The Pennsylvania State University. The Graduate School. Department of Chemical Engineering PHASE EQUILIBRIA AND DIFFUSION

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1 The Pennsylvania State University The Graduate School Department of Chemical Engineering PHASE EQUILIBRIA AND DIFFUSION IN HPMCAS-ACETONE-WATER SYSTEM A Thesis in Chemical Engineering by Sheng-Wei Chiu 015 Sheng-Wei Chiu Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 015

2 The thesis of Sheng-Wei Chiu was reviewed and approved* by the following: Ronald P. Danner Professor Emeritus of Chemical Engineering Thesis Advisor Robert Rioux Friedrich G. Helfferich Associate Professor Manish Kumar Assistant Professor of Chemical Engineering Phillip E. Savage Department Head and Walter L. Robb Family Endowed Chair Professor of Chemical Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT Thermodynamic properties and diffusion behavior in the hypromellose acetate succinate (HPMCAS)-acetone-water system with temperatures below its glass transition temperature were investigated using the capillary column inverse gas chromatography (CCIGC) technique. These properties are important for the optimization of the spraydrying processes in drug manufacturing. A modified CCIGC apparatus was developed to carry out studies ranging from the highly concentrated polymer region where infinitely dilute solvent was present, to polymer-solvent system with finite concentration of solvent, and further to ternary polymer-solvent-solvent systems. Results of thermodynamic properties were compared with prediction models based on the UNIQUAC functional-group activity coefficients (UNIFAC) method as well as the Flory- Huggins model. The diffusion coefficients were correlated with the modified free-volume model in the glassy state polymer in the highly concentrated polymer region and were predicted in polymer-solvent systems with finite concentrations of solvent and in ternary systems. Based on the experimental findings, acetone is a good solvent with a strong interaction with HPMCAS with very low diffusivities (~10-10 cm /s). The presence of water in the HPMCAS had little effect on the acetone behavior since acetone is much soluble than water. In contrast, water is a poor solvent with a weak interaction with HPMCAS and much higher diffusivities (~10-8 cm /s). When acetone was present in the HPMCAS, the partitioning of water in the HPMCAS slightly decreased due to a smaller interaction with HPMCAS compared to acetone. The diffusivities of water increased significantly with the presence of acetone, since acetone was more soluble and was able to turn the glassy state HPMCAS closer to the rubbery state with the plasticization effect.

4 iv TABLE OF CONTENTS List of Figures... vi List of Tables... xi Acknowledgements... xiii Chapter 1 Introduction... 1 Chapter Background Capillary Column Inverse Gas Chromatograhpy (CCIGC) CCIGC Model Parameter Estimation Methods Sensitivity Analysis of CCIGC Model Thermodynamics in Polymer-Solvent Systems Infinite Dilution Weight Fraction Activity Coefficients Flory-Huggins Model UNIFAC and Free-Volume Effects UNIFAC UNIFAC-FV UNIFAC-vdw-FV Free-Volume Theory in Polymer-Solvent System Vrentas-Duda Free-Volume Theory Mutual-Diffusion Coefficients Influence of Glass Transition Self-Diffusion Coefficients in Glassy Polymers Mutual-Diffusion Coefficients in Glassy Polymers Self-Diffusion in Ternary System Estimation of Free-Volume Parameters Solvent Free-Volume Parameters Pure Polymer Specific Critial Hole Free Volume Pure Polymer Free-Volume Parameters Flory Interaction Parameter Chapter 3 Experimental Procedure Application of Thermal Conductivity Inverse Gas Chromatography Apparatus Set up Experimental Procedures and Data Analysis... 58

5 3.3.1 Infinite Dilution CCIGC Finite Concentration CCIGC Ternary Systems CCIGC Data Analysis Materials Preparation and Characterization of Capillary Columns v Chapter 4 Infinitely Dilute Inverse Gas Chromatography Resutls Study of the Influence of Injection Volume in IGC Experiments HPMCAS-water System HPMCAS-acetone System HPMCAS-Acetone System HPMCAS-Water System Chapter 5 Finite Concentration Inverse Gas Chromatography Resutls Finite Concentration Chromatography with Elution on Plateau Modeling Equations Analytical Procedures HPMCAS-Acetone System Analysis of Thermodynamic Properties Free-Volume Analysis of Diffusivity Data HPMCAS-Water System Analysis of Thermodynamic Properties Free-Volume Analysis of Diffusivity Data Chapter 6 Ternary HPMCAS-ACetone-Water Inverse Gas Chromatography Resutls Infinitely Dilute Acetone in HPMCAS-Water System Infinitely Dilute Water in HPMCAS-Acetone System Chapter 7 Recommendations for Future Work Bibliography Appendix Summary of the Experimental Data

6 vi LIST OF FIGURES Figure.1: CCIGC model with cylindrical coordinates... 7 Figure.: Comparison of experimental and theoretical elution profile for (a) HPMCAS-acetone system at 40 C and (b) HPMCAS-water system at 70 C Figure.3: Subgroup structures for (a) HPMCAS-a; (b) HPMCAS-b; (c) Water; and (d) Acetone... 9 Figure.4: Vrentas-Duda free-volume concepts Figure.5: Characteristic of the specific volume for a polymer above and below the glass transition tmperature T g Figure.6: Variation of hole free volume in glassy polymers with addition of solvent and depression of T g with solvent concentration w Figure.7: Rheologial measurements of HPMCAS from Merck & Co., Inc using dynamic mechanical analysis (DMA) procedures Figure.8: Corelation of viscosity-temperature data with the modified Doolittle equation with WLF constants Figure 3.1: Schematic for the operation of thermal conductivity detector: (a) only the reference gas of helium flows through the filament and no thermal conductivity changes are detected; (b) effluent of the solvent vapor along with the makeup helium are now diverted to the filament and huge drop of thermal conductivities are detected Figure 3.: Schematic of the modified inverse gas chromatograph apparatus Figure 3.3: Schematic for bolts tightening according to the sequence of number Figure 3.4: Schematic of the manifold designed to interconvert experiments among infinite dilution, finite concentration, and ternary systems. 4 out of 5 on-off valves (with black knobs) and 1 metering valve (with white knob) are shown here. The other on-off valve is outside the stainless steel cover and is shown in Figure 3.5. Two fans were mounted to accelerate the air circulation inside the cover. The rectangular coordinates are applied to compare with Figure Figure 3.5: The overview for the modified HP 5890 Gas Chromatograph. The rectangular coordinates are applied to compare with Figure 3.4. Five on-off valves are labelled with numbers. The inserted thermocouples are located at a, b, and c. The dotted lines on the wall refer to the interior gas line

7 supplies. An insulation layer is attached below the stainless steel cover to form an oven. The thermocouple and one of the immersed heaters are connected to a PID temperature controller. The other two immersed heater along with another mounted heater below the cover (not shown in the figure) provides the makeup heating source with maximum 315 Watts and are controlled by the variable autotransformers Figure 3.6: Structure of hypromellose acetate succinate (HPMCAS) Figure 3.7: General procedures in sequence for capillary column manufacturing Figure 3.8: SEM image for the entire cross-section of the coated capillary column with a scale bar of 30 μm Figure 3.9: SEM image for part of the cross-section of the coated capillary column with a scale bar of 10 μm Figure 3.10: SEM image for part of the cross-section of the coated capillary column with a scale bar of μm Figure 4.1: (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 35 C Figure 4.: (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 40 C Figure 4.3: (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 50 C Figure 4.4: (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 60 C Figure 4.5: The impact of injection volume on partition coefficients and diffusivity for water at (a) 35 C and (b) 40 C Figure 4.6: The impact of injection volume on partition coefficients and diffusion coefficients for water at (a) 50 C and (b) 60 C Figure 4.7: (a) Elution profiles and (b) non-dimensionalized experimental data with varying acetone injection volume at 60 C Figure 4.8: Comparison of the elution profile and the CCIGC model regression for acetone in HPMCAS at 35 C Figure 4.9: Partition coefficients of infinitely dilute acetone in HPMCAS Figure 4.10: Diffusion coefficients of infinitely dilute acetone in HPMCAS vii

8 Figure 4.11: Correlation of averaged diffusion coefficients with free-volume model Figure 4.1: Comparison of the elution profile for before finite and after finite acetone for the 5µm column at 50 C Figure 4.13: Temperature dependence of Flory interaction parameter for HPMACAS-acetone system Figure 4.14: Overall elution profiles for certain circumstances: (a) 5µm column before finite. (b) 3µm column before finite. (c) 3µm column after finite acetone Figure 4.15: Comparison of the elution profile and the CCIGC model regression for water in HPMCAS at 60 C Figure 4.16: Partition coefficients of infinitely dilute water in HPMCAS Figure 4.17: Temperature dependence of Flory interaction parameter for HPMACAS-water system Figure 4.18: Elution profiles for HPMCAS-water system at different temperatures.. 96 Figure 4.19: (a) Diffusion coefficients of infinitely dilute water in HPMCAS; (b) Correlation of averaged diffusion coefficients with free-volume model Figure 5.1: Growth of acetone concentration and formation of plateaus at oven temperature 60 C with various activities Figure 5.: Relation between partition coefficient at infinite dilution and slope of isotherm at finite concentration Figure 5.3: Sorption isotherms for model polymer-penetrant system proposed by Vrentas and Vrentas53. Curve 1 and are at temperatures below T gm and curve 3 is the rubbery state polymer at all temperatures Figure 5.4: Non-dimensionalized elution profiles correlated with CCIGC model at column temperature 35 C with activity 0.19: (a) drifting baseline with larger D p and smaller S(C b ); (b) more stable baseline with smaller D p and larger S(C b ) Figure 5.5: Non-dimensionalized peaks correlated with CCIGC model at column temperature 50 C with activity 0.30: (a) before averaging the data led to larger D p and smaller S(C b ); (b) after averaging the data led to smaller D p and larger S(C b ) viii

9 Figure 5.6: Slope of isotherm decreases with increasing solvent concentration in the gas phase for HPMCAS-acetone system at various column temperatures Figure 5.7: Absorption isotherms for the HPMCAS-acetone system Figure 5.8: Partition coefficient of acetone in HPMCAS as a function of activity Figure 5.9: Volume fraction of acetone at equilibrium with HPMCAS. Solid and dashed lines are correlation and prediction from Flory-Huggins equation Figure 5.10: Weight fraction of acetone at equilibrium with HPMCAS. The data from Sturm at 35 and 50 C are plotted for comparison Figure 5.11: Comparison between weight fraction of acetone in HPMCAS with UNIFAC-FV, UNIFAC-vdw-FV, and Flory-Huggins model at (a) 35 C and (b) 50 C Figure 5.1: DSC results for HPMCAS-acetone system Figure 5.13: Glass transition temperature depression of HPMCAS by acetone with different weight fraction... 1 Figure 5.14: Comparison of experimental data with free-volume prediction of solvent mutual-diffusion coefficients above and below the isothermal glass transition for the HPMCAS-acetone system Figure 5.15: Comparison of non-dimensionalized elution profile and the CCIGC model at finite concentration of water (activity 0.01) in HPMCAS at 60 C Figure 5.16: Plot of the isotherm slopes as a function of water concentration in the gas phase for HPMCAS-water system at different temperatures Figure 5.17: Absorption isotherms for the HPMCAS-water system Figure 5.18: Partition coefficient of water in HPMCAS as a function of activity Figure 5.19: Volume fraction of acetone at equilibrium with HPMCAS. Solid and dashed lines are correlation and prediction from Flory-Huggins equation Figure 5.0: Weight fraction of water at equilibrium with HPMCAS Figure 5.1: Comparison between weight fraction of water in HPMCAS with UNIFAC, UNIFAC-vdw-FV, and Flory-Huggins model at (a) 50 C and (b) 60 C Figure 5.: Glass transition temperature depressions of HPMCAS by water with different weight fraction ix

10 Figure 5.3: Comparison of experimental data with free-volume prediction of solvent mutual-diffusion coefficients above and below the isothermal glass transition for the HPMCAS-water system Figure 6.1: Elution profile and the model regression fit for acetone diffusion in HPMCAS-water system at 50 C with weight fraction of water Figure 6.: Comparison for partition coefficient of acetone in binary (HPMCASacetone) and ternary (HPMCAS-water) system Figure 6.3: Comparison of experimental diffusion coefficients of acetone in HPMCAS-acetone-water system and the ternary free-volume prediction Figure 6.4: Elution profile and the model regression fit for water diffusion in HPMCAS-acetone system at 35 C with weight fraction of acetone Figure 6.5: Comparison for partition coefficient of water in binary (HPMCASwater) and ternary (HPMCAS-acetone) system Figure 6.6: Comparison of experimental diffusion coefficients of water in HPMCAS-acetone-water system and the ternary free-volume prediction x

11 xi LIST OF TABLES Table.1: Group Interaction Parameters for HPMCAS-Acetone-Water System... 8 Table.: Number of Subgroups Present in HPMCAS-Acetone-Water System Table.3: Solvent free-volume parameters for water and acetone Table.4: Group contribution methods to estimate molar volumes at 0 K Table 3.1: Thermal conductivities for acetone, water, and helium at 50 C Table 3.: The control of on-off valves for different experiments Table 3.3: HPMCAS grades Table 3.4: Details of HPMCAS and corresponding capillary columns Table 4.1: Diffusivity and Correction factor (Ratio) for Partition Coefficient with different water injection volumes... 8 Table 5.1: DSC results for HPMCAS-acetone system Table 5.: Isothermal glass transition composition in HPMCAS-acetone system... 1 Table 5.3: Isothermal glass transition composition in HPMCAS-water system Table A.1: Infinite Dilution Data for Acetone in 5 microns HPMCAS Determined using Infinite IGC-TCD Method (Before any Finite Concentration Experiments) Table A.: Infinite Dilution data for Acetone in 5 microns HPMCAS Determined using Infinite IGC-FID Method (Before any Finite Concentration Experiments) Table A.3: Infinite Dilution data for Acetone in 5 microns HPMCAS Determined using Infinite IGC-TCD Method (After Finite Acetone Concentration Experiments) Table A.4: Infinite Dilution Data for Acetone in 3 microns HPMCAS Determined using Infinite IGC-TCD Method (Before any Finite Concentration Experiments) Table A.5: Infinite Dilution Data for Acetone in 3 microns HPMCAS Determined using Infinite IGC-TCD Method (After Finite Water Concentration Experiments)

12 Table A.6: Infinite Dilution Data for Acetone in 3 microns HPMCAS Determined using Infinite IGC-TCD Method (After Finite Acetone Concentration Experiments) Table A.7: Averaged Infinite Dilution Data for Acetone in HPMCAS Table A.8: Infinite dilution WFAC for HPMCAS-acetone system Table A.9: Infinite Dilution Interaction Parameters for HPMCAS-acetone system Table A.10: Infinite Dilution Data for Water in 3 microns HPMCAS Determined using Infinite IGC-TCD Method (Before any Finite Concentration Experiments) Table A.11: Infinite Dilution Data for Water in 3 microns HPMCAS Determined using Infinite IGC-TCD Method (After Finite Water Concentration Experiments) Table A.1: Infinite Dilution Data for Water in 3 microns HPMCAS Determined using Infinite IGC-TCD Method (After Finite Acetone Concentration Experiments) Table A.13: Averaged Infinite Dilution Data for Water in HPMCAS Table A.14: Infinite dilution WFAC for HPMCAS-water system Table A.15: Infinite dilution Interaction Parameters in HPMCAS-water system Table A.16: Slope of isotherm for HPMCAS-acetone system Table A.17: Summary of finite concentration data for HPMCAS-acetone system Table A.18: Slope of isotherm for HPMCAS-acetone system Table A.19: Summary of finite concentration data for HPMCAS-water system Table A.0: Data for Infinitely Dilute Acetone in HPMCAS-Water Table A.1: Correction of the Nonlinearity Effect for Water in HPMCAS- Acetone Table A.: Data for Infinitely Dilute Water in HPMCAS-Acetone xii

13 xiii ACKNOWLEDGEMENTS It has been a fruitful and memorable two years research experience at Penn State. I especially want to thank my thesis advisor Dr. Danner for providing me the opportunity to be part of this project and building up my interest towards the field of polymer science. With his guidance and support, I was able to come through obstacles and frustrations during the experiments. I still remembered the day we had a fist bump at the end of the meeting since the experiments were finally able to be carried out in finite concentration systems with the modification of the gas chromatograph. All the encouragements have further provided me the confidence in conquering any upcoming challenges. I would like to thank Dr. Rioux and Dr. Kumar for taking time out of their busy schedule to serve on my committee. I also want to thank my labmates Ida and Derek. To Ida, for she took care of me in so many aspects once I joined the group. She also taught me the art of the procedures for coating a polymer thin film on the inner wall of the capillary column step by step. To Derek, for he brought his passion and valuable insights into this project. It has been a colorful lab experience with both of you. I especially want to thank Chris for his great assistance during the modification of the gas chromatograph. The modification would not have been possible without his help. In addition, I would like to thank Dr. Colby for offering me the opportunity to be trained to use the ARES rheometer. Special thanks to Fawzi for he provided me every details for operating the rheometer and offer me useful suggestions and information about the rheological measurements for this project. I also want to thank Dr. Janna Maranas for her

14 xiv kind offering to use the differential scanning calorimeter (DSC) in her lab. Many thanks to Dan for she trained me to use the DSC and special thanks to Lymaris Ortiz Rivera in the material characterization lab for letting me to use the automated press and providing suggestions about the hermetically sealed pan. Furthermore, I would like to thank my roommate Ritesh for letting me use the microbalance in his lab to obtain precise measurements for the weight of the pans throughout the DSC experiments. This work would not have been possible without the financial support from Merck & Co., Inc. and special thanks to Justin for providing us critical information for this project. Finally, thanks to my family in Taiwan (my mom, dad and brother) for their support and love. I could not have come all this way without them. I also want to thank my girlfriend Sche-I for her love and patience.

