vol. N. Passynski A.)1938.8.) 2004. (Acta Physicochem. 392. Acta Physicochim U. Asada M..(J...S. Soc. Lakshmanan A. Kuppuswami J. Z.. Vol 38.. (Bull. Bhuller S.. Ann-Sofi Warminska. Christian Riechardt. Sharma S.Umebayashi. Dorata Person Ingmar. 628-634. Fujimori. pp 7261-7271. Anorg.S. Kothai S and Kannapan V..437-441..385. 13.. mol.S 8. liquids vol.)1991.. issues 1-3.. ( J. No. M.T.( phys. 4. (Acoustica... Jap 38. Shin Chi Ishiguro.35. ‘Structure of Aqueous Electrolyte solutions and hydration of numbers at 25OC’.. phys. 292. pp.) 2008. 385. Ulström. 005 0.1 SOLVATION NUMBER Molality (m) 0.005 0.01 0.1 0.001 0.01 0.0075 0.01 0.1 0.01 0.15 0.001 0.005 0.01 0.1 0.001 0.005 0.001 0.15 0.0125 0.01 0.005 0.01 0.001 0.05 0.001 0.1 0.15 0.005 0.001 0.1 0.05 0.05 0.005 0.05 0.Table .005 0.001 0.05 0.1 0.05 0.15 5˚ C -168 -133 -34 -9 -3 -818 -138 -30 -6 1 -449 -110 -43 -5 5 4 -268 -44 -4 -8 -2 0 -640 -228 -64 -12 -10 -6 -534 -91 -91 -10 -4 -629 -84 -57 -33 -41 -255 -18 -17 -4 -1 0 15˚ C -94 -17 5 1 2 -391 -51 -6 2 4 77 -38 -10 5 3 6 -88 25 19 -1 1 -1 -396 -53 -42 3 0 -3 -417 -44 -12 -5 4 -97 -7 -18 3 -3 -281 -32 6 -1 6 1 25˚ C -244 -36 -12 -1 1 -168 10 12 1 4 -481 -25 -8 -15 7 5 -247 -6 9 -2 0 -1 -298 -53 -5 -2 -2 -1 -457 -83 -10 -5 2 -327 -9 -35 -14 -33 -260 -37 -11 -3 -1 0 35˚ C 34 28 -6 3 3 -84 -8 22 -4 4 21 15 59 9 11 6 -486 -21 11 1 4 1 200 76 53 10 4 7 117 83 9 8 7 -149 8 -4 20 0 -153 3 18 -1 2 2 45˚ C 250 73 24 3 4 153 61 48 11 8 254 73 10 2 11 8 84 53 32 6 5 2 754 165 110 18 12 9 603 74 62 23 7 114 49 30 28 12 214 68 52 8 3 3 55˚ C 377 91 35 7 5 366 123 47 6 18 274 70 44 28 5 8 -63 84 75 10 9 4 817 243 110 24 4 4 1151 248 88 31 17 381 101 70 51 18 230 -48 8 10 1 2 CALCIUM CALCIUM CALCIUM CALCIUM CALCIUM LEVULINAT LACTOBI PROPIONA CITRATE ACETATE E ONATE TE 9.05 0.01 0. CALCIUM ASCORBA CALCIUM CALCIUM PANTOT LACTATE HENATE 81 | P a g e .1 0. Table 2 The solvation number for Ca2+ ion in formamide at 35OC and 0. Study From Aqueous solutions at 25OC [6] CaClO4 in DMPA at 298 (from Raman spectroscopy)[7] Calcium ion in DMS (LAXS)[8] Ca2+ in Aq. Ammonium solutions (QM/MM simulation)[9] Ca2+ in DMF & DMA (Raman Spectroscopy & DFT calculations)[10] CaCl2 in water and methanol solutions (X-ray Diffraction and ab initio calculations[11] Ca2+ in water at 25OC (diffusion methods)[12] Mobility Experiments[13] Compressibility Study[14] Theoretical studies on divalent ions at 25OC[15] Solvation number.5-10.5 16 12.1m for all the samples Sample Calcium levulinate Calcium lactate Calcium pantothenate Calcium acetate Calcium propionate Calcium lactobionate Calcium ascorbate Solvation number 2 3 4 4 4 7 11 Table 3 The solvation number of Ca2+ reported from different studies in different solvents. 4 6 6 7.2 7 8 (water) 6 (Methanol) 9 7.3 82 | P a g e . deviation in adiabatic compressibility ( βad). A.V Sarmaa. The excess parameters are used to discuss molecular interactions between unlike molecules. intermolecular free length (Lf) and molar volume (Vm).9] The present paper deals with the study in the binary liquid mixtures of ethyl benzoate (1) + benzene (2). 313. G. Visakhapatnam.Appa Row Campus. Y.15K and 318. excess properties. 1.15K. DAR college. Introduction The thermodynamic study of esters has attracted increasing interest because these chemicals have an extensive variety of applications [1. The excess molar volume (VmE) and excess free length (LfE) are also evaluated for all the systems. + Chloro benzene. C. Andhra University. Nagarjuna. Further the data has been obtained at different temperatures with a view to understand the effect of temperature on these properties. The extensive uses of polymeric materials in technology have prompted ultrasonic studies to help to understand the structures of polymers and molecular interactions in solutions and nature of polymers[8.R.2. H.V. dipoles.11. multi polar and dispersion forces[4-7].M. V Apparaoa.bonding. + chlorobenzene (2).12]. c Department of Chemistry. The measured data used to compute adiabatic compressibility (βad). ABSTRACT : Densities. + nitrobenzene(2) at 303.15K. b Department of Physics.15 – 318. Dr.Ultrasonic study on binary mixtures of ethyl benzoate with benzene and substituted benzenes at different temperatures B. Experimental Details Ethyl benzoate (EB).15K. KEYWORDS: Ultrasonic velocity. benzene.15K. Nuzvid.V Ramaraob. Rambabuc a Department of Physics. 308. viscosity data furnish a wealth of information about the sum total of interactions between ions. ANU. These results were satisfactorily correlated by Redlich-Kister polynomial. Chlorobenzene and nitrobenzene were purified using fractionating column[10. deviation in viscosity ( η).3 Ultrasonic velocity together with density. 2. ultrasonic velocities and viscosities of ethyl benzoate + benzene. + nitrobenzene have been measured at temperatures 303. Nuzvid. 83 | P a g e . 4. 2 The molar volumes of the binary mixtures were calculated using the equation Intermolecular free length (Lf) was calculated from the measured density and ultrasonic velocity by 84 | P a g e .2. The adiabatic compressibility is proportional to strength of interaction between unlike molecules. The deviations in adiabatic compressibility are negative for all the three systems of ethyl benzoate with benzene.01%. adiabatic compressibilities can be obtained from the densities and ultrasonic sound velocities using the relation βad = (ρu2) -1 V = (X1M1+X2M2 ) / ρ using the following relation Lf = K/ uρ 1/2 ………… 3 where K is the temperature dependent Jacobson constant 13 and T is the absolute temperature.The accuracy in the measurement of density employing the specific gravity bottle method is better than + 0. The ultrasonic velocity varies non . India) working at 2 MHz. η and LfE have been calculated using the equation YE = Ymix .p. 1. Results and Discussion On the basis of a model for sound propagation proposed by Eyring and Kincaid[13]. Mittal enterprises.(X1Y1+X2Y2) 1 and 2 stand for the components1and 2.linearly with concentration without any maxima or minima at all temperatures [14] as evident from Table 1. 1 ………. In Ethyl benzoate + Nitrobenzene system. and X represent mole fraction of the component and subscripts ………. Velocities were determined using single crystal ultrasonic interferometer (Model M-81. The values are accurate to +0. ultrasonic velocity should decrease if the intermolecular free length increases as a result of mixing of components. 4 where YE is βad or VE or η or LfE.. velocity decrease as free length increases with concentration of ethyl benzoate. This fact is observed in the present investigation for Ethyl benzoate+ Benzene and Ethyl benzoate + Chlorobenzene systems. 3. The excess properties such as βad. Viscosity was determined by Ostwald’s viscometer. Theoretical considerations Assuming that ultrasonic absorption is negligible. VE . The βad values fall in the order Benzene > Chlorobenzene >Nitrobenzene …………….2. 2...2 and 3.001c. chlorobenzene and nitrobenzene as shown in Figs. 17] Excess molar volumes for ethylbenzoate + nitrobenzene system are more negative than that of ethylbenzoate + chlorobenzene system or ethylbenzoate + benzene system ( Figs.1.3.1.2. For the systems where dispersion and dipolar interactions were operating the values of viscosity deviations are found to be negative where as specific interactions tend to make deviations positive[20].4 and 3. 2.1.4. Benzene> Chloro benzene>Nitro benzene.1. As temperature increases dissociation of associated species takes place releasing more and more free molecules but because of favorable packing of ethyl benzoate and benzene or substituted benzene molecules into each other’s structure [18.4. suggesting an increase in interaction between component molecules[16. The η values have the following trends for binary mixtures with ethyl benzoate as common component. dipole-induced dipole interactions.1.1) The general trend in variation of excess molar volume of the mixtures follows the sequence.2. Nitro benzene > Chloro benzene > Benzene 85 | P a g e . The values of η for the whole mole fraction range for all the three systems are positive as evident from Figs.19] .3. interstitial accommodation and orientation ordering leading to more compact structure [15] The VE values become more negative at higher temperature( Figs. 1.1).1.The sign of deviation in adiabatic compressibility and excess free length plays a vital role in assessing the compactness due to molecular interactions in liquid mixtures through charge transfer. dipole-dipole interactions. 2 -Variation of deviation in adiabatic compressibility with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system 303.1 0.5 0.0 0.free length(LfE) Molef raction of Ethyl benzoate 0.15K 313.15K 1.4-Variation of deviation in viscosity with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system 86 | P a g e .3 -Variation of excess inter molecular free length with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system Fig 2.015 -0.1 .2.0 303.6 0.Variation of Deviation in viscosity with molefraction of Ethyl benzoate for Ethyl benzoate + Benzene system Molefraction of Ethyl benzoate Molef raction of Ethyl benzoate 0.6 0.10 0.15K 308.Variation of excess molar volume with molefraction of Ethyl benzoate for Ethyl benzoate +Chloro benzene system Fig 2.15K 318.Variation of excess intermolecular free length with molefraction of Ethyl benzoate for Ethyl benzoate + Benzene system Molefraction of Ethyl benzoate Fig 1.0 303.15K 308.2 0.15K 318.4 0.0 Molefraction of Ethyl benzoate -0.20 Deviation in viscosity (∆η) 0.014 0.2 0.4 0.0 0.5 0.mol.0 -1.0 Deviation viscosity (∆η) Molefraction of Ethyl benzoate 0.004 -0.2 0.020 303.006 -0.2 0.15K 308.0 Deviation in adiabatic compressibility(∆ β ad) Excess molar Volume(VE) 0.15K 318.15K 308.0 -1.0 Deviation in adiabatic compressibility(∆βad) 0.3 .mol.Variation of excess molar volume with molefraction of Ethyl benzoate for Ethyl benzoate + Benzene system Fig 1.8 1.5 0.15K Fig 2.5 0.5 -4.0 -2.0 -0.15K 313.free length(LfE) 0.005 -0.6 0.8 303.Molefraction of Ethyl benzoate 0.15K 313.15K 308.5 -2.6 0.15K -1.4 0.15K 308.15K 313.2 0.6 0.2 0.0 Fig 2.0 0.4 0.0 -2.4 0.0 Excess molar volume(VE) 0.010 -0.8 1.15K Fig 1.15 0.6 0.0 0.5 -3.0 Fig 1.4 .15K 318.0 -0.15K 318.0 -0.8 1.5 -2.002 0.Variationof deviation in adiabatic compressibility with molefraction Ethyl benzoate for Ethyl benzoate + Benzene system Excess int.2 0.0 -1.0 0.012 -0.8 1.2 0.15K 318.15K 318.5 -1.4 0.2 0.010 -0.0 -0.0 -1.5 -3.6 0.000 0.05 0.0 -3.15K 303.15K 313.1 .0 -1.8 1.6 0.0 -3.15K 308.008 -0.5 -4.4 0.15K 308.15K Excess int.5 303.15K 313.0 -0.0 303.8 Molef raction of Ethyl benzoate 1.0 0.15K 313.0 0.8 1.4 0.15K 0.15K 318.15K 313.000 -0.15K -1.00 0. 8 1.0 -3.00 0.016 -0.008 -0.0 Fig 3.3 -Variation of excess inter molecular free length with mole fraction of Ethyl benzoate for Ethyl benzoate + Nitro benzene system Fig 3.00 0.0 -2.6 0.15K 318.15K 318.4 -0.15K 0.0 -0.4 0.0 Excess m olar Volum e(VE) 0.15K 313.2 0.8 -1.0 -5.6 0.4 0.2 -Variation of deviation in adiabatic compressibility with molefraction of Ethyl benzoate for Ethyl benzoate +Nitro benzene system 303.0 1.15K 318.15K 308.004 -0.0 -4.0 0.0 0.2 303.0 Fig 3.0 303.15K 308.8 1.0 0.15K 308.15K 303.012 -0.1-Variation of excess molar volume with molefraction of Ethyl benoate for Ethyl benzoate + Nitro benzene system Molefraction of Ethyl benzoate Deviation in viscosity(∆η ) 2.2 -1.15K 313.50 1.6 0.15K 308.50 0.15K Molefraction of Ethyl benzoate 0.15K 318.15K 313.4 -Variation of deviation in viscosity with molefraction of Ethyl benzoate for Ethyl benzoate + Nitro benzene system 87 | P a g e .8 1.6 0.15K Fig 3.000 Excess int.m ol.00 0.6 0.free length(L fE) -0.0 -1.2 0.4 0.020 0.4 0.2 0.15K 313.Deviatio n ad iabatic co mp ressibility (∆ βad) Molefraction of Ethyl benzoate Molefraction of Ethyl benzoate 0.0 0.8 1. 18. 5. J. Nayak J N. 137. Parde J I & Urieta J S. 3. 13. J Chem Eng Data. Lande M K& Arbad B R. 2. J Mol Liq. 16. Proskaner E S. Oswal S L & Patel N B. 19. Organic solvents. 124(2009). Aminabhavi T M & Gopala Krishna B. J Mol Liq. M I. & Tariq M. 845(1995). Techniques in Chemistry. 455(2005). J Chem Eng Data. Anil Kumar Nain. Appa Rao Y V V. Indian J Pure & Appl Phys. 14. Weissberger A Ed. 13(2009). Chen J-T. 425(2000). Thakor & Mitesh C Patel. 37. 163(2009). Kincaid J F. 6. 64(2008). Perez E. NewYork) (1986). Aminabhavi T M & Aralaguppi. J Chem Phys. 8. Reddy B R & Reddy D L. 50. 11. 4. Subhash C Bhatia.144. 1306(2003). Bunger W B & Sokano T K. 10. Babu P. 620(1996). Andhra University. Rakesh R.References 1. 20. 47.40. 13(1999). Wankhede D S. New York (1955). Nandhibatla V Sastry. 1038(2005). 17. Riddick. Indian J Pure Appl Phys. J Chem Eng Data. Nikam P S & Kharat S J. Earnest Jayakumar. J Mol Liq. 50. Indian J Pure Appl Phys. Thirumaran S. 48. J Chem Eng Data. 38. Sharma H K& Singh W. 15. Shiah I-M & Chu H-P. 50. Ali A. 6. New York)(1989). 455(2005). Riddick J A & Toops E E Jr. Indian J Chem. 34A.Chem Eng Data. Cardoso M & Mainar A M. 856(1995). 88 | P a g e . Eyring H. Sekhar G C & Rao N P. Rachna Bhatia & Gyan P Dubey. 12. Rajni Sharma. Vol 2. 144. 144. 265. 1112(2003). A text book of practical organic chemistry. J Mol Liq. 48.40. Organic Solvents. 5th Edn (John Willey. 987(1995). Vol II 2 nd Ed. J Chem Eng Data. 4th Edn (John Willey. Anwar Ali & Swarita Gopal. J A. Pal A. 7. (2009). Ph. Wiley Interscience. 9. J Chem Eng Data. Vogel A I. Weissberger A.D Thesis. October (2009). Cuttack -753003.dignosis and imaging . Ravenshaw University. But when a sound wave of high amplitude propagates. non-linear effects occur such as harmonic distortion and acoustic scattering. wave form distortion and structural behaviour etc.[7].A number of information about some physical properties [5-6] of the liquid such as internal pressure.). but also the parameter which may provides some structure and state information of media.Obviously the study of acoustic nonlinearity parameter B/A in liquid binary mixture is very helpful in discovering the mixture law of acoustic nonlinearity parameter B/A in biological tissue as well as in developing and computing the theory of medical 89 | P a g e . Cuttack -754022. Dhaneswar Rath Institute of Engg. Physics. isentropic compressibility isothermal compressibility.E. coefficient of thermal expansion (α) are calculated for different frequencies. Odisha. Nath1 and R.G. The experimental values of sound speed have been fitted Ballou’s and Hartmann’s equation for non linearity parameter and variation of these parameters with the frequencies has been discussed in the context of molecular interactions. Tangi. clustering. 3MHz and 5MHz are presented for the binary mixture of di isopropyl ether (DIPE) and xylene (XY).can be obtained from the knowledge of this parameter.R.STUDY OF NON LINEARITY PARAMETER (B/A) AND THERMO ACOUSTIC PARAMETER OF BINARY MIXTURE AT DIFFERENT FREQUENCIES G. Researchers found that the acoustic non linearity parameter (B/A) was not only the parameter describing the degree of non linearity. Paikaray 2 of Engg.S.Now a days the acoustic nonlinearity parameter B/A is of potential possibility to be treated as a new parameter in tissue characterizing.M. 1Dept. ABSTRACT: Experimental data on speed of sound(C) values at 303K for different frequencies like 1MHz.I. binary mixture.Dept. coefficient of thermal expansion. KEYWORDS: Ultrasonic speed. India. India. heat capacity ratio. and Management Studies (D. Introduction: The propagation of acoustic waves of infinitesimal amplitude has been used to deduce most of the parameters involved in ultrasonic studies. isothermal compressibility (βT). From these experimental data for sound speed and density (ρ) of the binary mixture the thermo acoustic parameter like isentropic compressibility (βs). It has become of much interest to predict the extent of various kind of non-linear effects which are due to deviation from nonlinearity in ordinary acoustics [1-4]. acoustic scattering. of Physics. non linearity parameter 1. 2P. Odisha. intermolecular spacing. 71 × 10 −3 T 9 C 2 mix ρ = 1 1 4 4 3 Isothermal compressibility (β T )mixture = mix Coefficient of thermal expansion (α )mix 75. so the different factors like density .temperature and frequency of the sound wave may changes the sound speed [11-12].6 × 10 −3 T 9C 2 mix ρ 1 3 mix Heat capacity ratio (γ )mix = (β T )mix (β S )mix General formulation for the nonlinearity parameter in terms of the acoustical parameters of liquid has been made using the expression for the sound speed. coefficient of thermal expansion ( α) and the heat capacity ratio (γ ) from the well known thermodynamic relation[13-14 ] Isentropic compressibility (β S )mix = 1 ρC 2 1. there is a linear relation between the nonlinearity parameter of liquid and reciprocal sound speed as B (1. of experimental and theoretical studies have been performed on the nonlinearity parameter of liquid and liquid mixture but also to the best of our knowledge. The present work deals with the computation of thermodynamic parameters in one binary liquid mixture at different frequencies and at temperature 303K. Theory: Since sound propagation is an adiabatic process. In addition with this we have taken an attempt to compute acoustic nonlinearity parameter B/A of the binary mixture using two different method like Ballou’s empirical relation and Hartmann’s relation and the well known heat capacities ratio (γ ) is calculated at different frequencies which is well agreed the values for all the substances.isothermal compressibility(βT).ultrasonic and the theory of nonlinearity acoustics. 2. According to the empirical rule of Ballous employed by Hartmann [15]. computation of B/A at different frequencies has not been done so far.2 × 10 4 ) = −0.The experimental measured values of sound speed with different frequencies are used to compute the various thermo acoustic parameter like isentropic compressibility(βs ).5 + A C 90 | P a g e . During recent years [8-10 ] a no. 29 0.Hartmann [15] has shown theoretically the physical basis of Ballous equation assuming the intermolecular potential energy is the domain factor in determining the sound speed and derivatives in liquids. Thermal expansion coefficient and isothermal compressibility are obtained using the relation [13-14 ]. 65 0. isothermal compressibility and also coefficient of thermal expansion.The values of the nonlinearity parameter B/A of the binary liquid mixture have been calculated at different frequencies ranging from1MHz to 5MHz and at temperature 303K with the help of two different methods like Ballous empirical relation and Hartmann’s theoretically derived relation . 87 1 1M Hz 3M Hz 5M Hz Mole fraction of DIPE The variation of ultrasonic speed is supported by that of isentropic compressibility. 41 0.1 Variation of ultrasonic ve locity with mole fraction of DIPE Ultrasonic velocity 1500 1000 500 0 0 0.98 × 10 4 ) = 2+ A C 3.The ultrasonic speed is also increases with the increase of frequency for all concentration as shown in fig.1. Results and Discussions: Experimental values of ultrasonic speed and calculated values of density of the mixture has been used to determine the different parameters with the help of well known thermodynamic relation. But when the frequency increases from 3MHz to 5MHz. The expression for nonlinearity parameter due to Hartmann [15] is given as B (0.The values of isentropic and isothermal 91 | P a g e . The ultrasonic speed decreases with mole fraction of DIPE followed by an increase at higher mole fraction for all three frequencies. Fig.Considering the effect of frequency.The variation of these thermo acoustic parameter and nonlinearity parameter with frequency are plotted in figure1-7and discussed in the light of molecular interactions. the interaction between the molecules decreases so that they have small relaxation time [16] and move with high speed as compared to low frequency range. The decrease in ultrasonic speed is attributed to the depolymerisation of polarity in xylene caused by the addition of non polar DIPE. it is found that in low frequency range like 1MHz the molecules of the two liquid find greater time of interaction for which the ultrasonic speed is low. Mole fraction of DIPE Mole fraction of DIPE It is observed in low frequency like 1MHz. 0.70 mole fraction of DIPE and decreases thereafter for all three frequencies as shown in fig.4 1.compressibility increases up to ≈ 0. With increase of 92 | P a g e . 41 0 65 87 29 41 1 1 1MHz 3MHz 5MHz 0. in higher mole fraction of DIPE the dipolar association is observed between the DIPE molecules for which both the compressibility decreases. 8 0. 0.5 0 1MHz 3MHz 0 9 1 5 7 1 5MHz 1.70 mole fraction.45 1.55 1.3 Variation of isothermal compressibility with mole fraction of DIPE Isentro pic co m pressibility 3 1 0 1M Hz 3M Hz 5M Hz Isothermal compressibility 2 1MHz 4 2 0 3MHz 5MHz 0 0. 41 0. 87 1 0. 87 0. 29 0.4 it is found that the value of α increases with increase of mole fraction of DIPE up to 0. However. 0.35 0 0. But when the frequency changes from 3MHz – 5MHz the interaction between the unlike molecules is weak due to small relaxation time. the speed of the sound increases which decreases the value of α. Considering the variation of coefficient of thermal expansion as shown in fig. the interaction between the unlike molecules is very high for which both the compressibility are low.5 1 0. 2 0. 29 0. 65 0. speed of sound decreases which increases the value of α .The positive variation of both the profiles suggest that there is association of xylene molecules breaks up progressively with the addition of DIPE leading to expansion in volume and hence isentropic and isothermal compressibility increases. Again in higher concentration of DIPE as the density of the mixture decreases. 6 Mole fraction of DIPE well explained on the basis of the fact that with increase of density.4 Varitaion of coe fficie nt of the rmal e xpansion with mole fraction of DIPE Coefficient of thermal expansion Fig.3.This increases in α. which leads to in compressibility at every concentration of DIPE .5 1.5Variation of he at capacity ratio with mole fraction of DIPE Heat capacity ratio 2 1. then decreases in DIPE rich region. Such variation can be Fig. 4 Mole fraction of DIPE 0. 65 0. Fig.2 Variation of isentropic compressibility with mole fraction of DIPE Fig. increases the volume and hence both type of compressibility also increases up to certain mole fraction.2 and fig. (1975).32. R T Beyer. 211. 32. 87 0 1 1M Hz 3M Hz 5M Hz 20 15 10 5 0 param eter parameter 1MHz 3MHz 0.Acoust.On the basis of the above discussion it can be concluded that the variation of different thermo acoustic parameter and values of B/A by Ballos and Hartmann is not only affected by the variation of pressure but also with the frequencies.7 for Ballou’s and Hartmann’s. 65 0. Fi g.42-1. J.1 which decreases the value of α with increase of frequency. Physical Ultrasonic.65 mole fraction of DIPE and then deceases for higher concentration of DIPE . P S Westrvet. Academic Press.This is due to fact that at low frequency the speed of the ultrasonic sound is small for which the B/. 87 0 Mole fraction of DIPE Mol e fracti on of DIPE Again considering the variation of B/A with frequency it is observed that in low frequency the B/A value has high value in compare to the value obtained in high frequencies like 3MHz and 5MHz. 29 0.Soc Am. The authors have also put the interest to calculate the non linearity parameter B/A using Ballou’s and Hartmann’s relation. 65 0.Though it increases linearly with mole fraction of DIPE but its value varies from 1.This variation of B/A with mole fraction of DIPE in presence of xylene is only due to variation of ultrasonic speed in the binary mixture which is described earlier.Am. 94.6 and fig. R T Beyer and S V Letcher. Chem. 41 0.Acoust. With a close perusal of the data shown in fig. 719 (1960) 2. JDPandey and K P Thakur. (Neue Folge).270 (19780 4.Soc.6 which is well agreed with that of the result for other substances. 29 0. RPJain. 39. (1961) 3. The heat capacity ratio of the binary mixture is found to be increase in a linear trend with the mole fraction of DIPE as shown in fig. Acustica.6 Variation of Hartman n's n on l in e arity param e te r with m ole fraction of DIPE Hartmann'snon linear Fi g. 41 0.frequency from 1MHz-5MHz velocity increases as described on fig.A value is high as the value of B/A varies inversely with speed of sound in both the cases. it is observed that the nonlinearity parameter are increases with increase of mole fraction of DIPE up to 0. Z Phys.7 Variation of Ball ou's n on l i ne arity parame te r with mole fraction of DIPE B allou's non linear 20 15 10 5 0 0. Many authors have calculated this parameter with variation of pressure but in the present investigation the nonlinearity parameter are calculated with different mole fraction for different frequencies at a constant temperature. 2043. 5. References: 1. K P Thakur.8 (1960) 93 | P a g e 1 5MHz . 202. J.5 for all frequencies . New York. Indian J Phys.270. B Hartmann. 18. 2009 12. J.Phy Sci.34. Phys. 99. 117. 1392 (1979) 16.Pramana J.Int Acad . G P Dubey. Am. R Abraham and M A Abdulkhadar.52. Phys.. 678 (1998) 10. J.Phys. P Kuchhal.Phys. G P Dubey. 1051(1962) 7. G Nath and R Paikaray. V Sanguri and R Verma Indian J.321 (1999) 9. Acost Lett. JUSPS.36. 429 (2001) 15.N Tripathi and A KSingh J. 1309 (2009) 13. Soc.. Pramana J.83.Am. J D Pandey. J Acoust. 9.Acoust Soc. J D Pandey and R Verma Chem.83.Am.Acoust.45. R Kumar and DNarsingh . Soc. K C Sharma S Gupta M Sharma ands Chouan.221 (1995) 11. 21.1. 1.(1997) 14.233 (1995) 94 | P a g e . G Nath and R Paikaray. H Endo. 65.Pure and Appl. M S Chouhan. J Jugan. 2043(1986) 8.6. J L S Bellin and R T Beyer. However in MIBK there is an indication of complex formation in its the ternary mixture containing t-butanol and CCl4 KEY WORDS MIBK. thermo-acoustic parameters. Nayak2 and B. density and viscosity of the ternary mixture of MIBK/HAA+t-butanol+ CCl4 were measured at 301. internal pressure. B. Dash1. Although several reports are available for studying the molecular interactions in binary liquid mixtures [3. excess molar polarization ∆P and excess free energy of mixing ∆F for binary mixtures of MIBK in three apolar solvent viz. and . HAA. 1. Therefore attempt has been made towards investigations on thermo-acoustic 95 | P a g e . 1DESM. In an attempt to explore the nature of molecular interaction between the polar-polar. Swain3 Regional institute Of Education (NCERT). g. The molecular interactions are dipole-dipole. ACETYL ACETONE AND t. K. Karunamoy1*. CCl4 and p-xylene using dielectric studies. it is necessary to determine various thermo-acoustic parameters which are related to inter and intra molecular association with temperature as well as concentration variation. 15. available volume. S. Bhubaneswae-751006 ABSTRACT The ultrasonic velocity. In an earlier report [2] one of the author (SKD) have been evaluated the KirkwoodFröhlich linear correlation factor. T. K. polar-non polar species of the ternary mixture the excess properties were derived. The thermo acoustic parameters such as isentropic compressibility. free volume. Revenshaw University.BUTANOL WITH CARBON TETRACHLORIDE(CCl4). dipole-induced-dipole and dispersive type in the ternary mixtures containing HAA. Chintamaniswar Area. The molecular interaction between the like as well as unlike molecules in the given ternary systems have been studied in the light of several thermodynamic and acoustic parameters. To understand the molecular behavior of associating molecules.THERMO-ACOUSTIC STUDIES ON TERNARY MIXTURES OF METHYL ISO-BUTYL KETONE. Introduction Methyl-iso-butyl ketone (MIBK) and acetyl acetone (HAA) has been extensively used as extractant in various polar and apolar modifiers/diluents for extraction of actinides and lanthanides in atomic energy industry [1]. inter molecular free length.16 K. S. The ultrasonic velocity and dielectric constant of the organic phase changes by blending MIBK/HAA with polar and apolar liquids. Cuttack-753003 3Plot No. Bhubaneswar-751022 2Department of Chemistry. involving MIBK/HAA. 4] involving polar-polar and polar-apolar systems it is sparse in ternary liquid mixtures involving the nuclear extractant MIBK/HAA. benzene. t-butanol. ternary mixture. Some physico-chemical studies on thermo-acoustic properties of ternary mixtures on MIBK/HAA+t-butanol in the presence of CCl4 have been undertaken. relaxation time and relaxation amplitude were computed with the help of measured values of u. acoustic impedance. 9+0. Lf.1+0. the non linear variation in the values of βs.5). However.1+0.3) and (0.3) and (0.7+0.9). (0. (0. This shows molecular interactions as well as interstial accommodations among the polarpolar and polar-non polar components of the MIBK/HAA + t-butanol + CCl4 mixtures. For each set of compositional stoichiometry the ternary mixtures of MIBK/HAA + t-butanol + CCl4 was prepared with the decreasing mole fraction of CCl4.7+0. (0. Circulating water from thermostatic regulated bath around the sample holder with double wall maintained the temperature of the system constant with an accuracy of ± 0. viscosity() and density () of the ternary mixtures of MIBK/HAA+t-butanol +CCl4 in the polar compositional stoichiometry of (0. Further. and which is observed in the present study.1) with the function of mole fraction of CCl4 were measured at 303. Various thermo acoustic parameters such as such as isentropic compressibility(βs).1+0. (0.9).Some of the relevant data are presented in Table-1 and displayed graphically in Fig-1.7). purified by standard procedures [5] and redistilled before use.5).1) separately.3+0. the values of and α/f2 increases in (0. The density was measured by a digital microbalance with a pykonometer of 25 ml capacity with an accuracy of ±2x10-5 g cm-3. and Vf depends upon the combined effect of the increasing or decreasing trend of u. The binary mixtures of MIBK/HAA+t-butanol was prepared by weight for five sets of compositional (mole fraction) stoichiometry viz (0.16 K.9+0. Results and Discussion Ultrasonic velocity (u).9).e.internal pressure(πi). In perusal with Table-1. The purity of the sample was checked by comparing the measured value of density and viscosity with those reported in the literature [6].behavior in ternary mixtures on MIBK and HAA with t-butanol and CCl4 in the five polar compositional stochiometry for assessment of molecular interactions between the component molecules. 3. 2.7). (0. The viscosity was measured by Ostwald viscometer immersed in constant temperature water bath with an accuracy of ±10-6 Pas.5 ms -1. (0. The relaxation time ( τ) which is of the order of 10-12 s probably due to structural relaxation process [9] and in such situation it is 96 | P a g e . available volume(Va).1oC.8]. (MIBK/HAA + t-butanol) in all the ternary mixtures containing CCl4. πi. (0. free volume(Vf). relaxation time( τ) and relaxation amplitude (/f2) were measured by using standard relations [7.Experimental All the chemicals used in the investigations were of AR grade.7) while decreases in other compositions of polar solute non linearly with mole fraction of CCl4 in the ternary mixtures.5+0.3+0.5+0. inter molecular free length(Lf) acoustic impedance(Z). The ultrasonic velocity was measured by single crystal variable path interferometer at 2 MHz with an accuracy of ± 0.3+0. it is observed that the values of u and Va increases while that of and Z decreases non linearly with the increase in mole fraction of polar solute i. 75 mole fraction of polar solute thereafter shows positive in (0. it is observed that the values of βs shows negative in the entire range of concentration in (0.9+0.5)> (0. gMIBK = 1.1) with a decreasing magnitude (0.1+0.1) in the ternary mixtures containing HAA. HAA.7)> (0.3) and (0. in all the three protic liquids viz.3+0. In perusal with Fig-1. Further the values of VaE are negative in all the compositions while πiE are also negative in all compositions except in the compositions of (0.1) with a negligible variation in (0.3+0. MIBK and t-butanol reveals that Kirkwood-Fröhlich linear correlation factor.9+0.butanol are strongly associated polar liquids having dipole moment 2. it is observed that 97 | P a g e .7) > (0. The magnitude of ZE.7) compositions.3).3+0.5) compositions in HAA + t-butanol + CCl4 ternary mixtures.7+0.9) and up to 0. 11].9). gHAA= 1.66 D respectively.The values of LfE are observed to be negative in the entire range of mole fraction of CCl4 in the composition of (0.1+0.expected that molecules get rearranged due to co-operative process.9+0. 2.7+0. MIBK and t.5+0. On the otherhand Fig -1 shows that the values of ZE and VfE are positive for all the compositions except (0.7+0. it shows positive in the entire concentration range of concentration in (0. However the magnitude of negative values of βs decreases in the order of composition of (0. In the presence of t-butanol the molecular interactions between HAA and alcohol molecules takes place through the intermolecular Hbondings between O of two carbonyl group of HAA and H of hydroxyl group of alcohol CCl4 molecules are almost spherical in shape and can be easily trapped inside the interstitial voids of the interacting moieties containing HAA and probably favours the stronger molecular interaction in (0.1+0.3 gt-butanol =2.70 D and 1. the dipolar alignment of MIBK/HAA is influenced by nonspecific interaction due to the solvent effect and dipole-dipole interaction through H-bondings between H and O is also expected among the MIBK/HAA + t-butanol molecules.9)> (0. This indicates that the degree molecular interaction is relatively higher in the (0. g.91 D.5+0.7) of the ternary mixtures containing HAA.3).9+0. Further. In seemingly non-interacting medium like CCl4.9) composition in the ternary mixtures of HAA + t-butanol + CCl4.3+0.5+0. HAA/MIBK molecules are equilibrium mixtures of two tautomers such as keto and enol forms and the molecules are arranged in head-tail structure due to C and O linkage resulting intramolecular association. while it shows negative up to 0.3 mole fraction of CCl4 in (0.9) composition in the ternary mixtures containing HAA. From the close observation of Fig-1. HAA and t-butanol respectively which may be attributed by the presence of 3dimensional network of H-bondings among themselves and stacked together by head-tail arrangement [12].9)> (0.1+0. VfE and LfE are maximum in (0. This indicate that there is re-enforcement of parallel dipolar alignment among the like polar molecules of MIBK. The dielectric study involving HAA.18 is greater than one [10.5)> (0.1) compositions.1+0. However in other higher composition the values of LfE shows positive with the mole fraction of CCl4.56.1+0. 