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Sorption of organic vapors by copolymers of poly (styrene-butadiene) using a piezoelectric microbalance

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Title:
Sorption of organic vapors by copolymers of poly (styrene-butadiene) using a piezoelectric microbalance
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English
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Upadhyayula, Anant K
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University of South Florida
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Subjects / Keywords:
Qcm
Vle
Benzene
N-hexane
Dichloroethane
Chloroform
Dissertations, Academic -- Chemical Engineering -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Thickness shear mode (TSM) sensors, also known as quartz crystal micro-balances (QCM) are a class of acoustic wave sensors that have been used for gas phase sensing. In this thesis this device is used to measure vapor-liquid equilibrium data for copolymers of poly(styrene-butadiene) at 294K. Copolymers of poly(styrene-butadiene) with varying percentages of styrene (85%, 45% and 21 %) were studied with benzene, n-hexane, dichloroethane and chloroform as solvents. Literature data for pure polystyrene/benzene and polystyrene/chloroform and polybutadiene/benzene were obtained to complement the measured data. Obtained experimental data were fit with a modified Flory-Huggins model and compared with the predictions of three models (UNIFAC-FV, Entropic-FV, and GK-FV). Flory-Huggins model gave a good quantitative fit for the solvent activities in the copolymer solutions.
Thesis:
Thesis (M.S.)--University of South Florida, 2005.
Bibliography:
Includes bibliographical references.
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by Anant K. Upadhyayula.
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Title from PDF of title page.
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Document formatted into pages; contains 156 pages.

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Sorption Of Organic Vapors By Copolymers Of Poly (Styrene-Butadiene) Using A Piezoelectric Microbalance by Anant K. Upadhyayula A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering Department of Chemical Engineering College of Engineering University of South Florida Major Professor: Venkat R. Bhethanabotla, Ph.D. Babu Joseph, Ph.D. Scott W. Campbell, Ph.D. Date of Approval: March 30, 2005 Keywords: QCM, VLE, Benzene, n-hexane, dichloroethane, chloroform Copyright 2005, Anant K. Upadhyayula

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TATBLE OF CONTENTS LIST OF TABLES iv LIST OF FIGURES vii LIST OF SYMBOLS xi ABSTRACT xii CHAPTER 1 1 INTRODUCTION 1.1 What is sorption 1 1.2 Motivation 2 1.3 Thesis organization 3 CHAPTER 2 4 THERMODYNAMICS OF POLYMER SOLUTIONS 2.1 Introduction 4 2.2 Vapor liquid equilibrium calculations 4 2.3 Flory Huggins model 7 2.4 Free volume models 10 2.4.1 Elbro model (Entropic-FV) 10 2.4.2 Kontogeorgis model 11 2.4.3 UNIFAC-FV model 12 CHAPTER 3 15 QUARTZ CRYSTAL RESONATOR 3.1 Introduction 15 3.2 Piezoelectric effect 15 3.3 The quartz resonator 17 3.3.1 Natural and cultured quartz 19 3.3.2 Contouring and beveling 20 3.3.3 Base plating of quartz crystal 21 3.3.4 Mounting and bonding 21 3.4 The equivalent circuit model 22 i

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CHAPTER 4 24 EXPERIMENTAL SETUP 4.1 Introduction 24 4.2 Frequency change due to mass sorption 24 4.3 Calculation of film thickness 27 4.4 Effect of temperature 30 4.5 Effect of pressure 31 4.6 Experimental apparatus 31 4.6.1 Solvent cell 31 4.6.2 Sorption cell design 1 32 4.6.3 Sorption cell design 2 33 4.6.4 QCM parameter measurement and automation 35 4.6.5 Vapor dilution system 39 4.7 Calibration of dilution system 40 CHAPTER 5 45 EXPERIMENTAL PROCEDURES AND RESULTS 5.1 Introduction 45 5.2 Experimental procedure 45 5.3 Literature data 46 5.4 Data reduction 47 5.5 Activity of benzene in poly(85% styrene-15% butadiene) 49 5.6 Activity of n-hexane in poly(85% styrene-15% butadiene) 51 5.7 Activity of dichloroethane in poly(85% styrene-15% butadiene) 52 5.8 Activity of chloroform in poly(85% styrene-15% butadiene) 53 5.9 Activity of benzene in poly(45% styrene-55% butadiene) 54 5.10 Activity of n-hexane in poly(45% styrene-55% butadiene) 55 5.11 Activity of dichloroethane in poly(45% styrene-55% butadiene) 57 5.12 Activity of chloroform in poly(45% styrene-55% butadiene) 58 5.13 Activity of benzene in poly(21% styrene-79% butadiene) 59 5.14 Activity of n-hexane in poly(21% styrene-79% butadiene) 60 5.15 Activity of dichloroethane in poly(21% styrene-79% butadiene) 62 5.16 Activity of chloroform in poly(21% styrene-79% butadiene) 63 5.17 Summary 64 ii

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5.18 Effect of copolymer composition on benzene sorption 66 5.19 effect of copolymer composition on n-hexane 68 5.20 Effect of copolymer composition on dichloroethane 70 5.21 Effect of copolymer composition on chloroform 72 5.22 Summary 73 5.23 Activities of four solvents in poly(styrene-butadiene) (85% styrene) at 294 K 74 5.24 Activities of four solvents in poly(styrene-butadiene) (45% styrene) at 294 K 76 5.25 Activities of four solvents in poly(styrene-butadiene) (21% styrene) at 294 K 78 5.26 Summary 79 5.27 Resistance changes 80 CHAPTER 6 86 RESULTS AND CONCLUSIONS 6.1 Conclusions 86 6.2 Copolymer composition trends 86 6.3 Suggestions for future research 89 REFERENCES 91 APPENDICIES 93 Appendix A Experimental activity, weight fraction and chi values 94 Appendix B Comparison of different model errors 101 Appendix C Error Analysis 112 C.1 Weight fraction 112 C.2 Activity of solvent 113 Appendix D Comparison of USF, PNNL and DECHEMA data 117 Appendix E List of vendors 121 Appendix F 122 Fluctuations in frequency measurements Appendix G 134 Comparison of activities predicted by UNIFAC-FV, GK-FV and Entropic-FV iii

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LIST OF TABLES Table 2.1 Wagner equations constants 7 Table 2.2 Solvent virial coefficients of the solvents at 294 K 7 Table 2.3 Van der Waals volume parameters 9 Table 5.1 Poly (styrene-butadiene) (85 % styrene) 48 Table 5.2 Poly (styrene-butadiene) (45 % styrene) 48 Table 5.3 Poly (styrene-butadiene) (21 % styrene) 49 Table 5.4 Comparison of errors with all models for copolymer poly(styrenebutadiene)/ solvents 65 Table A1 Activity of benzene in poly (styrene-butadiene) (85% styrene) 94 Table A2 Activity of n-hexane in poly (styrene-butadiene) (85% styrene) 95 Table A3 Activity of dichloroehtane in poly (styrene-butadiene) (85% styrene) 95 Table A4 Activity of chloroform in poly (styrene-butadiene) (85% styrene) 96 Table A5 Activity of benzene in poly (styrene-butadiene) (45% styrene) 96 Table A6 Activity of n-hexane in poly (styrene-butadiene) (45% styrene) 97 Table A7 Activity of dichloroethane in poly (styrene-butadiene) (45% styrene) 97 Table A8 Activity of chloroform in poly (styrene-butadiene) (45% styrene) 98 Table A9 Activity of benzene in poly (styrene-butadiene) (21% styrene) 98 Table A10 Activity of n-hexane in poly (styrene-butadiene) (21% styrene) 99 Table A11: Activity of dichloroethane in poly (styrene-butadiene) (21% styrene) 99 Table A12 Activity of chloroform in poly (styrene-butadiene) (21% styrene) 100 Table B1 Comparison of activity of benzene in poly (styrene-butadiene) /(85% styrene) 101 Table B2 Comparison of activity of n-hexane in poly (styrene-butadiene) /(85% styrene) 102 Table B3 Comparison of activity of dichloroethane in poly (styrene-butadiene) /(85% styrene) 103 Table B4 Comparison of activity of chloroform in poly (styrene-butadiene) /(85% styrene) 104 iv

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Table B5 Comparison of activity of benzene in poly (styrene-butadiene) /(45% styrene) 105 Table B6 Comparison of activity of n-hexane in poly (styrene-butadiene) /(45% styrene) 105 Table B7 Comparison of activity of dichloroethane in poly (styrene-butadiene) /(45% styrene) 106 Table B8 Comparison of activity of chloroform in poly (styrene-butadiene) /(45% styrene) 107 Table B9 Comparison of activity of benzene in poly (styrene-butadiene) /(21% styrene) 108 Table B10 Comparison of activity of n-hexane in poly (styrene-butadiene) /(21% styrene) 109 Table B11 Comparison of activity of dichloroethane in poly (styrene-butadiene) /(21% styrene) 110 Table B12 Comparison of activity of chloroform in poly (styrene-butadiene) /(21% styrene) 111 Table D1 Activity vs weight fraction for benzene / PIB at 294K and its comparison with Dechema and PNNL data 117 Table D2 Activity vs weight fraction for n-hexane / PIB at 294K and its comparison with Dechema and PNNL data 118 Table D3 Activity vs weight fraction for cyclohexane / PIB at 294K and its comparison with Dechema and PNNL data 119 Table D4 Activity vs weight fraction for toluene / PIB at 294K and its comparison with Dechema and PNNL data 120 Table E1 List of vendors 121 Table F1 Fluctuations in frequency measurements for Benzene in poly(styrene-butadiene)/ (85% styrene) system 122 Table F2 Fluctuations in frequency measurements for n-hexane in poly(styrene-butadiene)/ (85% styrene) system 123 Table F3 Fluctuations in frequency measurements for dichloroethane in poly(styrene-butadiene)/ (85% styrene) system 124 Table F4 Fluctuations in frequency measurements for chloroform in poly(styrene-butadiene)/ (85% styrene) system 125 Table F5 Fluctuations in frequency measurements for benzene in poly(styrene-butadiene)/ (45% styrene) system 126 Table F6 Fluctuations in frequency measurements for n-hexane in poly(styrene-butadiene)/ (45% styrene) system 127 v

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Table F7 Fluctuations in frequency measurements for dichloroethane in poly(styrene-butadiene)/ (45% styrene) system 128 Table F8 Fluctuations in frequency measurements for chloroform in poly(styrene-butadiene)/ (45% styrene) system 129 Table F9 Fluctuations in frequency measurements for benzene in poly(styrene-butadiene)/ (21% styrene) system 130 Table F10 Fluctuations in frequency measurements for n-hexane in poly(styrene-butadiene)/ (21% styrene) system 131 Table F11 Fluctuations in frequency measurements for dichloroethane in poly(styrene-butadiene)/ (21% styrene) system 132 Table F12 Fluctuations in frequency measurements for chloroform in poly(styrene-butadiene)/(21% styrene) system 133 vi

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LIST OF FIGURES Figure 3.1 Arrangement of ions on QCM 16 Figure 3.2 Arrangement of ions on QCM under stress 16 Figure 3.3 SC-cut frequency vs. temperature plot 17 Figure 3.4 AT-cut frequency vs. temperature plot 18 Figure 3.5 Plano-convex and bi-convex beveled plates 20 Figure 3.6 Butterworth-Van Dyke equivalent circuit for the QCM 22 Figure 4.1 AT and BT cut quartz crystal plates 25 Figure 4.2 Simplified model of quartz crystal microbalance 26 Figure 4.3 Commercial QCM 30 Figure 4.4 Bubbler 32 Figure 4.5 Bubbler Cap 32 Figure 4.6 Sorption cell design 1 33 Figure 4.7 Sorption cell design 2 34 Figure 4.8 Overall automation programs 35 Figure 4.9 Initialization of all valves 36 Figure 4.10 First nitrogen purge cycle 37 Figure 4.11 Purge cycle control loop 37 Figure 4.12 Sorption cycle control loop 38 Figure 4.13 Vapor dilution system 39 Figure 4.14 Activity vs. weight fraction for benzene (1) / PIB (2) at 294K and its comparison with Dechema and PNNL data 41 Figure 4.15 Activity vs. weight fraction for n-hexane (1)/ PIB (2) at 294K and its comparison with Dechema and PNNL data 42 Figure 4.16 Activity vs. weight fraction for cyclohexane (1) / PIB (2) at 294K and its comparison with Dechema and PNNL data 43 Figure 4.17 Activity vs. weight fraction for toluene (1) / PIB (2) at 294K and its comparison with Dechema and PNNL data 44 vii

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Figure 5.1 Experimental activity of benzene (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 49 Figure 5.2 Experimental activity of n-hexane (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 51 Figure 5.3 Experimental activity of dichloroehtane (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 52 Figure 5.4 Experimental activity of chloroform (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 53 Figure 5.5 Experimental activity of benzene (1) in poly(45 % styrene 55% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 54 Figure 5.6 Experimental activity of n-hexane (1) in poly(45 % styrene 55% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 55 Figure 5.7 Experimental activity of dichloroethane (1) in poly(45 % styrene 55% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 57 Figure 5.8 Experimental activity of chloroform (1) in poly(45 % styrene 55% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 58 Figure 5.9 Experimental activity of benzene (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 59 Figure 5.10 Experimental activity of n-hexane (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 60 Figure 5.11 Experimental activity of dichloroethane (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 62 Figure 5.12 Experimental activity of chloroform (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 63 Figure 5.13 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on benzene at 294K 66 Figure 5.14 Flory-Huggins interaction parameter for benzene in poly(styrenebutadiene) with (85 %, 45% and 21% styrene) at 294K 67 viii

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Figure 5.15 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on n-hexane at 294K 68 Figure 5.16 Flory-Huggins interaction parameter for n-hexane in poly(styrenebutadiene with (85 %, 45% and 21% styrene) at 294.0K 69 Figure 5.17 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on dichloroethane at 294K 70 Figure 5.18 Flory-Huggins interaction parameter for dichloroethane in poly(styrene-butadiene) with (85 %, 45% and 21% styrene) at 294.0K 71 Figure 5.19 Effect of copolymer composition poly (styrene-butadiene)/ (85%, 45 % and 21 % styrene) on chloroform at 294K 72 Figure 5.20 Flory-Huggins interaction parameter for chloroform in poly(styrene-butadiene) with (85 %, 45% and 21% styrene) at 294.0K 73 Figure 5.21 Activity of four solvents in poly (styrene-butadiene) in (85% styrene) at 294K 74 Figure 5.22 Flory-Huggins interaction parameter for four solvents in poly(styrene-butadiene) with (85 % styrene) at 294.0K 75 Figure 5.23 Activity of four solvents in poly (styrene-butadiene) in (45% styrene) at 294K 76 Figure 5.24 Flory-Huggins interaction parameter for four solvents in poly(styrene-butadiene) with (45 % styrene) at 294.0K 77 Figure 5.25 Activity of four solvents in poly (styrene-butadiene) in (21% styrene) at 294K 78 Figure 5.26 Flory-Huggins interaction parameter for four solvents in poly(styrene-butadiene) with (21 % styrene) at 294.0K 79 Figure 5.27 Change in resistance of the equivalent circuit model of the QCM for poly(85% styrene15 %butadiene) copolymer film 80 Figure 5.28 Change in resistance vs. weight fraction for four solvents and poly(85% styrene15 %butadiene) copolymer system 81 Figure 5.29 Change in resistance of the equivalent circuit model of the QCM for poly(45% styrene55 %butadiene) copolymer film 82 Figure 5.30 Change in resistance vs. weight fraction for four solvents and poly(45% styrene55 %butadiene) copolymer system 83 Figure5.31 Change in resistance of the equivalent circuit model of the QCM for poly(21% styrene79 %butadiene) copolymer film 84 Figure 5.32 Change in resistance vs. weight fraction for four solvents and poly(21% styrene79 %butadiene) copolymer system 85 Figure 6.1 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/benzene systems 87 ix