15 Chapter 1 Introduction Knowledge of phase equilibria and diffusion properties for small molecules in polymers are of considerable importance in industrial applications, such as polymer synthesis, devolatilization, and drying of polymer films. The extraction rate of residual solvents and by-products are generally dictated by the diffusion coefficients of these components in the polymer matrix; while the total amount of these components remaining in the final product are determined by the chemical phase equilibria between the gas and polymer phase. In the pharmaceutical industry, hypromellose acetate succinate (HPMCAS), a synthetic polymer derived from cellulose, has been widely used as a solid dispersion polymer to stabilize the amorphous active pharmaceutical ingredients (APIs) and prevent them from turning into the crystalline phase, which is thermodynamically more stable 1. The combination of amorphous APIs and solid dispersion polymers are referred to as the amorphous solid dispersions (ASDs). Within the ASDs, the APIs are well dispersed in a polymer matrix and therefore less crystallization nuclei are likely to form. Consequently, the APIs can have higher apparent solubility and faster dissolution rate with good stability 3. Amorphous solid dispersions are primarily prepared in large scales as spraydrying process 4. APIs with the desired solid dispersion polymer are dissolved into

16 multiple solvents and fed through high pressure nozzle into the drying chamber. In the current studies, the solid dispersion polymer is HPMCAS, the solvents are water and acetone, and the chamber temperature is set between 30 to 70 C. Solvent evaporation occurs very quickly once the hot drying gas (usually nitrogen) contacts with the droplets. Within seconds, amorphous solid spray-dried dispersions (SDDs) 5 are formed, generally with around 5 wt.% acetone remaining. A secondary drying process is often applied to remove the residual solvents to meet regulations from the Food and Drug Administration (FDA). According to FDA, acetone is a class 3 solvent, which is regarded as less toxic and of lower risk to human health. However, it is still considered that the acceptable acetone intake should not exceed 50 mg per day. The oral antifungal medicine, Noxafil (Posaconazole), is an example if it was prepared with the spray-drying process. The preferable weight ratio of HPMCAS:Posaconazole in the amorphous solid dispersions is about 3:1 w/w HPMCAS/Posaconazole according to the patent US A1. The loading dose is 600 mg per day (three 100 mg delayed-release tablets twice a day). Thus, the corresponding intake for HPMCAS plus Posaconazole is 400 mg per day. To prevent patients from having more than 50 mg of acetone per day, the residual acetone weight fraction in the SDDs has to be controlled to less than wt.%. This can be achieved by controlling the acetone diffusivity and solubility within HPMCAS using the dryer temperature and concentrations of the solvents (both water and acetone) to further optimize the spray-drying process. Several techniques have been developed to measure thermodynamic and transport properties for polymer-solvent system, such as gravimetric sorption, differential pressure

17 3 decay (DPD), inverse gas chromatography (IGC), and nuclear magnetic resonance (NMR). NMR spectroscopy measures only the self-diffusion coefficient which is defined as the translational diffusion coefficient at zero gradient of the chemical potential. Both gravimetric sorption and DPD are developed mainly to determine mutual-diffusion coefficient in binary polymer-solvents at finite concentration of solvents, where chemical potential gradients takes place. IGC is generally applied to the important region of highly concentrated polymer, where the solvent concentration is virtually zero. However, with further modifications, IGC can be extended to study binary polymer-solvent systems at finite concentration of solvents as well as ternary polymer-solvent-solvent systems where a second solvent is present. The objective of this project was to develop a fundamental understanding of the phase equilibria and diffusion behavior in HPMCAS-acetone-water system at infinitely dilute and finite concentrations of both acetone and water by applying IGC. This was achieved with the following steps: (1) Modify the inverse gas chromatography apparatus to allow experiments at infinite dilution, finite concentration, and in ternary systems. () Obtain partition and diffusion coefficients of acetone and water in HPMCAS at the limit of zero concentration. (3) Obtain solubility and diffusivity of acetone and water at finite concentrations. (4) Obtain thermodynamic and diffusion properties for ternary systems based on the binary polymer-solvent system at finite concentration of solvents. (5) Compare experimental sorption and diffusion results with predictive models to extend the scope of the data available to optimize the spray-drying process.

18 4 The discussions of the work are organized in the following fashion: Chapter provides a review for the inverse gas chromatography technique, some background for the fundamentals of thermodynamics in polymer solutions, and the application of freevolume theory, particularly the Vrentas-Duda free-volume theory and its modification, used for semi-prediction of diffusion coefficients in polymer-solvents below glass transition temperature of the polymer. Chapter 3 describes the set up for the modified IGC apparatus as well as the experimental methods and procedures. In Chapters 4 to 6, the IGC results for infinite dilution, finite concentrations, and ternary systems are present. Results for the interactions between acetone and water in HPMCAS are presented. Prediction models for the sorption isotherms with specific HPMCAS subgroup structures are recommended to describe the phase equilibria over a larger range of the solvent concentration. Free-volume models both below and above the glass transition temperature of the polymer-solvent mixture are applied and the deviations with the experimental results are discussed. Finally, Chapter 7 offers some suggestions for future work.

19 5 Chapter Background This chapter will cover basically all the theoretical background required for this project, ranging from transport phenomena to thermodynamics. First of all, the Capillary Column Inverse Gas Chromatography (CCIGC) model derivation and the analytical procedures were covered. Second, thermodynamic properties corresponding to the polymer-solvent systems are discussed. Theoretical models based on Flory-Huggins theory, UNIFAC, UNIFAC-FV, and UNIFAC-vdw-FV are applied to correlate or predict the weight fraction of solvents in polymer at different activities. Small corrections were made from the original interaction parameters used in UNIFAC-based models due to a more complicated cellulosic based structure of the polymer. Details are covered in Section.. Finally, free-volume theory is covered to describe the transport properties of solvents in polymer. Since the operating temperatures in this project were all below the glass transition temperature, plasticization factors were introduced to optimize the prediction.

20 6.1 Capillary Column Inverse Gas Chromatography (CCIGC) A conventional gas chromatography technique is mainly for analytical purposes, since a sample containing multiple species is separated into its components on a stationary phase. Here, inverse gas chromatography (IGC) uses injection of a single species to probe the characteristics of a stationary phase polymer sample. The spread of the peak and the retention time measured at the column outlet can be further analyzed to obtain thermodynamic and transport properties in polymer-solvent systems. Two types of column can be applied: packed or capillary column. The packed column is filled with pure polymer particles (usually spherical) or inert particles that act as support and have been coated with a layer of polymer. It has been widely used to obtain the thermodynamic properties. However, difficulties occurred when applying packed columns to determine the diffusion coefficient due to the irregular distribution of the polymer in the column. The introduction of a more uniform coated capillary column made IGC a much more reliable technique to determine diffusion coefficients of solvents in the stationary phase. For this reason, in this work, CCIGC was used for collection of data. The only disadvantage for capillary column is a much more complicated preparation procedure, which is discussed in Section 3.5. Several analytical models 6 have been developed to describe the mass-transport processes occurring in the column. The most widely used model was published by Pawlisch et al. 7,8, which solves the continuity equation in both the gas and stationary phases. Details about the CCIGC model proposed by Pawlisch are introduced in the following section.

21 7.1.1 CCIGC Model The capillary column is modeled as a straight cylindrical tube with a polymer film deposited on the wall, as shown in Figure.1. R is the inner radius of the empty space in the capillary column, τ is the polymer film thickness, and L is the length of capillary column. r r = R+ τ z r = R Gas phase τ (polymer film) L Stationary phase Figure.1 CCIGC model with cylindrical coordinates The main mechanisms for mass transport are: (1) gas phase dispersion due to an axial concentration gradient of solvent in the carrier gas; () bulk absorption of the solvent in the polymer coating; and (3) adsorption onto the gas-polymer surface. Here, the adsorption effect was not included since Davis et al. 9 have shown that for capillary columns, even below the glass transition temperature, the effect is negligible. Additionally, several initial assumptions were made to simplify the model: 1. The column is kept isothermal.. The polymer coating thickness (τ) is much smaller than the column radius.

22 8 3. Gas phase diffusion is fast enough to keep the vapor phase well mixed in the radial direction. 4. No pressure drop over the column length. 5. The polymer phase diffusion coefficient (D p ) is constant. 6. The vapor phase diffusion coefficient (D g ) is constant. 7. The partition coefficient between the gas and stationary phase is constant. 8. The polymer film thickness (τ) is uniform everywhere in the column. 9. Diffusion in the polymer phase occurs only in the radial (r) direction. 10. The carrier gas is insoluble in the polymer. 11. No chemical reactions occur in the column. 1. The partial molar volume of the solvent in the polymer is constant. 13. Swelling in the polymer is insignificant. 14. The solvent injection can be modeled by a simple Dirac delta function. With these assumptions, the continuity equation and boundary conditions for the solvent in the polymer phase are simplified as: C t ' D p C r ' (.1) ' C 0 at t 0 (.) C ' KC at r R (.3) D g C r rr C r ' D p C r ' rr at 0 at r R r R (.4) (.5)

23 Where C is the concentration of solvent in the polymer phase, K is the partition 9 coefficient defined as the ratio between the concentration of the solvent in the polymer phase and in the gas phase at equilibrium, D p is the mutual binary diffusion coefficient in the polymer, and t is time. The gas phase continuity equation for the solvent along with its initial and boundary conditions are: C C U Dg t z C R 0 0 C z R rcdr rdr D R p C r ' rr (.5) (.6) C 0 at t 0 (.7) t C at z 0 C (.8) 0 C 0 at z (.9) The terms on the right side of Eq. (.5) refer to axial dispersion and bulk absorption respectively. No adsorption effect was considered. Here C(z,t) is the area-averaged concentration c(z,r,t) in the gas phase according to assumption 3, as shown in Eq. (.6). D g is the mutual binary diffusion coefficient in the gas phase, which was determined using the model developed by Fuller et al. 10, as shown in Eq. (.10): D 1 1/ 3 1/ 3 (.10) P 1 1 T M 1 M 0.5

24 where subscript 1 and are referred to as the diffusing species (solvent) and the concentrated species (polymer). D 1 refers to the diffusivity in unit of square meter per second, M i is the molecular weight of component i, T is the system temperature in unit of Kelvin, P is the system pressure in unit of Pascal, i refers to the group contribution values for diffusional volume of component i. In order to solve Eq. (.1) and Eq. (.5), they were transformed into a set of nondimensionalized equations by introducing the following dimensionless variables: Ut t (.11) L z z (.1) L r R (.13) CL C (.14) C U Where U is the linear velocity of the carrier gas, and C 0 is the strength of the injected pulse. With these variables, the non-dimensionalized continuity equation in the polymer phase along with the initial and boundary conditions can be expressed as: C ' 0 ' C L (.15) KC U 0 10 C t ' 1 C ' (.16) U (.17) LD p ' C 0 at t 0 (.18) ' C C at 0 (.19)

25 11 ' C 0 at 1 (.0) Here, β, a new dimensionless parameter related to the transport properties in the polymer was introduced, as shown in Eq. (.17). The non-dimensionalized continuity equation in the gas phase becomes: C C t z C z ' C 0 (.1) R (.) K D g (.3) UL C 0 at t 0 (.4) C ( t) at z 0 (.5) C 0 at z (.6) Two more dimensionless variables were introduced. α is the thermodynamic parameter related to the bulk absorption, while Γ refers to the gas phase transport properties. The last step is to convert the PDE to an ODE by solving Eq. (.16) and (.1) in the Laplace domain. New variables were introduced to make this transformation: C t z Ys z L,, (.7) ' C t, M s, L (.8)

26 1 Where the L{} refers to the Laplace transform function and s is the Laplace operator. The partial differential continuity equations in both gas and stationary phase were therefore transformed into a set of second-order linear differential equations: Gas phase: d M s M d (.9) Stationary phase: dy d Y dm Ys d z d z d 0 (.30) With new boundary conditions: s, Ys, z at 0 M (.31) dm s, d 1 0 at 1 (.3) s, z 1 at z 0 Y (.33) s z at z Y, 0 (.34) Laplace transform of the Dirac delta function is exactly 1, as shown in Eq. (.33). The derivative of the concentration in the polymer phase at the gas-polymer interface can be derived from solving Eq. (.9) with Eqs. (.31) and (.3): dm d 0 Y s tanh s (.35) Eventually, by substituting Eq. (.35) into Eq. (.30), the gas phase continuity equation in the Laplace domain becomes: d d z Y 1 dy d z s s Y tanh s 0 (.36)

27 The solution from Eq.(.36), (.33), and (.34) at the column outlet z 1 provides the theoretical solvent concentration profile for the effluent: 1 1 s s Y( s,1) exp s 4 tanh (.37) Parameter Estimation Methods In order to obtain thermodynamic and transport properties in the polymer, two methods can be applied. The first method is moment analysis, proposed by Macris in his PhD dissertation. Two moments of the concentration profile can be related to the transform solution. The first moment 1 represents the mean residence time; while the second moment is the variance of the concentration distribution: 1 t c 1 K (.38) R 4 3 K D g tc 1 K (.39) 3t cdpr UL R Moment analysis works well mainly for symmetrical peaks, it fails when applied to non-symmetric ones. Therefore, a second method, referred to as time-domain fitting, was applied in this work. It is capable of obtaining meaningful parameters with nonsymmetrical peaks. The essential concept is to fit the non-dimensionalized elution profile with the theoretical model in the time domain. However, the theoretical expression (Eq..37) is too complicated to be directly transformed from the Laplace domain to the time domain. Therefore, a numerical inversion of Eq. (.37) with a Fast Fourier Transform

28 14 (FFT) algorithm (subroutine FFTC from the International Mathematical and Statistical Library (IMSL)) was required. To obtain the parameters that lead to the best fit of the CCIGC model with the experimental data, a non-linear least square regression package from IMSL, based on a Levenberg-Marquardt algorithm, was used. Figure. shows examples of peak fittings done by this method. The results indicate that this technique can be properly applied to both Gaussian and considerably skewed peaks. Detailed procedures for peak fitting are discussed in Section

29 CL/C 0 U CL/C 0 U Acetone in 40 C CCIGC regression α = 0.8 β = 3.73 K = D P = 1.50E-10 cm /s R = t/t c Water in 70 C CCIGC regression α = 0.31 β = 0.09 K = 79.1 D P = 1.4E-07 cm /s R = t/t c Figure. Comparison of experimental and theoretical elution profile for (a) HPMCAS-acetone system at 40 C and (b) HPMCAS-water system at 70 C

30 Sensitivity Analysis of CCIGC Model It is critical to know the limitations of the CCIGC model as a source of thermodynamic and transport properties. Surana et al. 11 have done the sensitivity analysis and suggest that the parameter β should fall in the region between 0.03 and 5 to get reliable results. With β higher than 5 (low diffusivities), s tanh s reduces to s and Eq. (.37) becomes independent of β: tanh reduces to 1 and Eq. (.37) becomes: 1 1 s s Y( s,1) exp (.40) 4 Since γ is determined using Eq. (.10) independently, the elution profile with large β depends mainly on the product of αβ. Vrentas et al. 1 have shown that this model is unable to distinguish the individual contributions of these two variables. They suggest obtaining α from an extrapolation of the partition coefficients at higher temperatures, and then using it to estimate β. On the other hand, with β lower than 0.03 (high diffusivities), 1 1 s s Y( s,1) exp (.41) 4 Thus, the model becomes insensitive to β and reduces the reliability of D p. In addition, there is a lower limit for the partition coefficient: 10. Below this value, the solubility is so small that the gas phase diffusivity Γ becomes dominant in Eq. (.37) and the surface adsorption effect may no longer be negligible. Fortunately, all the experiments carried out in this project were within the sensitivity of CCIGC model and therefore reliable regression parameters were obtained.

31 17. Thermodynamics in Polymer-Solvent Systems The α parameter regressed from fitting a non-dimensionalized elution profile with the CCIGC model includes important the information about thermodynamic properties in polymer-solvent systems: the partitioning of solvent between gas and stationary phases. The data directly obtained from the elution profile are usually the partition coefficients or the retention volumes. They are not generally the parameters of direct application for characterizing the phase equilibria in polymer-solvent systems. Therefore, transformation of these values to more commonly used thermodynamic properties such as weight fraction activity coefficients (WFAC) and Flory-Huggins interaction parameters (χ) are covered in Section..1. In addition, pure predictive models including UNIFAC, UNIFAC-FV, and UNIFAC-vdw-FV are discussed to estimate vapor-liquid equilibria in polymer-solvent systems. Generally no particular model is able to best represent the whole spectrum of different systems, and thus all three models were applied in this project to obtain the most accurate predictions for the systems of interest...1 Infinite Dilution Weight Fraction Activity Coefficient (Ω 1 ) The partitioning of the solvent (with subscript 1) between the gas and stationary phase has been derived by Patterson et al. 13 as the ratio of net retention volume with zero column pressure to the stationary phase volume: 0 n1, poly V poly VN K (.4) n V V 1, gas gas poly

32 where K is the partition coefficient, n 1, polyand n, gas 18 1 are the moles of solvent in stationary and gas phase respectively, V and Vgasare the volume of stationary and gas phase poly respectively, and 0 V N is the net retention volume extrapolated to zero column pressure. The partition coefficient K is determined when the system reaches equilibrium, where the chemical potential of each component in the mixture are the same in both phases. For the solvent in the polymer-solvent system, it can be expressed as: (.43) gas poly 1 1 In addition, a more concrete physical property, fugacity, can be defined in terms of the chemical potential: 1 d ln f1 d (.44) RT According to Eq. (.43), the fugacity of the solvent must also be the same in both phases: gas poly f f1 1 (.45) In the gas phase, the fugacity can be directly related to the fugacity coefficient ϕ 1 : f gas 1 1P1 (.46) While in the stationary phase, the fugacity has to be defined differently since there is no easy model for ϕ 1 for liquid mixtures. Activity coefficient γ 1 is therefore applied to relate the deviation to some standard state fugacity f 0 1 to express the fugacity in the stationary: 0 f poly 1 1x1 f1 (.47)

33 19 Where x1 represents the mole fraction of solvent in the polymer phase. At infinite dilution, which is at essentially zero partial pressure, the fugacity coefficient ϕ 1 goes to zero. In combination of Eqs. (.45) to (.47), the mole fraction activity coefficient at the limit of infinite dilution can therefore be expressed as: P x (.48) 1 f1 With the net retention volume at zero column pressure 0 V N defined in Eq. (.4), the following expression can be obtained: P1 x 1 n, poly V 0 N RT n KV, poly RT poly W, poly KV M poly RT RT KM (.49) Where W, poly is the mass of polymer in the stationary phase, is the polymer density, and M is the molecular weight of the polymer. The standard state fugacity 0 f 1 can be related to the saturation pressure of pure solvent s P 1 at the system temperature T with a correction for the non-ideality effect by using the second virial coefficient B 11 as proposed by Everett and Stoddart 14 : f 0 1 P s ~ P 1 B11 V exp (.50) RT s 1 1 Where V ~ is the saturated molar volume of the solvent and R is the gas constant. Eventually, the mole fraction activity coefficient at the limit of infinite dilution can be obtained by substituting Eqs. (.49) and (.50) into Eq. (.48):

34 However, Eq. (.51) has difficulties dealing with high-molecular weight polymers. As pointed out by Patterson et al 13, the logarithm of the mole fraction activity coefficient decreases dramatically as the molecular weight of the polymer increases: s ~ RT P 1 B11 V1 1 exp s KM P (.51) 1 RT 0 ln as M (.5) 1 Therefore, they suggested using the weight fraction instead of the mole fraction. At infinite dilution, this can be easily done through the relation: 1 M 1 (.53) M 1 Here M 1 refers to the molecular weight of the solvent. Finally, the weight fraction activity coefficient at infinite dilution 1 RT KM P 1 is thus obtained as: s 1 1 P 1 exp s ~ B11 V1 RT (.54).. Flory Huggins Model The polymer-solvent system was modeled as a lattice structure by Flory and Huggins 15. Both combinatorial and energetic effects were considered in the model. The combinatorial contributions are related to the entropy of mixing. Provided that no volume change on mixing and monomers of both species can fit on the sites of the same lattice, the well-known Flory-Huggins expression for the entropy of mixing in a polymer solution can be obtained:

35 S k N 1 ln1 N ln (.55) 1 Here, N 1 and N are the number of solvent and polymer molecules, respectively, and the volume fractions ϕ 1 and ϕ are defined by the following expression: N 1 1 (.56) N1 rn rn (.57) N1 rn M ˆ M ˆ 1 r (.58) 1 where r is the number of segments in the polymer chain, defined as the ratio of molar volumes between the polymer and solvent. M i and ˆ i are the molecular weights and densities respectively. Thus, the activity of the solvent from the combinatorial contribution, comb a 1, is given by: On the other hand, the energetic effects were included to further account for the interactions between lattice sites. A residual term, 1 ln a comb 1 ln1 1 (.59) r res a 1, was therefore added to the model: res 1 ln a (.60) where χ is known as the Flory interaction parameter. The critical value of χ for miscibility of a polymer in a solvent is approximately 0.5. For values of χ below 0.5, there is a stronger attraction between species and therefore a single-phase mixture is favorable for all components. While for values of χ above 0.5, there is a stronger repulsion between species and two phases are more likely to exist. In addition, χ shows complex behavior as

36 a function of both concentration and temperature. As concentration increases from infinite dilution to finite concentration, small deviations are expected to be observed. The best way to study the difference is by correlating experimental sorption isotherm with the Flory-Huggins model to obtain χ at finite concentration. On the other hand, the temperature dependence of χ can be empirically written as the sum of two terms 16 : B T A (.61) T where A is independent of temperature and referred to as the entropic part of χ, while B/T is called the enthalpic part. There are mainly two types of contributions from A and B: (1) When both A and B are positive, χ decreases as temperature increased and thus phase separation take place on cooling. The highest temperature of the two-phase region is called the upper critical solution temperature (UCST). For any temperature above UCST, the homogeneous mixtures are stable; () When A is positive and B is negative, χ decreases as the temperature is lowered. The lowest temperature of the two-phase region is the lower critical solution temperature (LCST). Single phases exist for any temperature below LCST. The total activity of the solvent can be obtained from a summation of combinatorial (Eq..59) and residual terms (Eq..60): ln a 1 ln a comb 1 ln a res 1 ln r (.6) The solvent activity can be written in terms of the weight fraction activity coefficient: a (.63) 1 11

37 where 1 is the weight fraction of the solvent. By substituting Eq. (.63) into Eq. (.6), the weight fraction activity coefficient can be expressed as: 3 ln ln 1 1 r (.64) At infinite dilution ( 1), the Flory interaction parameter can be obtained by combining Eqs. (.54) and (.64): 1 ˆ 1 ln 1 1 ln r ˆ s ~ RT P1 B11 V1 ln s KM 1P1 RT 1 ˆ 1 1 ln r ˆ (.65) Finally, the partition coefficient, K, from infinite dilution IGC experiments can be converted to weight fraction activity coefficient, 1, and Flory interaction parameter, χ...3 UNIFAC and Free-Volume Effect Estimations of thermodynamic properties without any experimental data are essential to the advancement and implementation of the devolatilization process, particularly in multicomponent polymer-solvent systems where experiments are more difficult to carry out. Methods of prediction are usually classified into two categories: activity coefficient models and equations of state. Here, only activity coefficient models are considered due to the lack of parameters for HPMCAS in the group contribution lattice-fluid equation of state (GCLF-EoS) developed by Lee and Danner 17. The highly successful activity coefficient model UNIFAC (UNIQUAC Functional-group Activity Coefficient) proposed by Fredenslund et al. 18 was based on group contributions, from

38 which a large number of systems can be built with several functional groups. Both combinatorial and residual contributions are considered in the UNIFAC model. Later on, 4 Oishi and Prausnitz 19 found that the UNIFAC combinatorial contribution does not consider the free volume differences between molecules, which is important for polymersolvent systems. They, therefore proposed the UNIFAC-FV model by adding a free volume contribution derived from the Flory equation of state. Kannan et al. 0 recognized that the free volume percentage of water is less than that of most polymers, which is untypical for the free volume behavior of most solvents. Thus, they proposed the UNIFAC-vdw-FV model with a new free volume term derived from van der Waals partition function. Although UNIFAC-vdw-FV was originally proposed to correct for the failure of using UNIFAC-FV in aqueous solutions, it was found 0 to be able to give better predictions for most of the non-aqueous polymer systems. The following sections are the summary of these models. For this project, new interaction parameters were applied in the residual term of these models to account for the unique interactions between the cellulosic backbone in HPMCAS and water UNIFAC Model In the UNIFAC model, the combinatorial term developed by Staverman 1 accounts for the size and shape effects of the molecules, while the residual term derived from an extension of Guggenheim's quasi-chemical theory of liquid mixtures accounts for energetic interactions. The weight fraction activity coefficient of a solvent in a solution, i, in terms of these two contributions can be expressed as:

39 5 i C i R i ln ln ln (.66) where C i is the combinatorial term and term is given by the following: R i is the residual term. The combinatorial C i i im i ili ln i ln 5qi ln li (.67) M i where i is the molecular volume fraction of component i, i is the weight fraction of component i in the polymer phase, q i is the surface area parameter of component i, i is the molecular area fraction of component i, l i is a parameter for component i, based on i i j j the group volume and group area parameters, and M i is the molecular weight of component i. The molecular volume fraction, i, is given by: where r i is the volume parameter for component i: i where is the number of groups of type k, in component i, R k is the group volume k parameter of group k, and k is the number of distinct groups in the solution. The values of R k were determined from the van der Waals group volumes given by Bondi and have been tabulated by Danner and High 3. The molecular area fraction, i, is given by: M i i r (.68) j k r i j i M i j j ri k Rk (.69)

40 where q i is the surface area parameter for component i: where Q k is the group surface area parameter of group k, determined from the van der Waals group surface areas. The parameter l i is calculated using the volume and surface area parameters of component i: M i i q (.70) j k q i j i M i j j qi k Qk (.71) r q r l 5 1 (.7) i i i i 6 The residual contribution to the weight fraction activity coefficient, by the following: i i R i, is given R ln i k ln k ln k (.73) k where k is the residual activity coefficient of group k in the polymer solution and i is the residual activity coefficient of group k in a reference solution with pure component i. The residual activity coefficient, k, is given by: m km ln k Q k 1 ln m mk (.74) m m p pm p k

41 where m and p are the number of groups in the polymer solution, m is the group surface area fraction of group m, and 7 mk is the group interaction parameter between groups m and k. The group surface area fraction has the following form: m Q p m Q X p m X p (.75) where X m is the mole fraction of group m in the solution, given by: X m j j M j i m M p j j j j p (.76) j where is the number of groups of type m in component j and p is the number of m components in the mixture. The residual activity component of group k in a reference solution containing pure component i is calculated with the same equations above, but only considering the groups present in the pure component. The group interaction parameter function mn binary group pair, m and n, by the following equation: is determined for each possible a mn mn exp (.77) T where a mn is the group interaction parameter resulting from the interaction of main groups m and n, and T is the system temperature in Kelvins. Values for a mn are tabulated by Danner and High 3. Some of the tabulated values were not able to accurately describe the unique interaction between water and CH n O, OH groups on the cellulosic backbone

42 8 of HPMCAS. Therefore, new values measured by Ming and Russell 4 were introduced. Any other functional groups in the HPMCAS-acetone-water system remained the same as the tabulated values. Summarized interaction parameters in the HPMCAS-acetone-water are listed in Table.1. The parameters marked with an asterisk shown in tables and figures refer to the data obtained from Ming and Russell 4. Table.1 Group Interaction Parameters for HPMCAS-Acetone-Water System Main Group H O CH CO CH OH* COOH CH O CH O* CCOO H O * * 7.87 CH CO CH OH* * COOH CH O CH O* 007* CCOO Since HPMCAS is a synthetic polymer derived from cellulose, there is no exact formula for its monomer (details are covered in Section 3.4). A generalized structure was proposed in a patent by Lyon et al. from Bend Research Inc. 5, as shown in Figure.3. Here, two possible subgroup structures are present to account for the functional-group contribution methods. HPMCAS with structure (a) takes into account the main group CCOO including subgroups CH n COOH. While HPMCAS with structure (b) stresses the CH n O groups and thus the main group CCOO are replaced by CH CO, which includes subgroups CH n CO. Subgroup structures for water and acetone shown in (c) and (d) are much simpler. All the summarized subgroups composition and numbers for the HPMCAS-acetone-water system are listed in Table..

43 9 Figure.3 (d) Acetone Subgroup structures for (a) HPMCAS-a; (b) HPMCAS-b; (c) Water;

44 30 Table. Number of Subgroups Present in HPMCAS-Acetone-Water System Acetone Water HPMCAS-a HPMCAS-b Sub-group Component 1 Component Component 3 Component 3 H O CH 3 CO CH CO CH CH CH OH 0 0 COOH CH O CHO CHO* CH 3 COO CH COO UNIFAC-FV Model In the UNIFAC-FV model, a free-volume term 19 derived from the Flory equation of state was added to the original UNIFAC model: ln ln ln ln (.78) i C i R i FV i The free volume term, ln FV i, is given by the following: 1/3 v~ ~ i 1 v i 1 3C i ln ~ C 1/3 i 1 1/ 1 ~ 1 ~ (.79) vm vm vi FV i 3

45 where C i is an external degree of freedom parameter taken to be 1.1 for solvents, v ~ i is the reduced volume of component i, and v ~ M is the reduced volume of the mixture. The reduced volume of component i is calculated by the following equation: v M i i v ~ i br (.80) i 31 where v i is the specific volume (m 3 /kg) of component i and b is a proportionality factor taken to be 1.8. The reduced volume of the mixture is given by: v~ M vii i ri i b M i i (.81) where i refers to the weight fraction of component i UNIFAC-vdw-FV Model In the UNIFAC-vdw-FV model, a different free-volume term 0 was introduced based on the van der Waals partition function following Elbro et al. 6 and Flory 15 : fv h where i and i denotes the fraction of free-volume and hard-volume associated with component i, respectively, and x i is the mole fraction of component i. The fraction of free-volume and hard-volume are given by: ln ln ln ln (.8) i C i R i fv i fv h fv fv i i ln i i ln h (.83) x i i

46 where v i is the molar volume of component i and * fv xi ( vi vi ) i * x ( v v ) (.84) j 3 * v i is the molar hardcore volume of component i. The molar hardcore volume is determined by the following expression : j j j * h xivi i * (.85) x v j j j * 3 vi 15.17r ( cm mol) (.86) i where r i is the volume parameter for component i determined by Eq. (.69) and the value of group volume parameter R k for water, , is obtained from van der Waals group volumes given by Bondi, rather than the regressed value in UNIFAC, Free-Volume Theory in Polymer-Solvent System The original study of molecular diffusion controlled by free-volume was proposed by Cohen and Turnbull 7. They suggested a molecule is able to migrate when the following two conditions are fulfilled: (1) a void of sufficient size must appear next to the molecule and () the molecule has enough energy to break away from its neighbors and jump into the void. On this basis, the self-diffusion coefficient of a pure liquid can be described as the product of the probability of finding a hole of sufficient size and the probability of obtaining enough energy to overcome attractive forces from its neighbors: * E V 1 D1 D0 exp exp RT (.87) VFH E D01 D0 exp (.88) RT

47 where D 1 is the self-diffusion coefficient, D 0 is a pre-exponential constant, E is the critical energy that a molecule has to obtain to overcome attractive forces with its neighbors, * V1 is the critical molar free volume per mole required for a jumping unit of species 1 to jump, V FH is the average free volume per molecule in the mixture, and γ is an overlap factor introduced because the same free volume is available to more than one molecule. The pre-exponential factor D 01 in Eq. (.88) can be applied for regression purpose to reduce unknown parameters. Vrentas and Duda 8,9 further extended the Cohen and Turnbull theory of freevolume to describe molecular transport in the polymer-solvent system. A review of the concepts of the Vrentas-Duda free-volume theory is covered in the next section Vrentas-Duda Free-Volume Theory The Vrentas and Duda free-volume concept can be visualized in Figure.4, where the specific volume of a polymer is made up of three entities: (1) The solid circle in the figure refers to the specific occupied volume of the equilibrium liquid at 0 K; () The volume that exits between the solid circle and the solid line is the specific interstitial free volume Vˆ FI, which is supposed to be occupied by the atom s electronic cloud and therefore requires large redistribution energy and is uniformly distributed among the molecules that compose the liquid; (3) The volume between the solid line and the dotted line is the hole free volumevˆ FH one available for diffusion. The relationship is given by:, which does not require redistribution energy and is the

48 34 Vˆ Vˆ Vˆ FI Vˆ 0 FH (.89) Figure.4 Vrentas-Duda free-volume concept The average hole free volume proposed by Cohen and Turnbull in Eq. (.87) was further defined by Vrentas and Duda as the total free volume of the system divided by the total number of polymer and solvent jumping units. The following relationship was used: V FH Vˆ M FH (.90) 1 1 j M j where Vˆ FH is the specific hole free volume of a polymer with a weight fraction i of species i, and with jumping unit molecular weights of M ij. Here, i M ij accounts for the number of moles of jumping units for each species. Consequently, the self-diffusion coefficient of the solvent can be written by substituting Eq. (.90) into Eq. (.87): D 1 D 01 Vˆ 1 exp Vˆ ˆ * 1 V FH * (.91)

49 ˆ * * V1 V1 M 1 * ˆ * (.9) V V M 35 Here, a new parameter ξ is introduced to define the ratio of molar volumes of the solvent and the polymer jumping units. ˆi * V is the specific critical hole free volume of component i required for a diffusive jump. Vrentas and Duda further adopted the ideology espoused by Berry and Fox 30 and developed a relationship between the hole free volume available for diffusion and the volumetric characteristics of the pure components in solution: Vˆ FH Vˆ 1 FH 1 K11 1 Vˆ K1 K T T K T T 1 FH g1 g (.93) Where Vˆ FHi is the specific free volume of component i, K 11 and K 1 are the free volume parameters for solvent, K 1 and K are the free volume parameters for polymer, and T gi is the glass transition temperature of component i. Eventually, the self-diffusion coefficient of solvent in the mixture at temperatures above the glass transition temperature of the polymer can be expressed by substituting Eq. (.93) into Eq. (.91): D 1 D 01 exp K11 1 ( Vˆ Vˆ K 1 K T T K T T 1 * 1 1 g1 g * ) (.94) At infinite dilution IGC ( 1 0), Eq. (.94) can be simplified as: D 1 D 01 ˆ * V exp K1 ( K Tg T ) (.95)

50 36.3. Mutual-Diffusion Coefficients The self-diffusion coefficient discussed in the previous section is an intrinsic property in a homogeneous solution. That is, the mobility of a molecule within a uniform environment, such as in infinite dilution IGC, can be related to the Brownian motion. However, at finite concentrations, the molecular mobility is mainly driven by the presence of chemical potential gradients 1, most often related to the concentration gradients. In order to obtain this mutual-diffusion coefficient, based on the formalism of Bearman 31, Duda et al. 3 proposed an approximation for low solvent concentrations which couples the mutual-diffusion coefficient D to the self-diffusion coefficient D 1 : D D1 1 1 RT 1 T, P (.96) The derivative of the chemical potential in Eq. (.96) can be obtained from Flory- Huggins theory 15, and therefore the mutual diffusion coefficient D becomes: where 1 is the volume fraction of the solvent in the solution and is the Flory interaction parameter. 1 1 D D (.97) Influence of the Glass Transition The self and mutual diffusion coefficients discussed in Sections.3.1 and.3. are above the glass transition temperature of the polymer T g, where the polymer is in its equilibrium state. In contrast, at temperatures below T g, the polymer is in a nonequilibrium state where extra hole free volume is trapped due to the relatively slow relaxation rate of the polymer chains compared to the cooling rate. This non-equilibrium

51 Specific Volume 37 condition is referred to as the glassy state, and the passage from the amorphous to glassy states is denoted as the glass transition. A schematic representation of the specific volume changes as a function of temperature is illustrated in Figure.5. The thermal expansion coefficient (i.e. the slope in the figure) changes rapidly in the vicinity of the glass transition temperature, which can be idealized as a step change from α to α g at T g. The presence of the excess free-volume trapped in the glassy state enhances molecular transport, and thus two different modified free-volume models developed by Vrentas et al. 33,34 and Wang et al. 35 are covered in the following sections for self and mutual diffusion coefficients in glassy polymers, respectively. Non-Equilibrium Polymer Volume Equilibrium Polymer Volume Extra Hole Free Volume Tg α Hole Free-Volume α g α c α cg Interstitial Free-Volume Occupied Volume Temperature Figure.5 Characteristic of the specific volume for a polymer above and below the glass transition temperature T g

52 Self-Diffusion Coefficients in Glassy Polymers According to Vrentas et al. 33, at the limit of infinite dilution, the total free-volume including the excess free-volume trapped in the glassy state can be easily expressed by introducing a new parameter λ: Vˆ g FH K1 K T T g (.98) where Here, the extra hole free volume of the polymer can be estimated in terms of the difference between the thermal expansion coefficients of the amorphous and the glassy polymer ( and g, respectively). K 1 is the free volume parameters for the polymer. Based on Eq. (.99), λ is a characteristic quantity of the pure polymer and thus should be independent of the penetrant. However, g actually depends on the specific system history and cannot be related to the pure polymer properties alone. As a result, in this project, λ is determined by fitting the infinite dilution experimental data with the freevolume model for both HPMCAS-water and HPMCAS-acetone. Finally, the self-diffusion coefficients in glassy polymer can therefore be obtained by substituting Eq. (.98) into Eq. (.91): g 1 1 K (.99) D 1 Vˆ * D01exp D01exp ˆ g V K FH 1 K T Tg Vˆ * (.100)

53 Mutual-Diffusion Coefficients in Glassy Polymers The model for mutual-diffusion coefficients in glassy polymers proposed by Wang et al. 35 takes into account the plasticization effect. That is, the glass transition temperature of the polymer-solvent mixture, T gm, is greatly depressed with sorption of small molecules in a polymer matrix. Since in most cases the hole free volume of the solvent is greater than that of the polymer, the addition of the solvent can increase the total hole free volume and thus enhance the diffusion coefficient. However, the addition of the solvent can also lower the glass transition temperature of the mixture, and further reduce the excess hole free volume in the glassy state. The combined effect is illustrated in Figure.6. Typically, the increase of hole free volume from the solvent outweighs the loss of excess hole free volume related to the depression of glass transition temperature, and therefore the corresponding mutual coefficient would increase with increasing solvent concentration. Here, the polymer specific hole free volume at T < T gm can be given by: Vˆ g FH T 0 g Tgm Vˆ Tg f g c dt g cg dt T gm (.101) T where ˆ 0 V is the specific volume of polymer at the glass transition temperature and T g f g refers to the free volume fraction of polymer at the glass transition temperature T g. Wang et al. further simplified Eq. (.101) by assuming that the mobility of the polymer chain is so slow that the thermal expansion below T gm is approximately equal to that of the sum volume composed of the core and the interstitial volume: (.10) g cg

54 Specific Volume 40 Non-Equilibrium Polymer Volume Equilibrium Polymer Volume α w 1 Hole Free-Volume w 1=0 α g α c α cg Interstitial Free-Volume Occupied Volume T gm (w 1 ) T g (0) Temperature Figure.6 Variation of the hole free volume in glassy polymers with addition of solvent and depression of T g with solvent concentration w 1 Substitution of Eq. (.10) into Eq. (.101) leads to the following relation: Vˆ g FH Tg T f dt 0 Vˆ g g c (.103) T gm According to free-volume theory 9, Eq. (.103) can be further expressed as: Vˆ g FH 1 g K K T T (.104) where Tgm Tg (.105) T T g