002.9) in the extraction process.1+0.7+0.1+0.9+0. dipole-induced effective extractant in the presence o the modifier t-butanol and diluent CCl4 at compositional stochiometry of (0.5) (0.5) 0.1) in the ternary mixtures.3) (0.the values of βsE and LfE are negative throughout with the mole fraction of polar solute in compositions of (0.9+0.7) 4E-11 (N-1m2) 2E-11 0 (0.9+0.9) (0.1) X2 98 | P a g e .00 2. As such it is probable that there may be complex formation between the components present in the ternary mixtures of MIBK + t butanol + CCl4 system.3+0.9 ) (0.1+0. 150000 150000 (0.7+0.00 -4E-11 -6E-11 X2 (0.5+0.3) -2E-11 0. dipole induced dipole and dispersive type.00 X2 5E-11 (0.00 2.1+0.50 (0. mponents t-butanol 4.7) (0.3+0.7) and (0.3) (0.00 (kg m-2s-1 ZE x10-6 100000 100000 50000 0 -50000 0. then positive in other compositions in the ternary mixtures containing MIBK.3+0. From the trend of variation VfE with solute mole fraction it is observed that the values of VfE are positive in all the composition except (0.7+0.1+0. Further the values of ZE are positive while πiE and VaE are negative with the solute mole fraction in all the compositions of this ternary mixture.5+0.00 1.3+0.5+0.5+0. From such observation it is found that the magnitudes of the excess thermodynamic parameters are not prominent in any of the compositional stochiometry of the ternary mixtures containing MIBK.9) (0.5+0.7) (0. Although the molecular interaction of t t-butanol and MIBK is possible between O of MIBK with H of OH groups of alcohol the interstitial accommodation along with the dispersive forces between C of CCl4 and H of alcohols molecules cannot be overruled.50 1.Conclusion The present investigation reveals that the nature of molecular interaction involving MIBK/HAA with t t-butanol and CCl4 may be dipole-dipole.00 1.5 ) X2 6E-11 βsE x1010 (N-1m2) βsE x1010 (0.9+0.3+0.1) Z E x10 -6 (kg m -2 s -1 ) 50000 0 0.5) (0.1) 0 0.7 ) (0. As such HAA may be used as an dipole.00 -5E-11 (0.3) (0.5) while it shows partly negative.001. 00 912.00 1238.99 9. relaxation time ().1) X2 (b) Fig-1 Variation of Zβs πiEand Vawith mole fraction(X2) of (a) HAA+t-butanol+ CCl4 (b) MIBK+t-butanol+ CCl4 with compositions of (0.20 914.50 1.1+0.00 2.5+0.104921 1.47 0.0009 0.00 801.00 (0.33 9.0009 0.0011 0.3) πi Ex10-6… 1.32 1.0009 0.080300 1.0013 0.3) (0.5+0.10 914.00 1034. (0.82 10.9+0.28 3.451956 1.90 1.3) and (0. Table-1 Variation of density ().216950 1.53 6.98 9.71 9.451956 1.67 1.3+0.5) (0.00 1.894353 1.00 1588.23 2.284684 1.26 3.148 0.+0.7+0.53 8.15 1185.66 1.00 0.465 0.relaxation amplitude (α/f2) X2 free volume (Vf).25 0.00 2.5+0.78 9.02 9.5+0.0009 0.33 910.97 1588.0012 7.65 4. (0.00 869.00 1479.7).13 1.00 1115.384 0.3+0.273 0.08 (MIBK + t-butanol) + CCl4) 0.90 1.00 933.0010 0.74 3.00 949.67 99 | P a g e .815 0.00 -2E+08 -3E+08 -4E+08 (X2) 0 0 (0.47 5.68 8.95 2.33 2.713 0.00 1382.00 0.33 0.03 1.80 915.00 (0.9) (0.7+0.60 1037.49 0.80 0.47 2.58 0.69 0.00 2.348 0.22 1.18 0.30 1057.642 0.10 0.7+0.0009 0.1+0.9+0.26 9.1+0.17 0.00 1455.05 3.9).33 1.09 853 859 886 911 954 993 1060 1130 1220 1340 1510 853 872 891 910 933 1000 1005 1016 1.5) (0.0011 0.21 2.0010 0.00 -1E+08 0.5).5+0.577 0.09 1.0009 0.1) (X2) (a) (0.9) X2 (0.05 1108.09 2.3+0.0009 0.02 0.50 984.3) -2000 -4000 -6000 0.572 0.9).00 12.46 2.324050 1.00 7.261855 1.37 2.9+0.53 8.3) (0.00 0.00 1273.40 915.12 1.53 8.0009 0.420 0.00 1016.49 9.40 1330. adiabatic compressibility (βs).9+0.16 8.91 3.46 2.188102 1.9) (0.204 0.90 0.60 0.935913 0.618 0.81 3.17 1.7) (0.33 910.96 1.307 2.47 1.10 0.72 2.00 (0.14 6.1) VaEX105 (m3kmol-1) VaEX105 (m3kmol-1) -2000 -4000 -6000 0.156292 1.00 1164.00 967.0017 0.0009 0.20 951.02 1.5) (0.95 3. (0.37 0.33 5.7) (0.999842 1.96 3.00 934.0015 0.0009 0.502 0.10 7.03 1328.20 975.00 1408.9) (0.032255 0.00 1.45 2.00 997. available volume (Va) internal pressure (πi) and βsX1010 (N1m2) x1012 (s) α/f2×1014 (s2 m-1) VfX107 (m3mol1) VaX105 (m3kmol-1) πiX10-6 (pa) Z ×10-6 (kg m2 s-1) acoustic impedance (Z) with mole fraction(X2) of polar solute (MIBK/HAA+t-butanols)at(0.01 10.1).700 0.08 1.52 2.215120 1.89 4.3+0.31 4.1+0.7) (0.7+0. viscosity ().7) (0.30 8.58 2.127219 1.766 0. ( kg m-3) u (m/s) Nm-2s) (HAA + t-butanol) + CCl4) 0.0010 0.08 3.00 2.00 912.655 0.3+0.7+0.44 2.5) (0.985625 0.1) πi Ex10-6… 10000000 0 -1E+08 -2E+08 -3E+08 0.36 2.74 950.345890 1.9+0.022648 0.1+0.30 0.815 0.19 0.92 10.39 0.68 2.10000000 0 (0.54 10.ultrasonic velocity (u).50 1077.95 2. Das.90 1.Martin.83(11). S.Pure& Appl.B. V.50 1132.Atigas and F.64 (1995) 2636. [9] M. Indian J. 100 | P a g e .Tech 1 230 (1994).Das.Maheswari.84 0.79 4.Chalmers.Dash & B.Pure& Appl.00 782. [7] T.Swain. [12] S. W.Conosa.4thEdn.Dash. H.Rodrigucz and Z. Vol.K.Das.Bunger and T.83 10.K.(Wiley.Swain. .47 (2009) 782.Khopkar and R.Mol Liq.0014 0. 46 (2008) 712.99 2.01 9.67 13.71 (1997) 73.Pure& Appl.M. J. B.Swain.Inter Science.K. New York)( 1986).Rao.K Bhat.00 845.J .Indian .J.87th Edn.00 890.Dalai and B.53 1026 1046 1067 0.0.London.0021 10.J.K.K.B.78 3. [3] J. [10] J.K.K. [8] D.Dominguez.Shantafa.(CRC Press Boca Raton FL) (2006).0017 0. [11] S.Riddick.96 1.K.Uma. [6] CRC Handbook of chemistry and physics edited by DR. 45 (2007) 210.381(2002) 181. Indian J. S.Dash.N.27 4.923375 0.34 2.B.phys.B.Swain.Dey.60 1037.phys.Sravana Kumar and D.225 0.886294 References [1] A.phys.11 8. J. [5] J.1557 (2009).50 0.Dash.Sakano.Sumathi and J.80 0.Lide. [2] J.S.S.A. A. 1970).J.B. Indian J. Fluid phase equilibrium 156 (1999) 57.Mohanty & B.50 1082.A.K.Acharaya.Physical Socity of Japan Vol.K. Organic Solvents. Indian J.M.Chem.156 0.Selva Kumar and D. Solvent extraction of metals (Van-Nostrand-Reinhold. Phys.tozo. Thermochemica Acta.04 10.Royo.Chakravortty and B. [4] M.914712 0. S. Several unsuccessful attempts made so far to deduce a comprehensive model.T. to incorporate the depression in the dielectric constant of the dielectric continuum . Pin Code – 508116 . and the plots of thermodynamic parameters .P.Glueckauff [1] & Von Hippel [2] showed that the dielectric constant in the vicinity of the central ion is modified by the volume fraction of the ions in layer of the solvent around the central ion. a host of earlier workers . mainly because of so many shortcomings. 2 Jawaharlal Nehru Technological University (Jagtyal Campus) Jagtyal. tend to reduce the value of the dielectric constant of the electrolytic solution.N. and to modify the D-H Theory for an electrolyte solution were cited. Satara. about the findings of Gucker et. Discrete variation in the slopes of the straight line graphs are explained.U. The author used the relevant equations modified by him . Jawaharlal Nehru Technological University. and the need to use M. Gucker’s equations . T. by a host of others. Margaret Robson Wright & Robinson and Stokes pointed that the internal field around the central ion of the ionic atmosphere created by the charged solute ions in the solvent of the electrolytic solution. Gunavardhan Naidu 1. in their respective different types of studies in the very recent literature.For a volume fraction φ to ( φ +d φ ). Monte Carlo Simulations . Ion-pairs in aqueous electrolytes. since the parameter of the dependence of dielectric constant on concentration is missing in them . in the presumptions of the theory & its later developments.Using these equations. where φ = 101 | P a g e .GLUECKAUFF’S MODEL FOR LOWERING OF DIELECTRIC CONSTANT OF ELECTROLYTIC SOLUTIONS & ISOENTROPICCOMPRESSIBILITY AND ION ASSOCIATION STUDIES WITH AQUEOUS ELECTROLYTIC SOLUTIONS USING ULTRASONICS .Simulations. P.An excellent evidence for all of the concepts of all the cited workers is reported .. Isentropic compressibility. Bommalaramaram (M). ( 1** Email ID for all correspondence: profvrbr1@hotmail. Debye Huckel theory. HYDERABAD-500072. Shanaz Batul 4 Matrix Institute of technology. are incomplete & naïve. The plots clearly show an excellent agreement with many of the recent cited findings.al. 4 Main campus.Rajendra 3 . from literature Several correlating arguments cited by. Electrolytic ions entering into the solvent of the dielectric constant “D” creates an internal field around the central ion of the ionic atmosphere & the average effect of all ± such ions is to reduce the effective value of D to ( D − D) of the solvent of the electrolytic solution. due to solute-solvent interactions was outlined KEYWORDS: Glueckauff’s model.C. as the concentration increases.. T. the mechanism of formation of three types of ion pairs envisaged earlier by Eigen et. Jawaharlal Nehru Technological University HYDERABAD. 3 LNBC Institute of Engineering and Technology.Brahmajirao 1**.Raigaon. Lowering of dielectric constant of dielectric continuum Introduction The departures exhibited in the properties of electrolytic solutions. correlating them with the prevailing concepts proposed by several scientists. by the Debye Huckel model even with its several recent modifications that were developed during the last half a century.ION-PAIRS (CHLORIDES) V.A.al. . Treating the solvent as a continuously non uniform system having spatial distribution of the ions .Srikanth 2 . Cheekatimamidi (V). using equations for partial molal compressibility & apparent molal compressibility. Maharastra . observed in the plots is explained on firm grounds. cannot be satisfactorily explained.com ) 1 Abstract This paper reports the specific evidence of the formation of three types of Ion pairs from the ultrasonic studies in aqueous solutions of six chlorides from our laboratories in J. S.8π Nr 3 ) . is the dielectric constant. are parameters corresponding to 2 ∂p ∂p infinite dilution. χ = [(π N e ) (1000 D kT ) 0 2 ] 1 2 and N is Avogadro Number . [4]. with the increase in concentration. This will be invalid. The author opines that: the inherent change of slope of the plot reveals conspicuously the interactions between the ions and the solvent in a discrete way namely the ion-solvent-ion interactions. to account the solute solvent interactions.Simulations . In this β = [− ( )] = 2 . The integration of this within suitable limits yield [dD / d log(1 − φ )] = [3D( Dφ − D) /(2 D + Dφ )] . and. B. without rigorous explanation of the same. These shortcomings in the Gucker’s equations are to be attributed mainly to the solvation and the ion-ion & the solvent-ion interactions. SK becomes a function of concentration and dielectric constant. and “D”.C. The model for viscosity of electrolytic solution by Lencka et. leading to χ 6 (∑ν i zi )3 2 [ β 2 + 2( 2 i 15 ∂D 2 6 ∂ 2 D ∂β 6 β ∂D )T − ( )T + 2 ( )T − ( 2 )T ] D ∂P D ∂P ∂P D ∂P Hence ( φK vs C ) plot cannot be linear in view of the modifications made. Wang & Anderko [16]for water as solvent was later improved into a comprehensive model for calculating the viscosity of aqueous or mixed-solvent electrolyte systems ranging from dilute solutions to fused salts. The B coefficients data for a large number of aqueous species used by Wang & Anderko was determined by analyzing extensive experimental viscosity data by Marcus [14] for a number of ions in pure organic 102 | P a g e . S K = (6. dφ = 2 N (4π r 2 dr ) and “r” is the distance of the point of calculation from the centre of the 3 reference ion. since several recent findings are not taken care of. G 0 2 . in the solvent and the details are available in literature Gucker et. as the electrolytic ions enter the solvent. Also according to Gucker [3] & Gucker et. Further the thermodynamic variables that can be estimated from ultrasonic data. and φK2 = φK + S K C . and several concepts in the approaches are useful to be applied in the M. and needs a total review.R.al.al. pointed out the deviations in the Gucker’s equations qualitatively. as detailed in the discussion of the results. [3]& [4] established with standard notation the equation for the partial molal compressibility as: ∂2 ∂ 0 (G2 − G 0 2 ) = (V2 − V 0 2 ) = ( K 2 − K 0 2 ) . Marks [8]. [12] Attempted to arrive at a modified Poisson-Boltzmann Equation but for no complete avail. Mason [11]. Treating the dielectric constant as a variable it can be shown that. Krishnamurthy [6]. Padmini& Rao [10]. This equation is used for the estimation of lowering of the dielectric constant. where δ is independent of the ion-solvent-ion interactions as per the deductions arrived by the cited workers above. (which is a variable.Rao & K. V2 . consequent of internal field modifications around the central ion inside the ionatmosphere.al. In this K 0 2 .Rao [7]. in which S K = (∂SV / ∂P )T + ( SV β 2 ) . Bhimasenachar & Subramanyam [9]. 2 D ∂P D ∂P D ∂P V ∂P v ρ is the isentropic compressibility. is informative .These Also the apparent molal equations clearly reveal that compressibility is φk = ( SK = Cversus K 2 − K 2 ( ) plot will not be linear ∂φv2 ∂p 0 )T .3 X 10−10 )δ is a constant. Harned & Owen [5]. as ( 3 6 per the new revelations ).al [13]. Borukhov et. are related to the modification to the free energy of the central ion. the partial molal compressibility 1 ∂V 3 5 ∂D 2 1 ∂ 2 D β ∂D 1 0 Gets modified to: ( K 2 − K 2 ) = χ [ 2 ( ) + ( 2 ) + ( )] . ρ is the density. Discussion of the results: All the plots record three conspicuous gradient changes per each electrolyte.R. and a contribution of specific interactions between ions or neutral species. a contribution of individual ions. Results have been explained in terms of various modes of solvation interaction. tend to reduce the value of the dielectric constant of the electrolytic solution. having failed to incorporate the solute solvent interactions. The bridge used has a cell constant of (1.et.Waddington & J. [25] Studied properties of solutions of binary aqueous mixtures from the standpoint of solute-water and solute-solute interactions. organic or mixed water-organic solvents and aqueous acids or bases up to the pure solute limit. their values have been determined from experimental viscosity data at low electrolyte concentrations (usually below 0.39). of our ultrasonic studies using Ultrasonic pulse echo technique similar to that of Mc Clements & Fairley [17] in aqueous solutions of sulphates. Still these models find little use. The effect of electrolyte concentration on viscosity is modeled by combining a long-range electrostatic term obtained from the Onsager-Fuoss theory.solvents at 250 C.al & Singh . Solute solvent interactions of several mixed solvent systems with many electrolytes are studied by Maitra & Bagchi [24]. to make the model applicable to ion pair formation analysis. The analysis is applied to kinetic data describing the dependence on the ethanol mole fraction of the first order rate constant for the solvolysis of 103 | P a g e 0 . Blandamer. at three concentrations. Formulations have been developed for the contributions of individual ions and species-species interactions. the formation of solvent separated. solvent shared & contact pairs in tune to the expectations of Eigen [21] and is different from the findings reported earlier in literature. in “Clanguage” and details of analysis of variations in thermodynamic parameters. These graphs record distinct changes in slope.al & Mishra et . Avery exhaustive review on the Ion association & complexation studies is available by Covington & Lilley [23]. using a programme.al. The temperature dependence of the B coefficients can be expressed using the equation of Out and Los [15]. The conductance data was obtained using the ‘PHILIPS’ Conductivity Bridge Model P. The ionic polarization effecting the Conductivity measurements is balanced the usage of an inbuilt oscillator generating 1 KHz signal. applied to the bridge network as a whole The experimental details for dielectric determinations are given else where [20] The ultrasonic. However it is necessary to develop it further in the light of recent findings about solute solvent interactions Experimental and Calculations: This paper reports the data.05 M) in pure solvents using a method described by Lencka et al. D. strong evidence is obtained for clustering of both aqueous and non-aqueous components. using pair wise interaction parameters. where s is the solubility has been found to depend on various modes of solute–solvent interaction and also on the Hildebrand solubility parameter representing the cohesive energy density (solvent–solvent interaction) of solvent. as ordinates separately. dielectric and conductance data of the author were used in the calculations. The Gibbs energy of solvation. The Wang & Anderko [16] model incorporates a mixing rule for calculating the viscosity of solvent mixtures and a method for predicting the effect of finite electrolyte concentrations. With an increase in the amount of solute. Each gradient change corresponds to the formation of a type of ion pair. corresponding to.-9500 similar to the one used by Power et. J. as given by log s. Density measurements are made using the bicapillary pyknometer.Dole B coefficients. For systems for which the B coefficients are not available in literature sources. A dimensionless quantity has been defined to represent the deviation of the observed log s values from the mole fraction average.al. which is quantified by the Jones. [18] And Bikash Kumar Panda et. M. The model reproduces the approach to viscosity of systems such as salts in water. are presented as graphs with C as abscissa and φK2 & ( K 2 − K 2 ) .al. These trends are explained in terms of preferential solvation of initial and transition states using Kirkwood-Buff integral functions. As pointed out by Eigen& DeMaeyer [22] the internal field around the central ion of the ionic atmosphere created by the charged solute ions in the solvent of the electrolytic solution. Burgess et. [19]. with no modification attempted for accounting the solvent solute interactions.O”M. &Kraus et. In the reported plots.From the plots of [ C versus φK2 ] Gucker showed that lim φ K c →0 represents the reduction in the hydration number. b = e 2 / aDkT . They showed that at the critical distance defined by q = [( z1 z2 e 2 ) / 2 DkT ] . in which a is ionic diameter.al.N.nh v10 β 0 in which n1 is the total number of molecules of water and n2 is the number of moles of electrolytes and nh is the hydration number which is the number of water molecules in the primary hydration sheath round the central ion. [31]. ⇒ log K A = [log 4π Na 3e 2 ] ⇒ A plot between log K A as ordinate and (1/D) as abscissa. An equation for association constant was deduced. and T is the absolute temperature . Consequently Fuoss’ equations fail to predict the behavior of the ion pairs to a better extent the graph between log K A versus (1/D) will not have constant slope and so its analysis reveals valuable information about Ion-pair formation.O”M. [30] The outlines of the same are available at Brahmajirao. & J. f is Debye-Huckel activity coefficient .Hence this theory requires modification in the light of the Glueckauff’s model. Bockris & Amulya K. α is the fraction of the (1-1 ) electrolyte present as free ions and K A is the association constant . This fulfils the condition that the energy required to separate the ion pair is comparable to the thermal energy. Fuoss [32]. The liquids include aqueous solutions of multivalent electrolytes. Robinson and stokes[28] . et.since [ z1=z2 ]. It is shown that. (26) discussed the aqueous systems for which measurements of the complex electric permittivity (103 Hz ≤ ν ≤ 1011 Hz) and of the attenuation coefficient of acoustic waves (105 Hz ≤ ν ≤ 3 109 Hz) had been recently experimented over a broad range of frequencies. He obtained for the degree of association (1 − α ) = K Acα 2 f 2 . 104 | P a g e . J. applying the method devised by Boltzmann to the equilibrium between ion pairs and free ions.D is the dielectric constant. of micelles and bilayers. Bockris et.The qualitative explanation of the mechanism of formation of the three types of ion-pairs. The decrement in the dielectric constant makes the value of ‘q’ greater than the ionic diameter. k is Boltzmann’s constant . if D remains constant But the solvent mixture is treated as a dielectric continuum. that would lead to the continuous variation of the dielectric constant as the solute concentration gradually increases . the potential energy of the ion pair is “2kT”. had to be a 3000aDkT straight line with constant slope. this intercept is obtained on the φK2 axis . Kaatze. where c is concentration. Also we can write lim φ K = c →0 (v f − n1 v10 ) n2 β = .al.This decreasing intercept clearly signifies the reduction in the number of water molecules around the central ion. [33] showed that the solvent with lower dielectric constant favours ion-pair formation to a more marked degree. al. Reddy [29]. the two spectroscopic methods can be favourably used to yield complementary aspects of structural properties and interesting molecular dynamics of liquid mixtures . was detailed by Margaret Robson Wright [27] . and of small organic molecules. of transition metal chlorides. In many cases.For 1-1 electrolyte he deduced K A = [4π Na3eb ]/[3000] .t-butyl chloride in aqueous solution. . recently in their dielectric relaxation studies over a wide range of frequencies and concentration ranges similar to those of the author recorded marked evidences of the simultaneous existence of double-solvent-separated. Using studies in infrared. [37] in their X-ray diffraction & NMR studies in a series of papers 1990’s studied ionic solvation. Rohman [38] in his Ph. record more than two or more gradient changes at places of formation of solvent separated as well as solvent shared ion pairs.al [42]. and intend to report our findings shortly.al. Buchner et.al [39]. 105 | P a g e .Several workers [34] in addition to Fuoss and Kraus used mixtures of solvents aqueous as well as non aqueous and established the ion pair formation in each of them. However their work is to be extended to other sources of data to ensure generalizations. We are attempting to use this model. Petrucci et . Very recently Honggaing Zhao et.al [40].Weingartner [41]. and contact ion pairs at all the ranges of temperatures studied. Raman spectra. supported by dielectric and ultrasound relaxation and related thermodynamic evaluations attempted a systematic analysis of Ionpair mechanism.” published voluminous data with non -aqueous solvents also.al [39]. Ohtaki et. with nearly the same stability. so that the pairing process could be generalized to accommodate unsymmetrical electrolytes in such a way as to divide ions uniquely into uncharged "molecules" with minimal internal distances. and Collie [20] made an attempt to give a mathematical shape to the logical structure of mechanism of ion pair formation for a symmetrical electrolyte. used a dielectric relaxation technique that restricts the thermodynamic analysis of the individual ion pairs . and conductance measurements.al [36].. Buchner et. Exactly in the similar lines in our ultrasonic studies. thesis “Ultrasonic Velocities and Transport Properties of Aqueous and Nonaqueous Electrolytes. our plots with GKG parameters reported in this paper.They concluded that both the ions influence solvent water molecules beyond the first hydration sphere.D. attempted the development of an equation of state that considers the statistical conditions to account for association contribution of the solute to the solvent through the reduction of the dielectric constant. Hence their observations are incompetent to explain the ion-solvent interactions Stillinger [35] using the dielectric measurements of Hasted. & H.. solvent-shared. KCl was chosen for numerical analysis. However the fact that the dielectric constants of the solvent continuum changes once the solute ions enter it is not implanted into their analysis and observations. since the slopes at these places of formation corresponding to the value of SK is not much different. They concluded that both the ions influence solvent water molecules beyond the first hydration sphere. Results for sulphates appear separately at Brahmajirao et. with tendency for the formation of contact pairs to be more as the temperature increases. Ritson. exactly in the same lines and hence Fuoss and Kraus theory was applied therein. Their interpretations are yet to be confirmed in detail.Afanasievet.al. It is predicted from the scaled particle theory that the solvent exclusion effect caused by the introduction of solute into solvent is an important factor of the hydrophobic effect. density. In his studies on structural and thermodynamic aspects of the hydrophobic effect. Pitzer et.al. The results show that the model can accurately correlate the interactions in aqueous solutions of glycine and NaCl. for small ions due to the electrostriction of the solvent were obtained from an iterative shell-by-shell calculation from a continuum model of the solvent. reported apparent molar volumes and transfer of isentropic compressibility’s of l-alanine from water to aqueous potassium di-hydrogen citrate (KH2Cit) and tri-potassium citrate (K3Cit) from ultrasonic measurements.’s [50] formalism. from a detailed analysis of a series of lengthy molecular dynamics simulations of alkali-halide solutions carried out over a wide range of physiologically relevant concentrations find evidence for pronounced non ideal behavior of ions at all concentrations in the form of ion pairs and clusters which are in rapid equilibrium with dissociated ions. from analysis of the solvation structure around solutes and various water models by the RISM integral equation method. [48] With their extensive measurements of the speed of ultrasound.Several observed deviations were attributed to the change in the dielectric permeability of water in direct proximity to ions. this shows that some reorganization of water occurs in response to the change in solute size. evaluated parameters including hydration numbers and osmotic virial coefficients . studied the properties of electrolytes in solutions and observed the interactions of the constituent ions with solvent and other ions. [47] and Gardas et. and isobaric heat capacity. [43].al. The interactions with the solvent alone are manifested at infinite dilution. Gardas et. From the measurement of partial molar volume. For a given electrolyte.al.al. isentropic compressibility of aqueous solutions. 106 | P a g e .al. ion pairing sets in under certain circumstances of ionic charge and solvent permittivity. leading to Ionic hydrophobic influence.[49] Worked out Monte Carlo simulations of the hydrophobic effect in aqueous electrolyte solutions which reveal several structural characteristics of the solvent around the central ion during ion pair formation. developed in a series of papers has been put to use and a model was developed by Soto et. over wide temperature and concentration ranges. The phenomenology for ion pairing seen in these simulations is congruent with the multistep scheme proposed by Eigen and Tamm based on data from ultrasonic absorption. it was shown that the dependence of cluster populations on concentration can be described through a single set of equilibrium constants. additive ionic contributions. They confirm the conclusions of Fuoss and co-workers. Jönsson et. but have a promising scope to understand the solvent behaviour. Soda [45] concluded that with increasing solute radius from 0 to 3A. It was found that the apparent molar isentropic compressibility and the apparent molar volume of alanine in both KH2Cit and K3Cit aqueous solutions is negative and increases by increasing temperatures and salt concentrations. the molar electrostriction of the solvent is calculated & compared with the experimental values. based on conductometric experiments. is reported. However the attempts are yet in the primary stage of development. et. & density. the average orientation of hydrating water varies from an inward to an outward orientation. Ion pairing results as a balance between the favorable Coulomb interactions and the unfavorable partial desolvation of ions needed to form a pair. and good agreement for many univalent ions in both single solvents and in some binary solvent mixtures. Ion pairs and clusters form on length scales where thesize of individual water molecules is as important as the hard core radius of ions.Rahmat Sadeghi et. [46]. Chen. apparent molar volume and isentropic compressibility of glycine in aqueous solutions of NaCl. The solvation number ‘S ‘ defined by the ratio of the solvent shrinkage per mol of ions to. based on detailed experimentation with ultrasonic techniques.al compared their results with that of X-ray data analysis in the solid phase.al. He opines that when no appreciable preferential solvation takes place. Very recently in the ionic volume measurements Marcus [44]. [51] to correlate the activity coefficient. 107 | P a g e . Part 2. 32 835 (1960). (2) VONHIPPEL.P. Solution Chem. 426.Soc 55 2709 (1933) & Chem. 25(9). BLANDAMER & J. J .Mol. Chem. 5(4). 31 936(1960. U. 1 (1948).al..S.Faraday.Chem.J.Molecular.” The Physical Chemistry of Electrolytic solutions “: Reinhold publishers (1958).al.”Interaction and Activation in Aqueous mixtures “. New York & London (1965). (8) MARKS J. J. (4) GUCKER&BACHEM Zeits. Trans. Res.Let.Rev. J. 42 3495. Res. Fluid Phase Equil. 49(2) pages 225-248(2001). Ind. 9B 215(1951). 1863 – 1867 (1972). New York(1963).Soc. (3) GUCKER. Can. . (1970). 41 570(1936). Phys.Electrochem. Interscience. Ibid. (16)WANG & ANDERKO” Modeling Viscosity of Aqueous and Mixed-Solvent Electrolyte Solutions” Presented at‘14th International Conference on the Properties of Water and Steam in Kyoto ‘: Proceedings’ pp116-121 (2004)..S. Acous.F.R.T.al . “Ion Properties “.Of Sci. “Dielectric materials and applications “. (9) BHIMASENACHAR & SUBRAMANYAM J.. (19) PANDA et. (12) BORUKHOV et.RAO J. Study of solute-solvent and solventsolvent interactions in pure and mixed binary solvents J. 16. Can. ‘Complexes of 8-Amino-2-methylquinoline with cobalt (II)’ Australian Journal of Chemistry. 9 (1980) 19. (18) POWER et. “Digest of literature on dielectrics” Nat.Amer.Soc. 29 (1) Pages 58-62. (20) HASTED. Ind.Amer.BURGESS. Ibid (2003).. and COLLIE. Chapter 6.. 52.al. Advances in Molecular Relaxation Processes. (21) EIGEN. (6) KRISHNAMURTY J. (5) HARNED &OWEN. (13) LENKA et al.Molecular. Inorganic. (11) W. J.Chem. (1981).Acad. (26) KAATZE et. Marcel Dekker Inc. (1973). Liquids. Advances in Molecular Relaxation Processes. (25) M. 572(1964). J . Volume 1. Ibid (2001). vol VIII. Z. Chem. 203 141. 10B 149(1952). PP15-39. Intl.Phys. New York 1997.al. Revs 15 111. 2(1). 34 565(1960). ‘European Journal of Inorganic Chemistry’ 2004(1) 178-184. Acous. J.M.D. (23)COVINGTON & LILLEY.MASON “Physical Acoustics”.RAO& K. (1). (1991).24 25 . Theomophys.By Royal Society of Chemistry.. (27)MARGARET ROBSON WRIGHT: “An Introduction to Aqueous Electrolyte 108 | P a g e .Liquids (1992).al. 17B 444(1958).79 (3) pp435-438(1997). The Technology Press.al.. Article 5 on “: Ion pair and complex formation” (1970) . 20(8) 27112713. J. 60 1637.Physik.Frankfurt vol. J.Sci. Electrochemistry. Phys. Z.. Pages139-152 Blandamer et. 101 541(1936).al.Amer. Ind.. J. pp1-40Blandamer et. 54. Sci.(22)EIGEN& EMAEYER “Investigation of rates and mechanisms of reactions in“Techniques of Organic Chemistry “. Colloids and Surfaces. SINGH et. 19 367(1998). (7) B.Faraday. 48. 1563(1976).Hills. Ind. 1 176(1954). (1954). M.A. Discussions . Pub. Massachusetts. Liquids 137(1-3)10 131-137(2008). (10) PADMINI& RAO. pp333-338 Blandamer et. (14)MARCUS et.Soc. Res. (15)OUT and LOS. National research council Washington . J.Phys. Vol-II.Soc.Chem.Academic press.Chem.REFERENCES: (1) GLUECKAUFF. MISHRA et. Specialist periodical reports / Chemical Society Edited by G. Eng. (17)McCLEMENTS & FAIRLEY Ultrasonics.. Fluid Phase Equil. Ibid (2002). 186 103.al. (24)MAITRA & BAGCHI.al..I. Chapter 18.C. RITSON.. 45 24592462(1967). Chem. Saest. (31) BRAHMAJIRAO. I Solutions in p-Xylene and Benzene Interactions between benzene. B. Mol. D. . July1982.Chem. MARCUS. JAPAN. J.GKG and Dagget equations “. Assam.al.12 Formation of Ion pairs from free ions. “Ion Solvation.al.al. . GOVER et.78 169. the Dibrugarh University.(SULPHATES) “Paperpresented to NSA-2010..(1963)“Mechanisms underlying the equilibrium reactions between ions and ion pairs In solutions of electrolytes.Chem.Ibid “Application of Glueckauff’s model of variation of dielectric Constant to association constant – Calculations in relation to Ion pair Formation “Proceedings of 2nd International symposium on Industrial and Oriented Electrochemistry.Bunsenges.Pure & Appl. Ibid 70 706 Pyridine (1948). Ibid (1989) Ber. “Influence of variation of Dielectric constant. 5100-5107 ..Ibid “Ultrasonic studies in solute solvent interactions….) 93. 18. D. 286. B..Amer. B.Ghosh Memorial symposium held at Calcutta. Rev (Washington. .” Wiley Interscience.126 244503(2007). Phys..Solution Chem. 1998. Soc.N. held at Brighton U. EL-AGGAN et. Appl.. Phys. John Wiley & Sons Ltd. Chem. Rishikesh.) . 46-50. Ibid J. and the paper immediately following it.113 762. Am. Ibid (2010) Molecular Structure and statistical Thermodynamics Selected papers of Kenneth S Pitzer’ World Scientific. “Glueckauff’s model for lowering of dielectric const. “Ultrasonic Velocities nd Transport Properties of Aqueous and Nonaqueous Electrolytes “.al. 110(30): 14961-70. J. Proceedings of Eighth International Conference on Nonaqueous Solutions..Chem.Chem.C.O”M. II The effect of temperature”. 111(23): 646978 (2007). 103 (1996). Pages 392 & 429(2002).al. (36)PETRUCCI et. J Phys Chem. pure & Appl.Chem.B.J.Soc 77 225.( 48) GARDAS et.Chem.Solutions” Art. (1968) J. 3858. Solution. 87. Newyork (2002) .. Ibid (2001) Adv. vol 73 No.Second revised edition.. Ibid on ‘ionic Solvation in Aqueous and Nonaqueous Solutios. pages 200-7(2006).Bunsenges. et. J Phys Chem.al. 1007(1989). REDDY: “Modern Electrochemistry”. ethylenediamine (1955).al. 141. (30) J.al.al. J.Chem. 5701 (1974). (2006). REYNOLDS et.( 46) CHEN et. Proceedings of International Conference on Nonaqueous Solutions.pp1to32. (1963) 49(2):141-6. (1994) J.Ibid “Study of …in chosen electrolyte solutions “ Proceedings’ of Sir J. Ibid “Solute –Solvent interaction and Ion pair formation in the light Of depression in Dielectric constant” Proceedings of VIth International Symposium on Solute–Solvent–Solute…Interactions. (41) WEINGARTNER. (28)ROBINSON AND STOKES “Electrolytic Solutions “. 1157 (1993). Soc Japan 56: 443: . 103 738.” J.(33) KRAUS et.Phys.(43) RAHMAT SADEGHI et. 19 (1981) 254.Chem. Ibid J.al. Plenum Press Chapter3 on “Ion –Ion “interactions: & Chapter 4.Ibid “Analysis of solute. held at New Delhi.( 49) Jönsson et. Pages 62-68. in August 1984. 95 1579.Phys. Ibid 2000). 88. 41 & 51.A -2010. Ibid 0 1709 acetone (1948).5059– 5061(1958). Ibid (1981).( 47) AFNASIEV et..C. Singapore Ion interaction approach: Theory and data 109 | P a g e .Phys. Soc Japan 65: 1445. Of.A.. Chem..al. 1977 edition.97 (1997). Nantes (Cedex) FRANCE.al. Ibid (1999). B.Phys. J Phys Chem.. J.III.Soc. Sydney AUSTRALIA.Gucker’s equations…” Proceedings of International Conference onUltrasonics.Chem. (29)J. acetic acid (1954).al. BURGESS et.Chem.Appl. Chem.. Pennnsylvania. (35) STILLINGER et. Ibid (1981) “Application of Glueckauff’s model for depression in Dielectric . WEST GERMANY.al.V. Nov 11th to 13th. Chem. 2140(1972).KRAUSet.. With aqueous … using Ultrasonic’s . B. Liquids.Pure. 29 1-54(1993).D Thesis. Bull Chem.S.. 268 (1973).al.al Ibid 76 3247.The Equilibrium between Ion Pairs and Free Ions”.Chapter9. J.. By Springer wein. (Aug 1980). Chi Chester.