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Figure 6.2 GK-FV predictions for copolymers with 85%, 45% and 21 % styrene/benzene systems 88 Figure 6.3 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/benzene systems 89 Figure G.1 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/n-hexane systems 134 Figure G.2 GK-FV predictions for copolymers with 85%, 45% and 21 % styrene/n-hexane systems 135 Figure G.3 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/n-hexane systems 136 Figure G.4 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/dichloroethane systems 137 Figure G.5 GK-FV predictions for copolymers with 85%, 45% and 21 % styrene/dichloroethane systems 138 Figure G.6 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/dichloroethane systems 139 Figure G.7 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/chloroform systems 140 Figure G.8 GK-FV predictions for copolymers with 85%, 45% and 21 % styrene/chloroform systems 141 Figure G.9 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/chloroform systems 142 x

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LIST OF SYMBOLS Symbol Vaporf1 Fugacity of solvent in the vapor phase Solutiionf1 Fugacity of solvent in the solution SatfP1, System pressure (torr), saturated vapor pressure 11B Second virial coefficient of the solvent (cm 3 /gmole) R Gas constant T System temperature iw Weight fraction of component i iV Van der Waals volume parameter of component i iX Mole fraction of component i tM Total mass absorbed at time i M Total mass absorbed after infinite time gT Glass transition temperature E Activation energy CV Critical molar volume of solvent (cm 3 /gmole) 1a Activity coefficient 1 Activity coefficient of component 1 (solvent) based on weight fraction i Volume fraction of component i iN Number of moles of component i EG Excess Gibbs free energy f Frequency shift due to sorption of solvent (Hz) 0f Frequency shift upon coating of a poly (styrene-butadiene) xi

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SORPTION OF ORGANIC VAPORS BY COPOLYMERS OF POLY (STYRENE-BUTADIENE) USING A PIEZOELECTRIC MICROBALANCE Anant K. Upadhyayula ABSTRACT Thickness shear mode (TSM) sensors, also known as quartz crystal micro-balances (QCM) are a class of acoustic wave sensors that have been used for gas phase sensing. In this thesis this device is used to measure vapor-liquid equilibrium data for copolymers of poly(styrene-butadiene) at 294K. Copolymers of poly(styrene-butadiene) with varying percentages of styrene (85%, 45% and 21 %) were studied with benzene, n-hexane, dichloroethane and chloroform as solvents. Literature data for pure polystyrene/benzene and polystyrene/chloroform and polybutadiene/benzene were obtained to complement the measured data. Obtained experimental data were fit with a modified Flory-Huggins model and compared with the predictions of three models (UNIFAC-FV, Entropic-FV, and GK-FV). Flory-Huggins model gave a good quantitative fit for the solvent activities in the copolymer solutions. All models UNIFAC-FV, GK-FV and Entropic-FV gave good predictions for poly(85% styrene-15% butadiene) copolymer/solvent and poly(45% styrene-55% butadiene) copolymer/solvent systems. All models could not predict well for poly(21% styrene-79% butadiene)/ chloroform system, yet the same models gave good predictions for the same copolymer with benzene, n-hexane and dichloroethane systems. xi i

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All models predicted very well for 21% styrene in copolymer and n-hexane system and did not do well with chloroform as solvent. GK-FV and entropic-FV predicted better for 21% styrene in copolymer and solvents except chloroform. A fully instrumented and automated test-bed consisting of a temperature controlled vapor dilution system, a precision impedance analyzer, and computer for data acquisition in Labview was developed in-house to evaluate the performance of the coated TSM devices in sensor applications as well as in sorption data measurement. xi ii

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CHAPTER 1 INTRODUCTION Sorption of gases or organic vapors by polymers was studied considerably after 1960. The highly non-ideal behavior of polymer / solvent solutions in comparison to lower molecular weight solutions was another reason of study of vapor sorption by polymers. Understanding the properties of solutions of polymers in solvents of variable quality has been an outstanding problem in polymer science for decades. These systems are of fundamental interest as model systems for the statistical mechanics of fluid binary mixtures and also are of enormous practical interest for predicting processing properties. 1.1 What is sorption The general term sorption includes both adsorption, the process by which a solute clings to a solid surface, and absorption, the process by which the solute diffuses into a porous solid and clings to interior surfaces, (according to Fetter). When the attachment of the solute is accomplished by means of a chemical reaction with the solid, the process is called chemisorption. Many materials can be used as sorbents, but activated carbon is so effective primarily because of its sorbent properties. The total process of a solute diffusing through a carbon particle to attach to an inner surface is most accurately referred to as absorption, though the actual attachment of the solute at the site is actually 1

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adsorption. It should be noted, however, that the term adsorption seems to be used rather freely to refer to sorption processes in general. 1.2 Motivation Thin film materials are currently used in a wide range of industrial applications. For example thin films can be use as drug encapsulants, protective layers, or as catalysts. The characterization of the properties of such materials is essential in determining their applications in these areas. It is challenging to characterize such thin films because of the small thickness and mass of the material. Conventional techniques such as reflectance spectrometry or x-ray fluorimetry have disadvantages such as long preparation and analysis times, require vacuum environments, and have excessive associated costs. Because of its inherent sensitivity, TSM sensors are ideal for characterizing film properties. TSM sensors have the ability to monitor small amounts of thin films accurately with time. Determination of polymer properties is also important for polymer processing plants and other manufacturing processes. Properties of polymer materials such as weather resistance, resilience, toughness, durability, and spinability are vital in manufacturing processes; however, since these polymers may be exposed to various solvents during manufacturing or in applications, information concerning polymer solvent interactions is also essential. In particular, analytical methods, such as activity coefficient models, can be used to predict the phase behavior of polymer solutions. These models include three free volume models: UNIFAC-FV [14], Entropic-FV [13], and GK-FV [4]. Polymer solvent systems depict highly non-ideal behavior. Furthermore, for copolymer system, there are little literature data available. This thesis 2

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work determines the activity of benzene, n-hexane, dichloroethane, and chloroform vapors in poly (styrene-butadiene) copolymers with varying percentage levels of styrene (21 %, 45 %, and 85 %). In this work it is also determined how well the experimental data are fit with Flory-Huggins model and compared to the activity predicted by various models (UNIFAC-FV, Entropic-FV, and GK-FV). 1.3 Thesis organization This thesis work is subdivided into six chapters. Chapter 2 discusses thermodynamics of polymer solutions and different models used to calculate the activity coefficients. Chapter 3 presents rudiments of quartz crystal resonator principles and applications. It also gives insight into quartz crystal microbalance properties. Chapter 4 has detailed description of the experimental setup and mathematical calculations for interpreting the data. It describes the automation of the entire experimental setup. Also, it talks about sorption cell development, discussing pros and cons of different designs. Chapter 5 presents the results and data. Chapter 6 is mainly discussion of the experimental observations made and suggestions for future work. 3

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CHAPTER 2 THERMODYNAMICS OF POLYMER SOLUTIONS 2.1 Introduction This chapter describes methods for analyzing experimental data. Section 2.2 reviews vapor-liquid equilibrium calculations for concentrated polymer solutions used in determining the activity of solvents in poly(styrene-butadiene). Sections 2.3 describes Flory-Huggins model. Section 2.4 describes different free volume model used to compare the experimental data. 2.2 Vapor liquid equilibrium calculations Activity of the solvent is calculated by equating the fugacity of the solvent in vapor with that of the solvent in liquid solution phase at equilibrium. solutionvaporff11 (2.1) Where: vaporf1 = Fugacity of the solvent in vapor phase solutionf1 = Fugacity of the solvent in solution lfxPy1111^1 (2.2) Let 11PPy (2.3) 4

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Fugacity coefficient for component 1 in the gas phase for a two-component mixture is [16] 331113231112expBBByBRTP (2.4) When 01y 011B 3313112exp0BBRTPyLimit (2.5) Where, are second virial coefficients, R is the gas constant, P is the total system pressure and T is the system temperature. is the second viral coefficient of the solvent at system temperature and is estimated using the corresponding states correlation of Tsonopoulos [20] 331113,,BBB 11B )()()1()0(11RRccTfTfPRTB (2.6) Here, andPTcc, are the critical temperature, critical pressure and Pitzers accentric factor, respectively. are the reduced temperature and pressure. are given by [20] RRPT, )1()0(andff 32)0(0121.01358.0330.01445.0)(RRRRTTTTf (2.7) 332)1(0073.0097.05.046.0073.0)(RRRRRTTTTTf (2.8) Liquid: llfxf1111 (2.9) 5

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SatSatlSatSatlPPRTVExpPf11111 (2.10) SatSatlSatSatlPPRTVExpRTPBExpPf1111111 (2.11) For VLE SatSatlSatSatPPRTVExpRTPBExpPxBBByBRTPExpP11111111331113231112 (2.12) Hence SatSatlSatSatPPRTVExpRTPBExpPBBByBRTPExpPax11111133111323111111112 (2.13) Where is the activity coefficient based on weight fraction, is the saturated vapor pressure of the solvent at the system temperature. In writing this equation, it is assumed that the fugacity of the pure solvent at the temperature at the system pressure equals the fugacity at saturation and that for low or medium pressures it can be estimated using the truncated viral equation of state. 1 SatP1 SatT1 satP1 for pure solvent calculated from Wagners equation [19]. 635.11....1lnxVxVxVxVxPPPDPCPBPAcvp (2.14) Where P is in torr and T is the solvent temperature or system temperature in Kelvin (K). The second viral coefficients of the solvents at 298.15 K and 323.15 K were obtained from the correlation of Tsonopoulos [20]. 6

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Table 2.1 Wagner equations constants Solvents PAV PBV PCV PDV Benzene -6.98273 1.33213 -2.62863 -3.33399 Chloroform -6.95546 1.16625 -2.13970 -3.44421 n-Hexane -7.46765 1.44211 -3.28222 -2.50941 dichloromethane -7.35739 2.17546 -4.07038 3.50701 Table 2.2 Solvent virial coefficients of the solvents at 294 K Solvents gmolecmB311 at 298.15K Benzene -1758.7 Chloroform -2053.0 n-Hexane -1841.0 dichloromethane -1315.5 2.3 Flory Huggins model Polymer-solvent interactions are analyzed using the Flory-Huggins theory of the activity of the solvent as [5] [12] [15]. 22221.111lnlnra (2.15) Where 2 is the volume fraction of polymer and r is the ratio of molecular volumes. 12VVr (2.16) 7

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Where V 1 = Molecular volume of solvent V 2 = Molecular volume of polymer 2V and were estimated by assuming Van der Waals group volumes [6]. 1V kkikiRV. (2.17) Here, ik is always an integer, and is the number of groups of type k in molecule i. kR is the Van der Waals group volume of group k [6]. i the volume fraction can be expressed as: 2211111XVXVXV (2.18) 2211222XVXVXV (2.19) Where and are the mole fraction of the solvent and polymer, respectively. 2X 2X 8

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Table 2.3 Van der Waals volume parameters Molecule i iV Benzene 3.1878 n-Hexane 4.4998 Dichloroethane 1.988 Chloroform 2.87 Poly(styrene-butadiene) 85% styrene 4443 Poly(styrene-butadiene) 45% styrene 21742 Poly(styrene-butadiene) 21% styrene 17758 In cases where appears to be composition dependant a linear model for this dependence was assumed to represent the data are, assuming. 21 BA (2.20) in 221222111).(2ln.ln.BBAXNXNRTnGE (2.21) Where are the number of moles of solvent and polymer respectively. Taking partial derivatives w.r.t provides an expression for the activity of solvent 1N 2N 1N 221221).(2111lnlnBBAra (2.22) The parameter was used as a measure of the strength of interaction between the sorbing vapor and the polymer film. Hence, could be used as a guide for many thermodynamic properties of polymer solutions such as solubilities, swelling equilibria and colligative properties. 9

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2.4 Free volume models A new equation for an activity coefficient a so-called free volume activity coefficient which includes combinatorial and free volume contributions has been derived from a Van der Waals free volume type of expression [4] [13]. The new expression is analogous to the Flory-Huggins combinatorial term. The free volumes of solvents and polymers are compared, and it is shown that even for mixtures of solvents the free volume effect cannot always be ignored. For polymer solutions with energy interactions a UNIQUAC residual term is added. The energy parameters are obtained from small-molecule homologues. The results obtained with this new equation compared favorably with the Holten-Andersen equation of state and the UNIFAC-FV model by Oishi and Prausnitz [15]. 2.4.1 Elbro model (Entropic-FV) Equation 2.15 is used for the reduction of experimental data are. In practice, the parameter exhibits considerable variation with temperature, pressure and concentration which is the result of not taking free volume differences between the solvent and polymer into consideration [4]. Two Simple assumptions were made to derive the free volume activity coefficient equation. First )(*vvnVf (2.23) where = the molar volume calculated from Van der Waals volumes *v v = the molar volume and n is total number of moles Second The mixture volumes are found from linear mixing rules 10

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iiimixvxv** (2.24) iiimixvxv (2.25) From equations 2.24 and 2.25, an expression for combined combinatorial and free volume contributions, the free volume activity coefficient FVi can be calculated, ifviifvifvixx1ln (2.26) jijjiiifvvvxvvx** (2.27) Equation 2.26 is analogous to Flory-Huggins combinatorial term and contains only pure component properties, which enables to predict solvent activities from the molar volumes and the Van der Waals volume of components for polymer solutions without any energy interactions. 2.4.2 Kontogeorgis model The basis for this model is the Elbro model discussed above. Free volume, the available volume at the center of mass of a molecule is defined [13] as ifVVV (2.28) WiVV (2.29) Where V is the liquid molar volume and V i is inaccessible volume. It is assumed that the inaccessible volume is equal to the Van der Waals volume (V w ). The Van der Waals volume of a molecule is defined as the space occupied by this molecule, which is 11

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impenetrable to other molecules with normal thermal energies. The expression for the activity coefficient of component i is resifviilnlnln (2.30) Where the free volume part is given by equation 2.26, and are the free volume fractions for component i. fvi jfvifiifviVxVx (2.31) The residual part of the Elbro free volume model is given by UNIFAC. The interaction parameters are assumed to be temperature dependant through a linear relationship. 01,2,TTaaamnmnmn (2.31) 2.4.3 UNIFAC-FV model The UNIFAC model is based on the UNIQUAC model [15], contains two contributions to the activity )()(lnlnlnresidualRiialcombinatorCiiaaa (2.32) Where combinatorial term accounts for molecular size and shape differences and it given by 1111111111112ln21lnlnqMzqMzxaCi (2.33) Since 2211111mx 111111112112ln2lnlnqMzqMzaCi (2.34) 12

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Where m is, the number of segments per polymer molecule divided by the number of solvent molecules. Subscripts 1 and 2 represent solvent and polymer respectively. iiiiiqwqw (2.35) jjiiiqwqw (2.36) ir = volume parameter for species i i = surface fraction for species i iq = surface area parameter for species i i = volume parameter for species i z is the coordination number set equal to 10 The residual term accounts largely for energy differences. Which is computed from the below equation, kikkikRiva)(lnlnln (2.37) Where is the number of k groups present in species i and is the residual contribution to the activity coefficient of group k in pure fluid of species i molecules. ikv )(lnik mnnmnmkmmmkmkkkQMln1ln (2.38) mW = weight fraction of group m in mixture mM = molecular weight of the functional group m mnnmmmQWQW = surface area fraction of group m 13

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and TakTuumnnmmnmnexpexp (2.39) Where is a measure of the interaction energy between m and n and the sums are over all groups in the mixture. mnu 14