55 41 The plasticization factor, β, was introduced, which can be estimated from the depression of the polymer glass transition temperature induced by the plasticization effect. On the other hand, the solvent specific hole free volume is independent of the glassy state polymer and therefore remained the same as: Vˆ FH T g 1 Summation of Eqs. (.104) and (.106) leads to the specific hole free volume of the polymer-solvent mixture below T gm : K K T (.106) ˆ ˆ ˆ (.107) g g VFH 1V FH 1 VFH Finally, the mutual-diffusion coefficient in glassy polymers can be obtained by substituting Eq. (.107) into combination of Eqs. (.91) and (.97): * * ( 1Vˆ 1 Vˆ ) D D01exp ˆ (.108) g V FH.3.4 Self-Diffusion in Ternary Systems The basic free-volume expression for the solvent self-diffusion coefficient in Eq. (.91) can be further extended to ternary polymer-solvent-solvent systems. Vrentas et al. 36 developed expressions for the self-diffusion coefficients D 1 and D of the two solvents in a ternary system (subscripts 1 and refer to the two solvents and subscript 3 refer to the polymer):

56 4 Vˆ * Vˆ * Vˆ * D D exp 1 01 Vˆ FH (.109) Vˆ * Vˆ * Vˆ * D D exp 0 Vˆ FH (.110) 3 Vˆ FH K1 i i K i Tgi T (.111) i1 (.11) Here D 0 i is the pre-exponential factor for component i, K 1 i and K i are the free volume parameters for component I, and Vˆ FH here to the average hole free volume per gram of mixture, including contributions from the two solvents as well as from the polymer. The parameters 1 and 1refer to the ratio of the jumping units between the two solvents. They can be easily determined from the ratio of the jumping units between polymer and each solvent 13 and 3, as shown in Eq. (.11). All the other symbols have their usual meanings..3.5 Estimation of Free-Volume Parameters for HPMCAS-acetone-water System In this project, all the operating temperatures are below the glass transition temperature of the polymer-solvent mixtures. Therefore, Eq. (.100) was applied for infinite dilution IGC, Eq. (.108) was applied for finite concentration IGC, and Eqs. (.109) and (.110) were used for ternary systems. In order to precisely correlate and semi-predict the diffusion coefficients using these equations in the HPMCAS-acetonewater system, it is necessary to determine the following parameters: K, K, 11 1

57 * K 1 Tg1, K Tg, V ˆ *, V,,, D 01,, and, where subscript 1 is denoted as 1 ˆ the solvents (acetone and water) and subscript refers to the polymer (HPMCAS). Almost every parameter was able to be estimated independently using rheology information or group contribution methods, except D 01, ξ, and λ, which have to be obtained by correlation of infinite dilution IGC diffusion data. With the regressed ξ parameter, the mutual-diffusion coefficients at finite concentration were consequently able to be predicted based on the infinite dilution self-diffusion coefficients. Methods for estimating the majority of the parameters (excluding β) were summarized by Hong 37. Application of these methods and the corresponding values obtained are covered in the following sections. The plasticization factor β is determined by the depression of T gm with solvent concentration. Details are discussed in Chapter Solvent Free-Volume Parameters K 11 /γ, K 1 -T g1, and V ˆ The free volume parameters for the common solvents acetone and water were obtained directly from the tabulated value from Hong 37, as shown in Table.3. * 1 Table.3 Solvent free-volume parameters for water and acetone Solvent V ˆ (cm 3 /g) * 1 K (cm 3 /gk) K 1 Tg1 (K) 11 Water E Acetone E

58 .3.5. Pure Polymer specific critical hole free volume V ˆ * 44 The specific critical hole free volume of HPMCAS required for a diffusive jump can be determined as the specific volumes at 0 K. Sugden 38 has proposed the group contribution methods to estimate molar volumes at 0 K, and a summary of the methods is shown in Table.4. Table.4 Group contribution methods to estimate molar volumes at 0 K Component Sugden (cm 3 /mol) H 6.7 C 1.1 O 5.0 O (in alcohol) 3.0 Double bond 8.0 According to the generalized structure of HPMCAS shown in Figure.3, there are 78 hydrogen atoms, 5 carbon atoms, 3 oxygen atoms, 11 oxygen atoms in alcohol, and 9 double bonds within a HPMCAS monomer. Therefore, the molar volume for HPMCAS at 0 K was calculated based on the Table.4: Vˆ (6.7) 5(1.1) 3(5.0) 11(3.0) 9(8.0) 799. cm mol (.113) The molecular weight of the HPMCAS monomer was also calculated: M w, mon 146 g mol (.114) ˆ * The critical volume for HPMCAS, V, was obtained combining Eqs. (.113) and (.114): Vˆ 0 Vˆ * cm g (.115) M w, mon

59 Pure Polymer Free-Volume Parameters K 1 /γ and K -T g The pure polymer free volume parameters were determined by correlating the viscosity data of HPMCAS provided from Merck & Co., Inc with the modified Doolittle equation 39 using Williams, Landel and Ferry (WLF) constants 40,41. Doolittle proposed an empirical equation to represent the dependence of the liquid viscosity on free-space: where η is the liquid viscosity, A and B are empirical constants, V is the total volume of the system, and V f is the free volume. Vrentas and Duda further modified the Doolittle equation in terms of the free-volume theory. The term V-V f refers to the hard-core of the * molecule, which can be represented asv ˆ. The free volume V f can be considered as the polymer free volume, which is given by the expression: B V V f Aexp (.116) V f Vˆ FV K1 ( K T T) (.117) g The modified Doolittle equation can therefore be expressed as: Vˆ * / K1 ln ( T) ln A (.118) ( K T ) T Furthermore, the parameters K 1 /γ and K -T g can be related to the extensively reported WLF constants as follows: g K1 Vˆ.303C * 1 C (.119) K C (.10)

60 46 Substituting Eqs. (.119) and (.10) into Eq. (.118) leads to the final regression model:.303c1c ( T) A exp (.11) C Tg T The temperature dependent polymer viscosity data can be obtained from rheological measurement using dynamic mechanical analysis (DMA) procedures. Three parameters are monitored in terms of the angular frequency ω: (1) the storage modulus, G, which measures the stored energy, representing the elastic portion; () the loss modulus, G, which measures the energy dissipated as heat, representing the viscous portion; (3) the complex viscosity, η *, a frequency-dependent viscosity related to the complex shear modulus: " ' * G ( ) G ( ) ( ) i (.1) The amorphous polymer can be viewed as a viscoelastic material. The viscoelastic liquid in the low-frequency limit has the loss modulus G proportional to the angular frequency and the proportionality constant can be referred to the viscosity 16. Furthermore, according to the Cox-Merz rule 4, the complex viscosity at the low frequency limit (no elastic contribution) overlaps with the steady shear viscosity at the low shear rate limit: " G ( ) * lim lim 0 0 (.13) The rheological measurement of HPMCAS done by Merck & Co., Inc is plotted in Figure.7. The plate diameter and the gap are 5 and 5 mm, respectively. The frequency were measured from 0.5 to 500 rad/s and temperatures were done at 140, 160 and 180 C.

61 G', G" (Pa) η* (Pa s) 47 1.E+07 1.E+06 1.E+06 1.E+05 1.E+05 1.E+04 1.E+04 G'_140 C G"_140 C G'_160 C G"_160 C G'_180 C G"_180 C Eta_140 C Eta_160 C Eta_180 C 1.E+03 1.E+03 5.E-01 5.E+00 5.E+01 5.E+0 ω (rad/s) Figure.7 Rheological measurements of HPMCAS from Merck & Co., Inc using dynamic mechanical analysis (DMA) procedures The viscosity data can therefore be determined according to Figure.7 and Eq. (.13) at three temperatures. Correlation of the viscosity data with the regression model in Eq. (.11) is shown in Figure.8. The regressed WLF constants C 1 and C in Eq. (.11) as well as the calculated V ˆ in Eq. (.115) were further substituted into Eqs. * (.119) and (.10) to obtain the pure polymer free volume parameters. For HPMCAS, the regressed K 1 /γ is 3.E-04 cm /s and K -Tg is K.

62 Eta (Pa s) 48 1.E+07 K 1 /γ = 3.E-04 cm /s K -Tg = K 1.E+06 1.E+05 Merck & Co., Inc Regression model 1.E Temperature (K) Figure.8 Correlation of viscosity-temperature data with the modified Doolittle equation with WLF constants Flory interaction parameter χ The Flory interaction parameter can be obtained by two different approaches. First, it can be derived from the partition coefficient obtained from infinite dilution IGC, as shown in Eq. (.65). Second, it can be determined by correlating the sorption isotherm from finite concentration IGC with the Flory-Huggins model, as shown in Eq. (.6). The first approach was applied in this project since the original Flory-Higgins model in Eq. (.6) in some cases has difficulties precisely describing the thermodynamic properties for glassy polymer due to the plasticization effect. Details are discussed in Section 5.1.

63 49 Chapter 3 Experimental Procedure This chapter covers the experimental details used throughout this project. First of all, the thermal conductivity detector (TCD) used for the gas chromatograph signal detection is described. Second, the experimental set up for the inverse gas chromatography (IGC) technique is covered. The modification of the gas chromatograph used for finite concentration studies is explained with schematic details. In addition, the experimental procedures and analysis for infinite dilution, finite concentration, and ternary system experiments are presented. At the end, the polymer being studied in this project, hypromellose acetate succinate (HPMCAS) is introduced. The corresponding capillary column for HPMCAS was made and the detailed procedures for column preparation, characterization, and conditioning are explained.

64 Application of Thermal Conductivity Detector The thermal conductivity detector (TCD) has been used for gas chromatography studies due to its simplicity, versatility, and inexpensiveness compared with other detectors. The TCD works by measuring the thermal conductivity of the column effluent and compares it to a reference flow of carrier gas (ultra-high purity helium was used in this project). Since most compounds have a thermal conductivity much less than that of helium, a detectable signal is produced when the solvent vapor elutes from the column. The thermal conductivities for solvent acetone and water as well as the carrier gas helium are tabulated in Table 3.1. These values were obtained from the software developed by American Petroleum Institute Technical Data Book (API TDB). The difference of the thermal conductivities between acetone and water enables the applicability of the IGC technique in ternary system experiments, where one solvent at infinite dilution is injected into an equilibrium mixture of the second solvent and the polymer. Table 3.1 Thermal conductivities for acetone, water, and helium at 50 C Compound Thermal conductivity (W/m-k) Acetone Water Helium A schematic diagram for the TCD operation is shown in Figure 3.1. The TCD contains an electrically heated filament in a temperature-controlled cell. The filament temperature is kept constant while alternate streams of reference gas and column effluent

65 51 pass over it. The two gas streams are switched over the filament five times per second. When the column effluent is diverted to bypass the filament, as shown in Figure 3.1(a), only the reference gas helium is detected and thus no change of thermal conductivities is present. When the solvent vapor elutes and is diverted to the filament channel, as shown in Figure 3.1(b), the drop of the thermal conductivity forces the filament to heat up to maintain the temperature and consequently changes the resistance. This resistance change is measured and further produces the voltage change, which is recorded as the readout. (a) (b) Figure 3.1 Schematic for the operation of thermal conductivity detector: (a) only the reference gas of helium flows through the filament and no thermal conductivity changes are detected; (b) effluent of the solvent vapor along with the makeup helium are now diverted to the filament and huge drop of thermal conductivities are detected.

66 5 In order to optimize the TCD performance, two important factors need to be considered: (1) the detector cell temperature should be operated at the lowest possible temperature, which is limited by the boiling temperature of the injected solvent so as to prevent any condensation in the detector. This temperature can provide the highest sensitivity and meanwhile increase the filament lifetime. In this project, the detector cell temperature was always kept at 160 C; () For the 5890 GC, the reference flow should be three times the total flow of the column plus makeup gas flow. It is recommended that the total flow (column plus makeup) be around 5 ml/min, and therefore the reference flow should be set to 15 ml/min. Here, the column flow rate was around ml/min. All the flow rates were measured by using the Humonic Optiflow 40 digital bubble flowmeter. To prolong the lifetime of the filament in the TCD and prevent any damage, the detector was turned off whenever adjustments were made affecting gas flows through the detector. In addition, no exposure to oxygen was allowed. The marker gas used was methane. 3. Inverse Gas Chromatography Apparatus Set Up Most of the commercial GC units are designed for analytical purposes. Here, in order to probe the characteristic of the polymer-solvent system of interest, the conditions at which IGC experiments are conducted are slightly different. As shown in Figure 3., modifications were made to the Hewlett-Packard 5890 GC to enable studies for infinite dilution, finite concentration, and ternary systems.

67 53 Figure 3. Schematic of the modified inverse gas chromatograph apparatus The key difference was the addition of a saturator for finite concentration and ternary systems, where a uniform mixture of helium and saturated solvent was present before entering the column. The saturator consisted of a stainless steel vessel with the solvent of interest, and a gas diffusing stone that dispersed the inlet helium uniformly into the solvent. The level of the solvent was set between half to three-fourth of the vessel height, which covered both the diffusing stone and the immersion heater. To avoid any leaks from the saturator, it is crucial to apply an adequate O-ring surrounded with high vacuum grease (Dow Corning ) between the vessel and the lid to make it hermetically sealed. Both acetone and water were used for this project, and thus O-rings made of ethylene propylene (O-ring Warehouse) were used. In addition to O-ring, the bolts used to seal the vessel and the lid were tightened in a starfish pattern, as shown in Figure 3.3.

68 54 On the other hand, in order to obtain a uniform concentration in the gas phase with the solvent activity of interest, the temperature of the saturator was precisely controlled within 0.1 C by using a PID temperature controller (Omega CN76000) connected to a type J thermocouple probe and a 100-Watt heater immerged in the solvent. A cooling plate (Thermoelectrics Unlimited, Inc.) was used when the desired saturator temperature went below room temperature. Furthermore, a reusable and removable insulation blanket (Hot Caps TM from Ohio Valley Industrial Services, Inc.) was applied to surround the vessel to minimize any heat exchange with the environment. A magnetic stir bar was put inside the saturator and was driven by the cooling plate to minimize the temperature gradients within the solvent. The lining in the outlet of the saturator was heated at least 15 C above the saturator temperature with heating tapes to avoid any cold spot and condensation from the saturated solvent vapor. Figure 3.3 Schematic for bolts tightening according to the sequence of number The modifications also required a manifold designed to provide for experiments at infinite dilution, finite concentration, or in ternary systems, as shown in Figures 3.4 and

69 The manifold was composed of five on-off valves (screwed-bonnet brass needle valves from Swagelok ) and one metering valve (Brass Low-Flow Metering Valve from Swagelok ) that were connected by two tees, one union cross, and two straight fittings, as shown in Figure 3.4. The metering valve was applied to control the optimal flow rate of helium passing through the saturator. On the other hand, to prevent any condensation of the saturated solvent vapor, all the gas supply lines in the outlet were controlled at a temperature 15 C above the saturator temperature or at the column temperature. This was done by changing the original gas chromatograph plastic cover to a stainless steel cover lined with high temperature calcium silicate insulation sheets, which are able to operate in temperatures ranging from 0 to 95 C. The PID temperature controller (Omega CN76000) connected to a type J thermocouple and a 100-Watt heater was used to control the temperature inside the cover. Three additional heaters, 315 Watts in total, were set as the makeup heating sources and were controlled by variable autotransformers. One of the makeup heaters is not shown in Figure 3.5 because it was mounted directly below the top of the inner wall of the cover. Two AC axial compact fans (ebm-papst inc Z) in Figure 3.4 were used to provide air circulation inside the cover to minimize any temperature gradients. Temperatures within the cover were measured by three additional type J thermocouples which were inserted through three small holes shown as a, b, and c in Figure 3.5. The biggest temperature differences measured were within an acceptable range of 5 C.

70 56 Figure 3.4 Schematic of the manifold designed to permit experiments at infinite dilution, finite concentration, or ternary systems. 4 out of 5 on-off valves (with black knobs) and 1 metering valve (with white knob) are shown here. The other on-off valve outside the stainless steel cover and is shown in Figure 3.5. Two fans were mounted to provide air circulation inside the cover. The rectangular coordinates are applied to compare with Figure 3.5.

71 57 Figure 3.5 The overview for the modified HP 5890 Gas Chromatograph. The rectangular coordinates are applied to compare with Figure 3.4. Five on-off valves are labelled with numbers. Thermocouples were located at a, b, and c. The dotted lines on the wall refer to the interior gas line supplies. An insulation layer is lined the stainless steel cover to form an oven. The thermocouple and one of the immersed heaters were connected to a PID temperature controller. The other two immersed heater along with another mounted heater below the cover (not shown in the figure) provided the makeup heating source with a maximum 315 Watts and were controlled by the variable autotransformers.