( 34) FUOSS and KRAUS J. (40) HONGGAING ZHAO et. J. Stat.Chem 60 330.93 1058.. 80 (19).al. Phys. The Atrium.al.page 238:“Theoretical Interpretation of Chemical Potentials &Influence of ion solvent interactions on Ion atmosphere” and Also” Ion Association”: Chapter11&14. to be held during AUG23rd TO 27th of (2010). 19th to 23 rd July 1982 . India (2000). Phys. Chem.Ionpairs”Procedings of ICNAS-IX Held at Pittsburgh. 551019and21dioxan-ater mixtures (1933)).Procedings of International Symposium on Electro analytical Chemistry Held at Chandigarh. HNIZDAet. (42) BRAHMAJIRAO et. 76. Southern Gate. 18 12 (1980) 1021. Ibid “On GLUECKAUFF’S model for variation of dielectric constant of electrolyte Solution. 2092 ethanol (1958). 98. B 110(30):14961-70.14 646. 124(3). 28.al. Ind.Phys.C. HIBBARDet. RADNAI & YAMAGUCHI (2003) Chem. Phys. Proc Natl Acad Sci U S A... pub. England(2007) . vol. n-propenol1956).solvent interactions …in relation to ion pair formation”. Ind.K.6 on “Influence of Ionic Atmosphere on Ionic Migration”. Ibid (1999) J Phys Chem. Ibid 71 1565. J.Chem. pp 26. (50)PITZER et. (2008) . 30th JUNE to 2 nd JULY 1981.U.O”M. page 17.( 37) OHTAKI.110(17): 8782-8(2006).Am.al. Proceedings’ of ‘Ultrasonics International-81’. 28 435. and p-xylene (BTX) during their biodegradation. (2006) .Phys 116 1. 13(1): 212-23 (2009). Chem Soc. page1733 (2001). Ibid (1980).Chem . (2010). held at Regensburg.Amer..BOCKRIS et. 14(2) (1979)53. 112(11):338089(2008). ICNAS-7. (1985) . INDIA).Soc. Phys. Pure. JONES et. 8234-8244.al J Phys Chem. “Ionic Solvation Numbers from Compressibilities and Ionic Vibration Potentials Measurements. p. 48. Phys. J.FUOSS “Ionic Association. Toluene.. J Phys Chem.1. Ibid (1995) J. New York. liquidammonia (1949). Variation of Dielectric. Ibid (1980) “Application of …. J. ICEU-July 1980. Adv Biophys..Ion pair formation”. 11.Feb1982..( 44) MARCUS Biophys. Rev.( 45) SODA. (1-2).. . Tokyo..Phys.Phys.‘ION PAIRS ‘. Chem. ‘Highlights in solute-solvent interactions’editor: Wolfgang Linert.Phys.al. INDIA.. “Cationic motilities of electrolytic solutions-Ion pairs–EIGENmechanism”Transactions. INDIA (Dec 1980) (32). J.Chem. . (39) BUCHNER et.. determined by acoustic tools & onfirmation of Eigen Mechanism of ION PAIRS “Paper presented to: I. 96. Ibid (1991). Ibid (1980). Lett. INDIA.( 38) ROHMAN. Ibid J. Ibid “Electrostatic Potential energies of Ion pairs in nonaqeous media from” Ultrasonic measurements”. Isentropic ompressibility Studies …. “Mechanisms underlying the equilibrium reactions between ions and on pairs in Solutions of electrolytes. Bull Chem. Phys.. Ind. J Phys Chem. Mol.BOCKRIS & AMULYA K. and its Influence on thermodynamic variables. Ph. INDIA December1982. Ibid (1976). West Sussex PO19 8SQ.C. (Washington.Soc. Ber. J. Held at Karaikudi. 77. 74(3): 165-73 (1998). (2010) pp.. Biophys. Boca Raton.Chem. 2 “– Editor: Pitzer KS. Florida.’ In: “Activity Coefficients in Electrolyte Solutions. 110 | P a g e . 75–153. al. USA: CRC Press.correlation. (51) SOTO et. Jawaharlal Nehru Technological University. as well as other possible interactions . 3 LNBC Institute of Engineering and Technology.al.. correlating the concepts arrived at in the very recent literature. Hasted et. Buckingham [4].Raigaon. Gunavardhan Naidu 1. Correlating arguments cited by several earlier workers. Cheekatimamidi (V). Isentropic compressibility.. The graphs record an excellent agreement with many of the findings of the very recent work in the field of electrolytic research cited at the appropriate place . Debye Huckel theory. Bommalaramaram (M).and quantum physics . Monte Carlo Simulations .Srikanth 2 . They obtained valuable information with Monte Carlo Simulations and all of us land at concurrent & conspicuous conclusions.using thermodynamics. The author modifies the relevant equations and explains on firm grounds . T.P.e.GLUECKAUFF’S MODEL FOR LOWERING OF DIELECTRIC CONSTANT OF ELECTROLYTIC SOLUTIONS : ISOENTROPIC COMPRESSIBILITY AND IONASSOCIATION STUDIES WITH AQUEOUS ELEECTROLYTIC SOLUTIONS BY ULTRASONICS -Ion pairs (SULPHATES) V.Brahmajirao 1** . 2 Jawaharlal Nehru Technological University (Jagtyal Campus) Jagtyal. Satara. Lowering of dielectric constant of dielectric continuum Introduction Robinson and stokes [1]. Pin Code – 508116 . Discrete variation in the slopes of the straight line plots are explained. . Ion-pairs in aqueous electrolytes. since the dielectric constant dependence on concentration is to be installed into their arguments. are given in support.Rajendra 3 Shanaz Batul 1 4 Matrix Institute of technology. P.[2] . The data is presented as plots. molecular dynamics . Gucker’s equations . Jawaharlal Nehru Technological University HYDERABAD.al. ABSTRACT This paper reports the specific evidence of the formation of three types of Ion pairs from the ultrasonic studies in aqueous solutions of sulphates. 4 Main campus.com ) . and hence crudely neglects the short range interactions between ions and solvent molecules. [5] & [6] apparently are incomplete.the mechanism of formation of Three types of ion pairs i.showed that the first layer of the solvent molecules of type “B” round the central ion of type “A” of the ionic atmosphere cause short range interaction leading to the reduction in the bulk dielectric constant of the medium around the central ion. to account for the ion-solvent interactions missing in the prevailing theories of electrolytic state. point out that Debye. KEYWORDS: Glueckauff’s model. and 111 | P a g e ..A. (2) solvent shared and (3)contact types.. ( 1** Email ID for all correspondence: profvrbr1@hotmail. Maharastra . non deformable spheres of equal radius. (1) solvent separated.Glueckauff & Von Hippel [3]. by a host of workers trying to analyze similar interrelated problems in different angles . Also deductions by a host of others in the application of equations of Gucker et. T.which are responsible to create internal field around the central ion of the ionic atmosphere & the average effect of all such ions is to reduce the value of the dielectric constant of the electrolytic solution.. using equations for partial molal compressibility & apparent molal compressibility. HYDERABAD-500072. used this very important point for correction.Huckel theory treats the ions of the ionic atmosphere as hard. S. G 0 2 . and other factors. This data was used in the present work. and no rigorous explanation of these findings is available in the literature.Rao [9]. cannot be so. ∂φv 0 Also the apparent molal compressibility is [ φk = ( 2 )T . and Λ the value at the given concentration .R. in which ∂p S β S K = [(∂SV / ∂P )T + ( V )] Leading to 2 15 ∂D 2 6 ∂ 2 D χ ∂β 6 β ∂D 2 S K = (∑ν i zi )3 2 [ β 2 + 2( )T − ( )T + 2 ( )T − ( 2 )T ] D ∂P D ∂P 6 i ∂P D ∂P 0 Hence Cversus(φK ) plot cannot be linear. & solvent -solvent interactions. [6]. S K = (6. According to Gucker et. experimentally.al. is the iso-entropic compressibility.Rao & K.al.[14]. Marks [10]. that was confirmed to be reasonably accurate. and other factors that require attention. where δ is independent of the ion-solvent. and K A is the mass action term. ion-ion & and other interactions . Mason [13].Also the SK value showed irrational variation with the valence of the ion. are parameters corresponding to ∂p ∂p infinite dilution. [11]. Treating the dielectric constant as a variable it can be shown that 3 5 ∂D 1 ∂ 2 D β ∂D ( K 2 − K 0 2 ) = χ [ 2 ( ) 2 + ( 2 ) + ( )] . Prozorov[15]. Padmini& Rao [12]. 3 6 1 ] 2 and N is Avogadro Number .Association constatant is a parameter which gives an insight into the ion-ion and ion-solvent interactions With the notation used by Graham Kell &Gordon[17] . against the predictions of Gucker et. Gucker [5] established with standard notation the partial molal compressibility as 2 ∂ ∂ 0 [ 2 (G2 − G 0 2 )] = [ (V2 − V 0 2 )] = ( K 2 − K 0 2 ) .al. (which is a variable. as per the new expectations ).Barnartt[16] observed that the linearity of the above plots extends into higher concentration regions where the DebyeHuckel theory is not contemplated to be applied .] and [ φK2 = φK + S K C ].These equations clearly reveal That [ χ = [(π N e ) 2 (1000 D kT ) Cversus ( K 2 − K 2 ) ] plots that were expected to be linear previously. B. starting from Gibbs free energy given by G = ∂G ( ∂nA ) . & solvent -solvent interactions.developed a model to evaluate the depression in the dielectric constant. and “D”. Bhimasenachar & Subramanian et.But the above expression clearly shows that it is not so.’ E’ is the 112 | P a g e . Λ 0 the value at infinite dilution.al. leading to the ion pair formation as detailed in the discussion of the results. is the V ∂P v ρ dielectric constant.we can show that K A the association constant can be expressed in terms of conductances Λη the value corrected for volume effect on viscosity produced by the solute . V2 .by the equation Λη = [ Λ 0 + Eci log ci − S ci + Jci − K A ci f 2 Λη ] . The variations in its slope correspond to the ion-solvent. at constant nB temperature and pressure .This model was used earlier by the author to evaluate the dielectric data.3 X 10−10 )δ is a constant.Giacomini et. In this K 0 2 . of an electrolyte solution as the concentration of the solute increases. The variations in the slope correspond to the ion-solvent. 2 D ∂P D ∂P D ∂P 1 ∂V 1 In this β = [− ( )] = 2 . ρ is the density. Earlier Harned & Owen [7]. and. Krishnamurthy [8]. [39] Experimental and Calculations: This paper reports the data. but the ions are 113 | P a g e 0 .al.. .the formation of solvent separated.and ‘ f ’. )] . 2 F Λ0 We find that these equations do not incorporate the happenings around the reference central ion. In this stage the solvent co spheres are in contact . [19] And Bikash Kumar Panda et. [22]. in which n1 is the free charged ion number. dielectric constant and activity coefficient data for several aqueous as well as nonaqeous electrolytic systems partly his own and partly from Lobo [46] with the above equations. In addition if ion association comes into existence. These shortcomings of the respective citations detailed above find a systematic explanation by the author and are to be attributed mainly to the deficiencies in reckoning the electrical interactions. of our ultrasonic studies using Ultrasonic pulse echo technique similar to that of Mc Clements & Fairley [18] in aqueous solutions of sulphates. where F= F ( z ) = ( ) cos 2 [( ) cos −1 (−3 2.called the GKG equation. previously reported results The qualitative details of the mechanism of formation of ion pairs . entirely different from the cited . [20]. Density measurements are made using the bicapillary pyknometer. ‘J’is the relaxation term . in “C-language” and details of analysis of variations in thermodynamic parameters. to give finally 3 z Λ 4 1 γ = ( ) F ( z ) . around the central ion as the concentration increases Details are available at ref. It is now established that all these terms are discrete functions of dielectric constant. since the variety of influencing parameters and the equations to be probed with them is complex . Several findings from recent literature are in consonance with the conclusions from the author’s plots. and ‘c’ is c the concentration.al & Mishra et .R. applied to the bridge network as a whole The experimental details for dielectric determinations are given else where [47] The ultrasonic. in which’s’ is an independent variable 3 3 2 Λ0 Λ 2 given by z = ( S 3 )(cΛ )1 2 . Some of the prominent expectations of the recent trends are discussed below. . for each electrolyte were drawn. Brahmajirao et.This leads to ( ) = Λ 0 − [cΛ 2 f 2 K A ] /[Λ 0 F 2 ] .al & Singh . are presented as graphs with C as abscissa and φK2 & ( K 2 − K 2 ) .-9500 similar to the one used by Power et.et.al. Several plots.al. dielectric and conductance data of the author were used in the calculations. Paucity of space restricts the discussion about conclusions with this equation by the author here in this paper. solvent shared & contact pairs as envisaged by Eigen[21]and worked out by Eigen et.As a preliminary attempt the author used conductance. is briefed below : In the initial (first) stage an ion pair is formed with no disruption of the individual solvation sheaths of the individual ions.is the activity coefficient .al. ’S’ is the Onsager term. using a programme. are finding good utility at hand. From this equation γ can be obtained by a process of iteration. as ordinates separately.electrophoretic term. Only thermodynamics and statistical tools can help this . The ionic polarisation effecting the Conductivity measurements is balanced the usage of an inbuilt oscillator generating 1 KHz signal. The conductance data was obtained using the ‘PHILIPS’ Conductivity Bridge Model P. so that in the ion pair these solvation sheaths of the individual ions are in contact and solvent is present between the ions.Monte Carlo simulations. the expression for Λη becomes a cubic equation in γ (to be solved by n a method of continued fractions) where γ = [ 1 ] . Discussion of the results: All the plots record conspicuous gradient changes corresponding to . consequent of the interactions that generate long range and short range fields in the ion -atmosphere in the continuous dielectric medium of the solvent. inside the ionatmosphere. or at most two. In literature. solvent molecules lie between the ions. [27] showed that the solvent with lower dielectric constant favours ion-pair formation to a more marked degree. Ion-pair association constants calculated. A major factor contributing to enhanced association appears to be ion-dipole interaction. ion pair formation totally differs from complex formation when a complex is formed an intimate chemical interaction between the ions & electronic rearrangement occurs resulting in covalent interactions. A plot of [logK A] vs.In an outer-sphere ion pair one. [25] reported Conductivity data for solutions of [Co (NH3)5NO2] SO4 in water and aqueous dioxan. to reveal the reduction in the number of water molecules in the primary hydration sheath of the ion pair. and there is the possibility that different experimental methods may pick out and detect only one kind of ion pair. lim φ K represents the reduction in the hydration c →0 number. Because we can write lim φ K = c →0 (v f − n1 v10 ) n2 β = . [1/D] is found to have a slope considerably greater than that for simple 2:2 salts. In the last (third ) stage an ion pair is formed with total disruption of the solvation sheaths of the individual ions so that in the ion pair the bare ions are in contact and there is no solvent between the ions.Hence these are called SOLVENT SHARED ION PAIRS .Ion pairs formed in the first two stages are called outer-sphere ion pairs . However. at three places. Gucker showed that from the [ C versus φK2 ] plots. They showed that at the critical distance defined by 114 | P a g e . but for an inner-sphere ion pair bare ions are in contact and all solvent sheaths have been eliminated from between the ions.al. observed measurable difference for two models which are consistent with other magnetic relaxation and thermodynamic data for the solutions. Inferences made from thermodynamic and kinetic experiments have often been used. both inner and outer-sphere ion pairs are still solvated as the composite unit.... Fennell [30] and others. This is being attempted by the author in the lines of. and the ions are reasonably distant from one another In the intermediate (second) stage an ion pair is formed with partial disruption of the individual solvation sheaths of the individual ions and there is still some solvent present between the ions so that the ions of the ion pair share the solvent sheath between the ions . exactly in tune to the authors’ findings Master ton et. Fuoss [26] &Kraus et. However the effect of addition of electrolyte to the solvent is not considered. while conductance work and scattering of light experiments allow micelle formation to be picked up very easily. al.In this stage the solvent co spheres are in contact.al [24]. The slope gradually decreases for each plot. for which a theory is yet to be conceived. The ion pairs which can be found are thus not necessarily identical.nh v10 β 0 in which n1 is the total number of molecules of water and n2 is the number of moles of electrolytes and nh is the hydration number which is the number of water molecules in the primary hydration sheath round the central ion . Hence these pairs are called CONTACT PAIRS or inner sphere ion pairs . but they rely very heavily on being able to predict a model for the ideal solution. and the ions yet are not in contact . in contrast to the physical columbic electrostatic interactions involved in the formation of an ion pair. Also the Ultrasonic and spectroscopic methods probably allow a distinction to be made with reasonable certainty between outer and inner-sphere ion pairs. Larsen et al [29] and.reasonably distant from one another Hence these are SOLVENT SEPARATED ION PAIRS .in his admittance studies of aqueous sodium chloride and NMR relaxation rate of 7Li+ by Mn2+ or Ni2+ in aqueous solution . These are quite exceptional achievements in the field of ion association. Very recently Krishnan et.In an outer-sphere ion pair one. or at most two. solvent molecules lie between the ions .They pointed out from their admittance studies marked evidences for the ion pair formation. the ultrasonic studies is probably the only tool to detect the formation of all the three types However as pointed by Margaret Robson Wright [23]. They reported Enthalpy studies in electrolytes in methanol and dimethylformamide leading to similar observations . therein. An equation for association nt constant was deduced. in the N.D is the dielectric constant . f is Debye-Huckel activity coefficient . SrCl2.For 1-1 electrolyte he deduced K A = [4π Na 3eb ]/[3000] .R.al ion-solvent [29]. is in progress with the authors. and in each case. exactly in the ous same lines and hence Fuoss and Kraus theory was applied therein. k is Boltzmann’s constant . was applied. Association equilibrium constants (KA) were calculated and compared with two types of experiments. and T is the absolute temperature . .6 ns). where c is concentration. Hence their observations are incompetent to explain the ion solvent interactions Berman et. and small-large large small should be more dissociated.q = [( z1 z2 e 2 ) / 2 DkT ] . applying the method devised by Boltzmann to the equilibrium between ion pairs and free ions. and of small organic molecules. many multivalent electrolytes. and conductance data shows that the addition of a small amount of water causes transformation fr contact to from Solvent separated ion pairs Larsen et al [30] studied the ion solvent interactions in relation to dependence of Bjerrum length on several factors from the Restricted Primitive Model (RPM). tential A corresponding state between that of Yukawa case and unscreened coulomb case was conceived. was correlated using classical molecular using dynamics simulations.al.M. It is shown that.All spectra reveal a Debye Debye-type relaxation term with small amplitude. The relaxation term is 115 | P a g e . the potential energy of the ion pair is “2kT”. [32] reported ultrasonic absorption spectra at frequencies between 300 kHz and 3 GHz reported for aqueous solutions of MgCl2. However the fact that the dielectric constants of the solvent continuum changes once the solute ions enter it is yet to be implanted into their solute observations. NiCl2. Kaatze et. MC simulations of Yukawa potential for several other models in vogue to establish several lapses in RPM. From observations on the relative depths of the free energies of the contact ion pair (CIP) and the solvent-shared ion pair (SIP). ion Fennell et. favorably used to yield complementary aspects of structural properties and of the molecular dynamics of interesting liquid mixtures.Several workers [27] in addition to Fuoss and Kraus [28] used mixtures of solvents aqueous as well as non aqueous and established the ion pair formation in each of them. Consequently Fuoss’ equations fail to predict the behavior of the ion pairs to a better extent . He obtained for the degree of association (1 − α ) = K Acα 2 f 2 .Relaxation studies observed Contact ion association behaviour of per chlorate ion with Li + and Mg 2+ in a variety of solvents . with no modification he attempted for accounting the solvent solute interactions. corresponding with the τ values for solutions of Mg(NO3)2 and Ca(NO3)2 in water. But the solvent mixture is treated as a dielectric continuum. in which a is ionic 1 2 diameter .R. we test different parameter sets are tested for m modeling both the water and the ions. in many cases. from which equivalent Bjerrum lengths in the coulomb potential. molecules. th found a good shared they correlation with the proposition that small small-small and large-large should associate in water. along with related solvent structure analyses.since [ z1=z2 ]. Several different PMFs were compared. leading to the continuous variation of the dielectric constant as the solute concentration gradually increases . and CuCl2 . the two spectroscopic methods can be cies. of micelles and bilayers. . α is the fraction of the (1-1 ) electrolyte present as free ions and K A is 1 the association constant . This fulfils the condition that the energy required to separate the ion pair is comparable to the thermal energy. CaCl2.al [31] studied ion-ion interactions in water. and the Potentials of Mean Force (PMF) for the full set of alkali halide ion pairs.For Mg (ClO4 ) 2 in acetonitrile a combination of N.Hence this theory requires modification in the this light of the Glueckauff’s model. about the relative affinity of ions in solution depending on the matching of cation and anion sizes.They discussed such aqueous systems for which measurements of the complex electric permittivity (103 Hz ≤ ν ≤ 1011 Hz) and of the attenuation coefficient of acoustic waves (105 Hz ≤ ν ≤ 3 109 Hz) had been recently experimented over a broad range of frequencies. Work in the lines of Fennell et. of transition metals .2 ns τ 0. b = e / aDkT .M. and rigorously worked out . The decrement in the dielectric constant makes the value of ‘q’ greater than the ionic diameter. Collins "law of matching water affinities". The relaxation time values derived from the spectra display a small range only (0.al [27]. suggested to be due to the second step in the Eigen Tamm scheme of stepwise association and Eigen–Tamm dissociation of ions, namely the equilibrium between the complex of encounter and the outer sphere between complex. The relaxation amplitudes reflect special properties of the ions. Exactly similar observations are reported in our studies Recent ideas of the mechanism of dielectric relaxation in hydrogen bonded liquids are discussed. Comparison is made with some aspects resulting from computer simulation studies.. Concurring views as the authors of this paper that in many cases, the two spectroscopic methods (dielectric and ultrasonic) can be favorably used to yield complementary aspects of structural properties and of the yield molecular dynamics of interesting liquid mixtures were expressed. Gaiduk [33] suggested simple model of dielectric response due to the three-dimensional motion of ions inside a spherical ideally reflecting sheath is suggested. The present model termed the sphere confined ionic (SCI) model is combined with the so called sphere-confined hybrid model, previously used to describe dipolar orientational relaxation The wideband (up to 1000 cm−1) complex permittivity (ω) and absorption α(ω) spectra of NaCl NaCl-water and KCl-water diluted solutions are water calculated as the sum of the contributions due to cations and anions and to reorientation of polar H2O molecules. A modification of this model is also suggested, in which the walls may also vibrate. Honggaing also Zhao et.al, [34] developed an “ Equation of state for electrolyte solutions by combining statistical associating fluid theory & Mean Spherical Approximation for the non primitive model” .A major fraction of nonm the interactions between different ingredients of the electrolytic solution ,are attempted to be accounted in this . Specifically the Statistically A Associating Fluid Theory for Variable Range potentials (SAFT-VR) that ange describes long –range ( ion-ion ),( ion ion ion-dipole ), and (dipole-dipole ) interactions ,is combined with the dipole nonprimitive MSA model, in performing the MC simulations . The model yet requires modifications, which are aimed at by the author Wertheim [35], calculated the association contribution, statistically, by a double on summation over all the possible sites, and species, accommodating for the fraction of the ions that indulges in pair formation, at a given site .However the presumptions many times lead to unrealistic situations, and hence demand more in depth pursuance. M. J. Blandamer, D.Waddington & J. Burgess et.al. [36] Very recently examined the significance of the term ‘activity’ in the context of the properties of aqueous solutions for aqueous solutions containing neutral solutes, mixtures of neutral solutes and salts, and also binary aqueous mixtures... Properties of aqueous solutions binary aqueous mixtures from the standpoint of solute roperties solutewater and solute-solute interactions, using pair wise interaction parameters are studied . With an increase solute in the amount of solute, strong evidence is obtained for clustering of both aqueous and non non-aqueous components. These trends are explained in terms of preferential solvation of initial and transition states using Kirkwood-Buff integral functions. The analysis is applied to kinetic data describing the dependence on al the ethanol mole fraction of the first order rate constant for the solvolysis of t-butyl chloride in aqueous butyl solution. Work regarding the application of Kirkwood Kirkwood-Buff integral functions, to the data reported in this al paper is in progress at the authors end Pitzer et.al.’s [37] semi empirical Equations, developed for activity coefficient work.are used by Moggia et.al. [38] in a pseudo lattice approach using Gibbs-Duhem equation. Gibbs However a better alternative with a suitable modification , to develop MC Simulations ,using the Pitzer’s formalism with its versatile extensions for the force field calculations using Molecular dynamics simulations of ionic solutions is employ employed by Fyta et.al., [39] ,by optimizing ionic force fields based on single-ion and ion-pair properties simultaneously for five different salt solutions, namely, CsCl, KCl, NaI, pair KF, and CsI, at finite ion concentration. The force fields of these ions are systematically varied. From the systematically finite-concentration simulations, the pair potential is extracted and the osmotic coefficient is calculated, concentration which is compared to experimental data. They suggest that additional parameters are to be introduced into the modeling, for better results The author is attempting this model for comparisons with parameters ing, obtained with ultrasonic data. Choudhary et.al. [40] and Dougherty et.al. [41] [41]separately Calculated Entropic and enthalpy and excess free energy contributions to the hydrophobic interaction between hydrophobic solutes and water using o molecular dynamics simulations in the isothermal isobaric (NPT) ensemble with free energy perturbation isothermal-isobaric 116 | P a g e methodology. The stabilizing contribution to the free energy of association (contact pair formation) was found to be the favorable entropic part, the enthalpy contribution being highly unfavorable. The desolvation barrier is dominated by the unfavorable enthalpy contribution, despite a fairly large favorable entropic compensation. The enthalpy term was decomposed into a direct solute-solute term, the solute-solvent interactions term, and the remainder that contains pressure-volume work as well as contributions due to solvent reorganization. The enthalpy contribution due to changes in water-water interactions arising from solvent reorganization around the solute molecules is shown to have major contribution in the solvent induced enthalpy change. Their observations require in depth application to more data. The data used Dougherty et.al[41] with their model include: molecular orbital-molecular dynamics applied to electrolyte water systems; Raman spectra; infrared spectra; magnetic resonance spectra of ions; the apparent density of water; and the excess free energy of electrolytes in aqueous solutions. Molecular orbital-molecular dynamics calculations of relatively large water clusters containing a molecule of sodium iodide show that the solvent separated ion pair exists in a substantial potential well compared to other possible structures. Raman spectra of univalent electrolyte solutions as a function of concentration can be quantitatively modeled using only the spectra of pure water and electrolyte solution at the concentration of the solvent separated ion pair. This information supplements the author’s observations Buchner et.al [42], recently in his dielectric relaxation studies over a wide range of frequencies and concentration ranges similar to those of the author recorded marked evidences of the simultaneous existence of double-solvent-separated, solvent-shared, and contact ion pairs at all the ranges of temperatures studied, with tendency for the formation of contact pairs to be more as the temperature increases. Even our plots reported in this paper, with GKG parameters record gradient changes at more than two or more places of formation of solvent shared ion pairs, and with nearly the same stability, since the slopes at these formations corresponding to the value of SK is not much different. Buchner et.al, uses a technique that restricts the thermodynamic analysis of the individual ion pair’s .They conclude that both the ions influence solvent water molecules beyond the first hydration sphere. Soto et.al.,[43]developed a model based on the Pitzer et.al’s. [37] formalism developed in a series of papers to correlate the activity coefficient, apparent molar volume and isentropic compressibility of aqueous solutions of electrolytes , based on detailed experimentation wit ultrasonic techniques . The results show that the model can accurately correlate the interactions in aqueous solutions of glycine and NaCl. A positive transfer volume of glycine from a NaCl solution to a more concentrated NaCl solution indicates that the size of a glycine molecule is larger in a solution with higher NaCl concentration. The negative values of apparent isentropic compressibility imply that the water molecules around the glycine molecules are less compressible than the water molecules in the bulk solution. These effects are attributed to the doubly charged behavior of glycine and to the formation of physically bonded ion-pairs between the charged groups of glycine and sodium and chloride ions. The formation of ion-pairs, whose extents of binding reactions depend on the concentrations of both NaCl and glycine, alter the hydration number of glycine. This also explains the reason for the increase in the size of glycine with an increase in the NaCl concentration. Wang et.al. [44] Studied, the thermodynamic properties, like the mean activity coefficient, osmotic coefficient, and water activity,etc. for 129 complex aqueous electrolyte solutions using the modified three-characteristic-parameter correlation model., which considers ion association in a betterway, incorporating solute solvent interactions through thermodynamic parameters . This model is being worked out and the out come will be published soon elsewhere, because the technique is other than ultrasonic in nature. Wang et.al. also calculated the adjustable parameters of the Pitzer model and the Bromley model. and established that their modified model is fairly suitable for predicting the mean activity coefficient, osmotic coefficient, and water activity of these electrolytes, incorporating several interactions. This new model is much better than the Bromley model and shows a better result than the Pitzer model. especially for 3–1 and 3–2 electrolytes. Work on 117 | P a g e chlorides and sulphates and nitrates in aqeous and nonaqeous solvents and observations about thermodynamic and ion association parameters and other related evaluations by the author is available else where at [45] reference REFERENCES: (1)ROBINSON&STOKES“Electrolytic solutions“(second revised edition), DOVER publications NEWYORK, page231, chapter 9,” The limiting law ….Huckel “(2002); (2) HASTED et.al. J.Chem.Phys 16 1(1948). (3) GLUECKAUFF Trans.Faraday.Soc. 60 1637, 572(1964); “Digest of literature on dielectrics “....Nat. Acad, Of Sci., National research council Washington .D.C.; VON HIPPEL “Dielectric materials and applications “, The Technology press, M.I.T., Massachusetts, U.S.A. (1954); (4) BUCKINGHAM Disc.Faraday.Soc. 24 151(1957) ;( 5) GUCKER J.Amer.Chem.Soc 55 2709(1933) ; Chem .Revs 15 111(1933). ;( 6) GUCKER & BACHEM (1936) Zeits.F.Physik.101 541, Z.Electrochem. 41 570;(7) HARNED & OWEN “The Physical Chemistry of Electrolytic solutions “, Reinhold publishers, ;New York (U.S.A.) (1958);(8) KRISHNAMURTY, J. Sci.Ind.Res 9B 215(1951) ; Ibid10B 149;(9)B.R.RAO& K.S.RAO, J. Sci. Ind. Res. 17B 444(1958);(10) MARKS J. Acous.Soc.Amer. 31 936(1960) ;( 11) BHIMASENACHAR & SUBRAMANYAM J. Acous.Soc.Amer. 32 835(1960); (12) PADMINI& RAO Ind. J .Phys. 34 565(1960) ;( 13) W.P.MASON “Physical Acoustics”, Vol-II, Chapter 6, page 426; Academic press, New York & London (1965) ;( 14) GIACOMINI et.al. Ricerca. Sci. 11 606(1940). (15) PROZOROV Zhur.Fiz.Kim. 14, 384. 