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CHAPTER 3 QUARTZ CRYSTAL RESONATOR 3.1 Introduction A piezoelectric resonator consists of a piece of piezoelectric material precisely dimensioned and oriented with respect to the crystallographic axes of the material and equipped with one or more pairs of conducting electrodes. By means of the piezoelectric effect, and electric field applied between the electrodes excites the resonator into mechanical vibration. The amplitude of vibration is negligibly small except when the frequency of the driving field is in the vicinity of the resonators normal modes of vibration and resonance occurs. Near resonance, the amplitude of vibration increases and is the maximum at resonance. 3.2 Piezoelectric effect The discovery of the piezoelectric effect is generally attributed to the curie brothers and dates to 1880. The piezoelectric effect can be explained by considering a crude model of an arrangement of positive and negative ions of a quartz crystal in the plane normal to its optical axis as shown in Figure 3.1. The six ions are located at the corners of a regular hexagon. Assuming that the ions have charges +q and q, the net charge in the unit cell is zero. Due to the alternate arrangement of the positive and negative ions, the net dipole 15

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moment is also zero. If an external stress is applied causing a deformation in the crystal, the mutual forces acting between ions in the cell are such as to maintain both the distance apart of opposite pairs of ions, and also their co-linearity with the cell center. This deformation of the unit cell can be described in terms of the rotations of the lines joining the opposite pair of ions as shown in Figure 3.2 in the case of compression in the vertical direction. The ion pair in the horizontal direction is unaltered, but, the remaining two ion pairs are rotated towards the horizontal. Clearly, the center of gravity of the positive ion is shifted towards the left, whereas that of the negative ions is shifted towards the right, the combined effect being a non-zero dipole moment in the horizontal direction. Figure 3.1 Arrangement of ions on QCM Figure 3.2 Arrangement of ions on QCM under stress The reverse situation of a tensile stress in the vertical direction again leaves the horizontal ion pair unchanged but rotates the other two pairs away from the horizontal, producing a dipole moment oppositely directed to that produced by compression. Assuming a homogeneous strain, summing the dipole moments of all the unit cells throughout the material therefore results in an electric polarization that reverses with the strain, that is, piezoelectric and the phenomena is knows as the piezoelectric effect. 16

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3.3 The quartz resonator For many years quartz resonators have been preferred in satisfying needs for precise frequency control and selection than other resonators. This is because material properties of a quartz crystal are extremely stable and highly repeatable form one specimen to another. The acoustical loss or the initial friction of quartz is particularly low, leading to one of the key properties of a quartz resonator, its extremely high Q factor. Figure 3.3 SC-cut frequency vs. temperature plot Relative Frequency (ppm) Temperature (deg. C) Important cuts are the AT and the SC, which are manufactured range between 1.5MHz to several hundred MHz. The fundamental frequency of these cuts is inversely proportional to the wafer thickness. The frequency-temperature characteristics of both AT and SC cut resonators are cubic curves of the form: 3032020100)()()(TTATTATTAAff (3.1) 17

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Where A 0 A 1 A 2 and A 3 are constants. They depend upon quartz properties and the angle of the cut. T is the temperature and T 0 is the inflection temperature, which is approximately 25C for the AT-cut and 92C for the SC-cut. This equation gives the curves displayed in figure 3.3 and 3.4. Resonators with small frequency change over a broad temperature range can be designed with the help of these curves [8]. Figure 3.4 AT-cut frequency vs. temperature plot Relative Frequency (ppm) Temperature (deg. C) The second key property of the quartz resonator is its stability with respect to temperature variation. The most commonly used type of resonator is the AT-cut where the quartz blank is of the form of a thin plate cut at an angle of about 35 0 15 to the optical axis of the crystal. The AT-cut has a frequency-temperature coefficient described by a cubic function of temperature, which can be precisely controlled by a small variation in the angle of cut. The cubic behavior is in contrast to most other crystal cuts which show 18

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parabolic temperature characteristics, and makes the AT-cut well suited to applications requiring a high degree of frequency stability over wide temperature ranges. The third essential characteristic of the quartz resonator is related to the stability of its mechanical properties. Short and long term stabilities manifested in frequency drifts of only a few parts per million per year are readily available even from commercial units. Precision crystal units manufactured under closely controlled conditions are second only to atomic clocks in the frequency stability and precision achieved. AT-cut crystals are commonly manufactured in the frequency range from about 1 MHz to 200 MHz and above, and in this range are usually the optimum choice for most applications. In this thesis I have used AT-cut crystals for the experiment. 3.3.1 Natural and cultured quartz Quartz is one of the commonest naturally occurring crystalline materials, sand for example being largely made up of gains of quartz produced by weathering of large crystals. Despite this natural abundance, crystals of sufficient size and purity for processing into quartz resonators are very rare. Cultured quartz is now routinely grown from aqueous solutions under conditions of high pressure and temperature in massive underground steel autoclaves. The lower part of the autoclave if maintained at a temperature of about 400 0 C and contains nutrients in the form of pure silica. At this temperature and at pressures of the order of a thousand atmospheres, the solubility of silica is relatively high and a saturated solution is formed. Conversion currents transport the saturated solution up to the upper part of the autoclave which is maintained at a lower temperature of about 350 0 C. At this lower temperature, the solution is supersaturated and 19

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quartz is deposited on seed crystal, suspended in the cooler region of the autoclave. Over periods of many days or weeks crystals of substantial size can be grown. 3.3.2 Contouring and beveling Contouring the crystal to give a gradually changing thickness from the center of the edge of the blank is a well established empirical practice. The effect of contouring one or both major faces of a resonator, as shown in Figure 3.5, was recognized to be the restriction of the vibrating area of the plate to the central region, with the accompanying advantages of the ease of the mounting and reduced coupling to unwanted mode at the edge of the blank. A precise analysis shows that for a main response of a spherically contoured resonator, the amplitude of vibration falls away exponentially with the square of the distance from the center, rather than as a simple exponential function of distance. Figure 3.5 Plano-convex and bi-convex beveled plates 20

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3.3.3 Base plating of quartz crystal All resonators require some from of electrode structure. The most commonly used technique is by the electrode deposition directly on the quartz surface by vacuum deposition. For resonators of the very highest precision and stability, air-gap electrodes are used to avoid the instabilities associated with electrode stresses. The most commonly used electrode materials are silver, gold and aluminum, with copper having been used in some special applications. It is common to use a thin layer of chrome under silver or gold electrodes to improve the adhesion of the electrodes to the quartz. The disadvantage of using chrome is that it increases the stress in the electrodes and thereby provides additional source of long-term instability. The electrode materials can be deposited either by sputtering or by evaporation, the later being the more popular. The thickness of material deposited is controlled by detecting the change in frequency of monitor crystal exposed to the evaporant. 3.3.4 Mounting and bonding The basic requirements in mounting crystal resonators are that the crystal be provided with mechanical support, at the same time the mounting structure should impose minimal stress on the resonator and minimize damping of the mechanical resonance. Whatever mount is chosen, the blank has to be secured in place with some form of adhesive, which must provide both mechanical strength and resilience and also be electrically conductive. The most commonly used adhesives are silver loaded epoxy resin or silver loaded polyimide pastes, the latter being more useful for higher 21

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temperature applications. The paste or resin is applied with a syringe or needle, and invariably requires to be cured at an elevated temperature for further processing. It is important that the paste does not out-gas appreciably during the curing cycle and so contaminate the crystal. The paste should not contain any chemical that will attack electrode material. The crystals used in this experiment were found to be stable in spite of polymers and solvents on the surface of the quartz crystal and electrodes. 3.4 The equivalent circuit model Figure 3.6 Butterworth-Van Dyke equivalent circuit for the QCM Where C 0 Parallel capacitance C 1 Motional capacitance R 1 Motional resistance L 1 Motional inductance The conventionally accepted equivalent circuit of a crystal resonator at a frequency near its main mode of vibration is shown in Figure 3.6. The circuit elements L 1 C 1 R 1 are the electrical equivalents of the inertia, stiffness, and internal losses of the mechanically vibrating system. If the crystal were clamped in such a way that no vibration were possible, this arm would be absent, and hence L 1 C 1 R 1 are known as motional parameters of the crystal. The element C 0 presents the capacitance of the capacitor formed by the electrodes of the crystal and the quartz dielectric. It can be measured as the effective capacitance of the crystal unit at frequencies far removed from 22

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resonance, and is known as static capacitance. Static capacitance C 0 is essentially determined by the electrode size and separation and is thus independent of the overtone order. Typical values for AT-cut range from 1 to 7 pF. More important in practice is the ratio of C 0 and C 1 because this ratio effectively determines the sensitivity of the crystal frequency to changes in the external circuit parameters. 23

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CHAPTER 4 EXPERIMENTAL SETUP 4.1 Introduction This chapter describes the basics of frequency change due to the mass sorption and effect of temperatures and pressures on it. Section 4.2 talks about frequency change due to mass sorption. In Section 4.3, polymer film thickness calculations are discussed. Section 4.4 and 4.5 gives information about the effect of temperature and pressure on QCM. Section 4.6 talks about experimental apparatus, is further subdivided to talk in detail about solvent cell design, sorption cell designs, and the in-house software interface developed using Labview 7.0 to communicate with the instruments, for precise equilibrium cycle time control and to log the data continuously at desired time intervals. 4.2 Frequency change due to mass sorption Ever since the use of quartz crystal resonators for frequency control applications in RF communication equipments, the effect of added mass on the resonant frequency has been known. In the early years, many amateur radio operators knew that the frequency of quartz oscillator could be adjusted slightly downward or upward respectively, by smearing some pencil mark onto the surface of the resonator, or rubbing off the electrode material with a pencil eraser. The mode of vibration, which is most sensitive to the addition or removal of mass for quartz resonator, is the high frequency thickness-shear mode shown in Figure. 24

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When a voltage is applied along the y-axis, a shear vibration is produced which trends to change a rectangular cross section into a rhombus. To make the quartz plate oscillate in the thickness-shear mode, the plate must be cut in a specific orientation with respect to the central axes. These cuts belong to the rotated y-cut family shown in Figure [4.1]. For the purpose of micro-weighing, only AT and BT cuts are useful. In the thesis, only AT-cut crystals were used. When, a voltage is applied to the quartz crystal by means of thin metal electrode plates affixed to the crystal and connected to a periodic voltage source, the quartz crystal to vibrate at the frequency of the exciting voltage. If the frequency of the driving voltage is very close to one of the mechanical resonance frequencies of the quartz crystal, the amplitude of vibration reaches a maximum. The crystal can be made to oscillate at one of its resonance frequencies by placing it in the feedback network of a closed loop system containing an amplifier. Figure 4.1 AT and BT cut quartz crystal plates 25

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Figure 4.2 Simplified model of quartz crystal microbalance (a) At resonance, the wavelength equals half of the quartz plate thickness. (b) An increase in the quartz plate thickness in a decrease in the resonant frequency (an increase in the wavelength) (c) The mass of film deposited, treated as an equivalent amount of the quartz mass (a) Quartz (M q ) (t q ) (b) d t q (t q ) Quartz (M q ) (c) (t f ) (t q ) Quartz (M q ) Mass induced resonant frequency shift was investigated in the late 1950s by Sauerbrey [14] and can be described by the idealized physical model shown in Figure [4.2]. 26

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4.3 Calculation of film thickness For oscillation to occur the thickness of the quartz must be half of the wavelength as given in the following equation, 2qqt (4.1) where is thickness of the plate and qt q is the wavelength of shear-mode elastic wave in the thickness direction. Ignoring the effect of the electrodes on both side of the crystal equation 4.1 can be written as 2qqqtf (4.2) Because qqqf (4.3) where q is the shear wave velocity and is the resonance frequency. qf From equation [4.2], the resonant frequency shift caused by an infinitesimal change in thickness is qqqqtdtfdf (4.4) and in terms of quartz crystal mass and mass change qm qdm qqqqmdmfdf (4.5) The negative sign indicates that an increase in the thickness of the quartz crystal plate causes a decrease in its resonant frequency. 27

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According to Sauerbrey assumption for small mass changes, the addition of foreign mass can be treated as an equivalent mass change of the quartz crystal itself. Hence equation [4.5] becomes qqqmdmfdf (4.6) Where, is an infinitesimal amount of foreign mass uniformly distributed over the crystal surface. For a thin film, equation [4.6] can be rewritten as. dm qfqqcmmfff (4.7) Where, is the resonance frequency of the quartz crystal with the deposited material. In terms of area densities and cf fm qm (the mass per unit area) equation [4.7] can be written as qfqqcmmfff (4.8) Where fffptm (4.9) and qqqptm (4.10) Where is the thickness of the film, is the thickness of the quartz plate,and are the film density and the quartz density. ft qt fp qp Substituting equations [4.2], [4.9] and [4.10] into equation [4.8] yields 28

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22.qqqqcfffpfftp (4.11) or 22.qqqqcffpffm (4.12) which can be used to calculate the thickness and mass of the film. Equation [4.12] may be written as f fmcf (4.13) qcfff is the frequency shift and qqqfp f22 where c is defined as the mass sensitivity. For an AT-cut quartz crystal, for which 32650mkgp q and sm q 3340 the tor calculated from equation [4.14] mass sensitivity for a 10 MHz resona is gHzcm2810. This means that the addition of material with an areal density of 4.42 x26.2 2cmngonto such a resonator will cause a frequency shift of 1 Hz. The use of areal density rather than mass density in equation [ 4.12] is more onvenient because the vibrating area of an actual quartz crystal resonator does not ecessa shifts due c nrily extend to its entire surface and the exact area is hard to define. Sauerbrey thoroughly studied the amplitude of vibration and mass sensitivity for various locations on the quartz plate. He observed the amplitude of vibration at the center of the electrode to be of the order of 50 while outside of the electrode, it damped to zero very rapidly. It is very good approximations that the observed frequency 29

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to mass adsorptione region only. A typical mounting a4.3]. Figure 4.3 Commercial QCM cutting angle on the temperature dependence of frequency for an AT-cut rystal. The various curves are for cuts oriented within a degree for the AT cut direction. are therefore due to mass adsorbed on the electrodrrangement for commercial quartz is shown in Figure [ 4.4 Effect of temperature In addition to adhering mass, there are several other factors which will cause a change in resonance frequency. A change in the ambient temperature will generally cause a change in the resonance frequency. A slight change in the orientation of a quartz crystal plate with respect to the crystallographic axes generally does not alter the mode of resonance. However, the effects of temperature and stress on the resonance frequencies are found to be highly sensitive to the crystallographic orientation. Figure [3.3] describes the effect of the c 30

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4.5 Effect of pressure A shift in frequency is also associated wit the effect of hydrostatic pressure on the elastic moduli of quartz. Th is frequency change is linear in pressure and has been shown by Stockbridge [15] to be: torrperxTf1010015.035.18 f (4.14) Where T is in K. The pressure range of this work was small so that the pressure effect 4.6 Expratus hown in Figure and consists of four sections easuring automation ) Vapor dilution system 4.6.1 S ceramic sparger at one end, which is submerged into the solvent for better could be neglected. erimental appa The apparatus is s a) Solvent cell b) Sorption cell c) Frequency m d olvent cell 250 ml round bottom flask with two connecting ports for inlet and outlet respectively was used as a solvent cell. All the fitting are wrapped with Teflon to prevent any leakages from the stainless-steel tubes and glass surface of the flask. The main flask and connectors are shown in Figure 4.4 and 4.5, respectively. The glass tube shown in Figure 4.4 is the inlet of carrier gas to the solvent cell. Figure 4.3 shows the cap to the glass flash which is connected to the sorption cell with a stainless-steel tube. Inlet glass tube has 31

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d ispersion of carrier gas into the solvent, to achieve saturation of carrier gas with solvent apors. 4.6.2 Sorption cell design 1 of the frequency. With this cell design the frequency is stable within 100 Hz. The major drawback with this cell is large flow area around QCM, resulting in the following v Figure 4.4 Bubbler Figure 4.5 Bubbler Cap Figure 4.6 shows the first design of the sorption cell. It provides good stability for the QCM and the PCB and also has secure connections resulting into better stability 32