72 58 With the externally adjustable PTFE packing and the bonnet lock nut, all the onoff valves inside the cover were able to be controlled from the outer stainless steel wall with ease. By controlling these on-off valves, experiments were able to be run at infinite dilution or finite concentration. Table 3. shows the settings for the on-off valves (which are labelled with numbers from 1 to 4 in Figure 3.5) for infinite dilution and two types of finite concentration experiments. The detailed procedures to conduct experiments under infinite dilution, finite concentration, and ternary systems are discussed in the following sections. Table 3. The control of on-off valves for different experiments On-off valves with labelled numbers Experiments Infinite dilution x o o x o Finite concentration to column only Finite concentration to column, reference and makeup o o x o o o x o o o 3.3 Experimental Procedures and Data Analysis Before any experimental runs, the desired capillary column was installed in the GC with capillary column nuts (Part No ) and graphite/vespel ferrules (M-A, 0.8 mm ID from Supelco ) on both ends. On the inlet side, the column was inserted through the nut and ferrule and then cut down with a capillary column cutter since only 4 to 6 mm of the column can extend above the end of the ferrule. To avoid any

73 59 contamination from the nut or ferrule, the column was initially positioned around 3 cm (arbitrary) above the ferrule. On the other hand, the procedure for installing a capillary column into the TCD was similar. The column was inserted through the nut and ferrule with extra length to prevent contamination. The only difference was the column was gently inserted into the detector as far as possible, until it reached the bottom. Then the nut was tightened finger-tight to withdraw the column approximately 1 mm. Finally the nut was tightened with a wrench for an additional 1/4-turn. To make sure there was no leak coming from either end of the column, helium was set to a flow rate of ml/min and a gas leak detector (Sigma-Aldrich model 1-50) was used Infinite Dilution CCIGC During an infinite dilution experimental run, on-off valves labelled with number 1 and 4 in Figure 3.5 were turned off and only UHP helium was flowing through the capillary column at a flow rate of ml/min, which was determined by controlling the column head pressure. The makeup flow rate was set to make the summation of makeup and column to be 5 ml/min. Since the makeup flow control valve is an on-off valve, the only way to determine the makeup flow rate was by controlling the gauge pressure of the helium gas cylinder. The reference flow was set to around 15 ml/min and it was controlled by the reference control valve. After the flow rate setting settled, the desired oven temperature was set and the injection port temperature was set 50 C above the boiling temperature to insure fully evaporation for the solvent injection. The TCD temperature was set at 160 C. After all the temperatures reached stable conditions, the

74 60 equipment was ready to operate and the TCD was turned on. Once the detector was on, it took around a half hour for the baseline to become stable and retain constant in the output ranging from 3 to 6 mv. Then about 10μL of the marker gas methane was injected to determine the linear velocity of the carrier gas. After the methane injection, an injection of the liquid solvent was made and the elution profile was recorded with the program HP ChemStations Instrument 1 Online. This was followed by a second methane injection to check that the flow was constant. The above procedures were repeated with different injection volumes under different temperatures to exclude any non-linearity effect. Details are discussed in Section Finite Concentration CCIGC Two types of finite concentration experiments were designed and carried out: (1) The on-off valve labelled number 3 in Figure 3.5 was turned off and thus the column was saturated with the vapor solvent at a set activity, which was determined as the ratio of the solvent vapor pressure at the saturator temperature and that of the column temperature; () The on-off valves labelled number was turned off and the whole system including the reference and makeup gas were saturated with the solvent vapor. Only the former setup was able to maintain a stable baseline and thus an analyzable elution profile. The latter arrangement was rejected. Any leak from the saturator would lead to significant fluctuations or drifting of the output baseline, and therefore the first step before any finite experiments was to check the leak from the saturator. This was done by closing all the on-off valves except the one

75 61 labelled number 1. Then the UHP helium gas cylinder was turned on with the second stage pressure set at 5 psig and then immediately turned off. A pressure drop from the pressure gauge indicated to a leak. No leak detector was needed. If a leak was detected, all the bolts were loosen and re-tightened again in the pattern shown in Figure 3.3. An onoff valve was installed on the lid of the saturator to release the high pressure inside the saturator to the ventilation system. To make sure the saturator was essentially leak-free, the pressure should hold constant under observation for at least hours. Once there was no leak, the equipment was ready for the finite concentration experiments. Here, the flow through the column was the mixture of helium and solvent vapor of interest while the flow for both the makeup and reference streams were UHP helium. The same procedures as for the infinite dilution IGC were used to set the flow rate and the system temperatures. The TCD was turned on and approximately 1 to hours were required for the baselines to reach equilibrium. The equilibrium readout for the baseline was determined in terms of the solvent activities under different column temperatures. Then the marker gas, solvent of interest, and marker gas were injected in sequence to obtain the linear gas velocity and the elution profile under the equilibrium concentration of solvent in the polymer Ternary System CCIGC The experimental procedure for ternary system experiments were similar to that of finite concentration experiments, where UHP helium was passed through the saturator maintained at constant temperature and allowed to equilibrate with the polymer inside the capillary column. The injected solvent, however, was different than the solvent used to

76 6 saturate the polymer. This insured a multicomponent system where the pulse solvent (solvent 1) is diffusing in a solution of polymer and the saturator solvent (solvent ). In this way, the diffusion and partition coefficients were measured for a pseudo-ternary polymer-solvent 1-solvent system Data Analysis Generalized data analytical procedures for infinite dilution, finite concentration, and ternary systems are covered in this section. More detailed information for finite concentration and ternary systems are discussed in Chapters 5 and 6 respectively. The thermodynamic and transport properties were determined by correlating the non-dimensionalized elution profile with the theoretical response as described in Section.1.1. This was actually done with a FORTRAN program developed by a previous graduate student Peter K. Davis. Several initial parameters were required for input: (1) the capillary column length, L; () the polymer coating thickness, τ; (3) the inner diameter of the capillary column, (R+ τ); (4) the retention time of the marker gas, which was applied further to calculate the carrier gas linear velocity U, (5) the mutual binary diffusion coefficient in the gas phase D g, which was determined with the model described in Eq. (.10) that has been coded in the DIPPR manual program. The strength of the injected pulse C 0 used in the dimensionless concentration was determined directly with a numerical integration of the area under the elution profile. No additional calculations were needed. On the other hand, a baseline correction was applied since the CCIGC model assumes the baseline to be zero. This was done by subtracting

77 63 the average value of the frontal or rear baseline from the entire elution profile. Finally, the difference between the experimental non-dimensionalzed elution profile and the theoretical response expressed in the time domain obtained by a numerical inversion of Eq..36 was minimized using a nonlinear regression subroutine form the IMSL Library and consequently provided the regressed values of α and β with the best fit, from which the thermodynamic and transport properties were further calculated. 3.4 Materials The HPMCAS-acetone-water system was studied in this project. HPMCAS is a synthetic polymer derived from cellulose and stands for hypromellose acetate succinate. Figure 3.6 shows the structure of the HPMCAS molecule, which can be visualized as a polymer chain composed of -hydroxypropoxy groups (-OCH CH(CH 3 )OH), methoxy groups (-OCH 3 ), acetyl groups (-COCH 3 ), and succinoyl groups (-COCH CH COOH). Figure 3.6 Structure of hypromellose acetate succinate (HPMCAS) There are three grades of HPMCAS in terms of its substitution levels of methoxy and succinoyl groups, as shown in Table 3.3. In addition, each grade is available in fine (F) and granular (G) particle sizes. In this project, the HPMCAS-LF (L grade with fine particle sizes) provided by Merck & Co., Inc., was used. The following chapters refer to

78 64 HPMCAS-LF as HPMCAS for simplification. Summarized characteristics of HPMCAS are covered in Table 3.4. The density of HPMCAS was viewed as a constant instead of as a function of temperature due to the lack of data. Two capillary columns with different polymer coating thickness were prepared. The one with a 5µm film was made by colleague, Dr. Ida Balashova. High purity acetone designated for use in gas chromatography and distilled water were used as the solvents. Table 3.3 HPMCAS grades Grade Acetyl Content Succinoyl Content Methoxyl Content Hydroxypropoxy Content L 5-9 % % 0-4 % 5-9 % M 7-11 % % 1-5 % 5-9 % H % 4-8 % -6 % 6-10 % Table 3.4 Details of HPMCAS and corresponding capillary columns Polymer Capillary columns Density (g/cm 3 ) M w (g/mol) T g ( C) Length (cm) Film thickness (µm) HPMCAS , Preparation and Characterization of Capillary Columns The capillary columns for HPMCAS were prepared using a static coating technique in the modified gas chromatograph once connected to a vacuum source, as shown in Figure 3.7. There are four steps included, as described below:

79 65 (1) Prepare the polymer solution: A polymer solution with the desired amount of polymer was prepared and degassed by setting the Bransonic ultrasonic cleaner to the degas mode for about one hour. A magnetic mini stir bar is applied for faster and easier mixing. The selection of the solvent used to prepare the solution depends mainly on the miscibility of the solvent with the polymer. In general, low boiling point solvents are desired for a faster and safer preparation process. Tetrahydrofuran (THF) with a boiling temperature of 66 C was used to prepare the column for HPMCAS. The thickness of the film depositing on the wall of capillary column is determined by the concentration of the polymer solution. This can be easily calculated with an empirical equation based on the mass balance of the column, provided that all the polymer remains inside the column as a homogenous coating after evaporation: 4 C (3.1) D i where C is the concentration of the polymer solution, τ is the polymer thickness, ρ is the polymer density, and D i is the inner diameter of the column. Then a 0 cc-syringe is capped before filling with approximately 15 cc of the polymer solution. Make sure the syringe is clean and the piston can move up and down with little friction before filling. () Fill the column with the solution: Polymicro Technologies TM fused-silica columns with an inner diameter of 0.53 mm (TSP ) from Molex incorporated were used. The capillary column length can be calculated according to the equation: L DN (3.)

80 66 where L is the desired length of column, D is the average diameter of each round of the column, and N is the number of rounds. Before filling the column with the polymer solution, burn off around 7 cm of the exterior coating of the column and wipe off with wet paper towel gently for a clear and spotless end. The column section without the exterior coating becomes very brittle, and thus extra care is needed. Then tilt the syringe and loosen the nut so that air can escape while pushing the piston down into the syringe. With no air bubbles remaining in the syringe, connect the column to the syringe using Swagelok fittings along with the graphite ferrule. Do not tighten it too much but make sure there is no leak. Then turn on the syringe pump and fill the column completely with the optimized flow rate. A flow rate of 0.81 ml/min under speed position 5 is recommended. After the column is filled with solution, keep the syringe pump running for another two minutes to flush away any possible contaminants. Then turn off the syringe pump and disconnect the column from the syringe. To insure all the polymer solution is within the heated oven (here the temperature was set at 40 C), another 50 ccsyringe with 30 cc of air in it is connected to the column. The air/solution phase line can be moved inside the oven by pushing on the piston. (3) Form a tightly sealed end: The end of the column without the exterior coating is tightly sealed by using a commercial epoxy resin (UV Light Curing Adhesive-No. 40, Dymax Corportation, Torrington, CT) along with a buffer layer of distilled water. The degassed distilled water and UV-glue were placed in short and open containers separately to enable both the water and the glue to be sucked up easily. To exclude any formation of air bubbles, gently push on piston to form a small ball of solution on the end of the column before putting the column into the water. Then use the 50cc-syringe to suck up

81 67 water into the column to around cm (air/solution phase line should still be inside the oven). Similarly, before sucking in the glue, gently push on piston so that a small ball of water rest on the end of the column. Approximately 5 cm of the glue is then sucked up using the syringe. The glue is cured with UV light for at least 1 hour to provide tightly sealed end. There are two ways to check the sealing from the glue. A more straightforward way is done by pushing on the piston to see if the glue moves. The other way is by attaching the column to a UHP nitrogen cylinder and putting it under a pressure of 70 psig for one hour. It is best to check by both methods. If the glue moves or the pressure drops, the glue has failed to provide a tightly sealed end. Thus, cure the glue with additional time or cut off the end and suck up more glue to redo the sealing procedures. (4) Vacuum up the solvent: Once the glue is completely cured, attach the other end of the column to the vacuum apparatus. Before turning on the vacuum pump, close all the valves on the control board to avoid any abrupt evaporation. Then slightly turn on the valve connected to the column and check how the air/solution phase line moves. If the phase line keeps moving toward the vacuum end, the glue plug fails. Then close the valve, detach the column from the vacuum apparatus, reconnect the column to the 50cc-syringe, push the phase line inside the oven, and suck up more glue to repeat the sealing procedures. If the glue plug works fine, the air/solution phase line will move slowly away from vacuum and toward the sealed end, indicating the solvent is being evacuated to form a uniform coating as the polymer is deposited on the wall of the capillary column. As the solvent evaporates at the phase line, the polymer solution becomes more viscous. Due to the small diameter of the capillary column, the combination of the surface forces and the viscous forces are strong enough to resist any deformation driven by gravity. As a result,

82 68 the polymer film left behind is nearly symmetric. This evaporation process can take anywhere from one day to a week, depending on the solution. Here, the 3 micron column took around three days to fully evaporate the THF. Once the evacuation is complete, the glue plug is cut off while the vacuum pump is still on so that air will go through the column to sweep away any residual solvent. This should be done for 10 minutes. Then turn off the vacuum pump and detach the column from the vacuum apparatus. Finally, cut the column where the original phase line was (on the vacuum side) and where the column was out of the oven (on the glue side). Figure 3.7 General procedures in sequence for capillary column manufacturing

83 69 Before running experiments with any newly made capillary columns, it is critical to condition the column to eliminate residual solvent. This is done by installing the end of the column (on the glue side) to the injection port and turn on the UHP helium gas cylinder to make the helium flow through the column. The other end of the column should not be connected to the TCD while conditioning the column, since the residual solvent may cause contamination to the detector. Then increase the oven temperature gradually over a period of time up to the maximum experimental working temperature or any temperature below the thermal decomposition temperature of the polymer. Here, the oven temperature was set to increase from 35 C to 90 C with heating rate of 1 C/min. Two hours were maintained at 90 C and then gradually drop down to 50 C with the same rate of 1 C/min. Finally, the oven temperature was kept at 50 C overnight (around 1 hours) to insure all the residual solvent is evaporated. To confirm the uniformity of the coating as well as the thickness of the film, scanning electron microscope (SEM) figures were taken. Figure 3.8 shows the schematic of the capillary column and the regions measured with SEM. Figure 3.9 refers to the right region of Figure 3.8, which includes three layers: the exterior coating of polyimide, the fused silica, and the coating of HPMCAS. A seemingly uniform film was obtained, which indicates the preparation procedures for capillary column was successful. To further look at the coating thickness of HPMCAS, Figure 3.10 with a smaller measuring scale shows the left region of Figure 3.8. Thickness measured from SEM showed roughly 3±0.5μm over different sections of the 3μm-column. It is satisfactory to see such small deviations between the calculated film thickness and the real one.

84 70 Figure 3.8 SEM image for the entire cross-section of the coated capillary column with a scale bar of 30 μm Figure 3.9 SEM image for part of the cross-section of the coated capillary column with a scale bar of 10 μm

85 71 Figure 3.10 SEM image for part of the cross-section of the coated capillary column with a scale bar of μm

86 7 Chapter 4 Infinitely Dilute Inverse Gas Chromatography Results Partition coefficients and diffusion coefficients at virtually zero concentration of acetone and water in HPMCAS have been obtained by fitting the experimental data with the Capillary Column Inverse Gas Chromatography (CCIGC) model. Detailed information about the theoretical background and the experimental procedure are discussed in Chapters and 3. Studies of the injection volume were carried out to clarify the optimal sample size for the infinitesimal pulse of acetone or water injected to the column. The partition coefficient and diffusivity data were also measured after a finite concentration experiment to detect any effects from the water or acetone on the results. The partition coefficients obtained at different temperature are compared with the pure prediction models UNIFAC and UNIFAC-vdw-FV. A correlation has been made for the diffusivity data using the free-volume model. Flory interaction parameters for both HPMCAS-acetone and HPMCAS-water systems were derived using the weight fraction activity coefficient (WFAC) at the infinite dilution limit, which can be further applied for finite concentration systems to predict the absorption isotherm. Details are covered in Chapter 5.

87 Study of the Influence of Injection Volume in IGC Experiments Nonlinearity occurs when the solute concentration injected into the capillary column is too large. Under such conditions, interactions among the injected solute molecules as well as between solute and polymer become significant, and asymmetric peaks with different retention times may occur. The term infinitesimal for pulse injection is arbitrary and really depends on the type of detector being used. With their high sensitivity, mass spectroscopy and flame ionization detectors can go down to 0.01 to 0.0μL. The thermal conductivity detector that has been implemented here, however, requires a slightly bigger volume ranging from 0.1 to 0.3μL. Constrained by the sensitivity of the TCD, most of the time a larger amount of solvent had to be injected in order to get a more noticeable and analyzable peak for the finite concentration and ternary systems. Depending on the solvent activity and oven temperature, the injection volume was sometimes increased to 0. to 3μL. Aspler and Gray 43 have shown that the retention volumes vary with sample size for water in cellulose acetate at 5 C. It was critical to see how the increased injection volume from the syringe influenced the measured diffusion and partition coefficients HPMCAS-water System Water injections into the HPMCAS column were made ranging from 0.05 (limitation of the TCD resolution) to µl at temperature 35, 40, 50 and 60 C. Figures 4.1(a) to 4.4(a) are the elution profiles obtained from the readout with different injection volumes at different temperatures. Figures 4.1(b) to 4.4(b) are the non-dimensionalized

88 74 concentration at the exit with non-dimensionalized time. The elution profile becomes more Gaussian for smaller injections of water and becomes more skewed as the amount increases. All the elution profiles from large injection volumes show a typical behavior with a sharp front and a long diffusing tail. The main reason for the tailing is due to the sorption effect 44. The mobile phase velocity changes due to different ratio of the solute concentration in the column to the total concentration. The larger amount of injection leads to a higher finite vapor pressure of the sample and therefore causes a reduced partial pressure of the carrier gas with greater velocity in regions of the peak where concentration is higher. Accordingly, the center of the peak moves more rapidly through the column: a sharper front profile occurs. Another possible explanation is the adsorption effect. Some of the tails of the elution profiles from different injection volumes overlap, indicating a typical Langmuir type isotherm behavior that the retention of the solute is the result of solvent absorption in the stationary phase combined with the adsorption on the mobile-stationary interface 45. For infinitely dilution IGC, Henry s law is expected to apply. Therefore, only peaks that were not affected by any non-linearity were regressed. In HPMCAS-water system, the smallest injection volume within the sensitivity of the TCD, 0.05µL, was applied for any IGC experiments. Regressed partition coefficients and diffusivities obtained by fitting elution profiles with the CCIGC model with different injection volumes at different temperatures are listed in Table 4.1. Summary plots are shown in Figures 4.5 and 4.6. Negligible changes were observed for diffusion coefficients under different injection volumes; while there is a significant dependency between the partition coefficients and the injection volumes. The dashed lines are only visual guides. The

89 75 injection volume with 0.05µL provides the most representative partition coefficients within the region of linear chromatography; any other results are considered to be under non-linearity and concentration-dependent effects. Unfortunately, this concentration-dependent behavior was unveiled only after all the IGC experiments had been carried out, including the finite water concentration (Chapter 5) and ternary HPMCAS-acetone-water system (Chapter 6). A correction factor in Table 4.1, basically the ratio between partition coefficients at different injection volumes, therefore has been implemented to make sure the regressed partition coefficients or slopes of isotherm are closer to the real value. More details about the implementation will be discussed in Chapters 5 and 6.

90 CL/C o U V (mv) (a) 0.05 µl 0. µl 1.0 µl Time (min.) (b) 0.05 µl 0. µl 1.0 µl Figure 4.1 (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 35 C t/t c

91 CL/C 0 U V (mv) (a) 0.05 µl 0. µl 1.0 µl Time (min.) (b) 0.05 µl 0. µl 1.0 µl t/tc Figure 4. (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 40 C

92 CL/C 0 U V(mV) (a) 0.05 µl 0. µl 0.5 µl 1.0 µl Time (min.) (b) 0.05 µl 0. µl 0.5 µl 1.0 µl t/t c Figure 4.3 (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 50 C

93 CL/C 0 U V (mv) (a) 0.05 µl 0.1 µl 0. µl Time (min.) (b) 0.05 µl 0.1 µl 0. µl 1.0 µl t/t c Figure 4.4 (a) Elution profiles and (b) non-dimensionalized experimental data with varying water injection volume at 60 C

94 Partition Coefficient Diffusion coefficient(cm /s) Partition coefficient Diffusion coefficient(cm /s) 80 (a) E Partition Coefficient Diffusion Coefficient Volume for pulse injection (µl) 1.E-09 (b) Partition Coefficient Diffusion Coefficient 1.E E Volume for pulse injection (µl) 1.E-09 Figure 4.5 The impact of injection volume on partition coefficients and diffusivity for water at (a) 35 C and (b) 40 C

95 Partition coefficient Diffusion coefficient(cm /s) Partition coefficient Diffusion coefficient (cm /s) 81 (a) Partition Coefficient Diffusion Coefficient 1.E (b) Volume for pulse injection (µl) Partition Coefficient Diffusion Coefficient 1.E-08 1.E Volume for pulse injection (µl) 1.E-08 Figure 4.6 The impact of injection volume on partition coefficients and diffusion coefficients for water at (a) 50 C and (b) 60 C

96 8 Table 4.1 Diffusivity and Correction factor (Ratio) for Partition Coefficient with different water injection volumes T ( C) Injection Volume (µl) Partition Coefficient Ratio Diffusivity (cm /s) E E E E E E E E E E E E E E E E E E E E HPMCAS-acetone System The elution profiles from the TCD and the non-dimensionalized plot for acetone in HPMCAS in Figure 4.7 shows an entirely different behavior compared to water. The retention time and the tailing region all match for different injection volumes, ranging from 0.05 to µl. No concentration-dependent behavior was observed and therefore no correction factor is needed here.