391(1940); (16) BARNART J.Chem.Phys.20 278(1952). ; (17) GRAHAM KELL &GORDON J.Amer.Chem.Soc 79 2352(1957) ;( 18) McCLEMENTS & FAIRLEY Ultrasonics, 29 (1) Pages 58-62. (1991); (19)POWER et.al, ‘Complexes of 8-Amino-2-methylquinoline with cobalt (II)’ Australian Journal of Chemistry 25(9) 1863 – 1867(1972); SINGH et.al. (1976) Can. J. Chem., 54, 1563; Ibid, Inorganic.chem. (1981) 20(8) 2711-2713; (20) PANDA et.al. ‘European Journal of Inorganic Chemistry’ 2004 (1) 178 – 184 (2004); MISHRA et.al. Can. J .Chem. 45 2459- 2462(1967); (21) EIGEN Z.Phys.Chem.Frankfurt vol. 1 176; Discussions .Faraday.Soc.24 25 (1954). ;(22) EIGEN & De MAYER(1963) “Investigation of rates and mechanisms of reactions in “Techniques of Organic Chemistry “, vol VIII, Part 2, Chapter 18, Interscience, New York, ; (23) MARGARET ROBSON WRIGHT: “An Introduction to Aqueous Electrolyte Solutions” Art.1.12 Formation of Ion pairs from free ions, page 17, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chi Chester, West Sussex PO19 8SQ, England (2007) ;(24) KRISHNAN et.al Int .J.Electrochem. Sci. 2(2007) 958-972; Chemical Physics Letters (1973), 20 (4) Pages 391-393; J. Phys. Chem., (1971) 75 (23), pp 3606–3612; (25) MASTERTON et.al. J. Sol. Chem. 5(10) 721-731 (1976); (26) FUOSS (1958): “Ionic Association.III.The Equilibrium between Ion Pairs and Free Ions”, J. Am. Chem. Soc., 80 (19), 5059–5061, ;( 27) KRAUSet.al. “Mechanisms underlying the equilibrium reactions between ions and ion pairs” In ‘Solutions of electrolytes, II The effect of temperature “Proc Natl Acad Sci U S A. (1963) 49(2):141-6.Kraus et.al. (2006) “Mechanisms underlying the equilibrium reactions between ions and ion pairs in Solutions of electrolytes, I Solutions in p-Xylene and Benzene Interactions between benzene, Toluene, and p-xylene (BTX) during their biodegradation. ...” J Phys Chem. B. (2006)110(30):14961-70 ;( 28) FUOSS and KRAUS J.Amer.Chem.Soc, 551019and21dioxan-water mixtures (1933)); JONES et.al Ibid 76 3247, aceticacid (1954); HNIZDA et.al, Ibid 71 1565, liquid ammonia (1949); El-AGGAN et.al, J.Chem.Soc. 2092 ethanol (1958); GOVER. et.al, J.Phys.Chem 60 330, n-propenol (1956); HIBBARDet.al, J.Amer.Chem.Soc. 77 225, ethylenediamine (1955); REYNOLDS et.al; Ibid 70 1709 acetone (1948); BURGESS et.al, Ibid 70 706 pyridine (1948). ;( 29) BERMAN et.al “Contact ion association of perchlorate ion. Chlorine-35 nuclear magnetic resonance study. II. Solutions in mixed solvents”, J. Phys. Chem., 79 (23), 2551–2555(1975); (30) LARSEN et al J Chem. Phys. 65 3431(1976); Ibid (1978) J Chem. Phys. 68 4511(1978); Ibid (1974) Chem.Phys. Letters 27 47 (1974); Ibid (1980) J Chem. Phys. 72 2578(1980); Ibid (1974) J Chem. Phys. 7 530 (1977); (31) FENNEL et.al J Phys Chem. B.; 113(19) :6782-91 (2009):. ; (32) KAATZE et.al. Chemical Physics Letters, 384(4-6), PP 224228(2004) ; KAATZE& POTTEL (1992) J. Mol. Liquids, 52, PP 181-210; Ibid (1991) J. Mol. Liquids, 49 PP225-248;(33)GAIDUK “Dielectric Relaxation and Dynamics of Polar Molecules “published by World Scientific, Singapore Gaiduk (2000) J. Mol. Liquids, 80(1-3) PP81-10(1999)9 ; (34) HONGGAING ZHAO et.al J.Chem.Phys.126 244503 (2007); Ibid (2006) J.Chem.Phys.125 4504(2006) ; (35) WERTHEIM, J. Stat. Phys. 35 19, 35, (1984); 42, 459, 477 (1986);;(36) BLANDAMER & .BURGESS,” Interaction and Activation in Aqueous mixtures “ ColloidsandSurfaces, 48, (1990), Pages139-152; BLANDAMER et.al. Advances in Molecular Relaxation Processes, 5(4), pp333-338(1973), BLANDAMER et.alAdvances in Molecular Relaxation Processes, 2(1), pp1-40 (1970), ; Ibid . J.Molecular.Liquids (1992), 52, (1), PP15-39; BLANDAMER et.al (2005), Chem. Soc Rev. 34(5): 440-58 (2005), ;( 37) PITZER et.al.J. Phys. Chem., 77, 268 (1973); Ibid J. Am.Chem. Soc, 96, 5701 (1974); Ibid J.Solution Chem., 18, 1007(1989); Ibid (2010) Molecular Structure and statistical Thermodynamics Selected papers of Kenneth S Pitzer’ (2010) World Scientific, Singapore Ion interaction approach: Theory and data correlation.’ In: Activity Coefficients in Electrolyte Solutions. 2 – Editor: Pitzer KS, Boca Raton, Florida, USA: CRC Press; 1991. pp. 75–153. ;( 38) MOGGIA et.al. J Phys Chem. B. (2008); 112(4):1212-7; Ibid J Phys Chem. B. 111(12): 3183-91(2007).;(39) FYTA & NETZ et.al. J Chem. Phys. 132(2): 024911(2010). ;( 40) CHOUDHURY et.al. J Phys Chem. B. 110(16) 8459-63 (2006).;(41) DOUGHERTY et.al. Biophys. Chem. 105(2-3) pp: 269-78(2003). (42) BUCHNER et.al J Phys Chem. B. 110(30) (2006): 14961-70.; (43) SOTO et. al., Biophys.Chem. 74(3) 165-73(1998); SOTO et. al “Effect of cation …. Of an electrolyte on apparent molar volume, isentropic 118 | P a g e Compressibility…… in aqueous solutions”, Biophys Chem. (1999) 76(1): 73-82. ;( 44) WANG et.al J. Chem. Eng. Data, (2004) 49 (5), pp 1300–1302 ;( 45) BRAHMAJIRAO Ind.J.Pure. Appl .Phys. 14 646(1976) ; Ibid (1979), “Cationic motilities of electrolytic solutions – Ion pairs –EIGEN mechanism” Transactions. Of. Saest, 14 (2) (1979) 53; Ibid (1980), Ind. J. pure & Appl. Phys. 18 12 (1980) 1021; Ibid (1980), “Influence of variation of Dielectric constant.Gucker’s equations…” Proceedings of International Conference on Ultrasonics, ICEU-July 1980, Held at New Delhi. INDIA; Ibid (1980) “Application of ….. Variation of Dielectric.....GKG and Dagget equations “, Proceedings of International Conference on Non Aqueous Solutions, ICNAS-7, held at REGENSBERG, West Germany. (Aug 1980); Ibid (1981), Ind. J.Pure & Appl. Phys. 19 (1981) 254; Ibid “Application of Glueckauff’s model for depression in Dielectric …..Ion pair formation”, Proceedings’ of ‘ULTRASONICS INTERNATIONAL-81’, held at Brighton, U.K 30th JUNE to 2 nd JULY 1981;Ibid “Analysis of solute- solvent interactions …in relation to ion pair formation”, Proceedings’ of International Symposium on Electro analytical Chemistry Held at Chandigarh, INDIA December1982. ;Ibid “Study of …in chosen electrolyte solutions “, Proceedings’ of Sir J.C.Ghosh memorial Symposium, held at Calcutta, INDIA, Feb1982; Ibid “Electrostatic Potential energies of Ion pairs in nonaqeous media from Ultrasonic measurements”, Proceedings of Eigth International Conference on Nonaqueous Solutions, Nantes (Cedex) FRANCE, 19th to 23 rd July 1982;;Ibid “Ultrasonic studies in solute solvent interactions…..Ionpairs”Procedings of ICNAS-IX, Held at Pittsburgh, Pennsylvania, U.S.A. in August 1984; Ibid “Solute –Solvent interaction and Ion pair formation in the light Of depression in Dielectric Constant” Proceedings of VIth International Symposium on Solute –Solvent – Solute Interactions, Tokyo, JAPAN, July1982.; Ibid “Application of Glueckauff’s model of variation of dielectric Constant to association constant - Calculations in relation to Ion pair Formation “, Proceedings of 2nd International symposium on Industrial and Oriented Electrochemistry, Held at Karaikudi, INDIA (Dec 1980).;(46) V. M. M. Lobo “Handbook of Electrolyte Solutions”, “Elsevier Science Ltd” (1990); (47) Hasted et.al. J.Chem.Phys 16 1. (1948) COPPER COBALT 1.32 1.315 1.31 1.305 1.3 1.295 Contact pairs Solvent shared pairs 1.32 1.35 1.31 1.305 1.3 1.295 Contact pairs Solvent shared pairs 1.29 1.285 1.28 Solvent separated pairs 1.29 1.285 Solvent separated pairs 1.28 0.135 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.132 0.137 0.142 0.147 0.152 0.157 0.162 0.167 0.172 0.177 119 | P a g e 120 | P a g e . 1. 0. 7 0. 9 1 1. 1 1. 0. 0. 0. 3 0. 0.1 0. 0.0 0.1 0. 4 0.0 20. 0. 1. 0. 2 1. 0. 0. 5 0. 0. c With ‘C’ in gm moles per litre 121 | P a g e . 8 0. 6 0. 0. which are of different types. The colour of milk is due to the scattering of light by the fat globules. casein molecules. Bipin Bihari Post-Graduate College Jhansi. Milk also cantains certain enzymes. In this paper. The ultrasonic velocity decreases as temperature increases. Shrivastava* and Poonam Yadav Department of Physics. 1954). * Department of Chemistry. protein.P. colloidal calcium phosphate and to some extent by the pigments caroteine and riboflavin (Walstra and Jenness. To reduce the fat globules. impart a yellowish tint. These colours depend on the amount of caroteine present in the 122 | P a g e . B N P G College. milk creams very slowly.TEMPERATURE VARIATION ULTRASONIC VELOCITY IN COW MILK AT DIFFERENT FREQUENCIES Kailash. Hamirpur. INTRODUCTION The major constituents of milk are water.P. all long-life liquid milk products. The purpose of homogenization usually is not to make. are homogenized in practice. The main effect is the disruption of fat globules into smaller ones. S. Cost effective and fast methods for analysis of milk and milk products so that generated information can be effectively utilized for human health. Usually. Sensitive. This has motivated us to undertake the present study. U. The present day need is for development of simple reproducible. and are inactivated by heat. milk is homogenized. The intensity of yellow colour of cow milk depends upon size of the fat globules and fat percent. but to keep a product homogeneous (Jenness and Patton. After homogenization. which are present in the milk. apart from breed and feed (Harper and Hall. lactose. 1959). It revolves around the assessment of specific product and process attributes to confirm standards and specifications Very tiny work has been done to study the quality of milk using ultrasonic techniques. which slows down creaming (Burton. Milk ranger in colour from yellowish creamy white to creamy white to creamy white depending upon type of milk. the extent of colour depends on the ability of the cow to convert caroteine into vitamin A (Paterson. 1979). ash or mineral matter. Rath.com Milk is considered as an essential food constituent for a foremost segment of population. Quality Control may be defined as the operational techniques and activities that are used to fulfill requirement for quality. more generally. but is alos altered in other aspects. 1984). U. 1950). N. Email: kailashrath@gmail. All sterlised milks or. The caroteines. we have made detailed investigations of ultrasonic wave velocities in pure milk of Cow at different temperatures using multi frequency ultrasonic interferometer. fat. the transition in concept and organizational structure has moved from Inspection to Quality Control to Quality Assurance to Continuous improvement and finally to Total Quality Management. It revolves around the assessment of specific product and process attributes to confirm standards and specifications have been met. The technical requirements during dairy product distribution network must be considered by the organization for safe marketing and be included in the quality manual as operational guide. factors affecting milk vitamin and mineral content and the impact of packaging on quality. nature of products. cheese making. storage/ warehousing. The quality of milk reviews the health aspects of milk and its role in the diet. The impact of milk on the quality of yoghurt and cheese is also covered. The white colour of milk is an 123 | P a g e . its role in the diet and milk-based functional foods. retailing. Consumers demand quality milk with a reasonable shelf-life. including microbial spoilage and chemical deterioration. Guaranteeing the production of safe milk also remains of paramount importance. The present day need is for development of simple reproducible. The health aspects of milk. particularly when it is mainly concerned with final product analysis. must be obtained and recorded for periodical assessment and inducing further improvement in the system. In the newer context. marketing conditions etc. Improving the safety and quality of milk provides a comprehensive and timely reference to best practice and research advances in these areas. the dairy industry has ensured the quality of its products by employing inspection and test methods managed under the banners of ‘Quality Control’ and ‘Quality Assurance’. a requirement that can be met more successfully by the milk industry through use of improved processes and technologies. including milk microbial spoilage and chemical deterioration. Part two reviews essential aspects of milk quality. Traditionally. (Griffiths.milk. sensory evaluation and factors affecting milk vitamin and mineral content. infant formulas and applications of milk components in products other than foods. In its application Quality Control may become synonymous with the inevitability of product failure. The product examines sensory and nutritional quality of cow's milk and addresses quality improvement of a range of other milk-based products. Quality Control may be defined as the operational techniques and activities that are used to fulfill requirement for quality. M. The information on packaging. The sensory and nutritional quality of cow’s milk and addresses quality improvement of a range of other milk-based products. Chapters in Part three look at improving particular products. Milk is considered as an important food ingredient for a major sector of population. as well as the essential aspects of milk quality. We discusses various application requirements of milk such as milk quality requirements in yoghurt-maiking. 2010). transportation. Sensitive. sensory evaluation. Cost effective and fast methods for analysis of milk and milk products so that generated information can be effectively utilized for human health. goat milk and sheep milk. such as organic milk. excess enthalpies of binary and trinary systems. The range of multi frequency ultrasonic interferometer is 1-7 MHz. The molecular assembly in milk which results in whiteness’ ensures not only its purity. adiabatic compressibility and internal. a cortical and thermodynamic properties. Once quality of milk is assured. A number of maximum readings of anode current are passed on and their ‘n’ is counted the total distance (d) thus moved by the micrometer gives the value of wavelength (λ) with the help of the following relation: 124 | P a g e . The measuring cell is connected to the output terminal of the high frequency generator through a shielded cable the cell is filled with the experimental liquid before switching on the generator the ultrasonic waves moves normal from the crystal till they are reflected back from the movable plate and the standing waves are formed in the liquid between the reflector plate and the quartz crystal.expression of good qualities in which etiquette does not alter and thereby colours do not lose their identity in the white. The micrometer is slowly moved till the anode current meter on high frequency generator shows a maximum. latent heat of vaporization of liquids ultrasonic behaviour in liquid crystals molecular relaxation parameters. but also rejuvenates the hope of good nutrition. acoustic properties of substances near the critical and freezing temperature sinter molecular interaction. viscous-effects. MEASUREMENTS The multi frequency ultrasonic interferometer consist of the two parts.the high frequency generator and the measuring cell. pressure. Reaction rates and formulation of complexes. chemical and structural nature of liquid. transition study in liquids. it will make people pure and free from disease. A fine micrometer screw has been provided at the top. The high frequency generator is designed to excite the quartz plate fixed at the bottom of the measuring cell at its resonant frequency to generate ultrasonic waves in the experimental liquid in the “measuring cell”. The measuring cell is a specially designed double walled cell for maintaining the temperature of liquid constant during the experiment. as well as the colours merge in the white. excess volume and free volume. which can lower or raise the reflector plate in the cell through a known distance. insolvent interaction. It has a quartz plate fixed at its bottom the ultrasonic interferometer may be used for determination of ultrasonic velocity in electrolytic and non-electrolytic solutions sound absorption in medium observing liquid. phase. excess properties of binary and ternary systems. Therapeutic advances for microbial infections raise expectations that science is on the verge of understanding all manners of pathogenic microbes and their associated illness. It is the milk in which reside the rhythms and poetry. A micro ammeter to observe the changes in current and two controls for the purpose of sensitivity regulation and initial adjustment of micro ammeter is provided on the high frequency generator. 1984. 1959. and Patton. W. and Carl W. The graphs have been plotted between Temperature and velocity shown as in Figs. 21:194. Dairy Science: Its Principles and Practice. Burton. 1950. W. For this purpose we have take the pure milk of different animal. The Temperature variation of cow milk is effectual its nutrition quality so our aimed is to find at the Temperature in pure milk. inc Paterson. Dairy Chemistry and Physics. Jenness. Hall. 4. J. and jenness. Chicago. 1979. JI. A review of literature on ultrasonic studies reveals that ultrasonic velocity measurement is used to understand the nature of milk velocity. the ultrasonic wave velocities at different Temperature variation are given in Table I using the data of Table 1. Lippincot Co. Westport. 125 | P a g e . Sensitive. REFERENCES 1.d = n× λ /2 relation: V= λ ×f RESULTS AND DISCUSSIONS (1) Once the wavelength (λ) is known the velocity (v) in the liquid can be calculated with the help of following (2) Earlier we have introduced the significance of milk quality.: 519-128. On using the measurement techniques presented above. one can state that the ultrasonic velocity is decreases as Temperature variation one may say that the higher velocity is the indication of purity of milk. 1-7. 1954. It is clear from Table and Figs. 340. New York. The Equation between velocity and temperature are shown in the Table II. 2nd Ed. Walstra. Cost effective and fast methods for analysis of milk and milk products so that generated information can be effectively utilized for human health. 3. 5. J. R. AVI Publishing CO. Dairy Technology and Engineering. The present day need is for development of simple reproducible. H.357. We have made detailed investigations of ultrasonic Wave velocities in cow’s milk at different temperatures using multi frequency ultrasonic interferometer (1-7 MHz). of Dairy Res. Wiley and Sons: 160-167. 2. B. Jhon Wiley and Sons. P. Harper. ncipal of Dairy Chemictry. S. R. Colour Chenges in Heated and Unheated Milk I..e. S.0 1510.7 28 30 2MHz T(0C) V(m/s) 1538. Table I. G. 13.. Indian dairyman. 8. 54 (2002) 71...55 (2002) 30. 54 (2002) 47. Gau vansh poshan avam swasthya.. Designer milk nutritional and technological significance. Griffiths..K..8 28 30 3MHz T(0C) V(m/s) 1479. 15.5 1299. Indian Dairyman. Indian dairyma. Chemical quality of milk its relevance in present situation. Dhamendra B. 12. Indian Dairyman. Kamdhenu Kripa. Gaudugdh piye sau sal jiye. Garg A. 54 (2001) 33.. Milk production and reproductive performance of muraha buffaloes hormonally induced in to lactation. Kamdhenu Kripa.. January (2007) 13. M. 18. Kumar C. 52 (2000) 21. Venkatesh P. Sharma R.. Indian dairyman.4 1195. C. Singh M.2: 528. 16.0 30 32 6MHz T(0C) V(m/s) 1250.3 126 | P a g e . 54 (2002) 49.. Efficiency of additive and multiplicative correction factors for milk yield in karan fries cattle . October (2005) 3. 9.. Indian dairyman 54 (2004) 41.. 14. 54 (2002) 47-50. Chemical quality of milk its relevance in present situation.C.6. and Kohli R.. Indian journal of dairy science. K.6 1355. Our scriptures on cow milk.8 28 30 7MHz T(0C) V(m/s) 1211.V. Indian journal of dairy science. Indian dairyman. and Kanawjia S. Temperature variation of Ultrasonic velocity in cow milk 1MHz T(0C) 28 30 V(m/s) 1622. An odyssey on milk quality. Dube V. 11. 19. N. Gupta S. Lodhi R...56 (2003) 320. L. 10. Significance of ultrasonics in food industry-an overview. K. May (2006) 8.0 28 32 4MHz T(0C) V(m/s) 1415. Narang I. Bhattacharya T. and Rajput Y.V.. Murthy G.. 54 (2002) 71. An odyssey on milk quality.. Russian Agricultural Sci.. and Nair S.0 1189. 7.K.3 1428. Indian Dairyman. Improving the safety and quality of milk improving quality in milk Products. Kamdhenu Kripa. Improvement of quality of milk constituents by r DNA technology.. 2010. Ganguli N. Gay ka doodh hi amrat kyon.8 1609. Ganguli N. Sharma R.2 28 30 5MHz T(0C) V(m/s) 1324.. Lucknow. S. and Singh A. S. 17. Rajput Y. 6*103 T-4.6*102 T2 + 2.18*T4 + 12*T3 .00027*T5 .4*102T2 + 6.42*T + 2.8*104 V = 0. Freq.00036*T5 + 0.049*T4 .6 1041.4 1234.1.0014*T5 .96*T2 .4 1562.7* 103*T+2.6 978.1.3*104 V = 0.6 907.0 935.2 1436.2*103 V = -0.4 1337.5 1188.4 1544. 2. Equations showing relationship between V (m/s) and T (0C) S. 3.3*104 V = 0.0 1127.2 984.5 1082. (MHz) 1 2 3 4 5 6 7 Equation V = 0.8 1262.4 1458.2 Table II.1.2.00024*T5 + 0.28*T4 + 2.5 34 36 40 44 48 1129.0077*T4 + 1.0.3.4 1194.8 1158.8*T2 + 1.4 1472.9*103 T2*104 V = 0.045*T4 . 7. No.2*103 T+1.1*T3 . 6. 5.9 830.7 1304.0.2*T3 .6.7*103T .2*102T2 .001*T5 .1 1282.1*104 V = -0.053*T4 + 4.3.0 1036.6 32 36 40 46 48 1490.4 886. 1.1*105 Figure1: Frequency Variation of Ultrasonic Velocity in cow milk 1MHz 1630 Velocity 1620 1520 1610 Ultrasonic Velocity in m/sec 1600 1590 1580 1570 1560 1440 1550 1540 28 1420 28 Ultrasonic Velocity in m/sec 1500 1540 Figure2: Frequency Variation of Ultrasonic Velocity in cow milk 2MHz Velocity 1480 1460 30 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 30 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 127 | P a g e .0 33 36 40 42 48 1385.8*102T2 + 1.6 1589.0.0078*T3 + 0.4 34 38 42 46 48 1218.7*T3 +1.6 1480.4*102 T2 .5*104 T .7 1370. 4.32 34 38 42 47 1599.8 33 37 42 46 48 1062.2 1075.5 1574.8 36 40 42 46 48 1302.2.3*T3 + 1.1*T3 . Figure3: Frequency Variation of Ultrasonic Velocity in cow milk 3MHz 1480 Velocity 1460 1400 1440 Ultrasonic Velocity in m/sec 1420 1400 1380 1360 1340 1320 1300 1280 28 1150 28 Ultrasonic Velocity in m/sec 1350 1450 Figure4: Frequency Variation of Ultrasonic Velocity in cow milk 4MHz Velocity 1300 1250 1200 30 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 30 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 Figure6: Frequency Variation of Ultrasonic Velocity in cow milk 6MHz Figure5: Frequency Variation of Ultrasonic Velocity in cow milk 5MHz 1350 1300 Velocity 1250 1300 1200 Velocity Ultrasonic Velocity in m/sec 1250 Ultrasonic Velocity in m/sec 1150 1100 1050 1000 950 1200 1150 1100 1050 900 850 30 1000 28 30 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 Figure7: Frequency Variation of Ultrasonic Velocity in cow milk 7MHz 1250 1200 1150 Ultrasonic Velocity in m/sec 1100 1050 1000 950 900 850 800 28 Velocity 30 32 34 36 38 40 42 Temperature degree centigrate 44 46 48 128 | P a g e . impedance and viscosity evaluated from ultrasonic velocity and density measurements have been used to elucidate the structure and the nature of molecular interaction in aqueous and non-aqueous solutions [2].. Elastic constants of isotropic solid can be determined ultrasonically when both longitudinal and transverse wave velocities are known [3]. Department of Physics. India Email: kailash. KEYWORDS: Pathological. The graphical representation of the data has also been given. and Sucrose. Rath. as adjunct therapy and alternative medicine.in. Banda. Multi frequency ultrasonic interferometer is used for measuring ultrasonic wave velocity in pure Ethyl Acetate. Ultrasonic velocity. The acoustical properties. G. In addition to its use is as a 129 | P a g e . 210 431. Ethyl acetate is used for the concentration and purification of antibiotics. ultrasonic wave velocity is measured at room temperature using interferometric technique at different ultrasonic frequencies.P. 210 001. India 3.com ABSTRACT: The use of organic compounds in managing of pathology has increased in recent years. BN PG College.co. being used as a precursor to more complex chemicals [5]. U. Govt. K. In this work the measurement of frequencydependent ultrasonic wave velocity in these organic pathological compounds have been done from 1-8 MHz. jitendra_sharma50@yahoo. S.. Xylene. Herbicides Pigments. The measured data (frequency variation of ultrasonic wave velocity) has been tabulated.P. Antibiotics. College. U. 1 Introduction: Ultrasonic velocity has become a valuable tool for the study of various physical and chemical properties of the matter [1]. Hamirpur. Girls P. Bundelkhand University. Shrivastava2 and Jitendra Kumar3 1. U. Aniline. compressibility. Department of Physics. It is also used as an intermediate in the manufacture of various drugs [4]. One of the characteristic of these organic pathological compounds. Interpretation of data shown in graphs is presented through curve fitting and has been discussed widely.
[email protected] STUDY OF SOME ORGANIC PATHOLOGICAL COMPOUNDS Kailash1. India 2. 284 128. Extensive ultrasonic study about some organic pathological compounds has been reported in the recent past by some investigators to ensure their characterization and perfect use in medical industry. Ultrasonic interferometer. Aniline is the simplest and one of the most important aromatic amines. Department of Physics. Jhansi. The micrometer is slowly moved till the anode current meter on high frequency generator shows a maximum. the high frequency generator and the measuring cell. Sucrose is by far the most important disaccharide which is widely distributed in plants especially in sugar cane sugar beet and sugar maple [8].12 MHz in the medium. such as paracetamol. It is used in medicine as a hypnotic. Multi frequency 130 | P a g e . 2 Measurement Technique: The ultrasonic interferometer is simple in construction and operation and gives accurate and reproducible results. Acetaldehyde is a significant constituent of tobacco smoke. The high frequency generator is designed to excite the quartz plate fixed at the bottom of the measuring cell at its resonant frequency to generate ultrasonic waves in the experimental liquid in the measuring cell. increasing the onset and tenacity of addiction to cigarette smoking. λ/2.f . From these results. A micro ammeter to observe the changes in current is provided on the high frequency generator. In our experimental work we use multifrequency interferometer which can generate ultrasonic waves of several frequencies from 1 .precursor to dyestuffs. The aim of this work is to study the characterization of these organic pathological compounds using ultrasonic techniques. 3 Evaluation: One of the characterizations of organic compound. A fine micrometer screw has been provided at the top to lower or raise the reflector plate in the cell through a known distance. It has been demonstrated to have a synergistic effect with nicotine. Xylene is used as a solvent and in the printing. People who have a genetic deficiency for the conversion of acetaldehyde into acetic acid may have a greater risk of Alzheimer's disease. particularly in adolescents [7]. Once the wavelength is known the ultrasonic velocity v of the compound can be calculated with the help of the relation V= λ. It has a quartz plate fixed at its bottom the ultrasonic interferometer may be used or determination of ultrasonic velocity. The total distance d moved by the micrometer gives the value of wavelength λ with the help of the relation d= n. velocity is measured at room temperature using interferometric techniques at different ultrasonic frequencies (1-6 MHz and 8-9 MHz). The multi frequency ultrasonic interferometer consists of two parts. The measuring cell is connected to the output terminal of the high frequency generator and is filled with experimental liquid. On switching on the generator the ultrasonic waves moves normal from the crystal till they are reflected back from the movable plate and the standing waves are formed in the liquid in between the reflector plate and the quartz crystal. rubber and leather industries and as a cleaning agent for steel and for silicon wafers and chips. A number of maximum readings n are taken. one can readily determine the velocity of sound in a liquid with high accuracy [9-11]. a pesticide thinner for paint and in paints as varnishes [6]. It is clear from the figure that at 1-2 MHz velocity increases with increase in frequency. decrease in velocity is observed and at 6 MHz frequency. For 4 MHz frequency there is a highly decrease in velocity. It is clear from the figure that up to 2 MHz velocity increases with increase in frequency. Xylene. Aniline. The variation of ultrasonic wave velocity for Acetaldehyde is presented in Fig 4. The table shows that as well as on incensement frequency velocity increases. At 5 MHz frequency it increases slightly and at 6 MHz it decreases slightly. The variation of ultrasonic wave velocity for Xylene is presented in Fig 3. At 3-4 MHz frequency.4m/s. there is a slight decrease in velocity. The measured data (frequency variation of ultrasonic wave velocity) are shown in Table 1. The variation of ultrasonic wave velocity for Aniline is presented in Fig 2. Experimental findings shows that ultrasonic wave velocity is not increasing linearly with frequency. For 8 MHz frequency there is a highly increase in velocity.8m/s which is less than the ultrasonic velocity of water 1509m/s. there is a highly increase in velocity of ultrasonic wave and for 8-9 MHz an increase in velocity is observed. From 3-5 MHz frequency. At 5 and 6 MHz frequency there is a slight increase in velocity. The coefficients of the best fit polynomials of data shown in these figures are presented in Table 2. It is clear from the figure that for 1-3 MHz velocity increases with increase in frequency. the velocity increases. velocity shows slight variation. The ultrasonic velocity of Sucrose is more than the ultrasonic velocity of water that is 1509 m/s. because the density of Ethyl Acetate is much more than density of water. and Sucrose. It is clear from the figure that at 1-4 MHz velocity slight increases with increase in frequency. At 3-4 MHz frequency. At 8 MHz it again decreases and becomes 1412. At 5 MHz frequency there is a slight increase in velocity and for 6 MHz it again decreases. 5 References: 131 | P a g e . These studies can also be used to determined the extent of complexation and calculate the stability constants of these compounds [12]. The graphical representation of the data is also given in Figs. 4 Results and discussions: The variation of ultrasonic wave velocity with frequency for Ethyl Acetate is presented in Fig 1. The variation of ultrasonic wave velocity for Sucrose is presented in Fig 5 .ultrasonic interferometer is used for measuring ultrasonic wave velocity in Ethyl Acetate. that with increase in the frequency of ultrasonic wave. It is clear from figure. For Sucrose the ultrasonics velocity increases with increasing frequency. At frequency 8 MHz the velocity decreases highly to 1382. this is because of density. Acetaldehyde. the result shows a slightly deviation from the ideal case but over all these show that with increase in frequency of ultrasonic wave. At 5-8 MHz frequency increase velocity increases highly. there is a slight decrease in velocity. 1-5. Ultras. ‘Estimation of clamping force in high-tension bolts through ultrasonic velocity measurement’.0 1935. V. 2009. Stat. D. Oral Maxillofacial Path.8 Velocity (m/sec.42e+02 A2 -1. 50.0 1269. FRIEND.83 84..20e+02 -6. KANDYALA. Table 1. ‘Ultrasonic studies on charge transfer complexes of certain aldehydes with benzylamine and cyclohexylamine as doners in n-hexane at 303K’. 2007. J. 40. 2. 591.70e+03 4.2 1359. KUMAR et al..63 -67.0 1170. 149. 221. Comm. ‘Speed of sound as a thermodynamic property of fluids’. J. Phys. D.75e+02 A3 2.42e+02 5.3 1041. PHANI et al.17e+03 2. 44. 10.00e+03 -3.92e+02 -7. L. Phys. Y.06e+03 3.. M. 1968.8 1644. and Histochem. SEGURA et al. J.14 0.5 1215.34e+03 -2. KURAKEVYCH and V. MAO.4 1411. GANDHI.03 -4. ‘The use of Sucrose gradients in the isolation of cytoplasmic-polyhedrosis virus particles’. H. 2010. Solids..69e+03 6. GODEC.4 Sucrose 1518. 61.1.6 - Table 2.2 Acetaldehyde 1564. 2009. 2003. Arch..93 -76. J. 85. A. Y. ‘On the measurement of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials’. 11. Y. S. ‘Acetaldehyde adducts in the brain of alcoholics”. Toxicol. 14. I. Coefficient of Best Fit Polynomial for Ultrasonic Velocity Compound Ethyl Acetate Aniline Xylene Acetaldehyde Sucrose A0 -5. 11.2 1335. Ultras.88 3. O. 45. O. Methods Phys. 6.7 1016.5 1460. HAYASHI and F. ‘Elastic study of Potassium Sulphamate crystal using ultrasonic Pulse Echo Overlap Technique’. ‘Compression and thermal expansion of rhombohedral boron nitride at high pressures and temperatures ‘. 2169. K.2 1558. K.76 A5 0. B. 2010. 2006.38 3. S. ‘Xylene: An overview of its health hazards and preventive measure’.6 1615.6 1652. 327. NAKAMURA.66e+03 -2. 1339. 1935. 253. Invertebrate Path.0 2097. QUAN et al.9 1684.4 1866. BHADAURIA. Exp. 824. Sol.0 1158. G.6 1355. 12. K.) Xylene 1204. L.44e+03 -2. 4. 99.2 1563.16e+03 A1 2. 149.78e+03 1.2 962. H. IWAHASHI et al.81e+02 6. KANNAPPAN and N.2 1652. G. R. I. 2000. V. 8.8 1873.0 1599. GARCIA et al.. MOLERO. 77.4 2217. MIRAZ et al. ‘Volumetric properties and phase relations of silica-thermodynamic assessment’.99e+02 A4 -25. 237. 3. 9. Frequency Variation of Ultrasonic Velocity for Organic Pathological Compounds Frequency (MHz) 1 2 3 4 5 6 8 9 Ethyl Acetate 1093. SOLOZHENKO. 1.6 1605. ‘Dual trypan-aniline blue fluorescence staining methods for studying fungus-plant interactions’. 2010. VARUGHESE. 645.40 132 | P a g e .0 1725. ‘300-K equation of state of rhombohedral boron subnitride’. Chem. Biotech. Alloys Comp. P. Sol. 7.22e+02 0..96e+02 2. Sc. J.8 Aniline 1501.0 1382. 2001. SUNDMAN et al. JHANG.. M. Appl. BIRD.4 1638.2 1522. 2001. Pure.54 -10... 39.6 1255. 5.. T. Ind. State Comm. H.67e+02 -6. frequency for Xylene Fig. Velocity vs. Velocity vs. 1. 3. 4. 2. frequency for Aniline 1600 1900 1500 Velocity Velocity (in m/sec) 1800 Velocity Velocity (in m/sec) 1400 1700 1300 1600 1200 1500 1100 1400 1000 1 2 3 4 5 6 7 8 1300 Frequency (MHz) 1 2 3 4 5 6 7 8 Frequency (MHz) Fig. frequency for Acetaldehyde 2300 2200 2100 2000 1900 1800 1700 1600 1500 Velocity Velocity (in m/sec) 1 2 3 4 5 6 7 8 Frequency (MHz) 133 | P a g e . frequency for Ethyl Acetate Fig. Velocity vs.1900 1800 1700 1700 1650 Velocity Velocity Velocity (in m/sec) 1600 1550 1500 1450 1400 1350 Velocity (in m/sec) 1600 1500 1400 1300 1200 1100 1000 900 1 2 3 4 5 6 7 8 9 1300 Frequency (MHz) 1 2 3 4 5 6 7 8 Frequency (MHz) Fig. Velocity vs. Girls P... Pressure derivatives. Department of Physics. an attempt has been made to evaluate higher order elastic constants for TeO at an elevated temperature from 50K to 600K.P. thermal expansion.P.in. The data of SOECs. Higher order elastic constants. Govt. Divalent crystals. vir. BN PG College. In this work. G. Grüneisen numbers. jitendra_sharma50@yahoo. A number of theoretical and experimental measurements have been made on the anharmonic properties [6]. equation of state and phonon spectra. Jitendra Kumar2 and Virendra kumar1 1.rath@yahoo. In the last few years studies of anharmonic properties of solids have attracted the attention of the physicists since they provide much valuable information regarding crystal dynamics [1-5]. 210 001. and their dependence on temperature provides the fundamental data for determining the characteristics of cation-oxygen bonding interactions which are pertinent to the understanding and theoretical modelling of more complicated oxide compounds. U.HIGH TEMPERATURE STUDY OF ANHARMONIC PROPERTIES OF TeO Kailash1. Partial contractions. KEYWORDS: Anharmonic properties. The data of these oxides obtained through different techniques also give important and valuable information about internal structure and inherent properties of materials and can be used in future for different industrial purposes and further investigations of isostructural oxides. Banda. one may obtain ultrasonic velocities for longitudinal and shear waves which give an important information about its anharmonic properties. India 2.com.rath@yahoo. When the values of second and third order elastic constants and density for any material at a particular temperature are known. Rath. 210 431. one may get ultrasonic velocities for longitudinal and shear waves in different crystallographic directions which give important information about its anharmonic properties. While evaluating these properties it is assumed that the crystal structure does not change during temperature variation. College. Elastic properties are linked thermodynamically with specific heat. U.com ABSTRACT: A proper and systematic evaluation of anharmonic properties of isostructural oxides. Hamirpur. 