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SMA ThermocoupleM QC TeflonSheet PCB Gas Inlet/OutletSS Tubing Cross Section 0.5 "1.75" 2.75 Welded Top Screw 0.5 0.5 1.5 0.5" 0.5 0.25 "0.25 "1.5" PCB Screw 2/16 0.25 "Open 2.0" Screws Groove Figure 4.6 Sorption cell design 1 a) No streamlined flow across the QCM b) Took long time to rec) Channeling of N2 and resulting unstable baseline 4.6.3 Sorption cell design 2 To minimize the problems listed in 4.6.2 and improve the cell performance, a new cell was designed with smaller volume, better streamlined carrier-gas flow and smaller equilibration time. The design is shown in detail in Figure 4.7. ach equilibrium 33

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Figure 4.7 Sorption cell design 2 34

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4.6.4 QCM parameter measurement and automation Figure 4.8 Overall automation programs The flow diagram of the Labview program for automation and data logging is shown in Figure 4.8. The outer most while loop is to execute the program for desired number of time to check repeatability test. It gives flexibility to select the bubblers filled with four different solvents from one through four. Depending upon the need of the experiment it can be modified to run each solvent N times to test the repeatability of the 35

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experiment, it can also be used to run all the four solvents once and then come back to the first. The case can be modified with ease to run each concentration N times and purge the sorption cell before switching to a different concentration. The program consists of many while loops and cases which are described in detail in the next few pages. Figure 4.9 Initialization of all valves Figure [4.9] is the first sequence of the program, it has been noticed that i f the rogram is not shut down properly, then some of the relays remain on. To compensate any kind of possible erroneous behavior of these relays it is desired to set all the relays to alue to all the relays and henceforth setting them off p OFF position. This case sends false v before the main program starts. It has a time delay of 2 seconds. DAQ Assistant is for PCI 6025E (200 kS/s, 12-bit 16 analog input multifunction DAQ) connected with SCB100 (I/O connector block for 100-pin digital devices), is responsible for sending the analog outputs for all the relays and mass flow controllers. 36

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Figure 4.10 First nitrogen purge cycle Figure [4.10] is sequence two in the program and it starts nitrogen purge for 10 minutes. The purge time is controlled by changing the sequence delay time. For this experiment it is set as a constant. However, it can be changed to desired time delay. Figure 4.11 Purge cycle control loop 37

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Figure [4.11] is third sequence of the program and it has further two cases true and false. Loop iteration is case. Iteration number is divided by two and the quotient is checked for zero or greater than zero values. When quotient is zero true value is sent to both the cases, and when greater than zero false is sent to both the cases. Both cases are responsible for setting constant flow through the sorption cell. When the sequence is case1 one turns off all the relays except purge valve and case2 sets purge flow to desired value. used to determine the action of the Figure 4.12 Sorption cycle control loop Figure [4.12] is false case of the sequence 3. When the sequence is case1 one turns on the relays and solenoid values required depending upon the bubbler number selected. Case2 turns the purge valve off. This case increases flow thorough the bubbler by given value and it also reduces dilution of vapor by the same amount to maintain same flow rate to the sorption cell. 38

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4.6.5 Vapor dilution system The vapor dilution system consists of four glass bubblers containing different organic solvents. UHP nitrogen is used to generate different concentrations by varying the flow of nitrogen by four dedicated MKS-made mass flow controllers, which are controlled by the Labview program developed in-house. Four solvent cells are maintained nstant temperature using a water bath. at co Figure 4.13 Vapor dilution system ematic of the entire test bed has been shown in Figure 4.13. This system can be used to measure the activity at elevated temperatures. All the stainless steel lines can be wrapped with heating tape to maintain the higher temperature. For the experimental study Sch 39

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where the solvent cell temperature would be more than ambient and has the possibility of vapor condensation, this system can be used very well. 4.7 Calibration of dilution system Reproduction of the literature data gave a clear indication of proper functioning of dilution system. The equilibrium concentrations generated can be verified by charcoal bration. Charcoal bed is placed in the outlet of the solvent cell to absorb all the vapors generated, with the difference of initial and final weight of the charcoal bed giving the mass of solvent vapor generated at any given equilibrium condition. As the charcoal calibration is in progress, an alternate route was opted to ensure proper functioning of the vapor dilution system. Activity vs. weight fraction data form Dechema handbook and experimental data collected by Dr. Venkat R. Bhethanabotla at Pacific Northwest compared with our experimental data. Activity vs. weight fraction data for benzene, n-hexane, cyclohexane, and toluene are shown in Figures 4.14 to 4.17, respectively. All the ppendix-E. the cali national laboratories (PNNL) for the well-studied polymer PIB (poly-isobutylene) were activity, weight fraction values are listed in A 40

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41 Activity (a1) Figure 4.14 Activity vs. weig ht fraction for benzene (1) / PIB (2) at 294K and its mparWeight Fraction (w1) coison with Dechema and PNNL data

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Figure comparison with Dechema and PNNL data 1Activity (a1) 4.15 Activity vs. weight fraction for n-hexane (1)/ PIB (2) at 294K and its Weight Fraction (w) 42

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Figure 4.16 Activity vs. weight fraction for cyclohexane (1) / PIB (2) at 294K and its Weight Fraction (w comparison with Dechema and PNNL data Activity (a1 1 ) ) 43

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44 F igure 4.17 Activity vs. weight fraction for toluene (1) / PIB (2) at 294K and its comparison with Dechema and PNNL data Weight Fraction (w1) ) a 1 Activity (

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PTER 5 EXPERIMENTAL PRRES AND RESULT n 5.2 describes the experimterature data for benzene. Sections 5.4 to 5.15 show the experimental activity of four m) with poly(styrene-utadiene) with different percentages (85%, 45 % and 21 % ) of styrene; along with mass at constant temgases, increase in the mass of the polymer on the crystal causes a frequency change recorded. CHA OCEDU S 5.1 Introduction Sectio ental procedure. Section 5.3 shows the available li solvents (benzene, n-hexane, dichloroethane and chlorofor b flory-huggins fit and other predictive models activities. In further sections results are analyzed to see the effect on activity for each solvent with different percentage of styrene. Comparative studies of the activities of different solvents on single copolymer are presented. Experimental procedure Rudimental fact of micro-weighing with a quartz crystal balance is that mass of polymer coated on the surface of QCM causes frequency shift proportional to the coated perature and pressure. A crystal coated with polymer which absorbs directly proportional to the mass of the gas absorbed. The procedure for determining the weight fraction of solvent in the polymer phase is described below: 1. The frequency of the uncoated crystal at desired temperature and pressure is 5.2 45

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2. Uncoated crystal is thoroughly cleaned with chloroform a nd plasma cleaner until the frequency of the crystal is fairly constant. (styrene-butadiene). 4. 3. Poly(styrene-butadiene) was dissolved in chloroform to make a solution containing 0.05 wt% poly The crystal is then coated using a spray brush to achieve a uniform thin film. 5. All the solvent of the coating is then removed using a hot air gun. The coated crystal is then allowed to cool to desired operating temperature. Change in the frequency is noted and termed as0f 6 7. After achieving the desired solvent cell temperature, the coated crystal is placed ption cell. 8. UPH nitrogen is used to generate vapor of desired concentration 9. Carrier gas nitrogen is then allowed to pass thorou in the sorgh sorption cell, resulting in a change in the frequency of the crystal which is continuously logged into an Excel .3 Literature data The activity vs. weight fraction data are collected for pure polybutadiene and centages on poly(styrene-butadiene) copolymer in figure 5.15. No data on the pol spreadsheet. 5 polystyrene for benzene [12] [21] and it is used to show a complete study on effect of polystyrene per y(styrene-butadiene) for any composition and solvent are reported in the literature so far. Available data for pure polystyrene/chloroform system [12] is not utilized in this thesis, because data for pure polybutadiene/chloroform system was not found in the literature to make the study complete. 46

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5.4 Data reductio The linear relationship between the frequency decrease and the mass of material on the piezoelectric AT-cut crystal surface was discussed in detail in Ch n apter 3. Using rene-butadiene) was alculated using the equation Sauerbreys relationship, the weight fraction of solvent by poly (sty c )()(001ffMMw fM (5.1) here w = T f he frequency shift due to the solvent mass ( M ) sorbed by the poly (styrene-diene) on the crystal surface. 0ity of the solvent in vapor with that of the solvent in the liquid solution phase at equilibrium was discussed in detail in Chapter 2. buta0fof = The frequency change due to the initially applied poly (styrene-butadiene) film Calculation of the activity by equating the fugac M 2211.(2ln.ln.BAXNXNRTnG 22121)BE (5.2) Calculated point values for the weight fraction, activity, Flory-Huggins chi parameter, s of the copolymer were studied and each set of data were m and the estimated experimental errore listed in Tables [7] to [18] of Appendix A. Three composition rs in these variables a easured twice to ensure repeatability. The first data point was collected after 20 minutes of nitrogen purge. Typically, the system reached equilibrium within one minutes he total 10 minutes sorption and desorption cycle time. At higher weight fractions it s noticed that the QCM gets over loaded results in zero values in the logged frequency. of twa 47

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Flory-Huggins Chi parameter () is shown in Figure, 5.17, 5.19, 5.21, and 5.23. As appears to be composition dependant, a liner model for thwas assumed to represent the data as shown below: 21 is dependence BA (5.2) A and B were obtained by non-linear regression o f equation (2.22). Values of A and B for and 5.3. able 5.1 Poly (styrene-butadiene) (85 % styrene) Solvents Values of A Values of B different polymer and solvent interaction are listed in Tables 5.1, 5.2 T Benzene -0.1519 0.9244 n -Hexane -0.3852 0.7721 Dichlor oethane -0.1090 1.0244 Chloroform 0.1335 1.0254 Table 5.2 Poly (styrene-butadiene) (45 % styrene) Solvents Values of A Values of B Benzene -0.0867 1.1337 n-Hexane -0.3835 1.0507 Dichloroethane -0.5748 1.4306 Chloroform -0.2672 1.4214 48

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Table 5.3 Poly (styrene-butadiene) (21 % styrene) Solvents Values of A Values of B Benzene 0.0665 0.8520 n-Hexane -0.3176 0.7576 D ichloroethane -0.1268 1.1380 Chloro form 0.0027 1.1358 5.5 Activity of benzene in poly(85% styrene-15% butadiene) Activity (a 1 ) Figure 5.1 Experimental activity of benzene (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models Weight Fraction (w) 1 49

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Figure 5.1 shows experimental activity of benzene along with a fit to the Flory-Huggins model and comparison with various free volume models (UNIFAC-FV, Entropic-FV, and GK-FV). Sorption of benzene for weight fraction of different solvents in the range of 0.012 to 0.377 is measured. For poly (styrene-butadiene) with 85% styrene coating, frequency shift was 5012.5 Hz. The corresponding film thickness is cm5109352.2 for which the mass of copolymer is obtained using e quation (4.12). 5 Hz. The maximum uctuation in frequency is 39 Hz. The term maximum fluctuation is used further in the that these fluctuations are higher with higher solvent concentrations. The errors introduced in weight fractions with these fluctuations are reported in tables [8] through [19] which are in the order of 0.0001 to 0.001. Frequency shift due to solvent sorption ranged from 65 to 307 fl result sections, which is frequency changes after reaching equilibrium. When exposed to organic solvents it is observed 50

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5 .6 Activity of n-hexane in poly(85% styrene-15% butadiene) Figure 5.2 Experimental activity of n-hexane (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models Figure 5.2 shows experimental activity of n-hexane along with Flory-Huggins model and compared to the activity with various free volume models (UNIFAC-FV, Entropic-FV, and GK-FV) predictions. Sorption of n-hexane for weight fraction of different solvents in the range of 0.0139 to 0.379 and for poly (styrene-butadiene) with 85% styrene coatings to frequency shift 5012.5 Hz. The corresponding film thickness is for which the mass of poly (styrene-butadiene)/85% styrene is obtained Weight Fraction (w1) a1 Activity () cm5109352.2 51

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using equation (4.12). Frequency shift due to solvent sorption ranged fr om 71 to 3070 z. The maximum fluctuation in frequency is was 28 Hz. ene-15% butadiene) H 5.7 Activity of dichloroethane in poly(85% styr Figure 5.3 Experimental activity of dichloroehtane (1) in poly(85 % styrene 15% parison with three predictive activity models FV, Entropic-Fa1 Activity () butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and Figure 5.3 shows experimental activity of dichloroethane along with Flory-Huggins model and compared to the activity with various free volume models (UNIFAC-V, and GK-FV) predictions. Sorption of dichloroethane for weight Weight Fraction (w 1 ) com 52

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fraction of different solvents in the range of 0.0164 to 0.365 and for poly (styrene-butadiene) with 85% styrene coatings to frequency shift 5012.5 Hz. The corresponding film thickness is cm5109352.2 for which the mass of poly (styrenebutadiene)/85% yrene is obtained using equation (4.12). Frequency shift due to solvent sorption ranged Hz. The maximum fluctuation in frequency is was 20 Hz. ) st from 84 to 2889 5.8 Activity of chloroform in poly(85% styrene-15% butadiene Figure 5.4 Experimental activity of chloroform (1) in poly(85 % styrene 15% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models Figure 5.4 shows experimental activity of chloroform along with Flory-Huggins model and compared to the activity with various free volume models (UNIFAC-FV, Weight Fraction (w1) Activity (a1) 53

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Entropic-FV, and GK-FV) predictions. Sorption of chloroform for weight fraction of different solvents in the range of 0.0164 to 0.365 and for poly (styrene-butadiene) with 85% styrene coatings to frequency shift ilm thickness is foss of poly (styrene-butadiene)/85% styr tion (4.12). cy shift dulvent sorptiged from 304 to 4890 m fluctuation in frequency is was 19 Hz. 5.9 Activity of benzene in poly(45%ene) 5012.5 Hz. The corresponding f cm5 109352.2 r which the ma ene is obtained using equa Frequen e to so on ran Hz. The max imu styrene-55% butadi F igure 5.5 Experimental activity of benzene (1) in poly(45 % styrene 55% butadiene) ) at 294 K, its representation by a modified Flory-Huggins model and comparison with ree predictive activity models Figure 5.5 shows experimental activity of benzene along with Flory-Huggins model and compared to the activity with various free volume models (Entropic-FV, and Weight Fraction (w1) A ctivi ty (a 1 ) (2th 54

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GK-FV) predictions. In this case GK-FV and entropic-FV m odels predicted better than UNIFAC-FV model. Sorption of benzene for weight fraction of different solvents in the y (styrene-butadiene) with 45% styrene coatings to frequency shift 6125.0 Hz. The corresponding film thickness is for which the mass of poly (styrene-butadiene)/45% styrene is obtained using equation (4.12). Frequency shift due to solvent sorption ranged from 140 to 2266 Hz. The mum fluctuation in frequency is was 13 Hz. 5.10 Activity of n-hexane in poly(45% styrene-55% butadiene) range of 0.0223to 0.27 and for pol cm5108176.2 axim Figure 5.6 Experimental activity of n-hexane (1) in poly(45 % styrene 55% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models Weight Fraction (w1) Activity (a1 ) 55

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Figure 5.6 shows experimental activity of n-hexane along with Flory-Huggins model and compared to the activity with various free volume models (Entropic-FV, and GK-FV) predictions. In this case all models predicted very nicely. Sorption of n-hexane for weight fraction of different solvents in the range of 0.019 to 0.241 and for poly (styrene-butadiene) with 45% styrene coatings to frequency shift 6125.0 Hz. The corresponding film thickness is for which the mass of poly (styrene-iene)/45% styrene is obtained using equation (4.12). Frequency shift due to solvent sorption ranged from 119 to 1974 Hz. The maximum fluctuation in frequency is was 17 Hz cm5108176.2 butad 56

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5.11 Activity of dichloroethane in poly(45% styren e-55% butadiene) Figure 5.7 Experimental activity of dicbutadiene) (2) at 294 K, its representa (w hloroethane (1) in poly(45 % styrene 55% tion by a modified Flory-Huggins model and comparison with three predictive activity models Figure 5.7 shows experimental activity of dichloroethane along with Flory-Huggins model and compared to the activity with various free volume models (Entropic-FV, and GK-FV) predictions. In this case UNIFAC predicted values are greater than GK-FV and Entropic-FV however later gave very close values to the experimental values. Sorption of dichloroethane for weight fraction of different solvents in the range of 0.0159 to 0.305 and for poly (styrene-butadiene) with 45% styrene coatings to frequency shift 6125.0 Hz. The corresponding film thickness is for which the mass of cm5108176.2 Weight Fraction 1 ) Activity (a 1 ) 57