97 CL/C 0 U V (mv) (a) µl 0.05 µl 0.1 µl 0. µl 0.5 µl.0 µl µL Time (min.) (b) 0.05 ul ul 0.5 ul.0 ul t/t c Figure 4.7 (a) Elution profiles and (b) non-dimensionalized experimental data with varying acetone injection volume at 60 C

98 84 Although acetone has shown a linear chromatography behavior in the infinite dilution experiments, the peaks are still very asymmetric with long tails. This is caused by a non-ideal peak-spreading process 46. A huge mass transfer resistance in the stationary phase is usually the main reason for this type of peak broadening. It s particularly true for glassy polymer-solvent systems. Polymer chains at temperature below glass transition temperature are not sufficiently mobile to permit immediate penetration of the solvent to the polymer core, leading to a significantly smaller diffusion coefficient in the polymer phase compared to that in the gas phase. However, as a much smaller molecule, water can still easily penetrate in and out the polymer and therefore the spread of the peak was virtually symmetric since the concentration gradients are the same on each side of the peak, as shown in Figure 4.4 with 0.05µL. By contrast, as a bigger molecule, penetration for acetone is more difficult. Most of the injected acetone molecules do not diffuse into the polymer, eluting as a sharp front almost at the same time as the non-interacting gas. For those diffusing in, it took a long time to diffuse out due to the low diffusion coefficients, producing the severe tailing observed in Figure HPMCAS-Acetone System Data were collected for the partition coefficient and the diffusivity of infinitely dilute acetone in two capillary columns over a temperature range of 30 to 70 C by fitting the elution profile with the CCIGC model. One column had an inner wall film coating of 3µm and the other had 5µm. A typical comparison between the elution profile and the

99 CL/C 0 U model is shown in Figure 4.8. The open circles in the figure are the non-dimensionalized data points. The CCIGC regression providing the D p and K is shown by the solid line Experimental data CCIGC regression D p =1.06E-10 cm /s K= Figure 4.8 Comparison of the elution profile and the CCIGC model regression for acetone in HPMCAS at 35 C t/t c Data under different circumstances were obtained to check the consistency. Comparisons between partition coefficients and the pure prediction UNIFAC-vdw-FV model for both types of HPMCAS structures were made, as shown in Figure 4.9. The diffusivity data were correlated with the free-volume model to obtain ξ, D 01, and λ parameters, as shown in Figures 4.10 and The entire infinitely dilute data for acetone are listed from Tables A.1 to A.7. The 5µm column was made by a colleague, Dr. Ida Balashova. She obtained data using infinite dilution IGC with a flame-ionization detector (noted as 5 micron_igc w/ FID before any finite in the figures or tables). A set of measurements were made

100 Partition Coefficient of Acetone 86 afterwards from thermal conductivity detector (noted as 5 micron_before finite acetone ). There appears to be a slight difference between the two sets of data, but overall the deviation is small. The 5µm column was then exposed to finite concentrations of acetone for the finite concentration IGC experiments. A set of infinite dilution data (noted as 5 micron_after finite ) were measured to see if there were any detectable effects of the acetone on the results. Conditioning of the column was always made before any measurement by drying overnight at 50 C to make sure it had been thoroughly cleared of any acetone. Significant differences were observed: the partition coefficient essentially doubled and the diffusivity was decreased about half after the column was exposed to finite concentrations of acetone micron_before any finite 3 micron_after finite water 3 micron_after finite acetone 5 micron_before finite acetone 5 micron_after finite acetone 5 micron_igc w/ FID before any finite Averaged Partition Coefficient UNIFAC-vdw-FV_HPMCAS(b) UNIFAC-vdw-FV_HPMCAS(a) /T (1/K) Figure 4.9 Partition coefficients of infinitely dilute acetone in HPMCAS

101 Diffusion coefficient (cm /s) 87 Similar phenomenon was observed for a newly made 3µm column. A set of data were taken when the 3µm column was new and had not been exposed to either finite water or acetone (noted as 3 micron_before any finite ). After the column was exposed to finite concentrations of water (noted as 3 micron_after finite water ), the diffusivity again showed a significant drop; while this time the partition coefficient didn t change much. The last data set for infinitely dilute acetone was taken after several sets of finite concentration acetone experiments (noted as 3 micron_after finite acetone ). Negligible changes were observed for both partition coefficients and diffusion coefficients. 1.E-08 1.E-09 3 micron_before any finite 3 micron_after finite water 1.E-10 3 micron_after finite acetone 5 micron_before finite acetone 5 micron_after finite acetone 5 micron_igc w/ FID before any finite Averaged Diffusion Coefficient 1.E /T (1/K) Figure 4.10 Diffusion coefficients of infinitely dilute acetone in HPMCAS

102 Diffusion coefficient (cm /s) 88 1.E-06 1.E-07 1.E-08 Tg =11 C 5 micron_before finite 3 micron_after finite Averaged Diffusion Coefficient D 01 = 5.33E-04 cm /s ξ = 0.78 λ=0 1.E-09 1.E C 60 C 50 C 45 C 40 C 35 C 30 C λ= E-11 1.E-1 λ= /(K +T-Tg ) (1/K) Free-Volume correlation Figure 4.11 Correlation of averaged diffusion coefficients with free-volume model Figure 4.1 shows a comparison between the non-dimensionalized elution profiles before finite acetone and after finite acetone for the 5µm column at 50 C. According to the chromatogram, a greater mass transfer resistance was present in the stationary phase after exposure to finite concentration of acetone. An explanation for that may have something to do with non-equilibrium glassy state polymer undergoing a structural rearrangement after being saturated with finite concentration acetone and fully dried. A clear understanding of the effects of finite concentration remains unknown.

103 CL/C 0 U micron_before finite acetone D p =3.63E-10 cm /s K= micron_after finite acetone D p =1.93E-10 cm /s K= Figure 4.1 Comparison of the elution profile for before finite and after finite acetone for the 5µm column at 50 C t/t c Infinite dilution weight fraction activity coefficients (WFAC) were calculated by using the partition coefficient data. Detailed information is shown in Table A.8. It can be further applied at finite concentrations to check the consistency of the decrease of WFAC with increasing solvent concentration. The infinite dilution interaction parameters χ for HPMCAS-acetone system were determined using Eq. (.65), as shown in Table A.9. This value can be further applied to predict the sorption isotherm at finite concentration in Chapter 5 using Eq. (.6), provided that no significant changes occurred with increasing concentration. All the χ parameters obtained are below 0.5, indicating acetone is a good solvent for HPMCAS. The temperature dependence of χ in Figure 4.13 shows a negative slope (denoted as B in the figure) with positive intercept (denoted as A). According to Eq. (.61), this represents the case of lower critical solution temperature for HPMCASacetone system. As temperature goes up, a phase separation is expected to occur.

104 Flory interaction parameter χ χ A + B T A =.699 B = LCST y = x /T (K -1 ) Figure 4.13 Temperature dependence of Flory interaction parameter for HPMACAS-acetone system Figure 4.14 gives an overview of the non-dimensionalized elution profiles at different temperatures under certain circumstances: 5 micron_before finite acetone, 3 micron_before any finite, and 3 micron_after finite acetone. The spread of the peaks narrow down with increasing temperature, indicating a faster diffusion behavior at higher temperature. The 5µm column before finite acetone shows a similar elution profile with the 3µm column after finite acetone: a sharp front with a long tail. In contrast, the elution profiles for 3µm column before any finite concentration are more symmetric, particularly the one at 60 C. This may have something to do with the residual solvent THF in HPMCAS due to an inappropriate condition procedure in terms of the temperature and time for the newly made 3µm column. However, no definitive explanation can be provided.

105 CL/C 0 U CL/C 0 U CL/C 0 U 91 (a) C 35 C 50 C 60 C 70 C C (b) C t/t c 35 C 40 C 45 C 50 C 60 C 0. (c) C C 60 C t/t c 35 C 40 C 50 C 60 C t/t c Figure 4.14 Overall elution profiles for certain circumstances: (a) 5µm column before finite. (b) 3µm column before finite. (c) 3µm column after finite acetone

106 9 Overall, the partition coefficients for infinitely dilute acetone in HPMCAS are consistent regardless of the data from the 5µm column, and an Arrhenius behavior is observed: log of K varies linearly with the inverse of temperature. UNIFAC-vdw-FV models with two types of subgroup-structures in Figure.3 were applied here by setting a very small weight fraction of acetone in the polymer phase (10-8 ) to match up with the definition of infinite dilution (Figure 4.9). The prediction shows good agreement with the averaged partition coefficients (5µm after finite acetone data and 3µm before finite data are not included). Averaged diffusion coefficients were determined and the Arrhenius relationship was also observed (Figure 4.10), indicating the diffusion rates at infinite dilution systems were mainly limited by the diffusion activation energy. With the excess free volume trapped in glassy polymer, the diffusion coefficient in Figure 4.11 does not abruptly decrease. The λ parameter in free-volume model below the glass transition temperature was introduced and a value of 0.48 was obtained. The fitted ξ parameter here refers to the ratio of jumping unit between acetone and HPMCAS at absolute 0 degree. It is independent of temperature and concentration, so this fitted value, 0.78, was applied to the diffusion model in finite acetone concentration and ternary HPMCASacetone-water systems, which will be discussed in Chapters 5 and 6.

107 CL/C 0 U HPMCAS-Water System Partition and diffusion coefficients of infinitely dilute water in HPMCAS were measured with the new 3µm column from 35 to 70 C. A typical regression between the elution profile of water and CCIGC model is shown in Figure Experimental data CCIGC regression D p =6.85E-08 cm /s K= t/t c Figure 4.15 Comparison of the elution profile and the CCIGC model regression for water in HPMCAS at 60 C The water data for partition and diffusion coefficients are listed in Table A.10 to A.13, and the corresponding plots are shown in Figure 4.16 and The finite concentration effect was also investigated for infinitely dilute water in HPMCAS. Figure 4.16 shows good agreements among the data on the partition coefficient of the water measured before and after the finite concentration experiments, indicating no effects were observed due to the exposure of the column to finite concentrations of the solvents. A

108 Partition Coefficients of Water typical Arrhenius behavior of the data matches up perfectly with the predictive UNIFAC model, which is applied by setting the weight fraction of water in HPMCAS to be micron_before any finite 3 micron_after finite water 3 micron_after finite acetone Averaged Partition Coefficient UNIFAC_HPMCAS(b) /T (1/K) Figure 4.16 Partition coefficients of infinitely dilute water in HPMCAS With the partition coefficient data, the weight fraction activity coefficients (WFAC) at the limit of infinite dilution were calculated using Eq. (.54), as shown in Table A.14. Further calculations were made using Eq. (.65) to obtain the infinite dilution interaction parameters χ at different temperatures, as shown in Table A.15. The obtained values are all above 0.5, indicating water is a poor solvent for HPMCAS. Figure 4.17 shows the temperature dependence of χ at different temperatures. The same behavior of negative slope with positive intercept was observed. The case of LCST again indicates a phase separation is likely to occur at higher temperature.

109 Flory interaction parameter χ χ A + B T A = B = LCST y = x /T (T -1 ) Figure 4.17 Temperature dependence of Flory interaction parameter for HPMACAS-water system An overview of the elution profiles at different temperatures is shown in Figure The retention time of water increases significantly with decreasing temperature due to very large partition coefficients at lower temperatures (~1400 at 40 C). In contrast, the partitioning for acetone between the stationary and gas phase is much smaller (~170 at 40 C). Generally it can be directly interpreted as a stronger interaction between water and HPMACS than acetone and HPMCAS. However, the χ obtained for acetone and water in Table A.9 and A.15 shows an apparent contradiction: acetone has a much stronger interaction with HPMCAS. The main reason for water having a large partition coefficient but small interaction with HPMCAS is due to the fact that water is a small molecule with

110 CL/C 0 U high boiling temperature. The concentration of water in the gas phase was very small since the column temperature was controlled in the temperature range of 35 to 70 C, well below its boiling temperature, 100 C. Thus the partitioning of water was exaggerated. Meanwhile, the saturation pressure of water was much smaller compared to acetone at the same temperature. On the other hand, the small molecular weight of water made the parameter larger according to Eq. (.54) and further increased the value of χ. It is more typical for organic solvents to have high boiling temperatures with large molecular weights. In such cases, the obtained partition coefficients can be directly relate to the interaction between solvent and polymer. A good example is ethylbenzene in 1,4-cispolybutadiene published by Balashova et al C C C C 35 C t/t c Figure 4.18 Elution profiles for HPMCAS-water system at different temperatures

111 97 Data for diffusion coefficients in Figure 4.19(a) also follows the Arrhenius behavior with the log of D P decreasing with reciprocal temperature. Similar to acetone, the diffusion coefficient of infinitely dilute water appears to be consistently smaller after the column was saturated with a finite concentration of water, but the deviations are within the experimental error region. A correlation with free-volume model was made and three parameters were fitted: D 01, λ, and ξ. The fitted value D 01, 1.48E-03 cm /s, falls right into the region between the suggested value for water from Hong 37 and Zielinski 48, which are 0.86E-03 cm /s and 1.53E-03 cm /s respectively. According to Eq. (.99), λ is a characteristic quantity of the pure polymer and therefore should be independent of the penetrant. However, the difference between 0.68 for water and 0.48 for acetone implies a different amount of excess free volume was trapped. This can be expected when the thermal expansion coefficient of a glassy state polymer, α g, changes due to a different processing history of the system. The λ difference supports the presumption that an unknown structural rearrangement occurs in the glassy state of HPMCAS from the finite concentration effect. The jumping unit ratio ξ for water is 0.51, which is smaller than that of acetone (ξ=0.78) due to a smaller molecule size.

112 D p (cm /s) D p (cm /s) 98 (a) 1.E-06 1.E-07 (b) 1.E-08 3 micron_before any finite 3 micron_after finite water 3 micron_after finite acetone Averaged Diffusion Coefficient 1.E /T (1/K) 1.E-05 T g =11 C λ=0 1.E C 1.E-07 1.E C λ= E-09 1.E-10 1.E-11 1.E-1 D 01 = 1.48E-03 cm /s ξ = micron_before finite water 3 micron_after finite water 3 micron_after finite acetone Averaged Diffusion Coefficient Free-Volume correlation /(K +T-Tg ) (1/K) λ=1 Figure 4.19 (a) Diffusion coefficients of infinitely dilute water in HPMCAS; (b) Correlation of averaged diffusion coefficients with free-volume model

113 99 Chapter 5 Finite Concentration Inverse Gas Chromatography Results The previous chapter dealt with measurements at infinite dilution where the solvent concentration is low enough to prevent any inter-molecule interaction and therefore follows the condition of linear chromatography. Here the equilibrium thermodynamic properties and diffusion behaviors are probed at finite concentrations for both water and acetone, where nonlinear behaviors in the isotherm are observed. Several techniques for finite concentration experiments using gas chromatography have been discussed by Conder and Young 49, including frontal analysis (FA), frontal analysis by characteristic point (FACP), elution by characteristic point (EPC), and elution on plateau (EP). Only EP is applied here because this technique does not rely on detector calibration and the analysis is similar to that of infinitely dilution measurements. Details about the experimental procedures are covered in Section The following sections will discuss the theoretical background and analytical procedures. Thermodynamic properties at various temperatures and solvent concentrations are compared with the Flory-Huggins model and predictive UNIFAC, UNIFAC-FV, and UNIFAC-vdw-FV models. Diffusivity data are predicted using the free-volume theory based on the diffusivity at infinite dilution.

114 V (mv) Finite Concentration Chromatography with Elution on Plateau This method was first proposed by Reilley, Hildebrand, and Ashley 50. A solvent concentration plateau is successfully set up by saturating the capillary column with a continuous stream containing carrier gas and a steady amount of solvent. The dotted lines in Figure5.1 are the plateau concentrations of acetone at column temperature 60 C under different activities. Higher activity refers to a larger partial pressure of acetone, and therefore a higher concentration plateau is present Activity: Activity: Activity: Activity: Time (min.) Figure 5.1 Growth of acetone concentration and formation of plateaus at oven temperature 60 C with various activities After setting up the concentration plateau, a perturbation was made by injecting an infinitesimal amount of solvent to guarantee that essentially a linear portion of the isotherm is covered. As discussed in Section 4.1, a correction factor was applied to the

115 101 data obtained from finite water concentration experiments; while no correction for acetone was needed. Elution profiles from perturbation of the steady solvent concentration plateau were correlated with a modified CCIGC model proposed by Tihminlioglu, et al. 51 to obtain the slope of the isotherm at the plateau concentration S(C b ) and diffusion coefficient in the stationary phase D p. Unlike the infinite dilution CCIGC model, two new phenomena have to be accounted for in the continuity equation for the finite concentration model. First, the sorption effect discussed in Section results in an increased flow rate in the gas phase. Second, the distribution of the solvent between the stationary phase and the gas phase varies with concentration, the isotherm effect. As shown in Figure 5., the partition coefficient K obtained from an infinite dilution experiment in Chapter 4 is essentially the slope of isotherm at the initial value C 0 =0. As the solvent concentration increases to some finite value in the gas phase, changes in the slope of the isotherm at different plateau concentrations S(Cb) have to be taken into account. In most cases the slope of the isotherm increases with concentration, indicating that the penetrant spends more time in the stationary phase with increasing concentration. However, researchers 5 have found that the slope of isotherm actually decreases with concentration for glassy state polymers. That is, the sorption isotherm curves toward the activity axis with increasing concentration in the gas phase. A good example to demonstrate the changes of the slope of isotherm in transition from glassy state to rubbery state polymer is the sorption of water in poly(acrylic acid) (PAA) published by Peterson 53. PAA is a hygroscopic polymer with a glass transition temperature near 106 C. Data were collected by Peterson at room temperature and an obvious inflection point for the slope of

116 isotherms occurred at around T gm, whicg is the glass transition temperature of the polymer-penetrant mixture. 10 Figure 5. Relation between partition coefficient at infinite dilution and slope of isotherm at finite concentration Vrentas and Vrentas 54 have further proposed a nonlinear model for analyzing sorption behavior in glassy polymers by taking into account the effects of structural arrangements in the glassy polymer matrix after being plasticized by the penetrant. An additional term Flory-Huggins equation 55 : F e was introduced to determine the solvent activity a 1 in the original F 1 exp( (5.1) a 1 )e F ˆ ˆ dtgm M1 Cpg Cp d 1 T 1 RT Tgm (5.)