1 Introduction: Elastic properties of divalent compounds are important because they relate to the various fundamental solid state phenomena such as inter atomic potentials. TOECs and FOECs are used to evaluate the FOPDs of SOECs and TOECs. If the values of second order elastic constants and density at a particular temperature are known for any substance. and Debye temperature and Grüneisen parameters. No 134 | P a g e . SOPDs of SOECs and partial contractions. Department of Physics. India Email: kailash.co. TOECs and FOECs in Brügger’s definition and Voigt notations. While discussing higher order anharmonicities such as the FOPDs of TOECs. temperature variation of acoustic velocity and attenuation. 2.complete experimental or theoretical efforts have been made so for in obtaining the temperature variation of anharmonic properties of divalent crystals having various crystal structures. The elastic energy density for a deformed crystal can be expanded as a power series of strains using Taylor’s series expansion [7]. Selecting a few data obtained in this study. specific heat at higher temperature. U0 = U2 + U3 + U4 = [1/2!] Cijkl αij αkl + [1/3!] Cijklmn αij αkl αmn + [1/4!] Cijklmnpq αij αkl αmn αpq (1) Where Cijkl. 4. CIJK and CIJKL are the SOECs. 0 vib 0 vib C IJ = C IJ + C IJ . partial contractions and deformation of crystals under large forces. All these results are discussed widely and some of them are presented graphically in Figs. The coefficients of quadratic. Several physical properties and crystal anharmonicities such as thermal expansion. CIJK = CIJK + CIJK and 0 vib CIJKL = CIJKL + CIJKL (2) 3 Evaluation: The SOECs. the SOPDs of SOECs and partial contractions are evaluated utilizing data of Tables 1. CIJ. and the FOPDs of SOECs and Gruneisen numbers are directly related to SOECs and TOECs. For 135 | P a g e . 2 Formulation: The elastic energy density for a crystal of a cubic symmetry can be expanded up to quartic terms as shown below [8]. The FOPDs of SOECs and TOECs. 2 and the results are shown in Table 3. TOECs and FOECs in tensorial form. cubic and quartic terms are known as SOECs. 1–6. TOECs and FOECs at 300 K are given in Tables 1. the FOECs are to be considered extensively. Cijklmn and Cijklmnpq are the SOECs. The present paper is mainly focussed on the study of temperature variation of higher order elastic constants and their pressure derivatives up to an elevated temperature up to 600 K (near melting point) for Tellurium oxide (TeO) crystals using Born-Mayer and Coulomb potential starting from the nearest neighbour distance and hardness parameter. the values of SOECs. TOECs and FOECs respectively. TOECs and FOECs for TeO crystal are evaluated from 50-600 K. For TeO crystals the value of C11 and C44 increases and the value of C12 decrease as temperature increases and are represented in Fig 1. αij are the Lagrangian strain components. 4 Results and Discussions: It may state that all the SOECs are positive in nature. the SOPDs of SOECs. ZHAO and Q. 1381. Letters. Acoust. 2002. 5. E. Pure App. GHATE. 1947. Phys. C1112. Sol. KITTEL. 2886. C144 and C456 are positive in nature. dC112/dp. C1122. The value of all partial contractions W11. P. Rev. dC166/dp and dC456/dp increases as temperature increases. 2004. DOSSO and N. ‘Introduction to solid state physics’. 1965. decreases as temperature increases. A1666. C1144. Stat. These elastic constants are used to compute ultrasonic parameters such as ultrasonic velocities. R. 2004. BARSCH. 1. 6. 2005. H. C456 remaining constant. Z. Chem. the values of C111. C1255. 7. ‘Acoustic tracking of a freely drifting sonobuoy field’ J. 1981. JIANG. which is presented in Fig 6. C.. (b). ‘Temperature dependence of interatomic separation for alkali halides’ Phy. C1266. BIRCH. S. ‘Nonlinear pressure dependence of elastic constants and fourthorder elastic constants of cesium halides’ Phys. S. Rev. 4 References: 1. FANG. John Wiley. ‘Internal structure. J. Soc. F. 87. inherent ananharmonic properties of some mono. 111. 3. The value of C1456 remains constant. 8. 1967. 2166. C112 and C123 are given in Fig 2. C4444 and C4455 decreases as temperature increases. and the value of dC123/dp decrease as temperature increases. The ultrasonic studies [15] can provide interesting information on the specificities of ion-solvent interaction related to the structure of the solute and the reciprocal effects which arises in the solvent and the role of collinear and noncolinear phonons in anharmonic scattering processes and in ultrasonic attenuation for different structured solids [16].and di-valent materials’. 139. The value of d2C11/dp2 and d2C44/dp2 decreases and d2C12/dp2 increases as temperature increases and are presented in Fig 5. The first three are presented in Fig 3.C1155. 241. Ultra. P.Tellurium oxides. The value of dC11/dp and dC12/dp decreases and the value of dC44/dp increases as temperature increases. The variation of FOPDs of SOECs are given in Fig 4. ‘Crystal liquid interface energy and surface stress of alkali halides’. 4. 29. 27. COLLISION. Mate.. and the value of C1123 increases as temperature increases. K. E. The value of dC111/dp. The temperature variation of C111. thermal relaxation time etc [9-11]. 2. Rev. C123. KAILASH. Z. W12 and W44decreases as temperature increases but W11 decreases very sharply. 809. Am. The value of C1111. The data obtained in present investigation will be helpful to those workers who are engaged in studying the temperature variation of anharmonic properties [17–21] of solids at higher temperatures. CHANG and G. C112 and C166 are negative in nature. ‘Finite elastic strain of cubic crystals’ Phys. ‘Third order elastic constants of alkali halide crystals’ Phys.. dC144/dp. 136 | P a g e .. KUSHWAHA et al. 19. Newyork. 71. the value of C112. C144 and C166 increases. The values of C111. B. The variation of elastic constants [12-14] with respect to pressure can reveal many important features of the short range forces at high pressure.. M. while C123. P. A. P. ‘Interaction of collinear and noncollinear phonons in anharmonic scattering processes and their role in ultrasound absorption of fast quasi-transverse modes in cubic crystals’ J. 2007. 2009.45 447. 87. AYNYAS and S. Sc.109 22. S.096 1. 389. SINGH and D. ARYA. 1996. K..0 434. KAILASH.531 31.. 15. J. 114. 12. M.256 1..4 -79. 83. Tech. D.110 -102. 47. 198.414 0. SANYAL. zinc and gallium metals’ Ind. PANDEY and P. 21. SINGH. RAJU et al. 153. M. 2010. GHOZLEN and B. 22.. selected applications and perspectives’ Measur.711 22. Pure Appl. KETATA. D. Pure Appl. 403. J. SABU. S.725 -3. J. M. 20. Pure Appl.41 Table 3. UDO. P. REDDY.. Phys. Phys. J. ‘Elastic properties of intermetallic compounds under high pressure and high temperature’ Ind.9. 47.0 301. J. 45. The FOECs in 1010 N/m2 for TeO crystal at 300 K. A.346 -234. ‘High pressure behaviour of alkaline earth tellurides’ Ind. 270. UPADHYAY and B.. 095403. B. The FOPDs of SOECs and TOECs for TeO crystal at 300 K. dC11/dp dC12/dpP dC44/dp dC111/dp dC112/dp dC123/dp dC144/dp dC166/dp dC456/dp -5. 7. 47. PANDEY. 2009.1 -77. K. KARL. 434. 10. E. H.6 -74. Matter. M.826 32. d2C11/dp2 d2C12/dp2 d2C44/dp2 W11 W12 W44 137 | P a g e . 14. 47. 32. S. Phys. 502. S. N. ‘Ultrasonic investigation in intermetallics’ Pramana. M. Phys: Condens. H. HOSTEN. 50 . K. FRIECTER and L.256 33.967 -33. 19.F. ‘Elastic constants measurement of anisotropic Olivier wood plates using air-coupled transducers generated Lamb wave and ultrasonic bulk wave’ Ultras. D. I.48 387. 19.. 2009. RUKMANGAD. PUNDHIR.. 2010. ‘Structural and elastic properties of rare earth nitrides at high pressure’ Ind. ‘Ultrasonic investigation of amino acids in aqueous sodium acetate medium’ Ind.596 3. AWASTHI and V. 062001. Phys. C11 C12 C44 C111 C112 C123 C144 C166 C456 Table 1. 399. C1111 C1112 C1122 C1123 C1144 C1155 C1255 C1266 C1456 C4444 C4455 2392. 17. YUAN and Z. ‘Ultrasoniv attenuation in liquid mercury. AYNYAS and S.1 -74. Phys. Pure Appl. 2008. K. ‘Anharmonic properties of rock salt structure solids’ Physica B. E. 11. K. (K) 643 20.652 3. 2008. The SOECs in 1010 N/m2 for TeO crystal at 300 K.SANYAL. 13. KULEYEV et al. J. DING. B.23 -74. J.679 Table 2. Phys. 16.. Phys. 2007. J. ‘Finite element modeling of nano ndentation to extract loaddisplacement characteristics of bulk materials and thin films’ Ind. O.. 362. SHARMA. J. 2009. RAO and C. THIRUMARAN AND K. 18. DAHMEN. ‘Ultrasonic wave propagation in rare earth monochalcogenides’ Cent.01 452. K . 2009. ‘Ultrasonic velocity measurement in liquids with high resolution techniques. 2009. S. 2009..044 Table 4.881 -6.482 -88. G. K. Pure Appl. YADAWA. C. ‘Ab inito calculation of elastic properties of rock-salt and zinc-blend MgS under pressure’ Physica B. The SOPDs of SOECs in 10-9 m2/N and partial contractions in 1012 N/m2 for TeO crystal at 300 K. P. 54. 5 C11 C12 Fig. For TeO C111 C112 C123 -150 20.110 43.) 2500 2000 Fig.m.124 0. FOECs Vs Temp.5 0 -50 21.842 12. 2.380 0. For TeO dC11/dp dC12/dp dC44/dp 1500 1000 500 0 0 100 200 300 400 500 600 Fig.5 3000 0 100 200 300 400 500 600 0 100 200 300 400 500 600 FOPDs OF SOEC for TeO(dimensionless) Temperature(K) temperature(K) 2 1 0 -1 -2 -3 -4 -5 -6 -7 0 100 200 300 400 500 600 FOECs for TeO(in 1e10 N/sq. TOECs Vs Temp. For TeO Temperature(K) 0.m.101 10. SOPDs of SOECs Vs Temp.25 0.728 23 50 SOECs for TeO(in 1e10 N/sq. 5.35 0. For TeO Temperature(K) Fig.5 SOPDs OF SOEC for TeO(in 1e-9 sq.) 22.0.m.15 0.m. FOPDs of SOECs Vs Temp. 6.45 0.4 0. SOECs 21 C44 Vs Temp. 1.) ddC11 ddC12 ddC44 50 45 40 35 30 25 20 15 10 5 W11 W12 W44 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Temperature(K) Temperature(K) 138 | P a g e .1 Partial Contractions for TeO(in 1e12 N/sq. 3.2 0. For TeO -100 Fig.5 -200 20 -250 19. For TeO C1111 C1112 C1122 Fig. 4.m./N) 0.) 22 TOECs for TeO(in 1e10 N/sq.3 0. Partial Contractions Vs Temp. phonon–phonon interaction mechanism is dominating cause for attenuation. Govt. Rath. Akheiser loss and Gruneisen constants. phonon–phonon interaction and that due to thermo elastic relaxation. U. Department of Physics. 210 431. Oxides and silicates make up the bulk of the Earth’s mantle and crust. The most important causes of ultrasonic attenuation in solids are electron– phonon. G.rath@yahoo. Shrivastava2 and Jitendra Kumar3 1. Department of Physics. KEYWORDS: Attenuation.. India Email: kailash. 284 128. Girls P. India 2. In this work ultrasonic attenuation due to phonon–phonon interaction (α/f2)p-p and 139 | P a g e . Bundelkhand University. The two dominant processes that will give rise to appreciable ultrasonic attenuation at higher temperature are the phonon–phonon interaction also known as Akhieser loss and that due to thermo elastic relaxation are observed in calcium oxide crystal.
[email protected]. U. Banda. U. and thus it is useful to predict their behaviour. the ultrasonic attenuation techniques [5-7] are widely used as versatile tool in studying the inherent properties and internal structure of solids. Phonon-phonon interaction.co. Department of Physics.P.. BN PG College. College.com ABSTRACT: Ultrasonic velocity and attenuation parameters are well connected to the micro structural and mechanical properties of the materials. 1 Introduction: The ultrasonic attenuation study of the materials has gained new dimensions with the progress in the material science [1-4]. Thermo elastic relaxation. Temperature dependence of ultrasonic absorption in CaO crystal along different crystallographic direction reveals some typical characteristic features. At frequencies of ultrasonic range and at higher temperatures in solids. 210 001. In this work ultrasonic attenuation due to phonon–phonon interaction (α/f2)p-p and thermo elastic relaxation (α/f2)th are studied in CaO crystal from 100K-1500K along different crystallographic directions. S. K.in. Jhansi. The most important causes of ultrasonic attenuation in solids are electron–phonon.ORIENTATION DEPENDENCE OF ULTRASONIC ATTENUATION FOR CALCIUM OXIDE IN HIGH TEMPERATURE RANGE Kailash1. India 3. In recent years. phonon–phonon interaction and that due to thermo elastic relaxation.P. Hamirpur. The two dominant processes that will give rise to appreciable ultrasonic attenuation at higher temperature are the phonon–phonon interaction [8] also known as Akhieser loss [9] and that due to thermo elastic relaxation and are observed in calcium oxide crystal. d is the density and Vl.thermo elastic relaxation (α/f2)th are studied in calcium oxide at an elevated temperatures (100-1500 K) along <100>. 1 that the value of thermal relaxation time τth is very high at low temperature and decreases as temperature is increased along all crystallographic directions and of the order of 10-12 140 | P a g e . Several investigators have given different theories. 1–6. The behaviour of ultrasonic absorption and other parameters as a function of higher temperature have been discussed as the characteristic features of calcium oxide. <110> and <111> crystallographic directions. The temperature variations of all these properties are presented graphically in Figs. 3 Evaluation: The SOECs and TOECs for CaO has been evaluated at different temperatures (100 to 1500 K) following Brugger’s approach [12] and are presented in Table 1 at room temperature. 4 Results and Discussions: It is clear from the Fig. f is frequency of ultrasonic waves. here the one given by Mason has been used. For the evaluation of the ultrasonic coefficients the second and third order elastic constants (SOECs and TOECs) are also calculated using Coulomb and Born Mayer [10] potentials. Grüneisen parameters have been evaluated using Mason’s Grüneisen parameters tables [13] at different temperatures along different crystallographic directions with the help of SOECs and TOECs. The nonlinearity constants are evaluated using the average square Grüneisen parameters <γij>2 and square average Grüneisen parameters <γij2>. The values of <γij> and ultrasonic attenuation (α/f2)p-p and (α/f2)th along with Vl. Mason’s theory relates the Gruneisen constants with SOECs and TOECs.shear = 2 ρVs3 τ s and (α / f 2 )th = 4π 2 < γ ij > 2 KT 2 ρV 5 (1) where the condition ωτth <<1 has already been assumed. Vs. D in eqns. D 4π 2 E0 s 3 (α / f 2 ) Akh. Here E0 is thermal energy density. 2 Formulation: The expressions for ultrasonic attenuation coefficient due to phonon-phonon interaction [11] over frequency square (α/f2)p-p are as D 4π 2 E0 l 3 = 2 ρVl 3 τ l (α / f 2 ) Akh. Vs are the ultrasonic velocities for longitudinal and shear waves respectively.s are the Grüneisen parameters. (1) is given as 3C T D = 9 < (γ ij ) 2 > − v E 0 < γ ij > 2 (2) Where γij.long . τth and D are presented in Table 2 at room temperature along different crystallographic directions. J. 207.. K. SINGH. SINGH and R. K. Phys. The thermal ultrasonic attenuation along different directions is presented in Fig. A. P. Phys. From the above results one can reach to the conclusion that the thermal relaxation time. ‘On the absorption of sound in solids’. Ind. Phys. SRIVASTAVA. 1. while for shear wave it decreases. It is clear from the figure that the ultrasonic velocity for longitudinal wave increases as temperature increases. M. MAYER. R. SRIVASTAVA. Prinston. M. Phys. Along all these directions the ultrasonic attenuation increases with increase in temperature. ‘Effect of isotopy on thermoacoustical properties’. YADAV and KAILASH. ‘Acoustical investigation of magnesium oxide’. A. Phys. Figs. K. Phys. J. 67. Pure Appl. 3. MASON. 1939. ‘Ultrasonic attenuation in alkaline earth metals’. 479. Pure Appl. (USSR). 141 | P a g e . Current Appl. 3. 2003.. ‘Zur Gittertheorie der lonenkristalle’. 8.. 10. <1 1 0>) for which the ultrasonic attenuation decreases with temperature. Z Phys. KAILASH. It is clear from the figure that thermal attenuation increases with temperature along all these directions and of the order of 10-18 Nps2/m which is expected for the type of crystal under inspection. the situation is little different for shear wave along <110> direction (pol. SHARMA. W. 2. New Jersey. KOR. 9.. which is also expected. ultrasonic wave velocities and attenuation are the properties which depends on the crystallographic directions or one can say that these properties are orientation dependent which strongly supports the results given by other investigators [14] for the same type of crystals that all these properties are strongly dependent on direction of polarization. ‘Thermodynamic definition of higher order elastic coefficients’. The results obtained in this study can be used for further investigations [15. Pure Appl. Ulras. ‘Ultrasonic attenuation in dielectric crystals’. <110> and <111> crystallographic directions respectively.sec. J. D. M. KAILASH and K. 2 along <100> direction. R. 5 References: 1. PANDEY. 47. J. 351. 1950. A. ‘Theoretical study of temperature dependent lattice anharmonicity in TlCl and TlBr’. 2006. Soc. ‘Ultrasonic study of highly conducting metals’. K. 133. 28. Rev. 75. 1986. 6. 1. Phys. R. 2007. M. SINGH. 11. 5. 26. Van Nortrand Co.. 59.. K. J. DEY. GOTO and Y. Ind. Rev. Phys. UPADHYAY and B. 2004. RAJU and S. T. AKHEISER. RAJU. J. 81. ‘Piezoelectric crystals and their applications to ultrasonics’. BRUGGER. BORN and J. 1964. SINGH and R. 100. YANAGISAA. K. Ultras. NEMOTO. The temperature variation of ultrasonic velocities is presented in Fig.. 55. ‘Elastic properties of intermetallics compounds under high pressure and high temperature’. 115129. 1932. S. 44. T.. 12. 277. 362. 1053. S. (Germany). Inc. 7. B. J. 2009. 10. Jpn. 16] and industrial research and development purposes. K. K. K. 2010. S. P. ‘Ultrasonic investigation of Quadrupole ordering in HoB2C2’. J. 4. D. 230. 4 -6 represents the ultrasonic attenuation due to phonon-phonon interaction along <100>. 2006. R. Ind. A1611. <11 2 >) <γij> -0. Academic Press.838 14.599 4.601 -0. MALCOLM.124 6. Ultrasonic velocities Vs Temp.414 2. J. Melting Point (K) 2843 C12 12.520 6. 046618(1). ‘Temperature dependence of microwave loss in ADP-type crystals’.218 0.43 C166 -51.13.069 6.504 τth D 15.886 12. ‘Orientation dependence of ultrasonic attenuation’. Physical Acoustics. 2.203 -0.10 C123 20. 16. Table 1. Direction of propagation <100>long.039 -0.52 C44 12. 3.091 0.26 C456 4. RAJU.504 4. crystal quartz and silicon’.) 10 9 8 7 6 5 4 3 2 1 0 8 Ultrasonic Wave Velocities(in 1e+3 m/sec) Along <100> direction Along <110> direction Along <111> direction 7. Pure Appl.< 1 10>) (pol. E. shear(pol. A.786 13.5 0 500 1000 1500 0 500 1000 1500 Temperature(K) Temperature(K) Fig. 927.777 13. 1965.379 - Thermal Relaxation Time (in 1e-12 sec.665 -0. SCALES and A.71 C111 -252.71 Table 2. Phys. thermal attenuation in10-18 Nps2/m and p-p attenuation for long.673 -0. non linearity constants. Santiago de Chile. Rev E.529 (α/f2)th 0.375 9. New York. 2010.158 0.. C. 15. thermal relaxation time in 10-12 sec.88 C112 -65. Long.5 7 Vl Vs Vd 6. 66. Phys. K.34 C144 19. SRIVASTAVA. 1. ‘Laser characterization of ultrasonic wave propagation in random media’. 2003.5 6 5. Ind. and shear wave velocities in 103 m/sec. Thermal relaxation time Vs Temp Fig.171 3.135 - (α/f2)p-p 0.178 0.469 0.248 5.037 0.373 0. KAILASH and S.954 1. and shear waves in 10-16 Nps2/m. MASON. Vol.253 0. 14. III B. W. T.512 -0. Physics Procedia.836 0. ‘Effect of impurities and phonon-processes on the ultrasonic attenuation in germanium. shear <110>long.<001>) (pol. along <100> dir 142 | P a g e .115 8. 2009. J. International Congress on Ultrasonics.015 -0.082 V 7. M.782 1. P.<1 1 0>) <111>long. shear(pol. 67. K. UPADHYAY.171 9. 47. The SOECs and TOECs in 1010 N/m2 at roomtemperature. 237. 5 0.3 0.3 0. 5. along <111> dir 143 | P a g e . 3. Ultrasonic attenuation Vs Temp.long Akh.6 Akh.long Akh. 6.7 Ultrasonic Attenuation(in 1e-16 Nps2/m ) Along <100> direction Along <110> direction Along <111> direction 0.5 3 1 2 1 0.35 0. 4.15 0.4 0.Shear1 Akh.Shear2 5 2 4 1.1 0.2 0.05 0 Fig.45 0.long Akh.2 0.5 Akh.5 0 0 500 1000 1500 0 0 500 1000 1500 Temperature(K) Temperature(K) Fig.Shear 0. Thermal ultrasonic attenuation Vs Temp.4 0.1 0 0. along <100> dir 500 1000 1500 Temperature(K) Temperature(K) 3 0 500 1000 1500 7 6 Ultrasonic Attenuation(in 1e-16 Nps2/m ) Ultrasonic Attenuation(in 1e-16 Nps2/m ) Akh.Shear1 Akh.25 0.5 0.Shear2 2. Ultrasonic attenuation Vs Temp.Thermal Ultrasonic Attenuation(in 1e-18 Nps2/m) 0. Along <110>dir Fig. Fig. Ultrasonic attenuation Vs Temp. Molecular interactions. Introduction: Acoustic methods are the most powerful tools for the study of structural and physicochemical behaviour of liquids and liquid mixtures [1-3]. Eyring [10.. The molecular radius plays an important role in various liquid state theories [4.11] and Kittel [12]. 8]. India bDepartment of Physics. India ABSTRACT: The molecular radii of liquid mixtures of heterocyclic compounds viz. Besides these acoustic methods. D.MOLECULAR RADII OF PYRIDINE/QUINOLINE WITH PHENOL IN BENZENE USING ACOUSTICAL METHODS AT DIFFERENT TEMPERATURES Anjali Awasthia. College. Recently. Ernst and Glinski [7] have studied the effects of various physical parameters on molecular radius in pure liquids using several empirical relations. The applicability of Schaaffs or Rao’s method for the estimation of the molecular radii in ternary liquid mixtures has been authenticated. based on acoustic methods. the relation based upon the assumption that liquid system is made up of closely packed molecules with face centered cubic structures. Pandey et al. University of Lucknow. Tripathia. pyridine and quinoline with phenol in benzene have been computed at varying physical conditions using various acoustic methods. G. P. Bondi [6] provided a qualitative understanding of the nature of Van der Waals radii and proposed their qualitative values. Bhawana S. The study suggests the superiority of Schaaffs 144 | P a g e aMaterial . 5]. Ternary liquid mixtures 1. Lucknow-226 007. Rao [9]. Molecular radius has been utilized to compute various important parameters of liquid mixtures to explain the process of molecular association among their components. The results indicate that molecular radii of liquid mixtures evaluated from Rao’s method are in close agreement with the Schaaffs method. Rajiv K. KEYWORDS: Molecular radii. [13] has estimated the molecular radii of pure liquids and binary liquid mixtures using various acoustic methods. which reflects the structural features of pure liquids and liquid mixtures. A comparative study of the merits and demerits of various acoustic methods are discussed in the light of molecular structure and intermolecular interactions. A. Tripathib and Aashees Awasthia Science Research Laboratory Department of Physics. Lucknow-226 004. The molecular radius is an important parameter. has been used [6]. V. suggested by Schaaffs [4. These physico-chemical parameters have been used to study their effects on the intermolecular interactions. Ali et al. 2.2 Rao’s Relation: r = 3 M ρ N ⋅ 3 3 16π 1 − γRT Mu 2 . 1 + Mu 2 3γRT − 1 [ ( )( ( ) )] (1) 2.1 Schaaffs Relation: r = 3 M ρ N ⋅ 3 3 16π 1 − γRT Mu 2 . molecular radius and intermolecular free length of various liquids and their deuterium-substituted compounds.4 Kittel’s Relation: r = 3 M ρ N ⋅ (1 2 ) ⋅ 3 1 − (1 u ) ⋅ ( 3γRT M ⋅ 2 ) (4) For a system comprising of spheres of mass M/N in a close packed face centered cubic structure (CPFCC). Eyring’s and Kittel’s methods are based upon the assumption that the observed velocity of sound results from the propagation of sound waves inside the molecule and in free space between them. Dey et al. density and other related parameters. 145 | P a g e . the various acoustic methods for estimating the molecular radius have been extended to ternary liquid mixtures of pyridine/quinoline with phenol in benzene. [15] has studied the isotopic effects on non-linearity parameter.method for theoretical estimation of molecular radius over the remaining methods. Schaaffs and Rao’s methods are based upon the Van der Waals equation of state. Theory: Various methods can be employed to evaluate the molecular radii of liquid mixtures using ultrasonic velocity. any worker has made no such attempt as far as our knowledge is concerned. 1 + Mu 2 γRT − 1 2.3 Eyring’s Relation: ( ) ( ) (2) 3 r = 3 M ρ N ⋅ (1 2) ⋅ 3 1 − 1 − (1 u ). γRT M ⋅ 2 ( ) (3) 2. The deviations in variation patterns of molecular radii with changing temperature and concentration for ternary liquid mixtures have been studied. These acoustical methods for the computation of molecular radii of liquid mixtures are summarized as under: 2. In the present study. Earlier. molecular radius can also be obtained by the relation [7]. [14] have evaluated the molecular radii of binary liquid mixtures by employing acoustic and refractive index approaches. (5) 3. N and γ have their usual meanings. It may be due to bulkier structure of quinoline than pyridine. It is observed that the molecular radii data obtained from various acoustic methods are not found to change significantly with concentration at specific temperature for both ternary liquid mixtures.. It is also seen that at specific concentration and temperature. M. 14]. But. the availability of the unshared pair of electrons for sharing with acids is more than quinoline. Rao’s and CP-FCC method are slightly decreasing with increasing concentration at specific temperature while Kittel’s and Eyring’s relations exhibit a non-linear behaviour for pyridine-phenol system. higher values of molecular radii are obtained in quinoline-phenol system as compared to the pyridine-phenol system. Figures 1 (a-f) show the variation of molecular radii for both the ternary liquid systems as a function of mole fraction of phenol. Due to this reason pyridine show strong interaction with phenol showing decreasing trend of molecular radii in pyridine-phenol system while weak interaction in quinoline with phenol provide increasing trend of molecular radii in quinoline-phenol system.3 M 2 ρN where u. Since the superiority of Schaaffs method has been established by the earlier workers [7. a close perusal of the figure reveals that the molecular radii obtained from Schaaffs. N . The various acoustic methods for estimating molecular radii have been analyzed graphically at different temperatures. Since pyridine has greater pKα value than quinoline and resonating structures of pyridine and quinoline suggests that in pyridine. Results and Discussion: The molecular radii of both ternary liquid systems of pyridine/ quinoline with phenol in benzene have been computed at various concentrations and temperatures using relations (1-5).5 CP-FCC Relation: r = (1 2).. for quinoline-phenol system molecular radii increasing with the increasing concentration from all acoustic methods except Eyring’s relation showing non-linear trend. so it is considered as a reference for determining of molecular radii of both the liquid systems in the present study. QUINOLINE 146 | P a g e . PYRIDINE N . Theoretical values of molecular radii have also been evaluated. ρ. 13.2. [13] and Ali et al. These observations show that the assumptions of free space made by these relations have to be modified in the present cases [13]. Therefore. [13] have also emphasized the superiority of Schaaffs and Rao’s method for the estimation of molecular radii over other methods. The values of molecular radii obtained theoretically are in close agreement with the values obtained from Schaaffs and Rao’s method. Acknowledgements: 147 | P a g e .A significant inference has been drawn from the molecular radii data. This is because of thermal energy. [7] and Pandey et al. for pyridine-phenol system the molecular radii obtained from Eyring and Kittel’s relation shows an opposite trend. Moreover. It is observed from figure 1 (a-f) that on increasing the temperature values of molecular radii also increases for both the systems (except Kittel’s relation). and hence an increase in molecular radii is expected with temperature [13]. showing a non-linear behaviour with concentrations at specific temperature. In both liquid mixtures. The application of this equation for any liquid system should only be limited to compute the maximum possible values of molecular radii [13]. Ernst et al. It can also be seen that the values of molecular radii obtained from Rao’s method are in close agreement with Schaaffs method [13. Pandey et al. Eyring’s method may be successfully employed to explain intermolecular interactions in the ternary liquid mixtures. The molecular radii obtained from Kittel’s and Eyring’s methods have not been found to be in agreement with the Schaaffs method. obtained from Eyring’s relation. 14]. in order to get comparable results with the Schaaffs method. which weakens the molecular forces. Both methods are based on the assumptions that liquids behave like real gases. a correction term is needed which will take care of three body effects in the evaluation of molecular radii in these cases. Eyring’s and Kittel’s relation resulted in higher values of molecular radii than obtained by Schaaffs method. 4. This may be due to the fact that the CP-FCC method is based upon the assumption that there is no free space between the molecules. molecular association process is strongly supported by Eyring’s method. It is seen from the figures that the values of molecular radii obtained from CP-FCC method are always found to be higher than the values obtained from any other method. Conclusions: The variation pattern of molecular radii with the change in various physical parameters seems to be very convincing for both multicomponent liquid mixtures taken under investigation. [14] show similar observations in their studies. which provide minimum molecular radius at the same concentrations where maximum molecular association was observed [1]. e. Phys. Chem. D.. P. Fluid Phase Equilib. [15] R. M. Awasthi and J. 41 (2003) 477. Liqs. Liq.K. Eyring. J. Glinski. Rastogi. Schaaffs.L. [12] C. Eyring... Chem. References: [1] A. Soni. [2] M. 215 (2004) 119.V. F. c) Quinoline-phenol in benzene (d.. Chem. [13] J. [5] H. Phys. Shukla. 14 (1946) 614. Patel. 42 (2004) 117. Pandey. Dey and B. Tariq. P. J. Shukla. Acustica. Phys. [9] R. 33-34/2007 (SR)). R. J. Fig. A. [11] J. 114 (1939) 110. Kinkaid and H.. 242 (1969) 193.F. f) 148 | P a g e . No. H. Bisht and J. Bhatt. Ultrasonics. [6] A. 33 (1975) 272.1 Molecular radii versus mole fraction of phenol: Pyridine-phenol in benzene (a. N. 15th National Symposium on Ultrasonics (2006). A. Shukla. [10] J. R. M. J. Z. Phys. Pramana. [14] A. Phys. [4] W. J.. Singh.The authors gratefully acknowledge the University Grants Commission for providing financial assistance as a Major Research Project (F. Lebowitz. Chem.F. 5 (1937) 587. Chem. Awasthi and J. Chem. [8] W.K.. Frisch and J. 67 (2) (2006) 389. P. D. Schaaffs. 31 (1959) 369. B. Phys. Z. D.. Kinkaid and H. Nabi and Shahjahan. Ernst and J. Phys. J. Ali. 6 (1938) 620.L. Mol. Pandey. 13 (1981) 109. Gopala Rao and V. [7] E. Kittel.S. 111 (2004) 67. Bondi.. [3] A.Dey. Venkataseshaiah. Reiss.. Chem. Phys. b. Rastogi and J. Acustica. 68 (3) (1964) 441. Awasthi. 00 At 308. r (10-10 m) 3.08 (b) (e) mol. radius. radius.08 0.04 mole frac. (x 2) 0. (x 2) 0.1 1.15 K 3.06 0.00 At 308.02 0.00 0.02 0. r (10-10 m) At 318.08 (c) (f) 149 | P a g e .06 mole frac.7 2.4 2.0 2.1 1.1 1.8 0.1 1.02 0.1 1.0 2.04 mole frac.04 0.00 At 318. r (10-10 m) mol.8 0.0 2.4 2.7 2.02 0.04 mole frac.06 0.7 At 328.7 2.08 0. (x 2) 0.8 0.08 (a) 3.7 2.8 0. (x 2) 0.15 K 3. radius.04 mole frac. (x 2) 0.8 0.06 0.08 0.06 0.mol.15 K 0.0 2. (x 2) 0.15 K 2.1 1. r (10-10 m) 3.04 mole frac.4 2.02 0.00 (d) mol.4 2. r (10-10 m) mol. radius.8 0.0 2.15 K mol. radius.06 0. radius.4 2.4 2.7 2. r (10-10 m) 3.0 2.02 0.15 K 0.00 At 328. excess compressibility ( KEs). and various type of intermolecular interactions and their strengths [1. Intermolecular free length ( ). ***** Sujata Mishra. molar volume (V) acoustic 150 | P a g e . liquid mixtures and solutions is a useful technique for understanding its physico-chemical behaviour and molecular interaction which have demanding applications in many chemical and industrial processes. acoustic impedance ( Z). Acoustic and thermodynamic parameter have been used to understand different kinds of association. impedance dependence relation. In order to detect weak and strong molecular interactions in binary liquid mixtures consisting of polar as well as non-polar components. free length theory [6] and are compared with experimental values. Molecular interaction parameter ( χ) and also excess parameters such as excess velocity ( CE).co. 308K. 313K. Ultrasonic velocities calculated using Nomoto’s relation (NR) [3]. excess molar volume ( VE) and excess acoustic impedance (ZE) are computed for the binary mixture at different temperatures.in r_ paikaray@rediffmail. Variation of acoustic parameters with temperatures have been discussed in terms of nature and strength of intermolecular interaction existing in the binary system. molecular motion. Cuttack E-mail:
[email protected] mixture. Theoretical evaluation of ultrasonic velocity in binary liquid mixtures and its comparison with the experimental values reflects the molecular interactions in liquid mixtures.Ultrasonic and theoretical study of binary mixture of DEHPA (Di-(2. 1. Free length of interaction. The validity of these theoretical relations have been discussed for the present liquid system. impedance dependence relation ( IDR) [4].2]. The ultrasonic speeds calculated according to Nomoto’s relation.ethyl-hexyl) phosphoric acid) with n-hexane at different temperatures. INTRODUCTION Ultrasonic study of liquids. The acoustical parameters such as adiabatic compressibility ( Ks). Rita Paikaray Department of Physics Ravenshaw University. THEORETICAL CONSIDERATIONS The experimentally measured ultrasonic speed (C) and density ( ) are used to calculate the derived parameters like isentropic compressibility ( ). Molar Volume (V). excess free length ( LEf). Rao’s specific sound velocity relation and free length theory ( FLT) are compared with those obtained experimentally. Intermolecular free length ( Lf). the molecular packing. 2. Rao’s specific sound velocity Relation (R) [5]. acoustic parameters. Relative association (RA). 318K over entire composition range. Key words:. intermolecular interaction.com ABSTRACT Ultrasonic speed and density of binary liquid mixture of di-(2-ethyl hexyl) phosphoric acid ( DEHPA) with n-hexane has been determined at 303K. ultrasonic velocity measurement have been employed extensively. .. ). KEs.. M1 and M2 are molecular weight of DEHPA and n-hexane.(9) _________ x1V1 + x2 V2 Where X.. Interaction parameter (χ ) and excess parameters by using the = 1 ……………….(8) The empirical formula for sound speed in binary liquid mixtures given by Nomoto [3] can be written as CNOM = x1R1 +x2R2 3 ….. 151 | P a g e . molar sound speed and molar volume respectively.hexane. Rao’s specific sound velocity relation is given by CR = Σ ( xi ri ρ)3 ………(11) Where ri = Ci1/3/ρi is the Rao’s specific sound velocity of the ith component of the mixture. R = V C 1/3 and V represents mole fraction. ZE ). ρ EXP1/2 …. (4) Z = …………………………… (5) χ = ( C2exp/C2ideal)-1………………… . T is absolute temperature.. acoustic impedance and density of the ith component respectively. ( 1) C2 = k ( )1/2 ………………… (2) V= (x1 M1 + x2 M2 ) / mix ……….875 + 0. Sound Speed by Jacobson’s free length theory is calculated using the following CFLT = k________ (mix) . velocity in pure DEHPA at particular temperature. The theoretical values of sound speeds are evaluated using the following relationship . k (Jacobson’s constant) [ value. mix = 0 = density of DEHPA Co = Ultrasonic density of mixture. The sound speed in mixture is given by Impedance Dependence relation [4] CIDR = Σ xi Zi ………… (10) xiρi Where xi Zi and ρi are the mole fraction.. Relative association( following expressions.375T ) x 10-8 ...(7) Where x1 and x2 are mole fractions of DEHPA and n.... LEf..…(3) RA= (ρ /ρ o) (Co/C) 1/3 ……………. formula [ 6]. AE = Aexp – ( x1A1 + x2 A2)……. 93.(6) Where C ideal = x1C1 + x2C2 is ideal mixing velocity. AE stands for excess property of parameters ( CE.impedance (Z). VE. 5 1 molefraction of DEHPA Fig-2 molefraction of DEHPA DEHPA is an acidic extractant which is polar and its molecules exist as dimmers especially in pure form or in organic diluents due to intermolecular hydrogen bonding. But breaking up of associated structure of DEHPA releases several dipoles.3. New Delhi.RESULT AND DISCUSSIONS Measured values of density ( ρ) and ultrasonic speed (C) were used to calculate various thermodynamic parameters and their excess values using equation 1-7 at different temperatures. molefraction. with a circulating pump to an accuracy of + 0. Table-1 compares experimental and theoretical values of sound speed and deviations of these theories from experimental sound speeds at temperature 303k.[8] The effect of adding non-polar second component is primarily to disrupt the associated structure of DEHPA and strength of interaction decreases. Binary mixtures are prepared by mixing appropriate volumes of the liquid components in the standard flasks with airtight caps and the mass measurements are performed on high precision digital balance with an accuracy of +1mg.1msec-1. excess isentropic compressibility (KES). excess velocity (CE). excess free length (LEf). Velocity excess velocity 303K 308K 313K 318K 1 1.10C 4. Representative graphs of ultrasonic velocity (C). working at 3 MHz frequency with an accuracy of + 0.5 20 10 0 -10 0 0.velocity 1500 1400 1300 1200 1100 1000 900 0 0. Further ultrasonic velocity decreases with increase in temperature due to 152 | P a g e . The temperature of the sample was maintained stable by circulating thermo stated water around the interferometer cell that contains the liquid. excess molar volume (VE). which is supported by slow increase of relative association (RA) values and increase of ultrasonic velocity (fig-1). excess acoustic impedance (ZE) as a function of concentration and temperature represented in fig. EXPERIMENTAL The ultrasonic speeds in pure liquids and liquid mixtures have been measured using an ultrasonic interferometer (model Mx-83) supplied by Mittal Enterprises . which induce dipole moments in n-hexane molecules and there exist a dipole.induced dipole interaction between the component molecules.1-6. Density was determined by using a single capacity Pyknometer of bulb capacity 25 cm3 at different temperatures.5 Fig-1 molefraction ~excess velocity 30 303K 308K 313K 318K . Hence.5 1 -2 303K 308K 313K 318K 0. into the study of molecular interactions in a liquid mixture than derived parameters. The less negative magnitude of LEf itself suggests that the interaction between component molecules is not so strong i. As the concentration of DEHPA increases. releasing more and more dipoles which interact with each other. interstitial accommodation of n-hexane molecules increases which results positive excess velocity which increases with increase in temperature.2] shows negative deviation is low concentration region and positive deviation in high concentration region of DEHPA. Considering the effect of temperature. which shows that dipole-induced dipole interaction becomes stronger and the system is less compressible . The variation of excess isentropic compressibility ( KES) with mole fraction of DEHPA at all temperatures are shown in [Fig-3].5 1 -0. Variation of other parameters like acoustic impedance ( Z) and interaction parameter (χ) shows the presence of molecular interaction between component molecules of the system. strength of interaction increases .induced dipole interaction present in the system which dominates over the breaking up of associated structure of DEHPA.induced dipole interaction is responsible for contraction in volume and hence a decrease in KES. Similar observation made by Syal etal [9] and Subramaniyam Naidu and Ravindra Prasad [10]. with negative deviation over entire range of composition at all four temperatures .5 303K 308K 313K 318K -4 molefraction of DEHPA -1 molefraction of DEHPA Fig-4 Fig-3 Excess Thermodynamic parameters give a better insight. Mixing of n-hexane with DEHPA will induce breaking up the associated structures which leads to expansion in volume and hence increase in KES and dipole. The free length ( Lf) and compressibility ( Ks) decreases with increase in concentration of DEHPA and increases with temperature.thermal agitation of molecules. The negative deviation is due to breaking up of self association of DEHPA in high concentration of non-polar nhexane. The variation of excess velocity (CE) [Fig. Increase in temperature with rise of temperature [8. excess isentropic compressibility excess free length 0 0 molefraction~excess compressibility 0 0 molefraction ~excess freelength 0. Deviation in isentropic compressibility is negative with maxima at about ~ 0.9] 153 | P a g e promotes the breaking of associates present in pure liquids. it is clear that both KES and LEf become more and more negative with increase in temperature of the system. The variation of excess free length ( LEf) [Fig-4] is similar to that of KES.37 mole fraction of DEHPA from 303 to 318K.e a weak dipole. Table-1 shows that minimum deviations are observed in case of free length theory ( FLT).342 3.3 1328.5 CR ms-1 975.039 6.4 1380.0 1065.581 4.4 1436.0 1142.086 0.6 1065.1574 0.6 1074.003 0.003 0.3 1409.840 5.5 CNOM 0.816 8.8 1381.000 CR 0.160 6.2036 0.000 4.5 1 Fig-6 Fig-5 shows variation of excess molar volume ( VE) with mole fraction of DEHPA from 303 to 318 K.03 -0.9 1215.0000 CEXP ms-1 975.5 CIDR ms-1 975.249 2.7 1468. The negative ZE values indicate dissociation of self association of DEHPA and more than one type of interaction may be present in the system. -CH2-.0 1097.5 CFLT ms-1 975. which results decrease in VE.5 1468.000 CFLT 0. followed by impedance dependance relation ( IDR) and Nomoto Relation (NR).4 1211.0 1135.5 1 303K 308K 313K 318K -0.01 0 -0.7 1285.7 1328.093 0. The less magnitude of negative (ZE) values suggest that dipole .024 4.412 9.5 1468.induced dipole interaction dominates over dispersion forces which is in close agreement with the variation of LEf and KES with increasing concentration of DEHPA.000 0.497 6.4026 0.8 1170.000 3.235 3.3179 0.7349 0. The variation of excess acoustic impedance (ZE) is shown in fig-6 at all four temperatures.0 1131.763 7. It also shows presence of unfavourable interactions between different groups such as –CH3 .2 1468.0 1468.002 0.5 1253.0 1081. ∆C/C % Mole fraction of DEHPA (X1) 0.1717 0.8 1108.003 0.3 1141.0 1380.072 0.5785 0. The excess molar volumes are positive for the whole range of composition [7] and at all temperatures with a peak at about ~ . -OH of monomeric DEHPA Similar type of result shown by other Researchers [2.9 1253. Rao’s specific sound velocity relation 154 | P a g e .6 1074.05 molefraction of DEHPA 0.978 5.000 The theoretical values of ultrasonic speeds were calculated using theoretical and empirical relations [8-11].056 0.4 1217. The curves at all temperatures show that the self association of DEHPA molecules first breaks which results increase of VE and then the interaction between unlike components take place due to increase in mole fraction of DEHPA.469 1.6 1170.7].763 4.000 0.997 7.275 6.606 2.8 1298.041 3.000 2.0 1058.3 1119.04 -0.013 2.5 1360.761 3.5 CNOM ms-1 975.000 0.7 1109.4 1359.8 1395.excess acoustic impedance molefraction~excess molarvolume excess molarvolume molefraction~excess acoustic impedance 30 20 10 0 0 molefraction of DEHPA Fig-5 303 K 308 K 0 0.000 CIDR 0.02 -0.8 1415.954 0.9 1174.8 1090.4 1328.42 mole fraction.0 1254. The positive values increase with increase in temperature.0 1058.8312 1.0 1109.000 0. Table-1: Application of various theoretical approaches and percentage of deviation for DEHPA +n-hexane system at 303K. (20 -) 2010 (9) Syal VK. Yasmin A & Nain AK.45 . (8) S. 155 | P a g e . Ulagendran. 20 ( 1952) 957 (7) V. Indian J Pure Apply Phys. NR and RSSVR. Among four theoretical models. 419-423.shows maximum deviation. The temperature variation indicates that the strength of intermolecular interaction increases with rise of temperature. 43 ( 2005) 844 (10) Subramaniyan Naidu P & Ravindra Prasad K J Pure Appl. References:(1) Ali A. India J Pure Appl Physics Vol. Indian J Pure Appl Phys 40 ( 2002)315 (2) Kannappan V & Jaya Santhi R. S. Mishra & R. n-hexane acts as a structure breaker for DEHPA. Chauhan S & Uma Kumari. PP(210-220)2007 (6) Jacobson B. No-1. Kannappan proceeding of National Sympossium on Accoustics. Asian J Chem 7 ( 1995) 417 (5) D Sravana Kumar & D Krishna Rao.Vol-37. 27 ( 2005) 15. Kumar. 2007 PP. CONCLUSION: The variation of derived parameters and ultrasonic velocity with concentration of DEHPA and temperatures indicate the presence of molecular interaction between component molecules excess values reveal that the interaction mainly of dipole-induced dipole interaction which is weak. 13 ( 1958) 1528 (4) Shipra Baluja & parsania PH. Indian J Pure Appl Phys 43 (2005) 750 (3) Nomoto O. PP. Paikaray. J Accoustic Soc India. J Chem Phys. The order of applicability of the theories for the present system is as follows:CFLT > CIDR > CNOM > CR. Jayakumar & V. Ultrasonics. R. free length theory ( FLT) shows close agreement with experimental ultrasonic velocity values than IDR. J Phys Soc Japan. From these values.ACOUSTICAL STUDIES OF MOLECULAR INTERACTIONS IN BINARY LIQUID SYSTEM OF CINNAMALDEHYDE AND N-N-DIMETHYLANILINE AT 303 K Padmanabhan G1. internal pressure (πi). excess internal pressure (πiE). Department of Physics RKM Vivekananda College. Department of Physics. It is 156 | P a g e . Chennai – 600 014. Kumar R2. INTRODUCTION The acoustical investigation of liquids mixtures reveals the significance of molecular interactions that finds applications in several industrial. free volume (Vf). The New College. Sri Sankara Arts & Science College.com Abstract Ultrasonic velocity (u). excess impedance (ZE) were computed using standard relations. at 303K. It is observed that strong molecular interactions of dipole – dipole and complex formation types exist that depend on the concentration and also the structural aspects of the components in the mixture.Chennai-600 004. N – dimethylaniline (DMA) for the entire composition range. Cinnamaldehyde (CA) is an industrially important compound. E-mail: * jayakumar_5454@yahoo. Lennard – Jones potential (LJP). Loyola College. 3. 5]. Kanchipuram. 1. The results are interpreted in terms of molecular interactions between the component molecules. 4. 2. These structural dependent molecular interactions are also concentration dependent and this is well reflected by the behavior of the excess parameters [4. excess adiabatic compressibility (κE). Department of Physics. cohesive energy interaction parameter (χi) and excess thermodynamic parameters such as excess velocity (uE). molecular free length (Lf). The study of molecular interactions in terms of acoustical and excess thermodynamic parameters identifies the specific type of molecular interaction and the structural features of molecules in the solution. adiabatic compressibility(κ). excess molar volume (VmE). Chennai – 600 035. Jayakumar S3* & Kannappan V4 1. density (ρ) and Viscosity (η) were measured for binary liquid system of cinnamaldehyde (CA) and aromatic tertiary amine N. technological and biological fields [1 – 3]. Department of Chemistry. viscosity (η) and the computed values of acoustical parameters are tabulated in Table 1. The values of adiabatic compressibility and free length show similar variation that increase with 157 | P a g e . The ultrasonic velocity (u) was measured using Mittal ultrasonic interferometer of fixed frequency of 2 MHz with an accuracy of ± 0. It has electron deficient carbon. The whole range of compositions was studied between components of the binary system.used as flavouring agent in chewing – gum. It was reported that the non – linear variation of ‘u’ is an indication of solute – solvent type of interaction which may be of dipole – dipole nature through complex formation between components in the mixture [6. lipids and hormones. Carbonyl group is part of several biologically important molecules such as protein. N – dimethylaniline (DMA) and carbonyl group of CA. Thus. EXPERIMENTAL METHODS AnalaR grade samples are used in the present work. Chemicals are weighed using electronic single pan balance Shimadzu make and the materials are mixed stoichiometrically. 2.2 m/s. density (ρ). The variation of ultrasonic velocity and adiabatic compressibility with mole fraction of DMA is shown in Figures 1 & 2. ice – cream candy and beverages and also as fungicide. The interaction between polar groups such as carbonyl group of aldehyde and amino group is significant in practical applications. RESULTS AND DISCUSSION 3. The temperature of solutions was maintained constant by thermostat with an accuracy of ± 0. 3.1K. density (ρ) measurements were made using a 10ml specific gravity bottle and viscosity (η) measurements by rate of flow of solutions through Ostwald viscometer and digital stop watch with an accuracy of ± 0. which can function as electrophile. the formation of donor – acceptor complexes can be expected between amino group of N. insecticide and corrosion inhibitor in steel industries. The behavior of ultrasonic velocity is non – linear with the mole fraction of DMA as evident from Figure 1.1 Acoustical Parameters: The measured values of ultrasonic velocity (u). 7]. Amines behave as Lewis bases since they contain nitrogen as the basic centre with a lone pair of electrons.01s. 2 Excess Thermodynamic Parameters The computed values of excess thermodynamic parameters are summarized in Table 2. the void makes the system more compressible. This again supports our earlier view on the molecular interactions between component molecules and may also due to the difference in the molecular sizes. which might allow the fitting of CA molecules into the voids created by DMA molecules [13. Since the effective molecular area of the components decrease with concentration the viscous nature decreases and in turn that decreases the internal pressure of the system [8. CONCLUSIONS The behavior of acoustic parameters shows the existence of strong interaction among the component molecules of dipole-dipole nature through complex formation. It is also 158 | P a g e . The excess molar volume VmE is found to change sign from positive to negative. Though the interaction between the components is stronger. The observed viscosity deviations ηE are negative over the entire concentration range investigated. 9]. The larger negative deviations in uE and ZE from linear dependence on the mole fraction of DMA suggest the presence of complex formation between component molecules [11]. The existing strong interaction is weakened by the addition of DMA with CA this is due to the bulky size of the aromatic amine that makes the system more compressible. The increasing trend in both these parameters may be due to the increase in the void created by the aromatic amine. Both these parameters show almost positive deviations which may be due to the expansion in volume of the system by i) breaking of associated structure of dipolar molecules and ii) increasing concentration of aromatic component that creates void in the liquid mixture. Negative ηE from the rectilinear dependence on mole fraction may occur for the systems having components of different molecular size [12]. The weakening of unlike molecular interaction than that of strong like molecular association may also the reason for the positive values of these two parameters [11]. As CA are much smaller than those of DMA. The variation of excess velocity and excess compressibility versus mole fraction of DMA are shown in Figures 3 & 4. (Figure 5) 3.increasing concentration of DMA. A perusal of table 2 reveals that the behavior of excess compressibility with concentration is also well reflected with the behavior of excess free length. 14]. The observed values of cohesive energy are also in the reported range of dipole – dipole and hydrogen bonded types of interactions [10]. P. 12. Prahalada Rao et al. Nain A K.N and Kannappan V.K. S. Ind. R. Kannappan. Avneesh K Singh. Kumar. Liq. REFERENCES 1. Rambabu. 74B (2000) 63. Phys.. Ali A. Thiyagarajan R. J Phys. These conclusion can be drawn by the suggested variation of excess thermodynamic parameters. Phys. Jayakumar. Enathoor. 43 (2005) 755. K. Liq.found that there is a possibility of interstitial penetration of the CA into DMA. J Phys. Liq. Phys. J Pure Appl. J Pure Appl. A. June (2007) 48 – 57. Jaafar M. Isht Vibhu. Ali and A. Nain A. Mohamed Kamil. 7. Liq. Nain. Ind. Phys. Ind. Rama Rao. K. Mylapore. Sarma and C... V.74B (5) (2000) 351. J Mol. Kumar. J Pure Appl. Liq. 159 | P a g e . J Mol. 5. K. Phys. Arul G and Palaniappan L. Rajagopal E and Manoharamurthy N. 9. Manisha Gupta and Shukla J P. R. Chem. Sivaparasad V. 154 (2010) 69-75... Sci.G. Phys.E. 3. Chennai and the Management of Sri Sankara Arts and Science College.. Making sense of boiling points and melting points. Jayakumar .. 6. Kannappan and S. G. 115 (2004) 1. Resonance. 11. for their keen interest and support shown towards this work. Subramanyam Naidu P and Ravindra Prasad K. V. 40 (2002) 264. M.Yasmin A and Nain.Ali A. 37 (1999) 161. ACKNOWLEDGEMENT The authors thank the Management of R. Ind. Akilandeswari. 47 (2009) 195. J Chem. Ind. 2. Tiwari K. Chandra P and Pandey J D. 34 (1996) 761. 40 (2002) 315. J Mol. A. V. 10. Kanchipuram. Phys. S and Palaniappan L. Ind. J Pure & Appl. Ind. J Phys. 124 (2006) 1. Chem. 18(2) (2007) 81. Ind J Pure & Appl. Jayakumar and V.A. 46 (2008) 169. M. S. 13. K and Chakravorty V. 8. Ali A.... 42 (2004) 820. Vivekananda College. 4.S Karunanidhi . Hyder S and Nain A.. Chand D. 14. 3 1019.15K x2 0.595 1.0115 -0.761 -4.132 3.87 1.894 -0.6 8.3 1008.5996 0.433 -2.51 1.5 1032.43 2.0359 -0.4 -25.0999 0.346 -1.254 Vf 10-8 m3 5.695 65.838 -4.132 4.4206 0.3995 0.569 1.96 2.141 -0.401 -2.461 1.544 -6. density.124 59.984 1.425 56.595 1.402 -0.723 10.556 1.753 N.326 -1.676 45.776 -1.535 -1.318 3.5 1026.198 14.093 -1.2 -23.3 1000.0572 α πi 105 atm 4.634 47.44 5.4026 0.182 4.6 1018.483 4.374 Lf A0 0. viscosity and other acoustical parameters for cinnamaldehyde + N.035 6.176 -1.678 -0.052 4.716 43.300 -1.0999 0.831 3.2996 0.6 10-4 ηE Nsm-1 0.43 15.423 4.003 κE 10-11N-1m2 0.063 12.305 42.590 4.6996 0.33 2.943 2.0307 0.4065 0.0254 -0.6996 0.0106 -0.795 160 | P a g e .557 4. N – ZE 104 Rayl -1.13 11.133 -0.8 1509 1479.497 1.665 2.24 2.1998 0.8 19.970 -1.055 -1.254 -3.0731 -0.Table 1 – Ultrasonic velocity.4234 0.489 -0.43 3.8 969.313 4.9 1043.15K x2 0 0.308 55.7995 0.814 3.8 -57.388 4.6 -44.4050 0.733 7.4083 0.9 uE m/s -8.994 4.0331 -0.536 L fE 10-13 m 3.407 -1.50 κ 10-10 N-1m2 3.953 -6.4285 0.6 1555.772 7.187 6.8 1546 1528.285 1.181 0.4153 0.90 13.527 -1.485 3.6 1528.2 -27.7995 0.596 1.1998 0.6 ρ kg / m3 1058.197 0.5996 0.468 -2.6 1510.69 1.680 5.3995 0.252 2.613 3.726 62.168 4.30 6.155 6.508 1.941 10.4 1491.991 -4.629 -1.2996 0.586 -5.243 Table 2 – The values of excess thermodynamic parameters for cinnamaldehyde + dimethylaniline system at 303.145 5.03 1.924 4.28 15.904 -1.4997 0.8 -8.4997 0.335 4.163 πE 104 atm 0.798 4.140 50.3997 0.5 η 10-3 Nsm-1 3.693 -3.0112 0.014 8.2 1535.525 1. N – dimethylaniline system at 303.4183 Z 106 Rayl 1.9 1 u m/s 1537.537 1.126 -1.04 VmE -10 m-3 10 7.4 1512.628 1.100 4.801 -0.71 2.4164 0.65 CE KJ/mol 67.2 991 979. 8 1.FIGURE 1.6 0. B 1560 1540 U 1520 1500 1480 0.4 4.9 0.2 0.0 X2 FIGURE 2.4 0.0 X2 161 | P a g e .1 4.0 3.6 4.0 0.4 0.0 0.3 K 4.8 1.2 4.6 0. E 4.2 0.5 4. D 3 2 EXCESS K 1 0 -1 -2 0.2 0. X2 162 | P a g e .0 .FIGURE 3.6 0.6 0.4 0.0 X2 FIGURE 4.8 1. B 20 0 EXCESS U -20 -40 -60 0.2 0.0 0.8 1.0 0.4 0. FIGURE 5. K 70 65 CE(kJ/MOL) 60 55 50 45 40 0.0 0.2 0.4 0.6 0.8 1.0 X2 163 | P a g e CHARACTERIZATION OF NANOFLUID OF PLATINUM Virendra Kumar, Kailash and Jitendra Kumar1 Department of Physics, BN PG College, Rath, Hamirpur, U.P., 210 431, Bharat 1. Department of Physics, Govt. Girls P. G. College, Banda, U.P., 210 001, Bharat Email:
[email protected],
[email protected] Abstract: Nanofluids are attracting a great deal of interest with their enormous potential to provide enhanced performance properties, particularly with respect to heat transfer. Nanofluids are stable suspensions of nanoparticles in a liquid. In order to avoid coagulation of the particles, the particles must be coated with a second distance holder phase which in most cases, consist of surfactants that are stable in the liquid. An important application of nanofluid containing nanoparticles is as a coolant, since the addition of only a few volume percent of nanoparticles to a liquid coolant and significantly improves its thermal conductivity. Platinum nanoparticles with narrow size distribution dispersed onto smooth, non-catalytic surfaces are of interest as model systems for the investigation of particle shape and size dependence of the catalytic activity of platinum towards reactions of interest in fuel cell systems. Ultrasonic velocity is the speed in which sound propagates in a certain material. It depends on material density and elasticity. It is related in a simple way to the various coefficients of compressibility, isentropic, isenthalpic and isothermal, hence the importance of its measurement and modeling in temperature and pressure ranges are widely used. Measurement of ultrasonic velocity gives the valuable information about the physicochemical behaviour of the liquid and liquid mixtures. In this work we have measured the ultrasonic velocity at different temperature and frequencies of nanofluid of platinum using Interferometer technique. Key Words: Nanofluids, Ultrasonic velocity, Nanotechnology and Interferometer Technique. 1. Introduction Platinum is used in jewelry, laboratory, equipment, electrical contacts and electrodes; platinum resistance. Platinum occurs naturally in the alluvial sands of various rivers, though there is little evidence of its use by ancient people. The most important application of platinum is in automobiles as a catalytic converter, which allows the complete combustion of low concentrations of unburned hydrocarbon from the exhaust into carbon dioxide and water vapor. Platinum is also used in the petroleum industry as a catalyst. In the laboratory, platinum wire is used for electrodes; platinum pans are used in thermo gravimetric analysis. Nanotechnology is a most important and growing area in science. Nano-science, the science under pinning nanotechnology, is a multidisciplinary subject covering atomic, molecular and solid state physics, as well as much of chemistry. Nanostructures are known to exhibit novel and improved material properties. Nanotechnology is design, fabrication and application of nanostructures or nanomaterials, and fundamental understanding of the relationships between physical properties and material dimensions. 164 | P a g e Application of nanostructures and nano-materials are based on the peculiar physical properties of nanosized materials, the huge surface are the small size that offers extra possibilities for manipulation and room for accommodating multiple functionalities. In future, amazing nanotech-based products are expected, including extraordinarily tiny computers that are very powerful, building materials that withstand earthquakes, advanced systems for drug delivery and custom-tailored pharmaceuticals as well as the elimination of invasive surgery, because repairs can be made from within the body. Future developments and implemention of nanotechnology could certainly change the nature of almost every human made object and activity. Its ultimate societal impact is expected to be as dramatic as first industrial revolution and greater than the combined influences that aerospace, nuclear energy, transistors, computers and polymers have in this century. Nanotechnology development is the need to understand the techniques for atomic and molecular based study of matter in nanoscale [1-3]. Nanofluids are dilute liquid suspensions of nanoparticles with at least one of their principal dimensions smaller than 100nm. There is a growth in the use of colloids which are nanofluids in the biomedical industry for sensing and imaging purposes. This is directly related to the ability to design novel materials at the nanoscale level alongside recent innovations in analytical and imaging technologies for measuring and manipulating nanomaterials. This has led to the fast development of commercial applications which use a wide variety of manufactured nanoparticles. Nanofluids have higher thermal conductivity and single-phase heat transfer coefficients than their base fluids [4]. Nanofluids could be applied to almost any disease treatment technique by reengineering the nanoparticles properties. Several significant gaps in knowledge are evident at this time, including, demonstration of the nanofluid thermalhydraulic performance at prototypical reactor conditions and the compatibility of the nanofluid chemistry with the reactor materials [5]. Ultrasonic velocity has become a valuable tool for the study of various physical and chemical properties of the matter. Ultrasonic velocity measurement offers a rapid and destructive tool for the characteristics of materials. Various elastic parameters and estimation of grain size has been going on far the past several years. Elastic constants of isotropic solid can be determined ultrasonically when both longitudinal and transverse wave velocities are known [6, 7]. The aim of present work was to study the characterization of copper nanofluid using ultrasonic techniques. 2. Experimental Details Interferometry is the technique of diagnosing the properties of two or more waves by studying the pattern of interference created by their superposition. It is an important investigative technique in the fields 165 | P a g e of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, quantum mechanics, plasma physics and remote sensing. An ultrasonic interferometric sensor has been introduced for the measurement of suitable changes in the physical properties of fluids such as density, viscosity and bulk modulus [8]. The ultrasonic interferometer is simple in construction and operation and gives accurate and reproducible results. From these results, one can readily determine the velocity of sound in a liquid with high accuracy. Formerly, the absorption of sound in the liquid and the coefficient of reflection at the reflector surface have been obtained through a complicated analysis of the electrical and equivalent electrical circuits of the quartz crystal and the associated fluid column. In our experimental work we use multifrequency interferometer. This multifrequency generator can generate ultrasonic waves of several frequencies form 1 MHz to 12 MHz in the medium. The multifrequency ultrasonic interferometer consists of the two parts- the high frequency generator and the measuring cell. The high frequency generator is designed to excite the quartz plate fixed at the bottom of the measuring cell at its resonant frequency to generate ultrasonic waves in the experimental liquid in the measuring cell. A micro ammeter to observe the changes in current and two controls for the purpose of sensitivity regulation and initial adjustment of micro ammeter is provided on the high frequency generator. A fine micrometer screw has been provided at the top, which can lower or raise the reflector plate in the cell through a known distance. It has a quartz plate fixed at its bottom the ultrasonic interferometer may be used for determination of ultrasonic velocity. The measuring cell is connected to the output terminal of the high frequency generator through a shielded cable the cell is filled with the experimental liquid before switching on the generator the ultrasonic waves moves normal from the crystal till they are reflected back from the movable plate and the standing waves are formed in the liquid in between the reflector plate and the quartz crystal. The micrometer is slowly moved till the anode current meter on high frequency generator shows a maximum. A number of maximum readings of anode current are passed on and their n is counted the total distance x thus moved by the micrometer gives the value of wavelength λ with the help of the following relation; x = n× λ /2 of following relation; V= λ ×f (2) (1) Once the wavelength is known the ultrasonic velocity V of copper nanofluid can be calculated with the help 166 | P a g e Evaluation Ultrasonic velocity measurements have been successfully employed to detect and assess weak and strong molecular interactions present in nanofluids. Results and Discussions Ultrasonic velocity measurements are helpful to study the ion-solvent interactions in aqueous and non-aqueous solutions in recent years. The measured data of ultrasonic velocity for nanofluid of platinum at different temperature and frequencies are given in Table 1 . ultrasonic velocity is increase.5 MHz. on increasing temperature from 312K up to 318K. This shows linear and inverse relation separately between temperature and velocity. Temperature variation of ultrasonic velocity at 2 MHz frequency is shown in Figure 1(ii). Measurement of ultrasonic velocity gives the valuable information about the physicochemical behaviour of the liquid and liquid mixtures. Again increasing temperature till 327K. From Figure 1(i). Nanofluids are suspensions of nanoparticles in fluids that show significant enhancement of their properties at modest nanoparticle concentrations. which increases the thermal conductivity of the base fluid by a substantial amount [10. when temperature is reached slightly at 323K.2. one can say from this figure velocity is increase from temperature 312K to 315K but when we increase temperature at 318K. Temperature variation of ultrasonic velocity for nanofluid of platinum is given in Table 1 and frequency variation of ultrasonic velocity for this fluid is shown in Table 2. 4. at 1Frquency(F) in MHz. This shows proportionality relation between temperature and velocity. Ultrasound has been extensively used to determine the ion solvent interactions in aqueous containing electrolytes. Graphical representation of data is given in Figures 1 . semi-empirical formula and theories are available for the theoretical computation of ultrasonic velocity in liquid and liquid mixtures. the result is given in table 2. 11]. It is clear from Figure 1(iii).2. Several relations. velocity decreases. Frequency variation of ultrasonic velocity for this 167 | P a g e . the ultrasonic wave velocity is increase and when temperature again increase up to 320K. Ultrasonic wave velocity for nanofluid of platinum is measured at different frequencies ranging form 1 .3. Nanofluids contain suspended metallic nanoparticles. the velocity of ultrasonic wave is increase and up to 321K the velocity is slightly decrease and at 324K the velocity of ultrasonic wave is slightly increase and again at 327K the ultrasonic wave velocity is slightly decrease. Nanofluids are considered to offer important advantages over conventional heat transfer fluids. it is observed that at increasing temperature from 311K to 317K. velocity is increase but at 326K velocity again decrease. there is a slightly decreases. These studies can also be used to determine the extent of complexation and calculate the stability constants of such complexes [9]. at room temperature. 2010. Imperial College Press. Acknowledgement The authors are thankful to the University Grants Commission. Kumar and Y. Leon. Ind. Inter. Pramuanjaroenkij. 3187-3196. 2007. Applied Energy. Das and R. 143-150. ‘Ultrasonic velocity measurement in cylindrical rod material’ J. ‘Principles of nanotechnology’. Kannappan and N.Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Temperature (K) Frequency (F) 1 MHz 2 MHz 3 MHz 4 MHz 311 1343 1530 1520 1510 312 1330 1534 1534 1531 314 1363 1540 1510 1520 315 1380 1541 1548 1512 317 1398 1530 1590 1500 318 1400 1531 1586 1506 320 1390 1530 1530 1540 321 1390 1533 1507 1556 323 1394 1550 1520 1580 324 1400 1567 1552 1571 326 1364 1590 1600 1460 327 1300 1589 1542 1330 Table 2..C. ‘Review of convective heat transfer enhancement with Nanofluids’. 2566-2573.. Haur and A. Kumar. 391-412. 2009.I. Heat Transfer. velocity is decreases on increasing frequency to 5MHz. of pure and Appl. 86. 117. S. Singapore. of Heat and Mass Tran. Vajjha. Table 1 . J.T. 240-250. Phys. 128. ‘Ultrasonic Interferometer Technique’ Centre for NDE and Department of Mechanical Engineering. IIT Madras. 15-19. Sethuraman. 6. Singapore. 45. Buongiorno.D. Wong and O.. 2009. G. ‘Application of nanofluids in heating buildings and reducing pollution’. J.V. 2010 J. 2006.fluid is shown in Figure 2. Ultras. Advances in Mechanical Engineering. ‘Nanostructures and nanomaterials’. Gandhi. 45. Kakaç and A. Ind. ‘Convective Transport in Nanofluids’. 221225. It is observed that with increase in frequency from 1 MHz to 3 MHz.A. V. ‘Ultrasonic investigation of ion-solvent interactions in aqueous and nonaqueous solutions of transition and inner transition metal ions’. S. Pan Stanford Publishing. Phys. Mansoori. ‘Science at the nanoscale’. 