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poly (styrene-butadiene)/45% styrene is obtained using equation (4.12). Frequency shift due to solvent sorption ranged from 99 to 2691 Hz. The maximum fluctuation in frequency is was 18 Hz. 5.12 Activity of chloroform in poly(45% styrene-55% butadiene) Figure 5.8 Experimental activity of chloroform (1) in poly(45 % styrene 55% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models Figure 5.8 shows experimental activity of chloroform along with Flory-Huggins model and compared to the activity with various free volume models (Entropic-FV, and GK-FV) predictions. With this system, GK-FV and entropic-FV gave similar trends to the experimental activities but at a higher values of activity for a given weight fraction. UNIFAC-FV was very unpredictable for this system. Sorption of chloroform for weight Weight Fraction (w1) Activity (a1) 58

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fraction of different solvents in the range of 0.0457 to 0.321 and for poly (styrene-25.0 Hz. The corresponding film thickness is for which the mass of poly (styrene-butadiene)/45% Frequency shift due to solvent sorption ranged from 293 to 2895 Hz. The maximum fluctuation in frequency is was 9 Hz 5.13 Activity of benzene in poly(21% styrene-79% butadiene) butadiene) with 45% styrene coatings to frequency shift 61 cm5108176.2 styrene is obtained using equation (4.12). Figure 5.9 Experimental activity of benzene (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models Figure 5.9 shows experimental activity of benzene along with Flory-Huggins model and compared to the activity with various free volume models (UNIFAC-FV, Weight Fraction (w1) Activity ( a 1 ) 59

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Entropic-FV, and GK-FV) predictions. Sorption of benzene for weight fraction of different solvents in the range of 0.0293 to 0.282 and for poly (styrene-butadiene) with 21% styrene coatings to frequency shift 4943.7 Hz. The corresponding film thickness is for which the mass of poly (styrene-butadiene)/21% styrene is obtained using equation (4.12). Frequency shift due to solvent sorption ranged from 151 to 1972 Hz. The maximum fluctuation in frequency is was 12 Hz. 5.14 Activity of n-hexane in poly(21% styrene-79% butadiene) cm5103382.2 Weight Fraction (w1) Activity ( a 1 ) Figure 5.10 Experimental activity of n-hexane (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models 60

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Figure 5.10 shows experimental activity of n-h exane along with Flory-Huggins model and compared to the activity with various free volume models (UNIFAC-FV, Entropic-FV, and GK-FV) predictions. Sorption of n-hexane for weight fraction of to 0.291 and for poly (styrene-butadiene) with 21% styrene coatings to frequency shift 4943.7 Hz. The corresponding film thickness is for which the mass of poly (styrene-butadiene)/21% styrene is obtained using equation (4.12). Frequency shift due to solvent sorption ranged from 102 to 2050 Hz. The maximum fluctuation in frequency is was 9 Hz. different solvents in the range of 0.02 cm5103382.2 61

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5.15 Activity of dichloroethane in poly(21% styrene-79% butadiene) Figure 5.11 Expbutadiene) (2) a erimental activity of dichloroethane (1) in poly(21% styrene 79% t 294 K, its representation by a modified Flory-Huggins model and omparutadiene) with is Weight Fraction (w1) Activity (1) a cison with three predictive activity models Figure 5.11 shows experimental activity of dichloroethane along with Flory-Huggins model and compared to the activity with various free volume models (UNIFAC-FV, Entropic-FV, and GK-FV) predictions. Sorption of n-hexane for weight fraction of different solvents in the range of 0.017to 0.334 and for poly (styrene-b 21% styrene coatings to frequency shift 4943.7 Hz. The corresponding film thickness cm5103382.2 for which the mass of poly (styrene-butadiene)/21% styrene is obtained 62

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using equation (4.12). Frequency shift due to solvent sorption ranged from 85 to 2513 Hz. The maximum fluctuation in frequency is was 18 Hz. 5.16 Activity of chloroform in poly(21% styrene-79% butadiene) Figure 5.12 Experimental activity of chloroform (1) in poly(21% styrene 79% butadiene) (2) at 294 K, its representation by a modified Flory-Huggins model and comparison with three predictive activity models odel and compared to the activity with various free volume models (UNIFAC-FV, Entropic-FV, and GK-FV) predictions. Sorption of n-hexane for weight fraction of different solvents in the range of 0.053 to 0.399 and for poly (styrene-butadiene) with 21% styrene coatings to frequency shift 4943.7 Hz. The corresponding film thickness is Weight Fraction (w1) Activity (a1) Figure 5.12 shows experimental activity of n-hexane along with Flory-Huggins m 63

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cm5103382.2 for which the mass of poly (styrene-butadiene)/21% styrene is obtain ed sing equation (4.12). Frequency shift due to solvent sorption ranged from 102 to 2050 Hz. Maximum hysteresis between sorption cycles corresponding to weight fraction nce 0.0012. The maximum fluctuation in frequency is was 25 Hz. 5.17 Summary The following can be concluded from section 5.5 to 5.16 All models UNIFAC-FV, GK-FV and Entropic-FV gave better fit for poly(85% styrene-15% butadiene) and poly(45% styrene-55% butadiene) copolymer/solvent systems. 2. UNIFAC-FV, GK-FV and Entropic-FV show a large absolute average activity difference for poly(45% styrene-55% butadiene) copolymer/chloroform system. 3. UNIFAC-FV, GK-FV and Entropic-FV could not predict well for copolymer poly(21% styrene-79% butadiene)/chloroform system. UNIFAC-FV was also unable to predict for copolymer poly(21% styrene-79% butadiene) / benzene and dichloroethane systems, however for the same system GK-FV and Entropic-FV gave better predictions. 4. All predictive models showed fairly high absolute average activity difference for poly(45% styrene-55% butadiene)/chloroform and benzene system compared with other solvents systems. Rest of the system has shown better predictions. u differe 1. 64

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T able 5.4 Comparison of errors with all models for copolymer poly(styrenebutadiene)/ solvents 85 % styrene Solvents Flory-Huggins Unifac GK-FV Entropic-FV Benzene 0.007 15.56 16.26 16.89 n-hexane 0.0098 46.83 16.4 20.3 Dichloroethane 0.0048 17.57 16.42 23.99 Chloroform 0.004 8.73 32.78 18.78 45 % styrene Solv ents Flory-Huggins Unifac GK-FV Entropic-FV Benzene 0.0037 31.52 7.58 7.59 n-hexane 0.4525 16.68 17.79 25.87 Dichloroethane 0.675 24.65 10.32 11.68 Chloroform 0.2165 43.27 54.81 45.88 21 % styrene Solvents Flory-Huggins Unifac GK-FV Entropic-FV Benzene 0.0011 ** 17.91 17.63 n-hexane 0.5277 14.84 14.67 16.19 Dichloroethane 0.4033 99.43 23.76 21.09 Chloroform 0.1211 95.86 ** ** All the results discussed in section 5 .17 are put in table [7]. It represents how well UNIFAC-FV, GK-FV and Entropic-FV models were able to predict for different copolymer/solvent systems. It also shows errors with Flory-Huggins fit with the experimental data are. ** indicates that corresponding models could not predict for that particular copolymer/solvent systems. 65

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5.18 Effect of copolymer composition on benzene sorption Figure 5.13 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on benzene at 294K Figure 5.13 shows the experimers. Flory-Huggins fit, and comparison with other free volume models curves have been presented in Sections 5.5, 5.9, and 5.13 of this Chapter. Because of QCM limitations, in figure 5.13 it appears that higher percentages of styrene results in better sorption for the same activity, which is intriguing. This can be explained by the resistance changes in QCM, discussed in section 5.27. In case of 45% and 21% styrene systems the last two data points are missing, in this region QCM got over loaded and damped the signal. Sudden changes in the resistances are shown in figure5.27 to 5.32 and in tables from [37] to [48]. Figure 5.16 shows the chi () parameter linearly decreasing with weight fraction and that it is larger for copolymer with 45% styrene. Weight Fraction (w1) ental activity of benzene for different polym Activity ( a 1 ) 66

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Figure 5.14 Flory-Huggins interaction parameter for benzene in poly(styrene-butadiene) with (85 %, 45% and 21% styrene) at 294K W eight Fraction (w 1 ) 67

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5.19 effect of copolymer composition on n-hexane Weight Fraction (w1) Figure 5.15 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on n-hexane at 294K Figure 5.15 shows the experimental activity of benzene for different polymers. Flory-Huggins fit, and comparison with other free volume models curves have been presented in sections 5.6, 5.10 and 5.14 of this chapter. Figure 5.15 shows that polymer composition has almost no affect on the activity of n-hexane. Lower weight fractions has almost same activity, higher styrene percentages gave better sorptions and activity. However 45% styrene system shows lesser activity, which is due QCM limitations, during the test runs with 45% system, the QCM got over loaded and impedance analyzer ) Activity (a 1 68

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69turned zero values after the 0.24 Weight fractions. So if we take 0.24 weight fraction as the reference to compare still they do fall under the linear relationship with styrene percentages but the difference in activities are small. As said in section 5.18 the chi () is decreasing with weight fraction for the n-hexane system too however for this system it is greater for copolymer with 45% styrene. re Figure 5.16 Flory-Huggins interaction parameter for n-hexane in poly(styreneb utadiene) with (85 %, 45% and 21% styrene) at 294.0K Weight Fraction (w1) 69

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5.20 Effect of copolymer composition on dichloroethane Figure 5.17 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on dichloroethane at 294K Figure 5.17 shows the experimental activity of benzene for different polymers. Flory-Huggins fit, and comparison with other free volume models curves have been presented in sections 5.8, 5.11, and 5.15 of this chapter. Figure 5.17 shows that polymer composition has almost no affect on the activity of n-hexane. Lower weight fractions have almost same activity. No abnormalities are noted in this set of data are yet there is Weight Fraction (w1) Activity (a 1 ) 70

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n o linear relationship in activity and percentage styrene in polymer. The trends for chi () are same as described in section 5.18. Figure 5.18 Flory-Huggins interaction parameter for dichloroethane in poly(styrene-butadiene) with (85 %, 45% and 21% styrene) at 294.0K Weight Fraction (w1) 71

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5 .21 Effect of copolymer composition on chloroform Figure 5.19 Effect of copolymer composition poly (styrene-butadiene) / (85%, 45 % and 21 % styrene) on chloroform at 294K Figure 5.19 shows the experimental activity of chloroform for different polymers. Flory-Huggins fit, and comparison with other free volume models curves have been presented in sections 5.8, 5.12 and 5.16 of this chapter. Figure 5.19 shows that polymer composition has almost no affect on the activity of n-hexane. Lower weight fractions has almost same activity, higher styrene percentages gave better sorptions and activity. No abnormalities are noted in this set of data are yet there is no linear relationship in activity Weight Fraction (w1) Activity (a 1 ) 72

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a nd percentage styrene in polymer. The chi () values for 45% styrene/chloroform are very high compared to other two copolymer compositions. Figure 5.20 Flory-Huggins interaction parameter for chloroform in poly(styrene-utadiene) with (85 %, 45% and 21% styrene) at 294.0K 5.22 Summary Sections 5.18 to 5.21 describe the effect of copolymer compositions on four solvents. Three different composition of styrene in poly(styrene-butadiene) copolymer behave in same fashion. Based upon weight fractions and activity of all the four solvents dont show linear relationship. If we arrange them in ascending order of activity and weight fraction they will be 85 % styrene, 21 % styrene and 45 % styrene. Weight Fraction (w1) b 73

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5.23 Activities of four solvents in poly(styrene-butadiene) (85% styrene) at 294 K Figure 5.21 Activity of four solvents in poly (styrene-butadiene) in (85% styrene) at 94K Figure 5.21 is a plot for activity of four solvents (benzene, n-hexane, dichloroethane and chloroformChloroform shows a totally different trend compared to remaining 3 solvents. This kind of behavior is noticed with different copolymers. Chi values for benzene and chloroform fractions and activity data for both solvents are very close which is shown in figure 5.21. Weight Fraction (w) Activity (a1 ) 1 2 ) in copolymer poly(styrene-butadiene) (85% styrene). overlap on each other. That may be because the experimental data shows that the weight 74

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Figure 5.22 Flory-Huggins interaction parameter for four solvents in poly(styrene-butadiene) with (85 % styrene) at 294.0K Weight Fraction (w1) 75

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5 .24 Activities of four solvents in poly(styrene-butadiene) (45% styrene) at 294 K Weight Fraction (w1) Activity ( a 1 ) Figure 5.23 Activity of four solvents in poly (styrene-butadiene) in (45% styrene) at 294K Figure 5.23 is a plot for activity of four solvents (benzene, n-hexane, dichloroethane and chloroform) in copolymer poly(styrene-butadiene) (45% styrene). Clearly the difference in activities for benzene, n-hexane and dichloroethane is less; chloroform stays apart. 76

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Figure 5.24 Flory-Huggins interaction parabutadie meter for four solvents in poly(styrene-ne) with (45 % styrene) at 294.0K Weight Fraction (w 1 ) 77

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5 .25 Activities of four solvents in poly(styrene-butadiene) (21% styrene) at 294 K F2 igure our solvents in poly (styrene-butadiene) in (21% styrene) at 94 ne, rm) in copolymer poly(styrene-b) (21% styrene). Cless; chlorofActivity (a1) 5.25 Activity of fWeight Fraction (w 1 ) K Figure 5.25 is a plot for activity of four solvents (benzene, n-hexaand chlorofo dichloroethane utadiene arly the difference in activities for benzene, n-hexane and dichloroethane is lerm stays apart. o 78

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79 Figure yrene-butadie.26 Summary Sections 5.20 to 5.23 shows how the activity of four different solvents on varying percentage of styrene on poly(styrene-butadiene) copolymer. Clearly chloroform shows different behavior with 85% 45% and 21% styrene in copolymer. The predictive models show composition dependence, similar trends are not seen with the experimental data which is may be because the source of polymers are different. 45 % and 21% styrene are block copolymers were obtained from Sigma-Aldrich and 85% styrene was obtained from polysciences. 5.26 Flory-Huggins interaction parameter for four solvents in poly(stne) with (21 % styrene) at 294.0K Weight Fraction (w 1 ) 5

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.27 Resistance changes Changes in the resistance of the equivalent rcuit model can give a clear picture of the mass balance regime. Figures 5.27, 5.29 and 5.31 are plots of resistance changes due to solvent sorption. Figures 5.28, 5.30 and 5.32 are the plots of motional resistance with time. It is observed that there is a rapid increase in this resistance at higher weight fractions which is because of QCM going out of the mass balance regime. To explain more clearly the change in resistance is plotted against corresponding weight fractions for each time cycle. ci Figure 5.27 Change in resistance of the equivalent circuit model of the QCM for poly(85% styrene15 %butadiene) copolymer film Motional Resistance Time (Seconds) 80

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F igure 5.28 Change in resistance vs. weight fraction for four solvents and poly(85% styrene15 %butadiene) copolymer system Weight Fraction (w1) Change in Resistance 81

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Figure 5.29 Change in resistance of the equivalent circuit model of the QCM for poly(45% styrene55 %butadiene) copolymer film Motional Resistance Time (Seconds) 82

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Figure 5.30 Change in resistance vs. weight fraction for four solvents and poly(45% styrene55 %butadiene) copolymer system Change in Resistance Weight Fraction (w 1 ) 83

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Figure5.31 Change in resistance of the equivalent circuit model of the QCM for polyrene79 %ne) copoly Motional Resistance Time (Seconds) (21% sty butadie mer film 84