117 103 where subscript 1 and refer to solvent and polymer, respectively, M 1 is the molecular weight of the solvent, ω i and ϕ i are the weigiht and volume fraction of component i, Cˆ ˆ is the changes of the specific heat capacity from glassy state to rubbery state pg C p polymer. According to the model, isotherms for different temperatures below T gm are shown as dashed lines in Figure 5.3 along with a solid curve that represents the behavior of the rubbery polymer at nearly any temperature. All the dashed isotherms exhibit a characteristic shape that curve toward the activity axis (proportional to the penetrant concentration in the gas phase) with glassy region and then curve away after reaching T gm. Since T gm is a function of penetrant weight fraction, the larger the weight fraction is, the closer the glassy polymer matrix is to the equilibrium liquid configuration. Meanwhile, the transition weight fraction decreases with increasing temperature. Unfortunately, there were difficulties applying this model to HPMCAS-penetrant system since some key parameters for this nonlinear model were unknown. However, it s still informative to see how the slope of isotherm might change with increasing solvent concentration in the gas phase below T gm in both HPMCAS-acetone and HPMCAS-water systems. In addition, the slope in the linear Henry s law region shown in Figure 5.3 is smaller than the initial slopes of the glassy polymer at infinite dilution, particularly when T 1 is much lower than T g. This interesting behavior implies the partition coefficients obtained by infinite dilution experiments in Chapter 4 should be larger than that of the predicted values. As a matter of fact, the infinite dilution partition coefficients for acetone discussed in Figure 4.9 are all higher than the predicted UNIFAC-vdw-FV model and

118 also the averaged partition coefficients at lower temperatures show larger deviations. As for water, no significant deviations were observed due to its much smaller solubility. 104 Figure 5.3 Sorption isotherms for model polymer-penetrant system proposed by Vrentas and Vrentas 54. Curve 1 and are at temperatures below T gm and curve 3 is the rubbery state polymer at all temperatures Modeling Equations The continuity equation for the solvent in the gas phase can be written as: C C U U C t z z D g C z D R p C r ' rr (5.3) All the symbols in the above equation have the same meaning defined in Eq. (.5). The last term in the left hand side is added to the original CCIGC model derived from Pawlisch 7 due to the sorption effect. Since the total concentration in the gas phase, C Total, is constant, assuming that there s negligible pressure drop, and the system is isothermal, the overall continuity equation for the gas phase can be written as:

119 105 C Total U z D R p r rr (5.4) The mole fraction of the solvent in the gas phase is given by: C y (5.5) C Total Conder and Purnell 56 have further refined the mole fraction of the solvent in the gas phase by including the compressibility and imperfection of the gases. Two additional parameters a and j are introduced: ajy o (5.6) where In Eqs. (5.5) to (5.8), P i is the pressure at the column inlet, P A is the atmospheric pressure, B 11 is the second virial coefficient of the solvent vapor at the column temperature, and t r and t m are the retention times for the solvent and the marker gas, respectively. Both a and j usually have values very close to unity in capillary columns and therefore have negligible effect. The subscript o on y o refers to the mole fraction at the column outlet. 1 k(1 J a 1 k(1 J 1 3 y ) yop 1 yo ) B (1 J 1 o A 11 o ) k t t r RT y (5.7) r m (5.8) t y o PA B11( J 3 1) j J 3 1 RT (5.9) m n n P 1 i PA J m n m Pi PA 1 (5.10)

120 Combining Eqs. (5.1) to (5.4), the solvent continuity equation can be expressed 106 as: C C U t z D g z ' D (1 C R r C p ) rr (5.11) On the other hand, the solvent concentration in the stationary phase remains the same as the infinite dilution CCIGC model: C t ' D p C r ' (5.1) The appropriate initial boundary conditions for both gas phase and stationary phase are: C Cb at t 0, z 0 (5.13) C Cb ( t) C0 at z 0 (5.14) C Cb at z (5.15) C ' Cb 0 ( dc ' dc) Cb dc at t 0, R r R (5.16) C 0 ' b ' ' dc C ( dc dc) dc Cb ( ) at r R (5.17) dc C C C b b C t ' 0 at r R (5.18) Here C b refers to the plateau concentration, which is the steady state concentration of solvent in the carrier gas determined by the temperature of the saturator. The slope of isotherm at the plateau concentration ' (dc dc) C b can be noted as S(C b ). The rest of the

121 variables are defined in Chapter. Continuity Eqs. (5.9) and (5.10) and all the initial conditions as well as the boundary conditions from Eqs. (5.11) to (5.16) can be further non-dimensionalized using Eqs. (.11) to (.15). The only difference occurs in the dimensionless concentration in both gas and stationary phases due to the plateau concentration. New dimensionless variables C and ' C are: 107 ( C Cb ) L C (5.19) C U 0 C ' C ' b C S( C) dc L 0 (5.0) C S( C ) U 0 b These non-dimensionalized equations can be further transformed to the Laplace domain to obtain the theoretical elution profile for a finite concentration experiment. The same procedures are covered in Chapter and exactly the same expression as for the infinite dilution experiment is obtained: Y 1 1 s s exp s 4 tanh (5.1) The only difference is the definition of the thermodynamic dimensionless parameters due to sorption and isotherm effects. The other two parameters remained the same: R (5.) 1 ) S( C ) ( b U (5.3) LD p D g (5.4) UL

122 Analytical Procedures The plateau concentration at a certain activity can be calculated using the second virial coefficient to correct the non-ideality: yopcolumn C (5.5) RT P y B P column column P A y o o 11 P (5.6) 0 P1 (5.7) P column where R is the gas constant; T is the column temperature; B 11 is the temperature dependent second virial coefficient of solvent obtained from the DIPPR Compilation Access Program (DCAP); P column is the column pressure. A very small pressure drop P (0.1 psi) through the column was added to the atmospheric pressure P A, as shown in Eq. (5.6); yo is the mole fraction of solvent in the gas phase, which can be calculated from the ratio of saturated vapor pressure of the solvent at the saturator temperature column pressure P column, as shown in Eq. (5.7). 0 P 1 to the Since the correlated parameter from the CCIGC model no longer refers to K, but rather the product of ( 1 ) and S C ), the factor ( 1 ) from the sorption effect ( b should be first calculated using Eqs. (5.4) to (5.8) and consequently the slope of isotherm at the plateau concentration S C ) can be obtained by dividing the product by ( 1 ). ( b Finally the amount of solvent in the polymer at any given plateau concentration was calculated by integrating the slope of isotherm with respect to the plateau

123 concentration. The integral was evaluated with Mathematica by fitting to a second order polynomial function prior to the integration. 109 C ' 0 C b S( C ) dc (5.8) b The partitioning of the solvent between the stationary phase and the gas phase can therefore be calculated: K C C Cb ' S( Cb ) 0 C b dc (5.9) The weight fraction of solvent in the polymer can also be calculated as: C M ' 1 1 ' (5.30) 1 C M1 where M 1 denotes the solvent molecular weight and refers to the polymer density. 5. HPMCAS-Acetone System A series of experiments for acetone at different plateau concentrations was done to determine the sorption isotherm at column temperatures 35, 50, and 60 C. Some inherent problems took place at finite concentration of acetone because the diffusivity of acetone is so small in HPMCAS that the baseline fluctuation effect became significant particularly in the tailing region, which led to difficulties determining the most reliable elution profile. In contrast, the infinite dilution experiments were carried out on a

124 110 virtually flat baseline, and therefore the signal to noise ratio was insignificant even at the very end of the tailing region. Multiple measurements were made at a certain activity to obtain the most representative tailing region so that the whole peak can be adequately regressed with CCIGC model to get the most reliable data for the slope of isotherm and diffusion coefficient. Figure 5.4 shows the correlation between two elution profiles and the CCIGC model at a column temperature of 35 C with activity Both elution profiles were obtained at the same condition and the non-dimensionalized data were fitted properly. However, the actual tailing region in Figure 5.4(a) was shortened due to the downwarddrifting baseline illustrated as the dashed line in the zoomed-in real time elution profile. In this case, the regressed slope of the isotherm became smaller than the actual value while the regressed diffusion coefficient became larger. Figure 5.4(b) shows the accepted elution profile where the baseline was more stable throughout the measurement. In addition, the regressed slope of the isotherm was, as expected, larger than that from Figure 5.4(a) and the diffusion coefficient was smaller. The second approach to improve the experimental data was applied by averaging data points within a reasonable range to reduce the baseline oscillations before correlating the data with CCIGC model. This method became particularly important when the plateau concentration was high and the signal to noise ratio became small, which most often occurred when the saturator temperature was high. For example, the following command was applied in Excel to average every 0 points in the raw data obtained from column temperature 50 C with acetone activity 0.30 :

125 (C-C b )L/C 0 U (C-C b )L/C 0 U 111 =AVERAGE(INDEX(A:A,1+0*(ROW()-ROW($C$1))):INDEX(A:A,0*(ROW()- ROW($C$1)+1))). Figure 5.5 shows that the averaged data (b) have a much better correlation with the CCIGC model compared to the before-averaged one (a). (a) Experimental data CCIGC regression S(C b ) = 116 D P = 1.54E-10 cm /s t/t c (b) t/t c Experimental data CCIGC regression S(C b ) = 148 D P = 1.0E-10 cm /s Figure 5.4 Non-dimensionalized elution profiles correlated with CCIGC model at column temperature 35 C with activity 0.19: (a) drifting baseline with larger D p and smaller S(C b ); (b) more stable baseline with smaller D p and larger S(C b )

126 (C-C b )L/C 0 U (C-C b )L/C 0 U (a) Experimental data CCIGC regression S(C b ) = 59.9 D P =.5E-09 cm /s R = t/t c (b) Experimental data CCIGC regression S(C b ) = 74.6 D P = 1.44E-09 cm /s R = Figure 5.5 Non-dimensionalized peaks correlated with CCIGC model at column temperature 50 C with activity 0.30: (a) before averaging the data led to larger D p and smaller S(C b ); (b) after averaging the data led to smaller Dp and larger S(Cb) t/t c

127 dc'/dc Analysis of Thermodynamic Properties The data obtained for the slope of the isotherm S C ) and the factor ( 1 ) at different plateau concentration are listed in Table A.16. To obtain the acetone concentration in the stationary phase C ", Eq. (5.8) was used and the slopes of isotherm S( C b ) versus acetone concentrations in the gas phase C were fitted to a polynomial function to get the integral, as shown in Figure 5.5. From the plot, the slope of isotherm decreased with increasing concentration, and the changes were slightly larger at the lower temperature 35 C (circle) compared to higher temperature 60 C (triangle). These observations are in agreement with the sorption model in glassy polymers proposed by Vrentas and Vrentas, as shown previously in Figure 5.3. ( b IGC_35 C IGC_50 C IGC_60 C 10 0.E+00 1.E-04.E-04 3.E-04 4.E-04 5.E-04 6.E-04 C (g/cm 3 ) Figure 5.6 Slope of isotherm decreases with increasing solvent concentration in the gas phase for HPMCAS-acetone system under various column temperatures

128 Polymer phase concentration, C' (g/cm 3 ) 114 The HPMCAS-acetone isotherms calculated at 35, 50, and 60 C are shown in Figure 5.7 and all the thermodynamic properties and diffusivity data are listed in Table A.17. Comparisons with the UNIFAC-FV (dashed line) and UNIFAC-vdw-FV (straight line) models were made with two possible structures of HPMCAS. According to the experimental results in Figure 5.6 that slopes of the isotherm decrease with increasing concentration and therefore the isotherms curve toward the axis with acetone concentration in the gas phase (dotted line). The prediction models however, do not take into account the structural changes in the glassy region due to the plasticization effect, and all the predicted isotherms curve toward the axis with concentration in the polymer phase. 0.1 IGC_35 C 0.08 IGC_50 C IGC_60 C UNIFAC-vdw-FV_HPMCAS-a UNIFAC-FV_HPMCAS-a UNIFAC-vdw-FV_HPMCAS-b UNIFAC-FV_HPMCAS-b Gas phase concentration, C (g/cm 3 ) Figure 5.7 Absorption isotherms for the HPMCAS-acetone system

129 Partition coefficient of acetone 115 Figure 5.8 shows the acetone partition coefficient as a function of activity. Partition coefficient can be easily obtained using Eq. (5.9): the activity depends on the saturator temperature that dictates the partial pressure of acetone in the gas phase and the column temperature that establishes the saturation vapor pressure. From the experimental data shown in Figure 5.6, the acetone concentration increment in the stationary phase is much slower than that in the gas phase. Therefore, the partitioning of acetone between two phases became smaller with increasing activity. The discrepancy between experimental data and the prediction model here is again attributed to the relaxation effect below T gm C 50 C 60 C 100 UNIFAC-vdw-FV_HPMCAS-a UNIFAC-FV_HPMCAS-a UNIFAC-vdw-FV_HPMCAS-b UNIFAC-FV_HPMCAS-b Activity of acetone Figure 5.8 Partition coefficient of acetone in HPMCAS as a function of activity

130 A more general way to demonstrate the thermodynamic properties is by plotting solvent weight fraction or volume fraction as a function of activity. The solvent weight 116 fraction 1 is related to the solvent concentration in the stationary phase shown in Eq. (5.30), while the volume fraction 1 can be calculated from the weight fraction: (5.31) 1 1 where 1 and refer to the solvent and polymer density respectively. Figure 5.9 plots the acetone volume fraction as a function of activity. Correlations with the Flory-Huggins model (solid line) shown in Eq. (.6) were made to obtain the regressed interaction parameters,. Theoretically Eqs. (5.1) and (5.) should be used to fit the sorption isotherm in the glassy polymer-penetrant system; however, several unknown parameters prevented the application of this approach. On the other hand, predictions (dashed line) were made by applying the known parameters at different temperatures derived from infinite dilution partition coefficient (Table 4.9). Obvious discrepancies from the predicted values are observed. Additionally, as expected, there were difficulties correlating the experimental data with the standard Flory-Huggins model because the former curves toward the activity axis (dotted line) while the latter curves away.

131 Activity of acetone IGC_35 C IGC_50 C IGC_60 C χ increase Flory-Huggins_correlation Flory-Huggins_prediction Volume fraction of acetone in HPMCAS-LF Figure 5.9 Volume fraction of acetone at equilibrium with HPMCAS. Solid and dashed lines are correlation and prediction from Flory-Huggins equation The IGC results were compared with data obtained from a colleague, Derek Sturm, who used the differential pressure decay (DPD) technique 57 to measure both absorption and desorption process of acetone in HPMCAS at 35 and 50 C. A plot of the acetone weight fraction as a function of activity from both IGC and DPD are shown in Figure Small deviations between these two methods were observed at 50 C. A possible reason for getting slightly lower solubility from IGC may have something to do with the drifting bassline, as shown in Figure 5.4 and 5.5. This effect is likely to lead to a smaller slope of isotherm than the actual value. Overall, however, the data from IGC and DPD were in good agreement.

132 Acetone activity This work_igc_35 C This work_igc_60 C Sturm_DPD_desorption_35 C Sturm_DPD_desorption_50 C This work_igc_50 C Sturm_DPD_absorption_35 C Sturm_DPD_absorption_50 C Acetone weight fraction Figure 5.10 Weight fraction of acetone at equilibrium with HPMCAS. The data from Sturm at 35 and 50 C are plotted for comparison Further comparisons of the experimental data from both IGC and DPD at 35 and 50 C were made with UNIFAC-FV, UNIFAC-vdw-FV, and Flory-Huggins model, as shown in Figure Two possible HPMCAS structures were considered for UNIFAC- FV and UNIFAC-vdw-FV. The Flory-Huggins model was applied here by simply using Eq. (5.31) to convert the volume fraction of acetone shown as the dashed lines in Figure 5.9 into weight fraction. Overall, the predictive model obtained from UNIFAC-FV based on HPMCAS-a gave the best prediction of the experimental data.

133 Acetone activity Acetone activity 119 (a) This work_igc_35 C Sturm_DPD_absorption_35 C Sturm_DPD_desorption_35 C UNIFAC-vdw-FV_HPMCAS(a)_35 C UNIFAC-FV_HPMCAS(a)_35 C UNIFAC-vdw-FV_HPMCAS(b)_35 C UNIFAC-FV_HPMCAS(b)_35 C Flory-Huggins_35 C 0. (b) Acetone weight fraction This work_igc_50 C Sturm_DPD_absorption_50 C Sturm_DPD_desorption_50 C UNIFAC-vdw-FV_HPMCAS(a)_50 C UNIFAC-FV_HPMCAS(a)_50 C UNIFAC-vdw-FV_HPMCAS(b)_50 C UNIFAC-FV_HPMCAS(b)_50 C Flory-Huggins_50 C Acetone weight fraction Figure 5.11 Comparison between weight fraction of acetone in HPMCAS with UNIFAC-FV, UNIFAC-vdw-FV, and Flory-Huggins model at (a) 35 C and (b) 50 C

134 Free-Volume Analysis of Diffusivity Data As discussed in Section.3.3., the diffusivity data obtained below the glass transition temperature of the solvent and polymer mixture T gm can be described with a modified free-volume model from Wang, et al. 35 by taking into account the plasticization effect. The plasticization factor β was introduced to account for the changes of hole free volume in a glassy state polymer. According to Eq. (.105), an expression for how T gm varied with plasticization is required. Therefore, measurements were conducted using differential scanning calorimeter (DSC) to obtain the depression of the glass transition temperature as a function of acetone weight fraction. Results are shown in Table 5.1 and Figure 5.1. There were difficulties in obtaining high weight fraction data due to the sealing issue with the hermetic pans. Data were obtained only for the pure HPMCAS (sample 0) and near 1 wt. % acetone (sample 1 and ). All the weights were in units of milligram. The T g for pure HPMCAS measured here matched the literature value. Table 5.1 DSC results for HPMCAS-acetone system Sample 0 1 pan+lid (mg) HPMCAS (mg) Acetone+HPMCAS+pan+lid (mg) N/A Acetone wt.% N/A T onset ( C) Tg (inflection point) ( C) T endset ( C)

135 Heat Flow (W/g) Sample Sample Temperature ( C) Figure 5.1 DSC results for HPMCAS-acetone system A plot of the glass transition temperature of HPMCAS-acetone mixtures as a function of acetone weight fraction is shown in Figure The data point shown as an asterisk at around 10 wt. % acetone was provided from Merck & Co., Inc.. Although Chow 58 has proposed a theoretical model showing that T gm would decay exponentially with increasing solvent weight fraction, a more convenient linear approximation (dashed line) was used here due to the limitation of obtaining a wider range of wt. % data from the DSC. The acetone concentration dependence of T gm can therefore be represented as: T gm (5.3)

136 Glass transition temperature, T gm ( C) This Work_DSC Data from Merck Linear approximation Weight fraction of acetone in HPMCAS Figure 5.13 Glass transition temperature depression of HPMCAS by acetone with different weight fraction According to Eq. (5.3), the isothermal glass transition composition ω gm can be calculated for a given temperature. Above concentration ω gm, the pure polymer glass transition temperature is depressed below T gm and therefore the glassy polymer changes into the rubbery state due to the plasticization effect. Table 5. presents the ω gm in HPMCAS-acetone at 35, 50, and 60 C. Table 5. Isothermal glass transition composition in HPMCAS-acetone system T column ( C) gm The plasticization factor can therefore be expressed by using Eq. (.105): (5.33) T 11.17