1998. Vinayagam. Kulkarni.S. 52. A. 2010. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] G. velocity is increase. ‘Ultrasonic studies on charge transfer complexes of certain aldehydes with benzylamine and cyclohexylamine as doners in n-hexane ay 303K’. 2007. Shong. D. Balasubramaniama and S.. ‘Applications of Nanofluids: Current and Future’. V.W. 20. C. 5. 2007.K. J. London. Wee. 2006. J. Kannappan and S. New Delhi for financial support. Cao.P. 2006.. 1-28. D. K. 519659-519669. K.C. of pure and Appl.Frequency Variation of Ultrasonic Velocity in Nanofluid of Platinum Frequency [MHz] 1 2 3 4 Velocity [m/sec] 1329 1513 1570 1430 5 1414 168 | P a g e . World Scientific Publishing Co. Pure Appl. Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Figure 1(iii). Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Figure 1(ii).Figure 1(i). Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum Figure 2. Temperature Variation of Ultrasonic Velocity in Nanofluid of Platinum 169 | P a g e . Rath. it is interesting to prepare multiphase mixed crystals with new composition from miscible alkali halides. In addition. Kailash and Bharat Singh Department of physics. The mixed crystals of alkali halides are found to be harder than the crystals of end members and so they become more useful. melting point and Grüneisen parameter. 210 431. Lead Telluride is used in a number of industrial applications including infrared detection and imaging. Lead selenide nano-crystals embedded into various materials can be used as quantum dots. Bharat Email. mixed crystals with multiple phases have been found to be more interesting. Hamirpur. kailashrath@gmail. A mixed crystal has physical properties analogous to those of the pure crystals.com. and electronic devices. such as inter atomic potentials. Studies on mixed crystals are quite useful as they are of considerable technological importance in the field of storage cells. PbTe single crystals doped with VII A Periodic system group elements will continue to attract a widespread attention both for their fundamental electronic properties and for the applications in infrared optoelectronic [1-3]. Elastic properties are also thermodynamically related to the specific heat.Mayer potentials. College. the anions are substituted by other anions of nearly equal size without breaking the crystal symmetry and so any ratio of two components yields the mixed crystal.P. Key Words: Ultrasonic Properties. thermal expansion.rath@yahoo. Introduction In recent years considerable interest has been paid to the study of mixed crystal properties as they are useful in many technological applications such as mixed crystals of alkali halides are used for laser windows. Mixed Crystals and Partial Contractions. and phonon spectra. B. 1. Coulomb and Börn-Mayer Potentials. third and fourth order elastic constants of mixed potassium and rubidium fluoride and mixed lead selenide and telluride crystals at different temperature by using Coulomb and Börn . U.com Abstract: In the mixed crystal systems. optoelectronic. Further. Debye temperature. The evaluation of other ultrasonic properties such FOPDs of second and third order elastic constants. SOPDs of SOECs and partial contractions are computed using higher order elastic constants using this theory. The aim of this work is to give a detailed description of the behaviour of non-linear properties such as second.ULTRASONIC BEHAVIOUR OF MIXED CRYSTALS Virendra Kumar. The behaviour of the ultrasonic properties plays an important role in providing valuable information about the mechanical and dynamical properties. equation of state. Ultrasonic characterization of materials is a versatile tool for the inspection of their micro-structure and their mechanical properties.vir. This is possible because of the close 170 | P a g e .G. Elastic Constants.N.P. The mixed alkali halides find their applications in optical.. These coefficients are known as higher order elastic constants. the second. Similarly B for mixed (PbSe)X . also this technique offers the possibility of using different frequency ranges and many modes of vibration of the ultrasound waves to probe into structural level [4]. To study the ultrasonic behaviour of a deformed crystal.(PbTe)1-X and B1----B6 for its fractions. 2.(RbF)40. and the results are shown in Tables 4 – 5. the second. In last and present decade considerable interest has been taken in investigation of ultrasonic properties of materials [5-8]. third and fourth order elastic constants for A and B crystals are evaluated at different temperature. In present investigation. The FOPDs of SOECs and TOECs.(RbF)0.(RbF)60. Formulation As we presented earlier the elastic energy density for a crystal of a cubic symmetry can be expanded up to quartic terms as shown below [9]. Evaluation With the help of nearest-neighbour distance and hardness parameter. In this paper we represent mixed (KF)X (RbF)1-X as A and (KF)100 . CIJK = CIJK + CIJK . (KF)40 .(RbF)100 as A1----A6. (KF)80 . In this expansion. the elastic energy density is expanded by Taylor’s series expansions. and (KF)0 .(RbF)1-X and mixed (PbSe)X .association of the ultrasound wave with the elastic and the inelastic properties of the materials. U0 =U2 + U3 + U4 = [1 2!]C ijk l X ij X kl + [1 3!]C ijklmn X ij X kl X mn + [1 4!]C ijklmnpq X ij X kl X mn X pq These elastic constants have two parts as given below. third and fourth order elastic constants are the coefficients of second.(RbF)80. 0 vib 0 vib 0 vib CIJ = CIJ + C IJ . the SOPDs of SOECs and partial contractions for mixed crystals are evaluated utilizing room temperature data. some efforts have been made for obtaining SOECs. (KF)60 . the FOPDs of SOECs and TOECs. The values of SOECs at room temperature for A and B are given in Table 1 and third and fourth order elastic constants at 300K are given in Tables 2(i)-3(ii) for these crystals.(PbTe)1-X crystals. the SOPDs of SOECs and partial contractions of mixed (KF)X . TOECs and FOECs at an elevated temperature. One gets a series with higher order coefficients.(RbF)20. Elastic and dielectric properties of mixed ionic solids have been carried out by number of workers using different phenomenological models. 171 | P a g e . (KF)20 . third and fourth order terms. CIJKL = CIJKL + CIJKL (1) (2) 3. 215 3.647 3.016 A6 -4. From this figure. Figure 3 present the temperature variation of FOPDs of SOECs for B3.578 Table 2(ii) TOECs in 1011 dyne/cm2 at room temperature for B 172 | P a g e .20 1.4.340 -25.806 3.73 9.861 -26.679 A3 -100.418 5.831 3. From Figure 1.76 4. There are three SOECs for face centered cubic crystals. the value of C11and C44 increases and the value of C12 decreases as temperature increases for A1. Results and Discussions The temperature dependence of elastic constants has been a subject of study in a number of investigations.45 1. and d2C44/dp decreases as temperature increases and d2C12/dp decreases first and increases last for B4.052 Table 2(i) TOECs in 1011 dyne/cm2 at room temperature for A Fraction C111 C112 C123 C144 C166 C456 A1 -106.233 15.496 3.034 -24.59 9.38 4.952 -6.54 1. There are three FOPDs of SOECs for mixed crystals.450 2.535 -7.04 3.899 A5 -105.933 -15.902 -26.786 A4 -101.545 14.375 4. It may be stated that all the second order pressure derivatives of second order elastic constants are positive.591 2.67 14. C112 and C166 are negative in nature while C123.502 15.29 1.70 1.733 2. Acknowledgement The authors are thankful to the University Grants Commission.916 3.938 4.141 A2 -96. the value of C 112 is decreasing as temperature increases and C456 remains constant for A 2 .97 1. The values of C11 and C44 are increasing and the value of C12 is decreasing as temperature increases for A and B.022 -6.59 1. Figure 4 present the value of d2C11/dp. Ψ12 decreases as temperature increases and Ψ44 somewhere increases or decreases as temperature increases for B5 crystals. Table 1.109 4.266 -6.028 3.02 4.148 3.463 3.352 3.66 4.455 2. 5. Figure 2(i)-(ii) shows that the values of C 111.397 -7.80 5. The temperature variation of various ultrasonic are represented graphically for A and B.109 13. C123.88 8. From Figure 5.976 5. For all crystals the values of C111. C144 and C456 are positive in nature shown in Table 2(i)-(ii).141 -6. SOECs in 1011 dyne/cm2 at room temperature for A and B Fraction A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C11 C12 C44 9.147 -24. one can say that the value of Ψ11 .47 1.183 2.52 1.343 3. New Delhi for financial support. C 144 and C 166 are increasing.66 9.302 3.67 1.57 5.794 15.39 1.256 3.664 4.97 1. it is clear that the value of dC11/dp and dC12/dp decreases and the value of dC44/dp first increases than decrease as temperature increases. 77 -44.31 1.77 -89.86 -6.69 B3 -10.49 2.936 -2.12 -0.47 -18.63 B5 -10.83 -6.19 0.33 B4 -213.27 A2 -14.80 -7.03 1.34 21.63 -16.17 -70.98 -6.22 1.07 -3.83 -20.20 A4 -14.49 1.68 7.03 -18.73 -10.68 8.66 -21.53 7.02 -20.17 -0.89 -3.54 1.60 -87.95 2.50 -19.76 B5 -217.44 -6.53 2.43 -10.07 59.54 -6.14 -71.30 B2 -10.40 -6.78 2.32 207.60 22.07 -4.13 -15.90 119.49 -28.67 101.60 -6.42 9.50 32.49 18.03 -20.90 7.34 -17.12 71.11 -18.02 -17.47 A1 -14..72 -5.81 32.29 -0.86 24.06 -9.39 B4 -10.72 B2 -206.20 95.04 6.22 2420.40 -6.93 8.11 -26.53 -20.58 -6.57 1.00 -5.09 -7.53 -17.58 41.43 -7.47 -17.04 39.85 1.86 33.16 30.68 -6.67 B6 -10.33 89.37 8.35 42.22 37.33 92.88 8.14 107.08 8.233 A5 -14.36 98.02 0.16 0.10 -6.56 -24.234 A6 -10.73 -20.76 9.65 2457.232 2343.91 -204.98 53.69 -19.Fraction C111 C112 C123 C144 C166 C456 B1 -220.18 -30.26 34.789 B1 -9.85 -31.56 -6.03 -16.87 -18.01 -69.42 26.34 -0.23 35.43 -5.78 62.57 233.52 -17.20 -17.22 0.61 -18.02 0.44 -15.33 40.72 -5.18 -0.31 2.02 0.74 -206.48 -3.12 A6 169.88 -84.60 1.39 7.16 31.74 37.39 -19.56 2.87 40.42 -25.14 101.94 -6.233 2304.05 -22.37 87.48 -6.07 4.34 2.59 dC11 / dp dC12 / dp dC 44 / dp dC111 / dp dC112 / dp dC123 / dp dC144 / dp 173 | P a g e .23 -0.56 1.13 0.38 -17.20 2.97 -9.05 6.44 78.49 94.59 -15.75 45.06 -75.76 -7.02 35.08 6.09 -73.93 B3 -209.51 35.28 -3.07 -7.03 0.53 -16.56 73.59 -14.45 7.77 37.22 B6 -202.76 2.04 0.79 -27.22 -19.68 -6.51 -8.72 27.80 -15.41 Table 3(ii) FOECs in 1011 dyne/cm2 at room temperature for B Fraction B1 B2 B3 B4 C1111 C1112 C1122 C1123 C1144 C1155 C1255 C1266 C1456 C4444 C4455 Fraction B5 2382.84 A5 260.89 -31.15 -6.22 -9.20 -68.52 -203.64 111.38 121.95 -4.47 -7.61 18.46 104.47 7.29 0.17 -10.04 -22.39 83.41 183.86 -3.69 -3.02 0.40 88.29 8.05 48.27 1.39 -16.31 -205.56 Table 3(i) FOECs in 1011 dyne/cm2 at room temperature for A Fraction A1 A2 A3 A4 C1111 C1112 C1122 C1123 C1144 C1155 C1255 C1266 C1456 C4444 C4455 286.81 -16.63 37.13 25.88 -6. First Order Pressure Derivatives of the SOECs and TOECs for A and B A3 -14.20 2.234 Table 4.60 1.96 3.08 63.25 0.28 38.61 B6 2264.51 1.39 -86.07 -206.22 114.07 55.11 -72.39 -85.77 -19.64 -38.19 7.79 1.12 -20.06 52.14 -7. 42 1. Nunez.57 0. Kent.39 1. Ke.89 0. K. R.62 2. C.01 0. Srikanth.18 24.68 A5 3. E.63 2. (b). Rev.H. Srivastava and Kailash.48 2. Ding.10 0. Afifi.22 0. M.93 2.72 0.91 -7. N. Sinova.S.75 -0.S.24 0. 1996.74 2. K. ‘Lead selenide thin films from vacuum evaporation Methodstructural and optical properties’. Rajasekar and S. SOPDs of SOECs in 10-10 (dyne/cm2)-1 and Partial Contraction ( Ψ in 1013dyne/cm2) for A and B Fraction A1 2 A2 3. of Solids 69. 174 | P a g e . 2007.46 2. Philosophical Magazine. 270.22 3. E. 024304–024316. K. Ren.25 B2 2.19 23. 1668–1673. M. ‘Ab inito calculation of elastic properties of rock-salt and zinc-blend MgS under pressure’. and P. Trejo. Physica B. D. Yang. Raju. U.A. 60.59 0.45 2.75 0.60 2.L.Phonon Interaction in Polyacene Organic Transistors’.33 1.67 0.M. M. 2009. Pramana.05 3. F.04 -8.11 0. 89. ‘Anharmonic properties of rock-salt structure solids’.31 Table 5.54 -0.10 0.49 B3 1. Phys.78 0. 203–211. Stat. A. 403.99 1. Raju.85 -7. 2009.36 -0. Yuan and Z. B.71 B1 1. 2008. R. 230. C. Varsney. Kushwaha.18 25. X. Se Te ) alkaline earth chalcogenides’.623 1.59 2. 309-312. 445-450.28 -7.282 2.46 2. and Chem.271 2.97 -7. J.M.47 -6. E. Schliamann and A. J. 2002. Physica B.00 2. H. H.26 0. C.34 d C11 / dp 2 3. Mcdonald. S. References [1] [2] [3] [4] [5] [6] [7] [8] [9] S.dC166 / dp dC 456 / dp 2. 69. 2009. 2007.68 1. 6.20 -6. Phys. Physica B.276 2.K. Sol.20 -1.19 0. Gaafar. J. ‘Structural studies of some phospho-borate glasses using ultrasonic pulse echo technique DSC and IR spectroscopy’. Chen. F. P.26 2. 80. PbSe. ‘Temperature Variation of Higher Order Elastic Constants of MgO’.09 0.08 0.13 0. M. 2008.04 B6 2.65 A4 3. Mekawy.31 2.47 2.55 2.45 2.37 1.72 -6.G.19 22. Chalcogenides Letters. J. R.61 A3 3.S. Lin and M. J.75 d 2 C12 / dp 2 d 2 C 44 / dp 2 Ψ11 Ψ12 Ψ44 6. Phys. E. Zhang.00 2.85 B5 1. Case. J.93 2. Kailash.25 0.19 21. Kaurav.19 21. ‘Phase transformation and elastic behaviour of MgX ( X= S.72 A6 3.66 B4 1. ‘Electron. 143–167. Timm.07 5.96 -6. D.04 3. Curzio. ‘Temperature-dependent elastic moduli of lead telluride-based thermoelectric materials’. J. Kanatzidis. Ni.25 0.28 2.K.85 1. Sharma and R.35 1. 404. 390.23 0.12 -6. Srivastava and K. 2009. K.26 -1.96 2. Singh.97 -0.48 0.38 -1. ‘Thermodynamic properties of PbTe. Y. Prabahar.61 2. and PbS: First-principles study’.90 0. Figure 1 Temperature Variation of SOECs for A1 Figure 2(i) Temperature Variation of TOECs for A2 Figure 2(ii) Temperature Variation of TOECs for A2 Figure 3 Temperature Variation of FOPDs for B3 Figure 4 Temperature Variation of SOPDs for B4 Figure 5 Temperature Variation of Partial Contractions for B5 175 | P a g e . P. In sewage treatment facilities. Attenuation.P. Bharat 1. U. At room temperature. Rath. vir. electron mean free path is not comparable to phonon mean path and no coupling will take place. 1. phonon–phonon interaction and that due to thermo elastic relaxation. 2]. Hamirpur. Introduction Attenuation is the term used to account for loss of wave amplitude or signal due to all mechanism. Jhansi.TEMPERATURE DEPENDENDE OF ULTRASONIC ATTENUATION IN STRONTIUM OXIDE CRYSTAL Kailash. itself. BN PG College. scattering and mode conversion. Thus the attenuation due to electron–phonon interaction will be absent.rath@yahoo. Virendra Kumar and D. The strontium oxide crystal possesses face centred cubic crystal structure. Both these type of attenuation are observed in calcium oxide crystal. ultrasonic attenuation is used as a sensing mechanism to control pumps and maintain sludge levels in setting basins.. Bipin Bihari College.. is not relative. however.in. Ultrasonic absorption coefficients can be used for non-destructive techniques to characterize the materials. For the evaluation of the ultrasonic coefficients the second and third order coefficients are also calculated using Coulomb and Born Mayer potentials utilizing nearest neighbour distance and hardness parameter data.com Abstract: The ultrasonic attenuation is a measure of the relative amplitudes of a wave at two locations in space. The most important causes of ultrasonic attenuation in solids are electron–phonon.co. Akeiser loss and Gruneisen Numbers. Attenuation is a definite quantity for a particular mode of wave motion at a certain frequency in a given material under specific conditions. 284128. The two dominant processes that will give rise to appreciable ultrasonic attenuation at higher temperature are the phonon–phonon interaction also known as Akeiser loss and that due to thermo elastic relaxation [1.D. The ultrasonic attenuation gained very wide acceptance in scientific experiment. Bharat Email: kailash. The temperature dependent part of ultrasonic attenuation has been explained in terms of model where the acoustic phonon interacts with a number of thermal phonons in the lattice. Thermo elastic relaxation. In this work ultrasonic attenuation due to phonon–phonon interaction (α/f2)p-p and thermo elastic relaxation (α/f2)th are studied in strontium oxide at an elevated temperatures along <100> direction. 210 431. Gupta1 Department of Physics.rath@yahoo. Key Words: Attenuation. including absorption. It has been established that at frequencies of ultrasonic 176 | P a g e . Phonon-phonon interaction. U. Department of Physics. Vs = (C44/d)1/2 and 3/ VD = 1/ Vl 3 +2/ Vs3 Two relaxation times are related as 2 3 (3) (1/2)τl = τs = τth = 3K/Cv V D (4) Where τth is the thermal relaxation time for the exchange of acoustic and thermal energy. 3. The acoustic coupling constant D in eqns. (1) and (2) is obtained from the values of the SOEC and TOEC data using theoretical formulae for <(γij)2> and <γij>2 and given as D = 9 <(γij)2> – (3Cv T/ E0) <γij>2 (5) j are the Grüneisen parameters corresponding to particular direction of propagation and Where γi polarization. Vs are the ultrasonic velocities for longitudinal and shear waves respectively. Evaluation 177 | P a g e . Vs and VD are given as Vl = (C11/d)1/2. Cv is specific heat and VD is the Debye average velocity. The temperature dependent part of ultrasonic attenuation has been explained in terms of model where the acoustic phonon interacts with a number of thermal phonons in the lattice. The ultrasonic attenuation study of the materials has gained new dimensions with the progress in the material science [3-10]. d is the density and Vl. Formulation Here we use phonon-phonon interaction [12] for evaluating ultrasonic attenuation coefficient over frequency square (α/f2)p-p. The Vl. ω is the angular frequency (=2πf). In present work ultrasonic attenuation due to phonon–phonon interaction (α/f2)p-p and thermo elastic relaxation (α/f2)th are studied in strontium oxide at an elevated temperatures along <100> direction. thermal relaxation time τth and ultrasonic absorption coefficients over frequency square of the ultrasonic wave. Here E0 is thermal energy density. phonon–phonon interaction mechanism is dominating cause for attenuation. For the evaluation of the ultrasonic coefficients the second and third order coefficients are also calculated using Coulomb and Born Mayer [11] potentials.range and at higher temperatures in solids. 2. the expressions are given as: (α/f2)l = 4π2 E0( Dl/3) τl / 2dVl3 (1) 2)s = 4π2 E0( Ds/3) τs / 2dVs3 and (α/f (2) where the condition ωτth <<1has already been assumed. K is the thermal conductivity. The thermoelastic attenuation is obtained as (α/f2)th = 4π2 <γij>2 KT/2dV5 (6) We have calculated the SOEC and TOEC for the evaluations of acoustic coupling constants D. f is frequency of ultrasonic waves. Yadawa and A. J. 55. ‘Physical ultrasonics: current scenario and future prospects’. J. 29. (USSR). R. 4. Results and Discussion The elastic constants of an isotropic solid specimen can be accurately determined by measuring the velocities of transverse and longitudinal ultrasonic waves in the specimen. [2] A. 6. 1939. Jpn. 22. 1. K. 2000. The non-linearity constants D are evaluated using the average Grüneisen parameters <γij> and average square Grüneisen parameters <γij2> and are presented in Table 3 along with attenuation (α/f2)l. In the present study all the SOECs are positive. that the ultrasonic velocity for longitudinal wave and shear wave increases as temperature increases along <100> direction. New Delhi for financial support. It is clear from Figure 6 that the value of (α/f2)l and (α/f2)s increases with temperature. K. Phys. while among TOECs three are positive and three are negative in nature. ‘Attenuation of ultrasonic waves in V. Pure Appl. 5. Grüneisen parameters have been evaluated using Mason’s Grüneisen [15] parameters tables at different temperatures along <100> direction with the help of second and third order elastic constants.Pandey. The magnitude of second and third order elastic constants and their temperature variation plays a crucial role in the investigation of ultrasonic attenuation in Strontium Oxide. Acknowledgement The authors are thankful to the University Grants Commission. Soc. Alkeizer. 2. It is clear from the Figure 3 that the value of thermal relaxation time τth is very low at low temperature and increases as temperature is increased. The variation of the wave velocities with pressure can be used to determine the pressure derivatives of the elastic constants. R. K. Ultrasonics. Phys. [3] D. Cryogenics. S.. thermal relaxation time and non-linearity constants for Strontium Oxide along <100> direction are presented in Table 2. their temperature variation is presented in Figure 1. Singh. (α/f2)s and (α/f2)th. Using the formulation. 178 | P a g e . 207. Thangaraju. K. D. J. 277. the room temperature data of longitudinal and shear wave velocities. From Figure 5 one can see that non-linearity constants decrease as increase temperature. Gopal and B. It is clear from this Fig. Kor. debye average velocity. the values of (α/f2)l are found greater than those of (α/f2)s along <100> direction.The temperature dependence of second and third order elastic constants for Strontium Oxide has been evaluated at different temperatures following Brügger’s approach [13] and the method given by Mori and are presented in Table 1 along with melting point. similar behavior has been observed by other researchers in solids. 49. ‘On the absorption of sound in solids’. P. 1986. R. The theoretical [14] values of SOECs and TOECs in 1011dyne/cm2 at room temperature are also given in this Table for comparison. 12. ‘Ultrasonic attenuatio in dielectric crystals’. 2009. The temperature variation of ultrasonic velocities is presented in Figure 4. Yadav and Kailash. References [1] S. Yadav. [4] E. Nb and Ta at low temperatures’. [11] M.. stat. N.94 1. 47. S. Kim and K.327 4. Singh. Leisure. and chalcogenides of Pb and Sn. Inc. 237. 1932. 75. 2007. ‘Piezoelectric crystals and their applications to ultrasonics’. Point 24300C C11 18. 2004. D. crystal quartz and silicon’. [6] A. Debye Average Velocity in 105 cm/sec2.99 -2. ‘Thermodynamic definition of higher order elastic coefficients’.174 Dl 14. B. Mayer.038 τ th 7.[5] S. phys. [9] J. Zur Gittertheorie der lonenkristalle. M. Awasthi and V. 2009. P. New Jersey. P. 26. 1965. 2006. Pure Appl. Singh and R. J. 2003.18 1. Van Nortrand Co. 28.46 Reference This Work [14] Table 2. Singh. Brugger. Phys. 1950. K.85 -2.083 (α/f2)S 0. Pure Appl. 100.175 C44 10. p-p Attenuation for Longitudinal and Shear Waves in Nps2/cm and Thermal Attenuation in 10-20 Nps2/cm for SrO along <100> direction < γ ij > -0. [14] J.149 Table 3. Kor. 133. Liq. Z Phys. Table 1.495 5. D. 75.195 DS 2. Dey. III B. Yadav and D.310 C144 16. ‘Ultrasonic studies of CTAB in glycol’. [7] O.693 VD 5. sol.62 -22. ‘Effect of impurities and phonon-processes on the ultrasonic attenuation in germanium. F. Sharma.72 C456 15. ‘Effect of isotopy on thermoacoustical properties’. K. Cryst. 1964. A1612.18 17. Vol. [8] R.Cryst. Room Temperature data of Longitudinal and Shear Wave Velocities.35 C12 10. 677. 1.21 C123 16. 434. 392. [12] W. [15] W. Upadhyay and B. Phys. Pure Appl. [10] K. 362. Mol. J... [13] K. J. Thermal Relaxation Time in 10-12 sec and non linearity constants for SrO along <100> direction Vl 6. Ulrason. Ind. ‘Ultrasonic attenuation in alkaline earth metals’. Room Temperature data of Second and Third Order Elastic Constants in 1011 dyne/cm2 for SrO Mel. J. (a) 70.G.410 C166 -41. Ulrason. Phys. B.. Born and J. R. J. Rev. ‘Ultrasonic study of hydrogen motion in a Ti-Zr-Niicosahedral quasicrystal and a 1/1 bcc crystal approximant’. Prinston. Square Average Grüneisen Parameter. R. 2000. Academic Press New York.399 179 | P a g e .190 (α/f2)th 1. Pure Appl. 241. alkaline earth oxides. Pundhir..561 <( γ i j )2> 1.50 C112 -54.. J.66 1. Rev. Pandey. R. third and fourth order elastic constants for silver halides. A. Room Temperature data of Grüneisen Parameter.587 C111 -249. Physical Acoustics. 1982. Mason. ‘Elastic properties of intermetallics compounds under high pressure and high temperature’.218 VS 4. 45. 479.764 (α/f2)L 1. Shaklee. Y. 59. K. Kelto. Singh. ‘Ultrasonic attenuation in liquid mecury. Phys. P. Foster. zinc and gallium metals’. Shanker and J. 61. K. Mason. Ind. K. (Germany). Temperature Variation of TOECs 180 | P a g e . Temperature Variation of SOECs Figure 2.Figure 1. Temperature Variation of Ultrasonic Velocities Figure 5. Temperature Variation of Thermal Relaxation Time Figure 4.Figure 3. Temperature Variation of Ultrasonic attenuation 181 | P a g e . Temperature Variation of non-linearity constants Figure 6. 207 009(U. adiabatic compressibility. Gorakhpur University. P. The refractory titanium compounds like TiC and TiN is known for its extreme hardness (> 2500 VDH). Rao’s constant. Second and Third Order Elastic Constants (SOEC and TOEC). elastic constants. thermal conductivity INTRODUCTION: The ultrasonic properties can be used as nondestructive techniques for the detection and characterization of materials properties not only after the production but during processing as well [13]. India 2 Department of Physics. molar volume. intermolecular free path length.110 061. All calculated results have been discussed and comparision with available experimental results are drawn. ultrasonic velocities. D. Sahu2 1 Department of Applied Physics. Singh2 and S. The usual and interesting properties have attracted a large number of experimental. bulk modulus. van der Waals constant. New Delhi.ULTRASONIC WAVE PROPAGATION IN REFRACTORY MATERIALS Devraj Singh1*. acoustic impedance. For these materials. K. Ultrasonic attenuation due to phonon-phonon interaction mechanism is predominant over thermoelastic relaxation mechanism. Ravi S. Gorakhpur. and make it attractive as a structural material or as a coating for cutting tools. Yadawa1. thermal relaxation time. acoustic coupling constants are computed. KEYWORDS: Ultrasonic attenuation. Wada’s constant.P. theoretical and industrial investigations [4-6]. D. In present paper some characteristic microstructural thermophysical parameters those make considerable contribution to orientation and temperature dependence of ultrasonic attenuation in TiC and 182 | P a g e . Amity School of Engineering and Technology Bijwasan. high melting temperature and chemical inertness. elastic anisotropy. U.edu ABSTRACT: The ultrasonic attenuation of TiC and TiN are investigated at room temperature along <100>.amity. K. <110> and <111> orientations using Mason’s theory.) *dsingh1@aset. 8].e. e is the electronic charge. Rao’s constant. C144. Wada’s constant and van der Waal constant [14]. the ± sign apply like and unlike charge. second and third order elastic constant play a vital role. Mori. A is the strength parameter and b is the hardness parameter. The main causes of ultrasonic attenuation for perfect antiferroelectric and antiferromagnetic crystals are due to phonon-viscosity. C123. THEORY For the evaluation of ultrasonic attenuation. ultrasonic velocities. Since the crystalline form of stoichiometric titanium carbide and titanium nitride adopt the simple rocksalt structure. However at room temperature these remain only two types of losses. the thermal relaxation time and electron-phonon interaction. molar volume. Φµv(r) = ± (e2/r) + A exp (-r/b) Where. C112. acoustic impedance. Ludwig. intermolecular free path length. <110> and <111> orientations are discussed. Theory to evaluate ultrasonic attenuation has been discussed in our previous paper [12-13]. molar volume. 183 | P a g e . r the nearest neighbor distance. The loss due to electron-phonon interaction is only appreciable below 80K and hence it could be ignored safely at room temperature. adiabatic compressibility. With the help of second and third order elastic constant (SOEC and TOEC) . Here it is assumed that Φµv(r) is the interaction potential equal to the sum of the electrostatic potential ( Coulomb potential) and the Born-Mayer short range repulsive potential. which are due to phonon-viscosity and thermoelastic relaxation mechanism. The SOEC (C11. thermal relaxation time. the other physical parameters like zero pressure bulk modulus. van der Waals constant. C166 and C456) at room temperature (300K) are achieved by method developed by Leibfried. Rao’s constant. These titanium compounds have ionic metallic bonding. Ghate and Yadav [9-13] for NaCl-type crystal. All the formulations used in the computation of SOEC and TOEC of TiC and TiN are the same as those for previous paper [13]. Akhieser [15] has assumed that the equilibrium distribution phonons in a crystal can be distributed by the propagation of an acoustic phonon and the reestablishment of the equilibrium is the relaxation phenomenon. For this analysis. o We calculated SOEC and TOEC following Brugger’s definition of elastic constants at absolute zero (C IJ o and C IJK ) [7. i. acoustic impedance. Wada’s constant. adiabatic compressibility. We further assume A and b are the same for interaction between like (positive and negative) and unlike ions [11-13]. intermolecular free path length. C12 and C44) and TOEC (C111. we have also evaluated second and third order elastic constants. elastic anisotropy.TiN along <100>. acoustic coupling constants. adiabatic compressibility. acoustic impedance. From Table 1. [4]. The value of C12 is approximately 10 times less while value of C44 is approximately 5 times less than those obtained by others [4. Wada’s constant. adiabatic compressibility. van der Waal’s constant are of the same order as obtained for solids. The order of achieved SOEC is same as obtained by other investigators [16-20]. molar volume. 16-20]. Rao’s constant. elastic anisotropy. molar volume. and C44) are presented in Table 1 with available comparative experimental and theoretical values. Rao’s constant. The third order elastic constants are presented in Table 2. CONCLUSION On the basis of above discussion. intermolecular free path length. [4] used tight binding model. C12. intermolecular free path length. we conclude the following points: 184 | P a g e . Other physical parameter like bulk modulus. elastic anisotropy. The obtained values of C11. shows that the TiN has better mechanical strength than TiC.RESULTS AND DISCUSSION Evaluated Second order elastic constants (C11. Nguyen Manh used ab-initio calculation method [4] and Weber used phenomenological model theory. Results of various investigators are different because of they used different theoretical approach. TiN is more appropriate for general purpose. Table 1 depicts that the higher value of C11 for TiN. Ultrasonic attenuation values of TiN are less than those of TiC. C12 and C44 are good. The physical constants like bulk modulus. Hence TiN is more ductile than TiC. C12 and C44 are less because we have taken approximation upto second nearest neighbor. The obtained results are summary of various parameters involved during computing approaches. it is known that agreement between theoretical/experimental data of TiC and TiN for C11. Our results for C11 is very similar as Tan et al. The thermal relaxation time is of the order of the picosecond as expected for other NaCl-type materials []. For example Tan et al. The obtained values of wave velocities are in good agreement with other refractory materials and are comparable with literature [12-13]. while approximately half as ab-initio calculation [4] and experimental [16]. Wada’s constant. The ultrasonic attenuation due to phonon-phonon interaction is predominant over total attenuation. acoustic impedance. van der Waal’s constant were also evaluated by means of second order elastic constants and are presented in Table 3. On the basis of ultrasonic attenuation values of these materials. Eng. Tan. 133 (1964) 41611. C: Solid State Physics. G. Mayer. “Effect of platinum addition in coinage metals on its ultrasonic properties”. Z. Mat. A. Horsfield. The natures of ultrasonic velocities are found satisfactory. 3. Singh and P. 6. J. Born and J. Yadav. Acoust. Bretkovsky.1. “Carbon vacancies in titanium carbide”. E. appropriate and useful for its characterization and industrial applications. 5(1997) 187198. Pintschovius. Modelling Simul. Tiwari and D. K. Zhukov. A. P. Keith. 7. J. Scheerer. R. E. 54 (2010) 169–176. A. Sc. 150 (1958) 497. A. 1994. “Thermodynamic definition of higher order elastic coefficients”. 185 | P a g e . “Electronic Structure of Refractory Carbides and Nitrides”. 109(3) (2001) 1213. REFERENCES 1. Leibfried and H. D. D. M. R. L. we can say TiN is more ductile. Pettifort and A. Sutton. Obtained results of present investigation correlated with other physical parameters are applicable for further investigation. 2. K. Phys. Cambridge University Press. “Lattice dynamics of TiC”. V. but Coulomb and Born-Mayer potential is more appropriate to find out elastic constant of NaCl-type. 8. J. M.. A. Harris. D. Haln. Platinum Metals Rev. Soc. 75 (1931) 1. P. R. “Effect of pressure on ultrasonic attenuation in Ce monopnictides at low temperature”. Singh. Phys. Nguyen Manh. “A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone”. Z-Phys. The order of thermal relaxation time is found the order of the picoseconds. K. P. “Zur Gittertheorie der Ionen Kristalle”. Mat. Sc. 2. Although several potentials are available to evaluate elastic constants like Pseudo potential. 3. 5. 9. G. Cambridge. 11(1978) 1557-1562. 4. “Zur temperaturabhangigkeit der elastischen konstantaaen von alhalihalogenidkristallen”. Rev. M. Gubanov. Brugger. Morse-potential and Lenard-Jones potential. Am. 40(2005) 5319-5321. A. Phys. K. L. TiC and TiN as we found satisfactory results of SOEC and TOEC in present investigation. Ivanovsky and V. Yadawa. W Reichardt and B. Solid State Physics. 8(11) (1973) 5082-92. Phys. Tenchent and A.144 0. G.15 1. “An investigation of ultrasonic properties of NpX (X: S. N. Chang.Akhieser. On the absorption of ultrasound. Appl.(Moscow)1 (1939) 277-287. Phys. Sahu. 16.metal nitrides: TiN”. Ludwig. “Theoretical study of the elastic properties of titanium nitride”. Res.. Maosheng and H.83 [18] 5. W. L.Se and Te)”. Z.044 0. Chen. “Calculation of the third and fourth order elastic constant of alkali-halides”. B. 37 (1996) 3778. 17. D. “Phonon anomalies in transition.10. 12 (1964) 275. Hiki. 19. 18. “Behaviour of acoustic attenuation in rare earth chalcogenides”. Rev. S. Sci (Engl. Chen.0 1. Roedhammer. Rev. 20. Singh. J. W. Weber.383 Present work 6.287 186 | P a g e 5. J. TABLE 1. 15(5) (2001) 577-582. Jpn.Phys.06 1. Elastic Constants TiC TiC TiC C11 (x 1011 N m-2) C12 (x 1011 N m-2) C44 (x 1011 N m-2) Elastic Constants TiN TiN C11 (x 1011 N m-2) C12 (x 1011 N m-2) Present work 3. 45 (1978) 1449-1456. Kress. Phil Thesis submitted to Bundelkhand University. Grahm. S. Singh and D. Soc. Phys. 13.77 1. Christensen. Phys.978 1.594 1. “Theory of Anharmonic effect in cryatal”.1 1. Lett. Acta. Compared results of Second order elastic constants (SOEC) of TiC and TiN. 14. Y. K. M. J.) 22(2) (2009). Chem.79 [19] 4. Shi. E. J. Yu. 15. Jhansi.978 1. J. B. Z. Mori and Y. B 17 (1978) 111.125 Experiment [16] 5. Ming. 115 (2009) 65-68. R. Braz.8 [4] [19] . K. Chin. H.26 0. 12. 