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Figure 5.32 Change in resistance vs. wtion foents and% styrbutadienmer syst Weight Fraction (w1) Change in Resistance eight frac r four solv poly(21 ene79 % e) copoly em 85

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CHAPTER 6 6.1 Conclusions ties of b-hexane,thane, rm were measured at 294 K using quartz crystal microbalance. Experimlts leadollowing concluties of tnts studipendanttage ofin ymer. 2. A linear relationship is not noticed between percentage of styrene present in copolymer and activity. f solvents studied are independent of the film thickness. 6.2 Copolymer composition trends ties of model-FV, d Entropfor benzene in all three er systemown in1], [6.2].3] respectively. The remaining systems are listed in appendix-G. For these three models, the actis had thng trendrene-but% styrene) had the higty, polystadiene rene) hd higheity, andne-butad styrenewest acity decrewith the increasing composition of polystyrene in the copolymer. Also the predictions by GKRESULTS AND CONCLUSIONS Activi enzene, n dichloroe and chlorofo ental resu to the f sions: 1. Activi he solve ed are de on percen styrene copol 3. Activities o Activi predictive s UNIFAC GK-FV an ic-FV copolym s are sh figure [6. and [6 vity curve e followi s: polysty adiene (21 hest activi tyrene-bu (45 % sty ad the secon st activ polystyre iene (85% ) had the lo tivity. Activ ased 86

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FV and Entropic-FV are b etter than UNIFAC-FV. Except n-hexane the other three solvents showed similar composition dependence. Figure 6.1 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/benzene systems 1) Weight Fraction (w1) Activity (a 87

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Figure 6.2 GK-FV predictions for copolymers with 85%, 45% and 21 % styrene/benzene sy t FractiActivity (a1) stems Weigh on (w 1 ) 88

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Figure 6.3 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/benzene systems 6.3 Suggestions for future research 1. QCM has proved very reliable for collecting such thermodynamic experimental data. Due to its sensitive nature to small mass changes, accurate measurements at lower concentrations can be achieved. 2. This work is carried out at 294 K; with the existing facilities, effect of temperature on the activities of solvents for same solvent/copolymer system can be further investigated. a) Weight Fraction (w1) Activity ( 1 89

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3. Data for polystyren e and polybutadiene are available for only benzene. polymers, to make the study more complete. aratus should be utilized for measurements of a variety of other solvent ctivities in these co-pocternteracr solver sysciallymer systems for which data are scarce can be attempted with this apparatus. perature coefficients r the crystal employed in this cangated. e showr simtals no change in al free to tee fluctuations was observed [21]. Measurements for the other three solvents should be attempted for the pure 4. The app a lymers to chara ize the i tions. 5. Othe ent/polym tems, espe co-poly 6. Tem at room temper ature fo work be investi Literatur s that fo ilar crys cryst quency du mperatur 90

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NC 1. Method for estimating the activity coefficient of a component in a defined liquid ure., a predinual DImicrobalance." KSV technical note. ave Sensors-Theory, Design, and Physico-micalns, Acress. 4. Elbro, H. S., A. Fredenslund, et al. A New Simple Equation for the Prediction of ent A Polymions. Gmechling, et al. (1977). "Vapor-Liquid Equilibra Using 7. French, R. N. and G. J. Koplos (1990). "Activity coefficients of solvents in elastomers measured with a quartz crystal microbalance." Fluid phase equilibria 158-160: 879-892. 8. www.piezotech.com (technical information) 9. French, R. N. and G. J. Koplos (1999). "Activity coefficients of solvents in elastomers measured with quartz crystal microbalance." Fluid phase equilibria 158-160: 879 892. 10. Grate, J. W., S. N. kaganove, et al. (1997). Examination of mass and modulus contributions to thickness shear mode surface acoustic wave vapor sensor responses using partition coefficients." Farady discuss 107: 259-283. 11. Hao, W., H. S. Elbro, et al. "Polymer solution data collection, vapor-liquid equilibrium." Dechema Chemistry data series XIV(Part 1). 12. Huggins, M. L. (1941). J. Chem. Phy. 9: 440. REFERE ES mixt AIChe dat ction ma PPR. 2. (Nov. 2003). "W hat is a quartz crystal 3. Ballantine, D. S. (1996). Acoustic WChe Applicatio ademic P Solv ctivities in er Solut 5. Flory, P. J. (1941). J. Chem Phy. 9: 660. 6. Fredenslund, A., A. JUNIFAC." Elsevier Scientific Publishing. 91

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13. Kontogeorgis, G. M., A. Fredenslund, et al. (1993). "Simple Activity Coefficient Model for the Prediction of Solvent Activities in Polymer Solutions." Ind. Eng. 14. Oishi, T. and J. M. Prausnitz (1978). "Estimation of Solvent Activities in Polymer s Using a Group-Contribution Method." Ind. Eng. Chem. Process et al. (1986). Molecular Thermodynad Phaseria., Pre16. Prauznitz, J. M. (1969). Molecular thermodynamics of fluid-Phase Equilibria. lewoodew Jersy, Printice Hall. 2). "Advanced interface electronics and thods fo" Sensotuators : 543-19. Smith, J. M. and H. C. V. Ness Introduction to chemical engineering modyn 21. Wong, H. C., S. W. Campbell, et al. Sorption of benzene, toluene and chloroform by poly(styrene) at 298.15 K and 323.15 K using a quartz crystal balance. Tampa, FL 33620-5350, USA. Masters. Chem. Res. 32: 362-372. SolutionDes.Dev 17(3): 333. 15. Prausnitz, J. M., R. N. Lichtenthaler, flui mics of Equilib ntice Hall. Eng Cliff, N 17. Sauerbrey and G. Zeitschrift (1959). Physics 155: 206-222. 18. Schroder, J. and R. Borngraber (200me r QCM. rs and ac A 97-98 547. ther amics. 20. Tsonopoulos, C. (1974). EmAICHE J. pirical correlation of second virial coefficients. Department of Chemical Engineering. Tampa, University of South Florida, 92

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NDICI APPE ES 93

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Appendix A Experimental activity, weight fraction and chi values The following tables contain numerical values of all the experiments Table A1 Activity of bnzene -but(85% s = 5675 Hz e in poly (styrene adiene) tyrene) 0f 1 w 1w 1a 1 a 0.01277 0.00002 0.146238 0.063853 0.91057 0.040298 0.00015 0.264411 0.036292 0.88083 0.076457 0.00014 0.361896 -0.0068507 0.84178 0.10841 0.00007 0.443691 -0.014913 0.80728 0.141613 0.0 0010 0.513303 -0.014643 0.77144 0.17710.00021 0.573267 -0.0098062 0.73306 74 0.220809 0.00038 0.625459 -0.0069956 0.68599 0.267493 0.00094 0.671298 0.00018438 0.63564 0.315954 0.00124 0.711878 0.0097261 0.5834 0.377169 0.00185 0.748056 0.013442 0.51744 94

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Appendix A (Continued) Table A2 Activity of n-hexane in poly (styrene-butadiene) (85% styrene) 0f = 5675 Hz 1w 1w 1a 1 a 0.013932 03 0.155923 0.0630 0.000 123 .71243 0.045946 28 0.279076 0.0230 0.000 738 .66858 0.086364 15 0.378823 -0.0120 0.000 932 .61433 0.132873 23 0.461265 -0.0310.5534 0.000 089 0.163894 51 0.530552 -0.0080 0.000 9468 .51361 0.204905 59 0.589603 0.0020 0.000 4062 .46204 0.259177 00 0.640531 0.0050.3955 0.001 1634 0.311455 20 0.684907 0.0110.3332 0.001 434 0.37963 71 23919 0.0050 0.000 0.7 9025 .25446 able A3 Activity of dichloroehtane in poly (styrene-butadiene) (85% styrene) = 5675 Hz T 0f 1w 1w 1a 1a 0.016442 0.00003 0.143189 0.052035 1.307 0.046309 0.00006 0.259545 0.027594 1.2796 0.075437 0.00004 0.355969 0.013119 1.2521 0.107935 0.00008 0.437179 -0.0039652 1.2207 0.141466 0.00015 0.506515 -0.013112 1.1873 0.176365 0.00017 0.566404 -0.015122 1.1514 0.219357 0.00034 0.618653 -0.017656 1.1056 0.261138 0.00044 0.664638 -0.0079457 1.0593 0.311738 0.00078 0.705422 0.0045494 1.0007 0.365049 0.00096 0.741839 0.023111 0.93572 95

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Appendix A (Continued) Table A4 Activity of chloroform in poly (styrene-butadiene) (85% styrene) 0f= 5675.5 Hz 1 w 1w 1a 1 a 0.057046 14 0.162972 -0.0050 0.000 4212 .68548 0.10619 25 89673 0.0010 0.000 0.2 1278 .66644 0.155036 36 0.391018 0.0020 0.000 262 .64672 0.20415 45 73935 0.00060 0.000 0.4 8384 .62601 0.253454 36 0.543037 -0.0010.6043 0.006 3538 0.29838 79 01515 0.0020 0.000 0.6 2008 .58364 0.349262 90 0.651645 -0.00050 0.000 6717 .55918 0.39906 7 05 0.695097 -0.00120 0.001 206 .53406 0.449677 0.001 18 0.733124 -0.00190. 836 50725 0.493192 0.00104 0.766681 0.001916 0.48309 Table A5 Activity of benzene in poly (styrene-butadiene) (45% styrene) = 6125 Hz 0f 1w 1w 1a 1a 0.0223 0.00003 0.1462 0.019746 1.0871 0.0498 0.00006 0.2644 0.0087907 1.0645 0.0778 0.00005 0.3619 -8.88E-05 1.0412 0.106 0.00009 0.4437 -0.0045977 1.0173 0.1366 0.00018 0.5133 -0.0096128 0.99109 0.161 0.00025 0.5733 0.0023831 0.96985 0.2006 0.00048 0.6255 -0.0063094 0.93481 0.2461 0.00055 0.6713 -0.01098 0.89364 0.2701 0.00059 0.7119 0.0091834 0.87152 96

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Appendix A (Continued) Table A6 Activity of n-hexane in poly (styrene-butadiene) (45% styrene) 0f = 6125 Hz 1 w 1w 1a 1 a 0.0191 0.0000359 0.030. 0.15 157 99035 0.0486 0.0001 1 0.00620.9532 0.2791 091 5 0.0791 0.0001 6 0.3788 -0.006 101 0.9148 0.113 0.0001 6 -0.012897 0.8719 0.4613 5 0.144 0.0003 0 -0.0020.8326 0.5306 4015 7 0.1909 0.0003 5 -0.0048410.7730 0.5896 7 6 0.2412 0.0006 9 0.00290.7088 0.6405 141 8 Table A7 Activity of dichloroethane in poly (styrene-butadiene) (45% styrene) z 0f= 6125 H 1w w 1 1a 1 a 0.0159 0.00002 0.1432 0.049796 1.6491 0.0442 0.00008 0.2595 0.022532 1.6207 0.0723 0.00009 0.356 0.0019714 1.5916 0.0986 0.00008 0.4372 -0.006435 1.5635 0.1236 0.00010 0.5065 -0.006786 1.5359 0.1495 0.00014 0.5664 -0.0052077 1.5064 0.1816 0.00026 0.6187 -0.0085284 1.4685 0.2218 0.00058 0.6646 -0.010943 1.4189 0.2698 0.00080 0.7054 -0.0038612 1.356 0.3052 0.00015 0.7418 0.0201 1.307 97

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Appendix A (Continued) Table A8 Activity of chloroform in poly (styrene-butadiene) (45% styrene) f 0 = 6125 Hz 1 w 1w 1a 1 a 0.0457 0.000153 0.0151.0411 0.16 993 0.1003 0.0001 9 0.2897 -0.0045381.0158 2 0.1466 0.0001 9 0.391 -0.0066710.9931 8 0.1871 0.0002 3 0.4739 -7.56E-05 0.9721 5 0.2294 0.0002 7 0.543 0.00170.9491 719 1 0.2749 0.0003 7 0.6015 0.00030.9228 1802 9 0.321 0.0004 1 0.00080.8946 0.6516 7697 7 Te in poly (styrene-butadiene) (21% styrene) = 4943.75 Hz able A9 Activity of benzen 0f 1w 1w 1a 1a 0.029315 0.00004 0.146238 -0.0077869 0.80763 0.053389 0.00004 0.264411 0.007361 0.7902 0.082569 0.00005 0.361896 0.002578 0.76902 0.111111 0.00008 0.443691 0.0035164 0.74823 0.145007 0.00016 0.513303 -0.0036923 0.72345 0.176412 0.00019 0.573267 -0.00049536 0.70041 0.218261 0.00022 0.625459 -0.0078631 0.66957 0.257389 0.00044 0.671298 -0.0055144 0.64061 0.282846 0.00048 0.711878 0.011442 0.6217 98

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Appendix A (C ontinued) ty of n-hexane in poly (styrene-butadiene) (21% styrene) Table A10 Activi 0f= 4943.75 Hz 1 w 1w 1a 1a 0.019992 0.00002 0.155923 0.03048 1.0004 0.054642 0.00007 0.27907 6 0.0047199 0.96176 0.089253 0.00012 0.378823 -0.0070245 0.92172 0.124803 0.00014 0.461265 -0.01262 0.8771 0.174373 0.00027 3 0.50552 -0.00082921 0.8362 0.223723 0.00020 0.589603 -0.0013289 0.77412 0.270286 0.00029 0.64053 1 0.0082156 0.70729 0.29078 0.00002 0.684907 0.03048 1.0004 Table A11: Activity of dichloroethane in poly (styrene-butadiene) (21% styrene) 0f= 4943.75 Hz 1w 1w 1a 1a 0.016716 0.00002 0.143189 0.04 8554 1.4148 0.046711 0.00007 0.259545 0.020193 1.3869 0.075615 0.00006 0.355969 0.0035759 1.3593 0.1089 0.00007 0.437179 0.0016381 1.3337 16 0.131643 0.00009 0.506515 0.0059683 1.30 -34 0.16625 0.00016 0.566404 -0.014471 1.2673 0.20153 3 0.00039 0.618653 -0.013708 1.2292 0.242654 0.00054 0.664638 -0.0096668 1.1829 0.287546 0.00065 0.705422 0.0018419 1.13 0.334487 0.00080 0.741839 0.020514 1.0718 99

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A ppendix A (Continued) tyrene-butadiene) (21% styrene) = 4943.75 Hz Table A12 Activity of chloroform in poly (s 0f 1w 1w 1a 1a 0.0529 0.00000 0.163 0.005172 0.77607 0.1046 0.00001 0.2897 0.0036538 0.75455 0.1569 0.00000 0.391 -0.0025108 0.73167 0.2064 0.00059 0.4739 -0.0039223 0.7089 0.252 0.00032 0.543 0.00010005 0.68689 0.3014 0.00091 0. 6015 -0.0005472 0.66184 0.352 0.00091 0.6516 -0.0010087 0.63477 0.3987 0.00141 0.6951 0.0030225 0.60843 100

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Appendix B Comparison of different model errors The following table contains numerical values of error calcuFlroy-Huggins fit and predicted values by UNIFAC-FV, GK-FV and Entropic-FV. Table B1 Comparison of activity of benzene in poly (styrene-butadien = 5675 Hz lated for experiment data are; e)/(85% styrene) 0f 1w 1a Fry-HugginsUnifac GK-FV Entropic-FV lo 0.01277 0.146238 0.082384 0.059 0.0596 0.0557 0.040298 0.264411 0.22812 0.1734 0.1703 0.1655 0.0764 57 0.361896 0.36875 0.3013 0.2968 0.2908 0.10841 0.443691 0.4586 0.3967 0.393 0.3861 0.141613 0.513303 0.52795 0.4815 0.4794 0.4721 0.177174 0.573267 0.58307 0.5588 0.5591 0.5514 0.220809 0.625459 0.63245 0.6382 0.6413 0.6337 0.267493 0.671298 0.67111 0.7076 0.7135 0.7062 0.315954 0.711878 0.70215 0.7664 0.7744 0.7676 0.377169 0.748056 0.73461 0.8253 0.835 0.829 Absolute average activity difference 0.0070 15.56 16.26 16.89 101

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Appendix B (Continued) Table B2 Comparison of activity of n-hexane in p oly (styrene-butadiene)/(85% styrene) = 5675 Hz 0f 1w 1a Flory-HugginsUnifac Konto Elbro 0.013932 0.155923 0.0928 0.1192 0.0835 0.051 0.045946 0.279076 0.25534 0.3487 0.2195 0.1589 0.086364 0.378823 0.39175 0.5671 0.3637 0.2787 0.132873 0.461265 0.49235 0.7449 0.497 0.3969 0.163894 0.530552 0.5395 0.831 0.5701 0.4656 0.204905 0.589603 0.5872 0.9149 0.6509 0.5458 0.259177 0.640531 0.63537 0.9875 0.7357 0.6356 0.311455 0.684907 0.67347 1.0285 0.7986 0.7074 0.37963 0.723919 0.71802 1.0545 0.8601 0.7831 Absolute average activity difference 0.0098 46.83 16.4 20.3 102

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Appendix B ( Continued) in poly (styrene-butadiene)/(85% styrene) Table B3 Comparison of activity of dichloroethane 0f= 5675 Hz 1w 1a Flory-HugginsUnifac Konto Elbro 0.016489 0.0944 0.072546 42 0.1431 1154 0.06 1 0.0 0.04609 0.2590.23195 0.1701 0.1749 0.1466 3 545 0.075437 0.355969 0.34285 009 .26 0.2652 0.2281 0.107935 0.437179 0.44114 0.3502 0.3548 0.3106 0.141466 0.506515 0.51963 0.4309 0.4364 0.3873 0.176365 0.566404 0.58153 0.5043 0.5111 0.4591 0.219357 0.618653 0.63631 0.5823 0.5908 0.5375 0.261138 0.664638 0.67258 0.6471 0.6569 0.6043 0.311738 0.705422 0.70087 0.7135 0.7245 0.6746 0.365049 0.741839 0.71873 0.7717 0.7832 0.7376 Absolute average activity feren 0.0048 17.57 16.42 dif ce 23.99 103

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Appendix B (Continued) Table B4 Comparison of activity of chloroform in poly (styrene-butadiene)/(85% styrene) f 0 = 5675 Hz 1 w 1a Flory-HugginsUnifac Konto Elbro 0.057072 0.197 0.267243 46 0.1629 6839 0.20 4 0.2 0.10619 0.289673 0.28855 0.3165 0.4249 0.366 0.155036 0.3910 18 0.38876 0.3919 0.5434 0.4754 0.20415 0.4739 35 0.47325 0.452 0.6355 0.5631 0.2534 54 0.5430 37 0.54439 0.5042 0.7084 0.6349 0.29838 0.6015 15 0.59931 0.5479 0.7622 0.6899 0.349262 0.6516 45 0.65221 0.5953 0.812 0.7429 0.3990 67 0.6950 97 0.69632 0.6405 0.8521 0.7875 0.449677 0.7331 24 0.73511 0.6859 0.8859 0.8269 0.493192 0.7666 81 0.76477 0.7243 0.9105 0.8568 Absolute a veragferen0.004 8.73 32.78 18.78 e activity dif ce 104

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Appendix B (Continued) Table B5 Comparison of activity of benzene in poly (styrene-butadiene)/(45% styrene) 0f = 6125 Hz 1w 1a Flory-fac Konbro HugginsUni to El 0.0223 0.1462 0.12645 0.1833 0.1163 0.1162 0.0498 0.2644 0.25561 092 .35 0.241 0.241 0.0778 0.3619 0.36199 0.496 0.35 0.35 0.106 0.4437 0.4483 0.602 0.4441 0.4441 0.1366 0.5133 0.52291 0.6903 0.5313 0.5313 0.161 0.5733 0.57092 0.7457 0.5912 0.5912 0.2006 0.6255 0.63181 0.8144 0.6733 0.6733 0.2461 0.6713 0.68228 0.8702 0.7486 0.7485 0.2701 0.7119 0.70272 0.8924 0.7815 0.7815 Absolute a veragdifference e activity 0.0037 31.52 7.58 7.59 Table B6 Comparison of activity of n-hexane in poly (styrene-butadiene)/(45% styrene) = 6125 Hz 0f 1w 1a Flory-HugginsUnifac Konto Elbro 0.0191 0.1559 0.12433 0.0851 0.0841 0.0703 0.0486 0.2791 0.27289 0.2029 0.1976 0.1699 0.0791 0.3788 0.3849 0.3092 0.3007 0.2626 0.113 0.4613 0.4742 0.4114 0.4005 0.3544 0.144 0.5306 0.533 0.4923 0.4799 0.4293 0.1909 0.5896 0.59444 0.595 0.5816 0.528 0.2412 0.6405 0.63759 0.6837 0.6701 0.6171 Absolute average activity difference 0.4525 16.68 17.79 25.87 105

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Appendix B (Continued) Table B7 Comparison of activity of dichloroethane in poly (styrene-butadiene)/(45% styrene) 0f= 6125 Hz 1w 1a Flory-fac Konbro HugginsUni to El 0.0159 0.1432 0.093404 0.1289 0.0859 0.0794 0.0442 0.2595 0.23697 056 .31 0.2184 0.2056 0.0723 0.356 0.3540 3 0.459 0.3315 0.314 0.0986 0.4372 0.4436 3 0.5646 0.4231 0.4024 0.1236 0.5065 0.5132 9 0.6451 0.4991 0.4762 0.1495 0.5664 0.5716 1 0.7127 0.568 0.5436 0.1816 0.6187 0.6272 3 0.7789 0.6412 0.6159 0.2218 0.6646 0.6755 4 0.8413 0.7171 0.6916 0.2698 0.7054 0.70926 0.8942 0.7889 0.7642 0.3052 0.7418 0.721 7 0.9225 0.8312 0.8077 Absolute a veragdifference e activity 0.675 24.65 10.32 11.68 106

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Appendix B ( Continued) rison of activity of chloroform in poly (styrene-butadiene)/(45% styrene) Table B8 Compa 0f= 6125 Hz 1w 1 a Flory-HugginsElbro Unifac Konto 0.0457 0.163 0.14701 0.2802 0.2596 0.3593 0.1009424 0.5042 0.4716 3 0.2897 0.2 0.5149 0.1466 0.391 0.39767 0.5737 0.6358 0.5977 0.1871 0.4739 0.47398 0.6058 0.7215 0.6811 0.2293 0.7902 0.749 4 0.543 0.5412 0.6318 0.2749 0.6015 0.60118 0.8466 0.8059 0.6568 0.321 0.6516 0.65072 0.6817 0.8903 0.851 Absoe activity 0.2165 43.27 54.81 45.88 lu te averag difference 107

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Appendix B ( Continued) in poly (styrene-butadiene)/(21% styrene) = 4 Table B9 Comparison of activity of benzene 0f 943.75 Hz 1w 1a Flory-HugginsUnifac Konto Elbro 0.029315 0.146238 0.15402 0.4298 0.1722 0.1719 0.053389 0.264411 0.25705 0.6554 0.2916 0.2908 0.082569 0.3618 96 0.35932 0.8337 0.4139 0.4128 0.111111 0.443691 0.44017 0.9436 0.5138 0.5124 0.145007 0.513303 0.517 1.0227 0.6115 0.6099 00.573267 0.57376 1.0647 0.6855 0.6838 .176412 0.218261 0 .625459 0 .63332 1.0927 0.7643 0.7625 000.61 0.8199 .257389 .671298 768 1.1018 0.8216 0.282846 00.70.8504 .711878 0044 1.1024 0.8521 Aeragdifference 0.0011 ** bsolute av e activity 17.91 17.63 108

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Appendix B (Continued) Table B10 Comparison of activity of n-hexane in poly (styrene-butadiene)/(21% styrene) 0f= 4943.75 Hz 1w 1 a Flory-Huggins Unifac Konto E lbro 0.019992 0.155923 0.12 0.0766 254 0.0843 0.0861 0.054642 0.279076 0.20.1966 7438 0.2144 0.2161 0.089253 0.378823 0.30.3019 8582 0.3267 0.3285 0.124803 0.461265 0.40.3968 7392 0.4262 0.428 0.174373 0.530552 0.50.5098 3143 0.5424 0.5442 0.223723 0.589603 0.0.6032 59093 0.6363 0.6381 0.270286 0.640531 0.0.6768 63228 0.7086 0.7105 0.29078 0.684907 0.0.7052 63228 0.7362 0.738 Absolute avedifference ra0.5277 14.84 16.19 ge activity 14.67 109

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Appendix B (Continued) Table B11 Comparison of activity of dichloroethane in poly (styrene-butadiene)/(21% styrene) 0f = 4943.75 Hz 1 w 1 a Flory-Huggins Unifac Konto Elbro 000. .016716 .143189 094635 0.2832 0.1145 0.11 0.046711 0.259545 0.25 0.2795 393 0.634 0.2877 0.075615 0.355969 0.30.8461 0.4143 5239 0.425 0.101689 0.437179 0.40.5161 3554 0.9703 0.5283 0.131643 0.506515 0.50.6137 1248 1.0617 0.627 0.16625 0.5664 04 0.58081.1234 0.7191 0.7051 8 0.201533 0.6186 53 0.63231.1557 0.7933 0.7792 6 0.242654 0.664638 0.0.8463 67431 1.17 0.86 0.287546 0.705422 0. 70358 1.169 0.9138 0.901 0.334487 0.741839 0.0.9422 72133 1.158 0.954 Absolute ave radifference 0.4033 99.43 23.76 21.09 ge activity 110

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Appendix B (Continued) Table B12 Comparison of activity of chloroform in poly (styrene-butadiene)/(21% styrene) 0f= 4943.75 Hz 1w 1 a Flory-Huggins Unifac Konto E lbro 0.0529 0.163 0.100.6987 5783 .0529 0.7854 0.1046 0.2897 0.2 8605 0.0002 0.9848 0.8849 0.1569 0.391 0.3 0.9593 9351 0.0003 1.0599 0.2064 0.4739 0. 47782 0.0004 1.0904 0.9933 0.252 0.543 0.5429 0.0005 1.1032 1.0107 0.3014 0.6015 0. 60205 0.0006 1.1083 1.0218 0.352 0.6516 0.1.0285 65261 0.0007 1.1083 0.3987 0.6951 0. 69208 0.0009 1.1053 1.032 Absolute avdifference era0.1211 95.86 ge activity ** ** 111

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Appendix C Error Analysis E xperimental errors in w1, a1, and were estimated to first order using a propagation of C.1 Weight fraction error analysis. )(01fffw ) Taking partial derivatives w. r. t. (C-1 0f and f )(01ffffw ) (C-2 )(001ffffw ) Thus, the first order absolute error in w1 is (C-3 '020'201)()(ffffffffw (C-4) Where and are the functions in frequency measurement. The QCM is found stable with in 1 Hz after polymer coating. There for ignoring term in equation [C-4] reduces to f 0f 0'f '201)(ffffw (C-5) 112

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The error data are reported in table [7] through [18], equation [C-5] is used for .2 Activity of solvent 2.1write calculating the error. C From equation 3 we can at SatlVp1 RT SSatSatPPExRTPExPBBByBExpP11131123111111112Ecan b Bp11 3 (C-6) a RT P x 13 quation C-5 e rewritten as SatP1 SatP111 SatlPRTVRTBBBByBRTPExpPa13313231112) here P is given by wagner equation 2.14 11 1 x1111 SatP ( C-7 W 635.111lnxVxVxVxVxPPPDPCPBPAc (C-8) Where CTTx1 and T is sorption cell temperature. For eqution C-7 can be written as SatP 635.111lnxVxVxVxVxPPPDPCPBPAcSat ( C-9) Where CSatTTx1 and Sat T is sorption cell temperature 113

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Appendix C (Continued) The solvent second virial coefficient is given by RRCCCTfTfTRPB)1()0(11 (C-10) 8RT 3213.01445.RTf )0(0 00607.0 0121.058 330.0 )(RT RT RT (C-11) 8T 321(008.00073.0097.05.046.0073.0RRRRRTTTTf ) H critisure, is the critical ture, 3 ))(RT (C-12 ere CP is the cal pres CT emperat is the ace ntric fd ced tre. Partivatives oon C-111 witht actor an RT is the redu emperatu al deri f equati 0 and Crespec Sat T to 9432)0(006 07 .01358.3.0SatSatSatSatTTT ) 0121.0 030 SatT T f (C-13 984332)1(064.0269.1662.0SatCSatCSatCSatTTTTTTTf (C-14) Differentiating equation C-9 would give CCSatPRTTfTfTB.)1()0(011 (C-15) Similarly differentiating equation C-7 and C-8 xxVxVxVxVExpPTPPDPCPBPAC1635.1 (C-16) xxVxVxVxVExpPTPPDPCPBPACSatSat1635.11 (C-17) 114

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Appendix C (Continued) Solving equation C-15 and C-16 would result to 525.15623321.xxVxxVxxVxVPPDPCPBPAC (C P TT 2 1 -18) 525.11163321xxxxTPTPDPCPBPASatSat ) Taking partial derivatives of C-6 with respect to P and C V 5Vx 1PSat 2 2Vx Vx (C-19 11 1,,BPSat T 111111 .a RTVBPa ) P a Sat (C-20 RTVPaTaSatSatSat11111. ) B11 (C-21 SatPPRTaBa11111 (C-22) 121111.aRTVBTaSat (C-23) Applying the chain rule TPPaTa11 (C-24) SatSatSatSatSatSatTaTBBaTPPaTa1111111111 (C-25) For first order, the error in the activity due to fluctuations in the temperatures of solvent cell and the sorption cell is 115

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Appendix C (Continued) SatSatSatSatSatSatTTaTBBaTPPaTTP Pa1 a1111111 (C-26) 11 1 116

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Appendix D Comparison of USF, PNNL and DECHEMA data Ty vs weight fraction for benzene / PIB at 294K and its comparison with Nz able D1 Activitechema and PN D L data 0f= 10680 H USF Dhema DaL Data ata Dec ta PNN 1w 1a 1w 1a 1w 1a 0.006456 0.080964 0 0 0.00. 0096259 006600 0.020361 0.160448 0.0437 0.3007 0.0 0. 04313937 031500 0.034273 0.238495 0.0633 0.4078 0.0 0. 14352572 099400 0.049658 0.315145 0.0945 0.5189 0.0 0. 28159963 186200 0.06538 0.390436 0.1502 0.6936 0.0 0. 50160824 309800 0.082263 0.460.1516 0.7046 0.0 0. 4407 76218879 433000 0.101718 0.530.1842 0.7614 0.0. 7092 0913906 494400 0.123625 0.608527 0.2453 0.8558 0.108539908 0.555800 0.149578 0.678745 0.2453 0.8558 0.130003093 0.617000 0.177638 0.747777 0.2453 0.8558 0.130003093 0.617000 117

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Appendix D (Continued) Table D2 Activity vs weight fraction for n-hexane / PIB at 294K and its comparison with Dechema and PNNL data 0f = 10680 Hz USF D ata D a Dech em ata PNNL D ata 1w 1a 1 w 1a 1w 1a 0.014383 0.080039 0 0 0.0 0. 00890349 006700 0.029621 0.157539 0.0678 00.0 0.0 .281 04526218 32000 0.04495 0.232626 0.0948 0.404 0.0 0. 15439056 100800 0.061065 0.305415 0.1229 00.0 0. .505 30909645 188500 0.078085 0.376016 0.1659 00.0 0. .606 56157929 313200 0.0957 0.444528 0.2263 0.722 0.0 0. 87059902 437100 0.115703 0.511048 0.2502 0.0.1 0. 756 05994516 498800 0.138047 0.575666 0.2841 00.1 0. .805 28004822 560300 0.163247 0.638464 0.2841 0.805 0.10. 5807407 621600 0.186563 0.699522 0.2841 0.805 0.15807407 0.621600 118