11.13 2. Metall. A. P. Pandey. Wang and D. W. C.19 [20] 4. Phys. 2009. Jiawen. Phys.14 0. D. Bilz. J. Leibfried and W. J. (Communicated). Mat.1 ab initio [4] 6. D. Zhao.07 1.056 3. Mat. 876 8. Material TiC (x 1010 Nm-2) TiN (x 1010 Nm-2) C111 -614.279 C123 -3.572 1.132 2.544 2.99 C112 -7.83 C456 7.266 1.53 -30.23 -152.74 9.99 <110> Vl (x 105 cm/sec) 187 | P a g e .474 5.5 -13.206 1.813 0.681 1.99 2.46 C144 7.54 2.67 3.62 C166 -14.79 3.028 4. Material <100> TiC Vl (x 105 cm/sec) Vs (x 105 cm/sec) V (x 105 cm/sec) τth(x 10-12 cm) 7. Debye average velocity (V) and thermal relaxation time (τth) of TiC and TiN at room temperature.834 7.19 7.349 11.007 TABLE 4.676 11.214 2.TiN C44 (x 1011 N m-2) 0. Calculated ultrasonic parameters at room temperature Parameters Bulk modulus (x 1010 Nm-2) Elastic anisotropy Acoustic impedance (x 107 Kg m-2 s-1) Adiabatic compressibility (x 10-11 m Kg-1 s2) Molar volume (x10-5 m3 mol-1) Intermolecular free path length (x 10-14 m) Rao’s constant (x 102) Wada’s constant (x 102) Van der Waal constant (x 10-6 m3 mol-1) TiC 12.440 6.12 7.069 1. Longitudinal and Shear velocities (Vl and Vs).6 TABLE 3.849 2.51 TiN 10.65 5.131 5.760 7. Third order elastic constants (TOEC) are given below.392 1.681 TABLE 2.213 0.741 TiN 20.496 0. Vs1 (x 105 cm/sec) Vs2 (x 105 cm/sec) 2.24 <111> Vl (x 105 cm/sec) Vs (x 105 cm/sec) TABLE 5: Ultrasonic attenuation {(α/f2)long.2090 ♣=shear wave polarized along <100>.2252 0.79 7.9319 0.8250 0.1376 0.93 4. (α/f2)shear and (α/f2)th} of TiC and TiN at room temperature.46 6.67 10. # = shear wave polarized along <001>.0113 0.1441 0.3733 0.0632 0. $= shear wave polarized along and *= shear wave polarized along 188 | P a g e .65 5.7 2.2809 0.4706 0.9234 0.0134 0.2839 0.6941 0.0779 1.2179 0. Material <100> ♣ (α/f2)l (10-17Nps2/cm) (α/f2)s1 (10-17Nps2/cm) (α/f2)th (10-17Nps2/cm) Total <110> # $ (α/f2)l (10-17Nps2/cm) (α/f2)s2 (10-17Nps2/cm) (α/f2)s3 (10-17Nps2/cm) (α/f2)th (10-17Nps2/cm) Total <111> * (α/f2)l (10-17Nps2/cm) (α/f2)s4 (10-17Nps2/cm) (α/f2)th (10-17Nps2/cm) Total TiC 0.9989 0.5830 0..4743 0.92 6.5918 0.0520 0.0516 0.0406 1.0716 0.3735 TiN 0. India *Tel: +91-11-2806-2106/1487. ZnSe. specific heat. ZnSe. Introduction It is well known that II-VI semiconductor compounds have a large optical gap. We have developed a computer program to compute the elastic constants. Ultrasonic properties. Bijwasan.and third. Technological and theoretical interest in II-VI compound and their alloys is due to its appealing properties in electro-optical and electron acoustic devices [2-4]. in recent years. Actually. ZnTe and CdTe at room temperature.Ultrasonic wave propagation in II-VI hexagonal semiconductor compounds Pramod Kumar Yadawa* and Devraj Singh Department of Applied Physics. such as ZnS. may expand future prospects for the applications and study of these materials. Ultrasonic attenuation is very important physical parameter to characterize the material. AMITY School of Engineering and Technology.amity. these materials have been used as catalysts when studying photochemical reactions [6].edu ABSTRACT The paper presents a comprehensive computation of second. which is well related to several physical quantities like thermal conductivity. ZnTe and CdTe.order elastic constants and then velocities and attenuation of ultrasonic waves along unique direction in hexagonal II-VI group semiconducting materials like ZnS. Thermal conductivity. The 189 | P a g e . [1]. appear to be rather promising for applications in optical devices. Obtained results. but the feasibility of green-blue opto-electronic devices based on these materials has been demonstrated by Hasse et al. especially between the top of the valence band and the bottom of the conduction band at the Γ point. The comparison of our computed results has been made with available theoretical and experiment results. ultrasonic velocities and ultrasonic attenuation in C++ language. Due to the possibility of intense photoexcitation. Due to their wide direct band gap. The value of ultrasonic attenuation of ZnS is smallest in comparison to other chosen materials. Keywords: Semiconductors.wavelength radiation range from red to ultra-violet [5]. So ZnS is more ductile and more pure than the others. Elastic properties. Fax: +91-11-28061821 *E-mail: pkyadawa@aset. 1. their technological potential is very great. In addition to their use in optical devices operating in the short. the electronic properties of II-VI semiconductors. thermal energy density and higher order elastic constants [8]. New Delhi-110 061. they are used in solar cells [7]. together with other well known physical properties. .464 p B = 101. ∂e I ∂e J I or J = 1..168 p 2 B − 1..464 p 8 C ′ C66 = 9.9 p 2 B + 8..6 ∂e I ∂e J ∂e K where. y.6 (1) (2) C IJK = ∂ 3U . THEORY In the present investigation.924 p 4 B + 1. …6) is component of strain tensor.. I or J or K = 1.539 p 4 B 4 6 = 2.851 p 4 C ′ (3a) C111 = 126.007 p 4 C ′ C 333 = 5.695 p 6 B C155 = 1.. acoustic coupling constants.196 p 8 B (3b) 190 | P a g e . C IJ = ∂ 2U . The ultrasonic attenuation coefficient.309 p B C 344 = 3. I=1. in this work we predict the ultrasonic properties of hexagonal structured semiconductor compounds at room temperature.elastic constants provide valuable information about the bonding characteristic between adjacent atomic planes and the anisotropic character of the bonding and structural stability [9. 10]... U is elastic energy density .309 p 4 C ′ C12 = 5. higher order elastic constants. Therefore.1 Second-and third order Elastic constants The second (CIJ) and third (CIJK) order elastic constants of material are defined by following expressions. The obtained results are analyzed in comparison to other hexagonal structured materials. Eqs (1) and (2) leads six second and ten third order elastic constants (SOEC and TOEC) for the hexagonal close packed structure materials [8. eI=eij (i or j = x. C11 = 24.039 p 2 B + 9. The calculated ultrasonic parameters are discussed with related thermophysical properties for the characterization of the chosen semiconductors..617 p 4 B − 1. 2.918 p 4 C ′ C 33 = 3. 11]. thermal relaxation time and ultrasonic wave velocities for these semiconductors for unique direction of propagation of wave are calculated at 300K.155 p 6 C ′ C123 = 1.61 p 4 C ′ = 1. the theory is divided into two parts: 2.155 p 6 C ′ = 3. z...853 p 4 C ′ C113 C133 C144 C 222 C112 = 19..1 p 4 C ′ C13 = 1.925 p 6 C ′ C 44 = 2. 10. 2 Ultrasonic attenuation and allied Parameters The predominant causes for the ultrasonic attenuation in a solid at room temperature are phononphonon interaction (Akhieser loss) and thermoelastic relaxation mechanisms. m. The time for re-establishment of equilibrium of the thermal phonon distribution is called thermal relaxation time (τ) and is given by following expression: 2 τ = τ S = τ L / 2 = 3 k / C V VD ( ) (6) Here τL and τS are the thermal relaxation time for longitudinal and shear wave. D = 3 3E 0 < (γ ij ) 2 > − < γ ij > 2 C V T / E 0 is known as acoustic coupling constant. f: frequency of the ultrasonic wave. The Grüneisen number for hexagonal structured crystal along <001> orientation or θ=00 is direct consequence of second and third order elastic constants. Results and discussion 3. B = ψ a 3 / p3 . γ i j : Grüneisen number (i. which is the measure of acoustic energy converted to thermal energy. VS2) velocities. The expressions for ultrasonic velocities are given in our previous papers [11. b0=Lennard Jones parameter. When the ultrasonic wave propagates through crystalline material. C ′ = χ a / p 5 .1 Higher order elastic constants 191 | P a g e . (A /f2)Akh = 4π 2 3E 0 < (γ ij ) 2 > − < γ ij > 2 C V T τ / 2 ρ V 3 5 = 4 π 2 < γ ij > 2 kT / 2ρVL ( ) (4) (5) (A /f2)Th where.where p = c/a: axial ratio. 3. 12]. 12]: where ρ and θ are the density of the material and angle with the unique axis of the crystal respectively. χ = (1 / 8)[{nb 0 (n − m)}/{ a n + 4 }] ψ = − χ /{6 a 2 ( m + n + 6)} . The ultrasonic attenuation coefficient (A)Akh due to phonon-phonon interaction and thermoelastic relaxation mechanisms is given by the following expression [11. E0: thermal energy density. The ultrasonic velocities have been used for the calculation of ultrasonic attenuation and allied parameters in the chosen materials. j are the mode and direction of propagation). 2. the equilibrium of phonon distribution is disturbed. The Debye average velocity (VD) is well related to longitudinal (VL) and shear wave (VS1. k and CV are the thermal conductivity and specific heat per unit volume of the material respectively. VL: longitudinal ultrasonic velocity. n=integer quantity. V: ultrasonic velocity for longitudinal and shear wave. 508 5.10 -5.33 4.249 3.638 3.50 -6. the second order elastic constants are used for the determination of the ultrasonic attenuation and related parameters.151 11.78 -37.631. 1.643 10.366 2.015 9.54 -7.65 9.46 3. Second and third order elastic constants (SOEC and TOEC) & bulk modulus (B) in the unit of 1010Nm-2 of materials at room temperature.54 13.83 -4. The values of b0 for these materials are 7.02 1.570 14.31 C155 -7.42 B 6. C11 ZnS ZnSe ZnTe CdTe ZnS[12] ZnSe[14] ZnTe[15] CdTe[15] C111 ZnS ZnSe ZnTe CdTe -222.659 2.5 0K and 225.571 3. Also.22 C113 -7.731 6. 4.50 C12 3.13 2.The unit cell parameters ‘a’ (basal plane parameter) and ‘p’ (axial ratio) for ZnS. (3) and are presented in Table 1. 14.53 3. Table1.3 0K respectively.2x10-64 erg cm7.43 1.30 C112 -35.0x10-64 erg cm7 respectively.74 -7. It is obvious from Table 1 that.03 -139.60 -142. The SOEC and TOEC have been calculated for these materials using Eq. The value of m and n for chosen materials are 6 and 7.59 10.89 C344 -44.639.830 8.351 2. 14.509 -5.58Å and 1.301 1.73 -3. the comparison can be made with the value of Debye temperature of ZnSe and ZnTe.396 13.650 5.80 C44 3.46 C222 -176.88 -28.90 -4.65 -82.00 11.013 6. calculated using second order elastic constants.72 8.16 C144 -11.79 -3. 9.70 3.13 3.56 -139.53 C333 -180.71 -83. 4.635 [13] respectively.45 C13 2. 4.21 -30.18 -114.26 6. 1.91 3.54 -20. since they are related to hardness and therefore of interest in applications where mechanical strength and durability are important.59 C123 -9. 15].760 2.44 -22. ZnTe and CdTe are 3.927 2.49 2.424 2. ZnSe.350 4.869 1.244 4.12 -8. 1.4 0K respectively.144 1.41 -5.73 -112.2x10-64 erg cm7.37 -104.00 2.637. there is good agreement between the present and reported theoretical and experimental second order elastic constants of these semiconducting materials [12.28Å. The present value of Debye temperature for ZnSe and ZnTe are 269.19 C66 5.09 -4.56 6.50 2.81 -34. Thus our theoretical approach for the calculation of second order elastic 192 | P a g e .83Å.91 C133 -47.247 3.57 -16.9 0K and 218. The Debye temperature experimentally determined by Lee [14] are 278.47 -176.107 The elastic constants of the material are important. Also.19 C33 14.242 1.27 -27.0x10-64 erg cm7 and 20.02Å.99 -22.511 2. laves-phase compounds and other hexagonal wurtzite structured materials [8. The value of CV and E0 are evaluated using tables of physical constants and Debye temperature. Table 3: Comparative velocities (in 103 m/s) of hcp semiconductor materials. 11.2.876 0.977 0.92 1.710 0. 12.31 54. The combined effect of SOEC and density is reason for abnormal behaviour of angle dependent velocities. thermal conductivity (k: in Wm-1K-1) and acoustic coupling constant (DL. The thermal conductivity k and calculated acoustic coupling constants (DL & DS) are presented in Table 2. 16-18]. 193 | P a g e . Table 2: Density (ρ: in 103 kg m-3). The chosen semiconductors have shown similar properties with their crystal structure. 11.0 11.27 1.636 5. The nature of the angle dependent velocity curves in the present work is found similar as that for heavy rare-earth metals. CV 0.17 1.849 DS 1.09 5.46 k 27.constants for hexagonal structured materials at room temperature is well justified.0 6. The bulk modulus (B) for these alloys can be calculated with the formula B= 2(C11+ C12+ 2C13 + C33/2)/9. 3.72 54. Hence applied theory for the evaluation of higher order elastic constants at room temperature is justified. The comparative study of ultrasonic velocities is presented in Table. Ultrasonic velocity and allied parameters The density and thermal conductivity at room temperature have been taken from the literature. However.262 5.24 1. DS) of hcp semiconductor materials.65 1. 16-18]. 12.76 54. Figs 1–3 show that the velocities VL and VS1 have minima and maxima respectively at 45° with the unique axis of the crystal while VS2 increases with the angle from the unique axis.21 The computed orientation dependent ultrasonic wave velocities and Debye average velocities at 300 K are shown in Figs 1–4. thermal energy density (E0: in 108Jm-3).0 19.91 1.0 DL 53.600 E0 1.58 ρ ZnS ZnSe ZnTe CdTe 4. specific heat per unit volume (CV: in 106Jm-3K-1). third order elastic constants are not compared due to lack of data in the literature but the negative third order elastic constants are found our previous papers for hcp structure materials [8. The evaluated B for these alloys is presented in Table 1. 3. Ultrasonic attenuation due to phonon-phonon interaction and thermal relaxation phenomena In the evaluation of ultrasonic attenuation. VD of these materials are increasing with the angle and have maxima at 55° at 300 K (Fig.78 4.93 Hence values of velocities are in good agreement with experimental/theoretical values. The angle dependent thermal 2 relaxation time curves follow the reciprocal nature of VD as τ ∝ 3K / C V VD . therefore the angle variation of VD is influenced by the constituent ultrasonic velocities.45 2. VS1 and VS2 [8. it is supposed that wave is propagating along the unique axis [<001> direction] of these materials.00 3. The calculated thermal relaxation time is visualised in Fig.Velocity Present work theoretical Carl et al. Hence the calculated τ justifies the hcp structure of chosen materials at room temperature.99 2. shear long. Thus the present average sound velocity directly correlates with the Debye temperature.[21] theoretical ZnS ZnSe ZnTe CdTe long. 12].67 5.65 5. The τ for hexagonal structured materials is the order of pico second [18]. Thus it can be concluded that when a sound wave travels at 55° with the unique axis of these crystals then the average sound wave velocity is maximum.49 3.58 2.[20] experimental Bijalwan et al. The maximum VD at 55° is due to a significant increase in longitudinal and pure shear (VS2) wave velocities and a decrease in quasi-shear (VS1) wave velocity.25 2. 4). This implies that τ for chosen materials are mainly affected by the thermal conductivity.3.47 2. 3.93 4. The minimum τ for wave propagation along θ = 550 implies that the re-establishment time for the equilibrium distribution of thermal phonons will be minimum for propagation of wave along this direction. shear long.51 2.57 2. shear long. The attenuation coefficient over frequency square (A/f2)Akh for longitudinal (A/f2)L and shear wave (A/f2)S are calculated using Eq. Since VD is calculated using VL.74 3.[19] experimental Kim et al.29 3.35 1. shear 5.88 2. 5.83 3. specific heat and thermal energy density of theses materials. Thus the angle dependencies of the velocities in these materials are justified.92 6. (4) under the condition ωτ<<1 at room 194 | P a g e . Alloys (A/f2)Th (A/f2)L (A/f2)s (A/f2)Total ZnS 0.138 24.180 678. Table 4: Ultrasonic attenuation coefficient (in 10-17 Np s2 m-1) of hcp semiconductor materials. (A/f2)S. This reveals that ultrasonic attenuation due to phonon-phonon interaction along longitudinal wave is governing factor for total attenuation ((A/f2)Total =(A/f2)Th+(A/f2)L+(A/f2)S).288 907. Thus it may predict that at 300K the ZnS behaves as its purest form and is more ductile as evinced by minimum attenuation while CdTe is least ductile.930x10-17 Nps2m-1 and InN: 20. The values of (A/f2)L. (5). The thermoelastic loss over frequency square (A/f2)Th is calculated with the Eq. The total attenuation is mainly affected by thermal energy density and thermal conductivity.617 74.663 ZnSe 0.441x10-17 Nps2m-1.223 597.539x10-17 Nps2m-1) due to their large thermal conductivity and acoustic coupling constants [18. GaN: 14. we conclude following points: 195 | P a g e .596 Table 4 indicates that the thermoelastic loss is very small in comparison to Akhieser loss and ultrasonic attenuation for longitudinal wave (A/f2)L is greater than that of shear wave (A/f2)S. 4.691 832.698 ZnTe 0. 22]. (A/f2)Th and total attenuation (A/f2)Total are presented in Table 4. The total attenuation of these compounds are much larger than third group nitrides (AlN: 4.918 CdTe 0.543 621.738 57. This implies that the interaction between acoustical phonon and quanta of lattice vibration for these alloys is large in comparison to third group nitrides.temperature. Conclusions On the basis of above discussion.962 42.266 254.259 278. The minimum ultrasonic attenuation for ZnS justifies its quite stable hcp structure state. Since A ∝ V −3 and velocity is the largest for ZnS among CdTe thus the attenuation A should be smallest and material should be most ductile. Therefore impurity will be least in the ZnS at room temperature.513 554. P. Sol. Photobiol. 196 | P a g e . Strand. The mechanical properties of ZnS are better than those of CdTe. Appl. Yadav. Mater. M. Cleveland. Yao. [7] H. A. Phys. J. W. Lett.• • Our theory of higher order elastic constants is justified for the hexagonal structured materials. Our theoretical approach is valid for ultrasonic characterization of these alloys at room temperature. The order of thermal relaxation time for these materials is found in picoseconds. Qiu. Weber (Ed). L. M. Yadawa. Haase. X. Vac. M. K. Pandey. J. which justifies their hcp structure at 300K. J. Cheng. The acoustic coupling constant of these materials for longitudinal wave are found five times larger than third group nitrides. Y. These results. Ono. D. A 74 (1993) 85. Cheng. Louail. [10] L. 84 (1998) 4891. DePuydt. D. may expand future prospects for the application and study of these materials. T. Appl. H. 59 (1991) 3228 [4] M. [9] P. The Open Acoustic Journal 2 (2009) 80.III. Hasse. F. together with other well-known physical properties. References [1] M. O. [8] P. The re-establishment time for the equilibrium distribution of thermal phonons will be minimum for the wave propagation along θ = 550 due to being smallest value of τ along this direction. H. The ultrasonic behavior in these semiconductor materials as discussed above shows important microstructural characteristic feature. The ultrasonic attenuation due to phonon-phonon interaction mechanism is predominant over total attenuation as a governing factor thermal conductivity. Fast. Gu. A 7 (1989) 2975. D. Chen. A. Ravindran. Bagnall.A. K. Roumili. 70 (1997) 2230. Maouche. Soc. Appl. [2] M. Appl. Lett. K. Shock. Photochem. This shows general suitability of chosen materials. Technol. 1986. CRC Press. B. J. T. Handbook of Laser Science and Technology. Chen. A. [6] L. Vol. M. Cells 34 (1994) 19. R. Korzhavyi. Wills. Lett. A. Hence the conversion of acoustic energy into thermal energy will be large for these materials. J. Phys. Lett. J. Johansson. [5] D. Phys. Ali Sahraoui. Zhu. which are well connected to thermoelectric properties of the materials. Sci. [3] M. Matsuoka. DePuydt. general and industrial applications. • • • Thus obtained results in the present work can be used for further investigations. K. Singh. Energy Mater. because CdTe has low elastic constants and ultrasonic velocities. Misemer. 58 (2004) 2975. Phys. D. R. 59 (1991) 1272. J. F. J. Eriksson. W. [19] F. Kwun. Pandey. 53 (2009) 91. Mat. H. J. Singh. Yadav. Lett. 61 (2007) 5194. D. J. Pandey. 38 (4) (1967) 1944. Appl. N. V. Yadav. R. H. Zubkova. Lee. Yadav. D. J. R. K. Pandey. 61 (2007) 4747. Bijalwan. Semiconductors. S. N. Phys. K. Rev. Singh. Pandey. R. [16] D. [21] R. D. Mat. 62 (2008) 3258. Glenn. P. [13] T.4: VD vs angle with unique axis of crystal Fig. M. Rev. B 6 (1972) 4546. A. P. C. V. [17] D. 41 (2007) 886. [22] Landolt-Bornstein. J. Phys. D.. I. P. Yadav. [18] D. K. Yoon. K.[11] A. [15] R. Figure Captions: Fig. B 61 (9) (2000) 6036. D. L. K. R.3: VS2 vs angle with unique axis of crystal Fig. K. Mat. Yadav. Rusina. R. K. [14] B. Numerical Data and Function Relationship in Science and Technology. Yadawa. M. Carl. 11. Gorkavenko.1: VL vs angle with unique axis of crystal Fig. 16 (1983) 2537. Plat. [12] D.. G. Ram. Yadawa. R. P. Pandey. Phys. [20] E. Rev. M. Group III Vol. Harold. W. R. Met. Phys. K. K. S. H. Lee. Singh.5: Relaxation time vs angle with unique axis of crystal 197 | P a g e . D. Kim. R. C: Solid State Phys. Lett. Seo. Phys. D. 68 (2007) 766. Lett. Makara. Bellin Springer 1979. P. L. K.2: VS1 vs angle with unique axis of crystal Fig.K. Martin. Yadawa. 41 (1970) 2984. M. Appl. S. Acoust. Appl. Tiwari. 1.5 3 0 10 20 30 40 angle 50 60 70 80 90 Fig.6 5.5 ZnSe CdTe V L(103 m/sec) 5 4 3. 4 V S1(103 m/sec) 3 2 ZnS ZnTe 1 0 10 20 30 40 angle 50 60 70 80 90 ZnSe CdTe Fig. 198 | P a g e .2.5 ZnS ZnTe 4. 4.5 2 ZnS ZnTe 1.ZnS 3.5 1.5 0 10 20 30 40 50 60 70 80 90 angle ZnSe CdTe Fig. 4 3.5 3 V D(103 m/sec) 2.5 ZnTe ZnSe CdTe V S2(103 m/sec) 2. 199 | P a g e .5 0 10 20 30 40 angle 50 60 70 80 90 Fig.3. 5.11 10 ZnS ZnTe ZnSe CdTe Relax time (10-12s) 9 8 7 6 5 0 10 20 30 40 50 60 70 80 90 angle Fig. 200 | P a g e . Sound Velocity and Density.K. From the measured values of density and sound velocity. sodiumdodecyl sulfate (SDS) in aqueous solutions has been investigated with the help of density and sound velocity measurements at different temperatures (15.surfactant formulations are used extensively in industrial. CHAUHAN. Himachal Pradesh University. SDS.SOUND VELOCITY AND DENSITY STUDIES TO FIND THE EFFECT OF PEG ON AQUEOUS ANIONIC SURFACTANT (SDS) S. KEYWORDS: PEG. In the present work. Gurgaon-122018 ABSTRACT Polymer. Maruti Kunj. 20. a synthetic polymer. Intermolecular free length (Lf). pharmaceutical and cosmetic applications.S. KIIT College of Engineering. emulsification or solublization properties of the system under investigation. The versatility in such systems is achieved owing to the reason that polymer– surfactant interactions influence the behaviour of solution significantly and also these interactions can be modified to get the enhanced desired benefits. Interaction.A. Interactions of surfactant with polymer have been found to indicate the binding of surfactant with the polymer molecule at lower concentration followed by the usual micellization at higher concentration of surfactant. Shimla-171005.e. R. 30 and 35oC). the effect of Polyethylene glycol (PEG-6000).) have been calculated and their variations with different concentrations of PEG and SDS have been discussed. Molar sound velocity (Rm) and Relative association (R. Specific acoustic impedance (Z). And V. polymers are often added to control the rheology of the solution whereas surfactants can cause alterations in wettability. INTRODUCTION Ultrasonic velocity offers a rapid and nondestructive method for characterisation of materials and serves as a powerful. 25.In continuation with our 201 | P a g e . e.g. THAKUR and DEEPIKA KAUSHAL Department of Chemistry. the acoustical parameters namely. effective and reliable tool to investigate properties of polymer solutions. therefore.SYAL. on anionic surfactant i. R grade) from s. The values of R.in binary mixtures of DMSO-H2O system at 25oC.A. In case of carbohydrates (fructose and maltose) also.d.polymer interactions.surfactant interactions. in this paper. 202 | P a g e . Polyethylene Glycol (PEG) molecular weight 6000 (L. At 1% PEG.This difference in behaviour of Rm clearly shows that at lower concentration of PEG. 5. doubly distilled water of conductivity in the range <1-2 X10-7 Scm-1 was used in all sample preparation. however. the marked difference in the of plots reflect that the PEG concentration is also playing important role.surfactant interactions dominate and at higher concentration of PEG.A. polymer-polymer interactions prevail.The variation of Rm plots remains same at different temperatures studied. RESULTS AND DISCUSSIONS Density (d) and sound velocity (v) for surfactant SDS in the concentration range (1-15 mmol dm-3) have been measured in aqueous solutions of 1. The variation of Rm is non-linear at all concentrations of PEG. Densities and sound velocities were measured from Density and Sound Velocity Analyzer (DSA-5000) supplied by Anton Paar Gmbh. PEG. Graz. Austria which measures the speed and density of the solution simultaneously with a resolution of 1×10−1 ms−1 and 1×10−6 gcm−3 respectively and was thermostated with in ±0. However. At 5% PEG solution with [SDS]. The variation of R. the Rm value increases initially up to 4mmol [SDS] after which no effect of [SDS] is observed. after which the Rm value remains almost constant.A with SDS concentration as well as temperature is shown in [Fig 3]. values show a regular increase indicating considerable solute-solvent interactions [5]. 10 % w/v PEG over wide range (15-35oC) at interval of 5oC. EXPERIMENTAL Sodium dodecyl sulfate (Biochemical grade from BDH) was further purified as suggested in literature [4]. fine.002°C with Peltier heating device. however. This increase is again due to the fact that the polymer-SDS interactions dominate over polymer. at 10% PEG. the nature of graph shows no regular trend.previous work on polymers [1-3]. The Density (d) and sound velocity (v) data has been reported in Table 1-2. the R.Chem private limited was used for this study.we report various acoustical parameters for PEG-SDS system in order to explore polymer. there is decrease in Rm values up to 5mmol [SDS] and then occurs a significant hump in 6-10 mmol [SDS]. remain close to unity and show slight increase with the increase of [SDS] content in mixtures. However,on comparing the behaviour of R.A. at different PEG concentrations, a marked non-linear behaviour seems to be quite significant at 6-10mmol [SDS] at 1% PEG. This may be taken as a region of maximum structural changes which may involve micellization to greatest extent. In fact, PEG offers hydrophobic carbon moiety on which micellization of SDS seems to be facilitated and it seems true also as maximum such structural changes are significant in [SDS] range of 6-10 mmol as reflected by Rm and R.A. values at 1% PEG. At higher PEG concentration polymer-polymer interactions dominate. The variation of Lf with SDS concentration as well as temperature is shown in [Fig2]. From these plots, it is observed that Lf decreases regularly with concentration of surfactant but varies in magnitude with temperature. This kind of trend is similar to the behaviour of polymers PEG in AN- H2O mixtures [1] and polyvinylpyrrolidone in DMSO-H2O system at 25oC [2]. The variation of Z with SDS concentration as well as temperature is shown in [Fig4]. In the plots of Specific acoustic impedance (Z) w.r.t SDS concentration, it is observed that Z is also almost independent of concentration of surfactant but its magnitude increases with increase in temperature and also with concentration of PEG solution. All these parameters collectively show extent of solute- solvent interaction. REFERENCES 1. V.K. SYAL, A. CHAUHAN and S. CHAUHAN ‘Ultrasonic velocity and density studies of poly (ethyleneglycols)(PEG-8,000, PEG-20,000) in acetonitrile (AN) and water (H2O) mixtures at 25oC.’ J. Pure Appl. Ultrason. 27, 2-3 (2005). 2. V.K. SYAL, A. CHAUHAN and S. CHAUHAN ‘A study on solutions of poly (vinylpyrrolidone) in binary mixtures of DMSO+H2O at different temperatures by ultrasonic velocity measurements.’ Indian J. Phys. 80 (4), 379-385 (2006). 3. V.K. SYAL, A. CHAUHAN, POONAM SHARMA and S. CHAUHAN ‘Ultrasonic velocity and density studies on solutions of Poly(vinylalcohol) (PVA) in binary mixtures of dimethylesulphoxide (DMSO) + water (H2O) mixtures at 25oC.’ J. Polym. Mater. 22 363-368 (2005). 4. S. CHAUHAN, M.S. CHAUHAN, J.JYOTI and RAJNI ‘Acoustic and viscosity studies of sodium dodecyl sulfate in aqueous solutions of gelatin’ Journal of molecular liquids 148, 24-28 (2009). 5. V.K. SYAL, S. CHAUHAN and R.GAUTAM ‘Ultrasonic velocity measurements of carbohydrates in binary mixtures of DMSO + H2O) mixtures at 25oC’Ultrasonics 36, 619-623(1998). 203 | P a g e Table 1 Density d (g cm-3) for SDS in various aqueous PEG solutions at different temperatures. (ToC) [SDS] ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------(mmol dm-3) 15 20 25 30 35 15 20 25 30 35 15 20 25 30 35 1% (w/v) PEG 5% (w/v) PEG 10% (w/v) PEG ----------------------------------------------------------------------- ----------------------------------------------------------------------- ---------------------------------------------------------------------------1 1.00089 0.99994 0.99874 0.99730 0.99564 1.00746 1.00636 1.00502 1.00345 1.00168 1.015006 1.013726 1.012219 1.010503 1.008597 2 1.00094 0.99999 0.99879 0.99734 0.99569 1.00750 1.00640 1.00506 1.00349 1.00172 1.015105 1.013828 1.012317 1.010595 1.008685 3 1.00100 1.00005 0.99884 0.99740 0.99574 1.00754 1.00644 1.00510 1.00353 1.00176 1.015171 1.013884 1.012372 1.010652 1.008733 4 1.00105 1.00010 0.99889 0.99744 0.99579 1.00750 1.00640 1.00506 1.00349 1.00172 1.015172 1.013883 1.012369 1.010648 1.008735 5 1.00110 1.00015 0.99894 0.99749 0.99583 1.00762 1.00651 1.00516 1.00360 1.00182 1.015280 1.013989 1.012472 1.010749 1.008832 6 1.00117 1.00021 0.99899 0.99755 0.99589 1.00767 1.00656 1.00521 1.00364 1.00187 1.015230 1.013941 1.012424 1.010702 1.008788 7 1.00116 1.00019 0.99898 0.99753 0.99587 1.00771 1.00661 1.00525 1.00368 1.00191 1.015319 1.014028 1.012511 1.010786 1.008870 8 1.00120 1.00024 0.99902 0.99757 0.99590 1.00780 1.00669 1.00533 1.00376 1.00198 1.015348 1.014055 1.012536 1.010811 1.008895 9 1.00126 1.00030 0.99908 0.99763 0.99596 1.00781 1.00669 1.00534 1.00377 1.00199 1.015457 1.014162 1.012640 1.010913 1.008993 10 1.00139 1.00043 0.99921 0.99776 0.99610 1.00781 1.00670 1.00535 1.00378 1.00200 1.015453 1.014152 1.012637 1.010908 1.008990 11 1.00144 1.00048 0.99925 0.99780 0.99614 1.00787 1.00675 1.00540 1.00382 1.00204 1.015503 1.014205 1.012684 1.010905 1.009034 12 1.00149 1.00052 0.99930 0.99785 0.99618 1.00790 1.00679 1.00543 1.00385 1.00207 1.015438 1.014140 1.012620 1.010892 1.008973 13 1.00154 1.00057 0.99935 0.99789 0.99623 1.00793 1.00682 1.00546 1.00388 1.00210 1.015522 1.014222 1.012698 1.010969 1.009049 14 1.00158 1.00061 0.99938 0.99793 0.99626 1.00802 1.00690 1.00554 1.00397 1.00218 1.015594 1.014295 1.012769 1.011038 1.009116 15 1.00162 1.00066 0.99943 0.99797 0.99630 1.00802 1.00690 1.00554 1.00396 1.00215 1.015613 1.014313 1.012788 1.011056 1.009133 Table 2 Sound velocity v (ms-1) for SDS in various aqueous solutions of PEG at different temperatures. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1472.85 1473.06 1473.30 1473.38 1473.44 1473.54 1473.72 1473.73 1473.66 1473.79 1473.73 1473.82 1473.78 1473.76 1473.71 1488.45 1488.70 1488.66 1488.91 1488.95 1489.06 1489.16 1489.15 1489.07 1489.28 1489.24 1489.21 1489.26 1489.22 1489.18 1502.22 1502.48 1502.48 1502.63 1502.65 1502.74 1502.79 1502.76 1502.64 1502.94 1502.90 1502.85 1502.89 1502.86 1502.81 1514.21 1514.40 1514.40 1514.52 1514.52 1514.64 1514.59 1514.57 1514.42 1514.78 1514.74 1514.70 1514.70 1514.66 1514.62 1524.48 1524.66 1524.66 1524.71 1524.72 1524.82 1524.76 1524.70 1524.55 1524.95 1524.88 1524.84 1524.85 1524.78 1524.51 1497.21 1497.23 1497.44 1497.23 1497.51 1497.52 1497.53 1497.76 1497.55 1497.55 1497.58 1497.48 1497.46 1497.52 1497.38 1510.97 1511.03 1511.10 1511.03 1511.22 1511.23 1511.25 1511.33 1511.20 1511.19 1511.22 1511.14 1511.06 1511.05 1511.01 1523.00 1523.06 1523.10 1523.06 1523.20 1523.19 1523.20 1523.28 1523.11 1523.10 1523.15 1523.06 1522.96 1522.95 1522.90 1533.33 1533.36 1533.37 1533.36 1533.45 1533.47 1533.47 1533.55 1533.33 1533.31 1533.35 1533.27 1533.15 1533.18 1533.09 1542.04 1542.07 1542.07 1542.07 1542.14 1542.13 1542.13 1542.20 1541.97 1541.96 1542.00 1541.90 1541.77 1541.77 1541.69 1526.33 1526.70 1526.74 1526.69 1526.97 1526.76 1526.87 1526.78 1526.93 1526.81 1526.86 1526.55 1526.59 1526.61 1526.61 1537.80 1538.03 1538.15 1538.08 1538.34 1538.11 1538.23 1538.11 1538.28 1538.04 1538.17 1537.86 1537.90 1537.91 1537.91 1547.69 1547.87 1547.97 1547.89 1548.15 1547.88 1548.00 1547.88 1548.06 1547.78 1547.90 1547.61 1547.63 1547.64 1547.64 1555.98 1556.14 1556.22 1556.13 1556.36 1556.09 1556.21 1556.08 1556.25 1555.98 1555.86 1555.79 1555.78 1555.80 1555.79 1562.82 1562.95 1563.00 1562.90 1563.13 1562.84 1562.96 1562.83 1562.97 1562.70 1562.78 1562.49 1562.51 1562.51 1562.49 204 | P a g e -0.20 -0.25 1% w/v PEG -0.4 -0.6 -0.8 15 C o 20 C o 25 C o 30 C o 35 C o 5 % w/v PEG -0.30 -0.35 Rm (m s ) -0.40 -0.45 -0.50 -0.55 -0.60 -0.65 -0.70 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 -1.0 -1.2 -1.4 Rm (m s ) -1.6 -1.8 -2.0 -2.2 -2.4 -2.6 -2.8 -3.0 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 -1 15 C o 20 C o 25 C o 30 C o 35 C o -1 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1.0 -1.1 0 2 4 10 % w/v PEG Rm (m s ) -1 15 C o 20 C o 25 C o 30 C o 35 C o 6 8 10 -3 [SDS] (mol dm ) 12 14 16 Fig 1. Molar sound velocity (Rm) (m s-1) for SDS in various aqueous PEG solutions at different temperatures. 205 | P a g e 1.0008 1% w/v PEG 1.0007 1.0006 1.0005 1.0004 RA 1.0003 1.0002 1.0001 1.0000 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 15 C o 20 C o 25 C o 30 C o 35 C o 1.0007 1.0006 1.0005 1.0004 RA 1.0003 1.0002 1.0001 1.0000 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 5 % w/v PEG 15 C o 20 C o 25 C o 30 C o 35 C o 1.0007 10 % w/v PEG 1.0006 1.0005 1.0004 RA 1.0003 1.0002 1.0001 1.0000 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 o 15 C o 20 C o 25 C o 30 C o 35 C Fig 2. Relative association (R.A.) for SDS in various aqueous PEG solutions at different temperatures. 206 | P a g e Specific acoustic impedance (Z) (kg m-2 s-1) for SDS in various aqueous PEG solutions at different temperatures 207 | P a g e .152000 1% w/v PEG 154400 154000 151000 153600 153200 Z (kg m-2 s-1) 5 % w/v PEG Z (kg m-2 s-1) 150000 152800 152400 152000 151600 151200 150800 15 C o 20 C o 25 C o 30 C o 35 C o 149000 148000 15 C o 20 C o 25 C o 30 C o 35 C o 147000 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 157600 157200 10 % w/v PEG 156800 Z (kg m s ) -1 -2 156400 156000 155600 15 C o 20 C o 25 C o 30 C o 35 C o 155200 154800 0 2 4 6 8 10 -3 [SDS] (mol dm ) 12 14 16 Fig 3. 33E-011 4.35E-011 15 C o 20 C o 25 C o 30 C o 35 C 4.22E-011 4.17E-011 4.26E-011 4.16E-011 4.34E-011 Lf (m) Lf (m) 4.21E-011 10 % w/v PEG 4.32E-011 0 2 4 6 8 -3 10 12 14 16 0 2 4 6 [SDS] (mol dm ) 8 10 -3 [SDS] (m dm ) ol 12 14 16 4.15E-011 0 2 4 6 8 10 -3 12 14 16 [SDS] (mol dm ) Fig 4.29E-011 o 4.34E-011 4.27E-011 4.28E-011 15 C o 20 C o 25 C o 30 C o 35 C o 5 %w/v PEG 4.20E-011 4. 208 | P a g e .36E-011 4.4.18E-011 4.19E-011 Lf (m) 15 C o 20 C o 25 C o 30 C o 35 C o 4. Intermolecular free length (Lf) (m) for SDS in various aqueous PEG solutions at different temperatures.35E-011 1 % w/v PEG 4.25E-011 4.