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Appendix D (Continued) Table D3 Activity vs weight fraction for cyclohexane / PIB at 294K and its comparison with Dechema and PNNL data 0f= 10680 Hz USF D ata D a Dech em ata PNNL D ata 1w 1a 1w 1 a 1w 1a 0.014383 0.0.0 0.0 080039 0 0 01286315 06800 0.029621 0.0.1282 0.465 0.00. 157539 0622364 032200 0.04495 00.1653 0.5562 0.0 0. .232626 21012727 101500 0.061065 0.3 0.1883 0.6129 0.0 0. 05415 41384567 190100 0.078085 0.0.2349 0.6959 0.0 0. 376016 74335284 316200 0.0957 0.4 0.2806 0.7641 0.10.4 44528 1332432 41800 0.115703 0.0.3026 0.7853 0.1 0. 511048 35796638 504500 0.138047 0.570.4005 0.8769 0.1 0.5 5666 61108406 67000 0.163247 0.630.4005 0.8769 0.1 0. 8464 96808588 629400 0.186563 0.699522 0.4005 0.8769 0.196808588 0.629400 119

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Appendix D ( Continued) with Dechema and PNNL data = 10680 Hz Table D4 Activity vs weight fraction for toluene / PIB at 294K and its comparison 0f USF Data Dechema Data PNNL Data 1w 1a 1w 1a 1w 1a 0.014383 0.080039 0 0 0.000983719 0.006500 0.029621 0.157539 0.283 0.0342 0.004762791 0.030900 0.04495 0.232626 0.379 0.0563 0.015720081 0.097600 0.061065 0.305415 0.469 0.0861 0.030707544 0.182900 0.078085 0.376016 0.555 0.1281 0.054754523 0.304600 0.0957 0.444528 0.656 0.1775 0.083066641 0.426100 0.115703 0.511048 0.724 0.2211 0.099474165 0.486700 0.138047 0.575666 0.77 0.2611 0.118025482 0.547300 0.163247 0.638464 0.77 0.2611 0.141134543 0.607900 0.186563 0.699522 0.77 0.2611 0.141134543 0.607900 120

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Appendix E L ist of vendors Table E1 List of vendors PART AMOUNT SUPPLIER MFCs 1 MKS Power Supply and Readout 1 MKS MFC Cable 3 MKS OMEGA Solenoid Valve 9 ASCO Bubblers 4 Fischer Relays 9 OMEGA # Stainless Tube 30 FT. Swagelok Ferule Set 1 Swagelok Elbows 7 Swagelok Tees 8 Swagelok Unions 2 Swagelok Water Bath 1 USF Computer ( Serial and PCI slot) 1 DELL Serial Cable ( Connected to MFC) 1 MKS NI DAQ 1 NI Connector Block 1 NI Cable 2 m NI 121

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Appendix F F luctuations in frequency measurements The following table contains concentrations of vapor and its equivalent frequency shifts, weight fractions and frequency fluctuations, corresponding errors in weight fractions. These tables also show the resistance changes when QCM goes beyond the mass balance regime. Table F1 Fluctuations in frequency measurements for Benzene in poly (styrene-butadiene)/ (85% styrene) system = 5675 Hz 0f Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 49508.2 0.01277 65 9.9164 0.00002 10.878 89645.65 0.040298 211 19.728 0.00015 11.027 122842.8 0.076457 416 10.12 0.00014 10.912 150756.6 0.10841 611 3.541 0.00007 10.861 174555.3 0.141613 829 3.994 0.00010 11.19 195086.3 0.177174 1082 7.2836 0.00021 11.128 212979.6 0.220809 1424 11.113 0.00038 11.763 228712.6 0.267493 1835 23.988 0.00094 12.913 242654.5 0.315954 2321 28.734 0.00124 16.079 255094.5 0.377169 3043 39.66 0.00185 26.974 122

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Appendix F (Continued) T able F2 Fluctuations in frequency measurements for n-hexane in poly (styrene-butadiene)/ (85% styrene) system 0f= 5675 Hz C oncentrations Weight of vapor Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 93547.04614 0.013932496 71 11.866 0.00003 11.69 167911.8461 0.045946459 242 31.737 0.00028 11.6 228445.8411 0.086363636 475 9.7411 0.00015 11.67 278679.2481 0.132873167 770 9.8365 0.00023 11.647 321035.0692 0.163893511 985 18.572 0.00051 11.368 357231.6126 0.204905063 1295 18.051 0.00059 11.531 388521.3155 0.259177355 1758 26.049 0.00100 12.877 415838.6062 0.311455193 2273 28.163 0.00120 16.671 439894.8128 0.37962963 3075 15.169 0.00071 35.08 461240.9958 0 ** 0 0.00000 128.18 123

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Appendix F (Continued) T able F3 Fluctuations in frequency measurements for dichloroethane in poly (styrene-butadiene)/ (85% styrene) system = 5675 Hz 0f Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 50939.99759 0.016441574 84 9.2091 0.00003 12.002 92452.39166 0.046308597 244 7.253 0.00006 11.776 126932.6981 0.075436983 410 2.9001 0.00004 11.462 156028.2178 0.107935381 608 3.9288 0.00008 11.406 180909.0001 0.141465915 828 6.4067 0.00015 11.146 202429.0049 0.17636453 1076 5.9613 0.00017 10.993 221226.0896 0.219356843 1412 9.9817 0.00034 11.315 237786.3 0.261138068 1776 11.447 0.00044 12.009 252486.4985 0.311738118 2276 18.218 0.00078 13.446 265623.3918 0.36504928 2889 20.802 0.00096 16.846 124

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Appendix F (Continued) T able F4 Fluctuations in frequency measurements for chloroform in poly (styrene-butadiene)/ (85% styrene) system 0f= 5675 Hz C oncentrations Weight of vapor Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 176206.77 0.05704635 304 8.422 0.00014 11.896 313916.917 0.10618997 597 12.083 0.00025 11.527 424503.821 0.15503615 922 7.4227 0.00036 11.261 515262.336 0.20414951 1289 7.1411 0.00045 11.01 591086.587 0.25345417 1706 9.7988 0.00636 11.299 655382.492 0.29838034 2137 9.8285 0.00079 12.005 710593.462 0.34926185 2697 11.063 0.00090 13.36 758517.972 0.39906721 3337 10.815 0.00105 16.035 800509.175 0.44967692 4106 16.443 0.00118 24.949 837604.701 0.49319213 4890 19.638 0.00104 47.164 125

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Appendix F (Continued) able F5 Fluctuations in frequency measurements for benzene in poly (styrene-butadiene)/ (45% styrene) system = 6125 Hz T 0f Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 49508.2 0.0223 140 6.1872 0.00003 16.467 89645.65 0.0498 321 5.5614 0.00006 17.972 122842.8 0.0778 517 2.7828 0.00005 19.301 150756.6 0.106 726 4.072 0.00009 21.228 174555.3 0.1366 969 6.5355 0.00018 24.318 195086.3 0.161 1175 8.2342 0.00025 29.252 212979.6 0.2006 1537 13.384 0.00048 33.24 228712.6 0.2461 1999 13.545 0.00055 45.962 242654.5 0.2701 2266 13.865 0.00059 83.908 255094.5 0 0 0 0.00000 148.45 126

PAGE 141

Appendix F (Continued) able F6 Fluctuations in frequency measurements for n-hexane in poly (styrene-butadiene)/ (45% styrene) system T 0f= 6125 Hz C oncentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 93547.04614 0.0191 119 7.5078 0.00003 17.23 167911.8461 0.0486 313 10.409 0.00011 19.142 228445.8411 0.0791 526 9.4588 0.00016 23.075 278679.2481 0.113 780 7.0136 0.00016 27.573 321035.0692 0.144 1030 10.697 0.00030 29.632 357231.6126 0.1909 1445 10.263 0.00035 33.19 388521.3155 0.2412 1947 17.181 0.00069 47.783 415838.6062 0 0 0 0.00000 88.327 439894.8128 0 0 0 0.00000 227.69 461240.9958 0 0 0 0.00000 443.42 127

PAGE 142

Appendix F (Continued) T able F7 Fluctuations in frequency measurements for dichloroethane in poly (styrene-butadiene)/ (45% styrene) system = 6125 Hz 0f Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 50939.99759 0.0159 99 5.8853 0.00002 15.383 92452.39166 0.0442 283 7.5056 0.00008 16.887 126932.6981 0.0723 477 5.9858 0.00009 19.004 156028.2178 0.0986 670 3.996 0.00008 22.197 180909.0001 0.1236 864 3.8862 0.00010 26.293 202429.0049 0.1495 1077 5.0127 0.00014 30.119 221226.0896 0.1816 1359 7.8578 0.00026 32.473 237786.3 0.2218 1746 15.328 0.00058 35.757 252486.4985 0.2698 2263 18.683 0.00080 46.148 265623.3918 0.3052 2691 3.3974 0.00015 71.074 128

PAGE 143

129 Appendix – F (Continued) Table F8 Fluctuations in frequency measurements for chloroform in poly (styrenebutadiene)/ (45% styrene) system 0f = 6125 Hz Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 176206.77 0.0457 293 14.766 0.00015 16.349 313916.917 0.1003 683 9.2229 0.00019 19.86 424503.821 0.1466 1052 6.6548 0.00019 25.499 515262.336 0.1871 1410 6.7318 0.00023 30.908 591086.587 0.2294 1823 6.9588 0.00027 33.818 655382.492 0.2749 2322 8.6069 0.00037 39.325 710593.462 0.321 2895 8.9339 0.00041 53.685 758517.972 0 0 0 0.00000 84.68 800509.175 0 0 0 0.00000 158.15 837604.701 0 0 0 0.00000 280.62

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130 Appendix – F (Continued) Table F9 Fluctuations in frequency meas urements for benzene in poly (styrenebutadiene)/ (21% styrene) system 0f = 4943.75 Hz Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 49508.2 0.029315 151 6.945 0.00004 14.077 89645.65 0.053389 282 4.1144 0.00004 15.582 122842.8 0.082569 450 3.0572 0.00005 17.663 150756.6 0.111111 625 4.0132 0.00008 20.39 174555.3 0.145007 848 6.4367 0.00016 24.143 195086.3 0.176412 1071 6.571 0.00019 29.056 212979.6 0.218261 1396 6.3667 0.00022 36.26 228712.6 0.257389 1733 11.576 0.00044 49.991 242654.5 0.282846 1972 12.032 0.00048 76.309 255094.5 0 0 0 0.00000 144.47

PAGE 145

131 Appendix – F (Continued) Table F10 Fluctuations in frequency measurements for n-hexane in poly (styrenebutadiene)/ (21% styrene) system 0f = 4943.75 Hz Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 93547.04614 0.01999216 102 6.0461 0.00002 12.745 167911.8461 0.054641709 289 7.3225 0.00007 13.765 228445.8411 0.089253188 490 7.5375 0.00012 15.268 278679.2481 0.124803081 713 6.4531 0.00014 22.544 321035.0692 0.174372523 1056 9.4416 0.00027 23.572 357231.6126 0.223723024 1441 5.6716 0.00020 29.879 388521.3155 0.270286048 1852 7.4656 0.00029 46.761 415838.6062 0.290780142 2050 0 0.00000 88.334 439894.8128 0 0 0 0.00000 218.51 461240.9958 0 0 0 0.00000 387.01

PAGE 146

132 Appendix – F (Continued) Table F11 Fluctuations in frequency measurements for dichloroethane in poly (styrenebutadiene)/ (21% styrene) system 0f = 4943.75 Hz Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 50939.99759 0.016715831 85 4.6653 0.00002 12.449 92452.39166 0.046711153 245 7.5285 0.00007 12.898 126932.6981 0.075614716 409 4.5124 0.00006 13.66 156028.2178 0.101688825 566 3.8301 0.00007 14.541 180909.0001 0.131642932 758 4.1236 0.00009 15.899 202429.0049 0.166249792 997 5.8915 0.00016 17.785 221226.0896 0.201533057 1262 12.105 0.00039 20.593 237786.3 0.242653741 1602 14.9 0.00054 24.637 252486.4985 0.287546309 2018 16.007 0.00065 32.151 265623.3918 0.334486889 2513 18.198 0.00080 46.579

PAGE 147

133 Appendix – F (Continued) Table F12 Fluctuations in frequency measurements for chloroform in poly (styrenebutadiene)/(21% styrene) system 0f = 4943.75 Hz Concentrations of vapor Weight Fractions Frequency shifts Frequency fluctuations Error in Weight fraction Resistance change 176206.77 0.0529 279 0 0.00000 11.943 313916.917 0.1046 584 0.32435 0.00001 11.91 424503.821 0.1569 930 0 0.00000 11.875 515262.336 0.2064 1300 18.173 0.00059 11.859 591086.587 0.252 1684 8.4673 0.00032 11.982 655382.492 0.3014 2157 21.817 0.00091 13.585 710593.462 0.352 2716 20.108 0.00091 18.48 758517.972 0.3987 3315 29.497 0.00141 25.645 800509.175 0 0 0 0.00000 55.76 837604.701 0 0 0 0.00000 197.38

PAGE 148

134 Appendix – G Comparison of activities predicted by UNIFAC-FV, GK-FV and Entropic-FV Figure G.1 UNIFAC-FV predictio ns for copolymers with 85%, 45% and 21 % styrene/nhexane systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 149

135 Appendix – G (Continued) Figure G.2 GK-FV predictions for copolymer s with 85%, 45% and 21 % styrene/nhexane systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 150

136 Appendix – G (Continued) Figure G.3 Entropic-FV predictions for copol ymers with 85%, 45% and 21 % styrene/nhexane systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 151

137 Appendix – G (Continued) Figure G.4 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/dichloroethane systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 152

138 Appendix – G (Continued) Figure G.5 GK-FV predictions for c opolymers with 85%, 45% and 21 % styrene/dichloroethane systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 153

139 Appendix – G (Continued) Figure G.6 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/dichloroethane systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 154

140 Appendix – G (Continued) Figure G.7 UNIFAC-FV predictions for copolymers with 85%, 45% and 21 % styrene/chloroform systems Weight Fraction (wB1B) Activity (aB1B)

PAGE 155

141 Appendix – G (Continued) Figure G.8 GK-FV predictions for c opolymers with 85%, 45% and 21 % styrene/chloroform systems Weight Fraction (wB1B) Activity (aB1B)

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142 Appendix – G (Continued) Figure G.9 Entropic-FV predictions for copolymers with 85%, 45% and 21 % styrene/chloroform systems Weight Fraction (wB1B) Activity (aB1B)


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Upadhyayula, Anant K.
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Sorption of organic vapors by copolymers of poly (styrene-butadiene) using a piezoelectric microbalance
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by Anant K. Upadhyayula.
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[Tampa, Fla.] :
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2005.
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Thesis (M.S.)--University of South Florida, 2005.
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ABSTRACT: Thickness shear mode (TSM) sensors, also known as quartz crystal micro-balances (QCM) are a class of acoustic wave sensors that have been used for gas phase sensing. In this thesis this device is used to measure vapor-liquid equilibrium data for copolymers of poly(styrene-butadiene) at 294K. Copolymers of poly(styrene-butadiene) with varying percentages of styrene (85%, 45% and 21 %) were studied with benzene, n-hexane, dichloroethane and chloroform as solvents. Literature data for pure polystyrene/benzene and polystyrene/chloroform and polybutadiene/benzene were obtained to complement the measured data. Obtained experimental data were fit with a modified Flory-Huggins model and compared with the predictions of three models (UNIFAC-FV, Entropic-FV, and GK-FV). Flory-Huggins model gave a good quantitative fit for the solvent activities in the copolymer solutions.
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Adviser: Dr. Venkat Bhethanabotla.
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Qcm.
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Benzene.
N-hexane.
Dichloroethane.
Chloroform.
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x Chemical Engineering
Masters.
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t USF Electronic Theses and Dissertations.
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