137 13 Most of the free volume parameters for the HPMCAS-acetone system are covered in Section.3.5. The ξ parameter was obtained in Section 4. by correlating infinite dilution acetone data with free-volume model. It remained the same since it only depends on the solvent molar volume at 0 K. χ was derived from the infinite dilution partition coefficient, as shown in Table A.15. Based on the diffusivity measured at infinite dilution, diffusivity data at finite concentration were predicted with the free-volume model, as shown in Figure Below ω gm, Eq. (.108) was applied and the plasticization factor β was introduced. While above ω gm, Eq. (.97) was applied and no plasticization factor was considered. Diffusivity data obtained from IGC at 35 C fit reasonably well with the prediction; while deviation occurs at both 50 and 60 C. Two possible causes are discussed below. First, precision of the experimental data obtained from IGC at higher column temperature may be limited by the drifting baseline effect, as shown in Figure 5.5. Although improvements were made by averaging the data, the signal to noise ratio at the very end of the tailing part was still too small to give good accuracy. Therefore, slightly larger diffusivity data were expected to be obtained. Second, the modified free-volume model assumes the thermal expansion coefficient of the specific volume below T gm is equal to that of the sum of the volume composed of the core and the interstitial volume, as shown in Eq. (.10), by stating that a quasi-equilibrium state was reached in the glassy region since solvent molecules cannot be accommodated in the nonequilibrium domains for its large volume. However, in the real case, the unrelaxed domain still appears and contributes to acetone mobility in HPMCAS. Thus, the actual diffusion coefficients should have a higher value

138 Diffusion coefficient (cm /s) 14 than the predictions. With these two effects, the overall free-volume predictions were in good agreements with experimental data from IGC. A further comparison of diffusivity data obtained from IGC and DPD were made. It s typical to see some deviations between these two techniques. But here they present remarkably good agreement with each other at 50 C. No experimental data above the isothermal glass transition composition ω gm were obtained due to the high glass transition temperature of HPMCAS. 1.E-06 Free-volume prediction 1.E-07 1.E-08 ω gm = E-09 1.E-10 ω gm =0.074 ω gm =0.089 IGC_35 C IGC_50 C IGC_60 C Sturm_DPD_50 C 1.E Weight fraction of acetone in HPMCAS Figure 5.14 Comparison of experimental data with free-volume prediction of solvent mutual-diffusion coefficients above and below the isothermal glass transition for the HPMCAS-acetone system

139 (C-Cb)L/C0U HPMCAS-Water System The system of HPMCAS with water at finite concentration was less complicated compared to that with acetone, since water molecules diffuse two orders of magnitude faster than acetone in HPMCAS. The drifting baseline had little effect on the virtually symmetric elution profile. Also the water concentration in the gas phase is so low compared to acetone due to a higher boiling temperature that there is no need to average the elution data points as shown in Figure 5.5. A typical non-dimensionalized elution profile for finite water concentration IGC is shown in Figure The system was at column temperature 50 C with water activity All the thermodynamic and transport properties are listed in Table A Experimental data CCIGC regression S(C b ) = 88.1 D P =.88E-08 cm /s R = Figure 5.15 Comparison of non-dimensionalized elution profile and the CCIGC model at finite concentration of water (activity 0.01) in HPMCAS at 60 C t/tc

140 dc'/dc Analysis of Thermodynamic Properties Series of experiments for water at different plateau concentrations were done to determine the sorption isotherm at column temperature 40, 50, and 60 C. The influence of injection volume discussed in Section 4.1 was applied here. Correction factors for different injection volumes, for the sorption effect (1-Ψ), and for the corrected slope of isotherm S(C b ) are tabulated in Table A.18. A plot of the slopes of the isotherm as a function of water concentration in the gas phase is shown in Figure Compared to Figure 5.5, there were negligible changes in the slopes of the isotherm since the water concentration in the gas phase is so small (around one order of magnitude smaller than acetone) that the finite concentration region being studied was close to the infinite dilution region IGC_40 C IGC_50 C IGC_60 C E E E E-05.0E-05.5E-05 C (g/cm 3 ) Figure 5.16 Plot of the isotherm slopes as a function of water concentration in the gas phase for HPMCAS-water system at different temperatures

141 C' (g/cm 3 ) 17 Equation (5.8) was further applied to calculate the concentration of water in the stationary phase. Comparisons with UNIFAC, UNIFAC-vdw-FV models are shown in Figure As expected, no significant concave curves were observed. As discussed in Table.1, the main group interaction parameters applied for the HPMCAS-water system were slightly different than typical values due the interaction between water molecules and the OH, and CH O groups on the cellulosic backbone of HPMCAS..5E-0.0E-0 UNIFAC-vdw-FV_HPMCAS-a UNIFAC-vdw-FV_HPMCAS-b UNIFAC_HPMCAS-a UNIFAC_HPMCAS-b 1.5E-0 1.0E-0 5.0E-03 IGC_40 C IGC_50 C IGC_60 C 0.0E E E E E-05.0E-05.5E-05 C (g/cm 3 ) Figure 5.17 Absorption isotherms for the HPMCAS-water system The partitioning of water between stationary and gas phase as a function of water activity was also calculated and is shown in Figure Similarly, little changes were observed due to the virtually unchanged slopes of isotherm.

142 Partition Coefficient of Water UNIFAC-vdw-FV_HPMCAS-a UNIFAC-vdw-FV_HPMCAS-b UNIFAC _HPMCAS-a UNIFAC_HPMCAS-b IGC_40 C IGC_50 C IGC_60 C Activity of Water Figure 5.18 Partition coefficient of water in HPMCAS as a function of activity The volume fraction of water in HPMCAS as a function of activity is shown in Figure Correlations with the Flory-Huggins model were made to obtain the dependence of the interaction parameter on temperature for the HPMCAS-water system. Isotherm predictions were made by using the interaction parameter derived from the partition coefficient of water at infinite dilution. Good agreements between experimental data and predictions were observed. The weight fraction of water in HPMCAS is also plotted in Figure 5.0. Detailed comparisons between experimental data and the prediction models are shown in Figure 5.1. The dotted lines (UNIFAC-vdw-FV*) were derived using the original group interaction parameters without correction, resulting in a poor prediction. Overall, the UNIFAC-vdw-FV model with subgroup structure

143 Activity of water Activity of water HPMCAS-a provides the best prediction for the absorption isotherms in the HPMCASwater system IGC_40 C IGC_50 C IGC_60 C χ=1.67 χ=1.74 χ=1.76 χ=1.80 χ=1.83 χ=1.86 χ increase Volume fraction of water in HPMCAS Figure 5.19 Volume fraction of acetone at equilibrium with HPMCAS. Solid and dashed lines are correlation and prediction from Flory-Huggins equation IGC_40 C IGC_50 C IGC_60 C Weight fraction of water in HPMCAS Figure 5.0 Weight fraction of water at equilibrium with HPMCAS

144 Activity of water Activity of water 130 (a) IGC_50 C UNIFAC-vdw-FV*_50 C UNIFAC-vdw-FV_HPMCAS(a)_50 C UNIFAC_HPMCAS(a)_50 C UNIFAC-vdw-FV_HPMCAS(a)_50 C UNIFAC_HPMCAS(b)_50 C Flory-Huggins_50 C Weight fraction of water in HPMCAS (b) IGC_60 C UNIFAC-vdw-FV*_60 C UNIFAC-vdw-FV_HPMCAS(a)_60 C UNIFAC_HPMCAS(a)_60 C UNIFAC-vdw-FV_HPMCAS(a)_60 C UNIFAC_HPMCAS(b)_60 C Flory-Huggins_60 C Weight fraction of water in HPMCAS Figure 5.1 Comparison between weight fraction of water in HPMCAS with UNIFAC, UNIFAC-vdw-FV, and Flory-Huggins model at (a) 50 C and (b) 60 C

145 Glass transition temperature, Tgm ( C) Free-Volume Analysis of Diffusivity data Xiang et al. 59 have found that the glass transition temperature of HPMCAS would drop around 81K with increasing water content from 0.7 to 13. wt. % due to the plasticization effect. A plot of their data is shown in Figure 5.. T gm and the plasticization factor β can therefore be expressed as a linear approximation (dashed line) with water weight fraction ω 1 : T (5.34) gm (5.35) T Xiang et al. Linear approximation Weight fraction of water in HPMCAS Figure 5. Glass transition temperature depressions of HPMCAS by water with different weight fraction The glass transition compositions ω gm for water at column temperature 40, 50, and 60 C were calculated according to Eq. (5.34) and listed in Table 5.3. Diffusivity data

146 13 obtained from IGC were compared to the predictive free-volume model based on the diffusivity data at infinite dilution, as shown in Figure 5.3. Good agreements between experimental results and prediction values show an untypical behavior that diffusion coefficients slightly decrease with increasing water concentrations, particularly at 40 C. This may be explained by the strong intermolecular interactions due to hydrogen bonds among water molecules. Researchers 60 have found the hydrogen bonding may retard diffusion. Compared to infinite dilution, water molecules were no longer isolated with each other at finite concentration, and thus the effect of hydrogen bonding can be expected. From the free-volume perspective, the free-volume of water is less than that of the most polymers, as discussed in section..3, and thus there is a negative free-volume effect in HPMCAS-water system. Based on the theory of the mutual diffusion coefficients in glassy polymers discussed in section.3.3., the addition of water not only lowers the glass transition temperature of the mixture, but also decreases the total hole free volume in the system. As a result, these combined effects lead to the untypical behavior of decreasing mutual diffusion coefficient with increasing water concentration. Table 5.3 Isothermal glass transition composition in HPMCAS-water system T column ( C) gm

147 Diffusion coefficient (cm /s) E-06 Free-volume prediction 1.E-07 1.E C 50 C 40 C IGC_40 C IGC_50 C IGC_60 C 1.E Weight fraction of water in HPMCAS-LF Figure 5.3 Comparison of experimental data with free-volume prediction of solvent mutual-diffusion coefficients above and below the isothermal glass transition for the HPMCAS-water system

148 134 Chapter 6 Ternary HPMCAS-Acetone-Water Inverse Gas Chromatography Results So far previous chapters have been concerned with systems in which only one component is present in both gas and stationary phase. The ultimate goal of this project was to extend inverse gas chromatography to measure partition and diffusion coefficients in ternary HPMCAS-acetone-water system. It is critical to understand the second solvent effect during the devolitalization process for both acetone and water. Vrentas et al. 36 have shown that the addition of the second solvent can increase the free volume of the system and can thus facilitate removal of the volatile solvents. Experimental procedures for carrying out ternary system are discussed in Section The ternary system here was treated as a pseudo binary system, since one solvent was present at finite concentration in the polymer while the other was present at infinite dilution. The analytical procedures for a ternary system were exactly the same as infinite dilution IGC by assuming that the pulse injection of the solvent did not change the equilibrium of the second solvent in the column. Additionally, since the concentration of the pulse solvent was at infinite dilution, the thermodynamic effect is negligible and the partition coefficients are expected to follow Henry s law; while diffusion coefficient data can be viewed simply as the selfdiffusion coefficient. Prediction methods such as UNIFAC and free-volume model were applied to compare with experimental results.

149 CL/C 0 U Infinitely dilute acetone in HPMCAS-water System An infinitesimal amount of acetone was injected to a specific weight fraction of water at equilibrium with HPMCAS (obtained from finite concentration of water in HPMCAS). Similar to the finite concentration of acetone discussed in Section 5., the baseline drifting effect also took place due to the long-tailing shape characteristic of low diffusion coefficient of acetone in HPMCAS. Improvements were made accordingly by averaging the raw data before correlating them with the CCIGC model. Figure 6.1 shows the non-dimensionalized elution profile of acetone in HPMCAS-water system at 50 C with weight fraction of water and the CCIGC model regression results. The diffusion coefficient is 9.74E-10 cm /s and the partition coefficient is Experimental data CCIGC regression K = 85 D P = 9.74E-10 cm /s ω water = t/t c Figure 6.1 Elution profile and the model regression fit for acetone diffusion in HPMCAS-water system at 50 C with weight fraction of water

150 136 A summary of the partition and diffusion coefficients of acetone in HPMCASwater system at 40, 50, and 60 C is listed in Table A.0. Figure 6. shows the comparison of the partition coefficients of acetone in HPMCAS in binary (HPMCASacetone) and ternary (HPMCAS-water) systems at various temperatures. No comparison was made at 40 C since there was no data obtained for binary HPMCAS-acetone system at that temperature. The abscissa is the concentration of acetone and water in the cases of binary and ternary systems, respectively. The open markers represent the partition coefficient of acetone in binary HPMCAS-acetone systems; while the closed markers refer to the partition coefficient of acetone in ternary HPMCAS-water systems. UNIFACvdw-FV models in both binary and ternary systems were shown as dashed and solid lines, respectively. The experimental partition coefficients obtained in both cases slightly decreased with the addition of solvent in HPMCAS. The significant drop in the partition coefficients at 40 C is attributed to the drifting baseline effect. Longer tailing regions were expected at lower temperatures due to the slower diffusion rates; however, the drifting of baseline made it difficult to separate the peak from the noise. Thus, underestimated partition coefficients were obtained. Overall, no significant changes were observed between the binary and the ternary system, indicating the solubility of acetone in HPMCAS is approximately the same in the presence of acetone and water. A negligible second solvent effect within the relatively small solvent weight fraction region (0 to 0.0) was predicted by the UNIFAC-vdw-FV models for both binary and ternary systems.

151 Partition coefficient of acetone UNIFAC-vdw-FV_Ternary UNIFAC-vdw-FV_Binary 100 IGC_Ternary_40 C IGC_Ternary_50 C IGC_Ternary_60 C IGC_Binary_50 C IGC_Binary_60 C Weight fraction of solvent in HPMCAS Figure 6. Comparison for partition coefficient of acetone in binary (HPMCASacetone) and ternary (HPMCAS-water) system Figure 6.3 shows the measured experimental diffusion coefficients of acetone in the HPMCAS-acetone-water ternary system at different weight fraction of water in HPMCAS. Comparisons were made with the extended free-volume model for ternary system as described in Section.3.4. The parameters required for the free-volume model were obtained from the pure component polymer-solvent data as well as the binary polymer-solvent diffusion data. Here, the plasticization factor was introduced by using Eq. (5.35). The ξ 13 parameter between acetone (with subscript 1) and HPMCAS (with subscript 3) were obtained by fitting diffusivity data at infinite dilution with the freevolume model. The only additional parameter required for prediction is ξ 1, which is the ratio of molar volume required for jumping units of acetone and water (with subscript ). It can be easily calculated using Eq. (.11): (6.1)

152 Diffusion coefficient of acetone (cm /s) 138 Huge deviations between the experimental data and free-volume predictions were observed, particularly at the lowest temperature. The experimental diffusivities increased dramatically from infinite dilution with a very small weight fraction of water in HPMCAS; while gradual increments were observed afterwards. These were mainly caused by the drifting baseline effect, as discussed in Section 5... The actual tailing region was not able to be obtained due to the small signal to noise ratio at the very end of the peak. Situations got worse at lower temperatures since much longer tails were expected. On the other hand, the free-volume predictions were slightly underestimated since the free volume within the unrelaxed polymer domain were excluded. 1.E-08 IGC_40 C IGC_50 C IGC_60 C Free-volume prediction 1.E C 50 C 40 C 1.E Weight fraction of water in HPMCAS Figure 6.3 Comparison of experimental diffusion coefficients of acetone in HPMCAS-acetone-water system and the ternary free-volume prediction

153 CL/C 0 U Infinitely dilute water in HPMCAS-acetone System With the presence of the saturating acetone in the system, slightly larger amount of water (1~μL) were injected into the HPMCAS-acetone system to obtain elution profiles with better resolution. The weight fraction of acetone at equilibrium with HPMCAS was determined as shown in Section Correction factors were applied to exclude any non-linearity effect, as shown in Table A.1. For the much faster diffusion rate of water in HPMCAS, the drifting baseline effect was less significant. Figure 6.4 shows the non-dimensionalized elution profile for water in HPMCAS equilibrated with weight fraction of acetone at 35 C. Overall the peak obtained was very symmetric and the regression with CCIGC model was satisfactory in spite of some small deviations at the frontal region K = D P = 1.99E-8 cm /s ω acetone = Experimental data CCIGC regression t/t c Figure 6.4 Elution profile and the model regression fit for water diffusion in HPMCAS-acetone system at 35 C with weight fraction of acetone

154 Partition coefficient of Water 140 Summarized data for infinitely dilute water in HPMCAS-acetone are listed in Table A.. Comparisons were made for the partitioning of water in both binary (HPMCAS-water) and ternary (HPMCAS-acetone) systems at different temperatures, as shown in Figure 6.5. No experimental data were obtained for finite concentration of water at 35 C, and thus the comparisons were made only at 50 and 60 C. Here, a more significant second solvent effect is present due to a stronger interaction between acetone and HPMCAS. With the presence of acetone, the partitioning of water decreased slightly; while no significant changes were observed for water in binary system within a relatively smaller range of weight fraction. These observations matched up with the UNIFAC prediction models UNIFAC _Ternary UNIFAC _Binary 1000 IGC_Ternary_35 C IGC_Ternary_50 C IGC_Ternary_60 C 100 IGC_Binary_50 C IGC_Binary_60 C Weight fraction of Solvent in HPMCAS-LF Figure 6.5 Comparison for partition coefficient of water in binary (HPMCASwater) and ternary (HPMCAS-acetone) system

155 Diffusion coefficient of water ( cm /s) 141 Figure 6.6 shows the diffusion coefficient of water in HPMCAS-acetone mixture. The trend of measured diffusion coefficients increased with addition of acetone, which matched perfectly with the prediction from the free-volume model. Here, the plasticization factor was introduced by using Eq. (5.33) and the ratio of the molar volumes of the jumping units between water and acetone ξ 1 is exactly the reciprocal of ξ 1. In the binary water system with no presence of acetone (Figure 5.), the measured diffusion coefficients were barely increased and even slightly decreased with addition of water. Figure 6.6 shows that the second solvent, acetone, introduced extra hole free volume in the glassy polymer domain and therefore facilitated the devolitalization process of water. 1.E-06 1.E-07 1.E C 50 C 60 C Free-volume prediction 1.E Weight fraction of acetone in HPMCAS Figure 6.6 Comparison of experimental diffusion coefficients of water in HPMCAS-acetone-water system and the ternary free-volume prediction

156 14 Chapter 7 Recommendations for Future Work Several suggestions are made in this chapter for future investigations of this project. The possible influence of a non-uniform polymer film and the surface adsorption in the capillary column inverse gas chromatography (CCIGC) model presented in Section.1.1 should be investigated. Although these two effects have relatively small contributions to the shape of the elution profile, it would be interesting to see how sensitive the regressed thermodynamic and diffusion properties are to these effects. To characterize the non-uniformity of the coated polymer film in capillary columns, Pawlisch et al. 8 have extended the CCIGC model by introducing two new parameters based on the ratio of the thinnest to thickest film dimensions observed at a particular cross section. In the SEM studies of this project, a film thickness ranging from.5 to 3.5 μm were observed for the 3-μm capillary column and the corresponding ratio is approximately On the other hand, the adsorption effect has been well described by Davis et al. 9 with a constant surface equilibrium constant. These modifications to the CCIGC model can be done by adding new syntax in the current program written in FORTRAN. The free-volume model applied for semi-predicting the solvent diffusion coefficient in the polymer film can be better described with more precisely measured

157 143 pure polymer free-volume parameters and the plasticization factor. The pure polymer free-volume parameters were analyzed with the rheology data provided from Merck & Co., Inc, where the lowest temperature measured was at 140 C while the slowest angular frequency was set at 0.5 rad/s. However, it is better to include data at lower temperatures (~130 C) and low frequencies (~0.01 rad/s) in order to precisely describe the pure polymer free-volume parameters when fitting the viscosity data with the modified Doolittle model shown in Eq. (.116). Several attempts were made by using an ARES rheometer; however, no reliable rheology data were obtained since the molded HPMCAS film degraded severely due to the oxidation effect under high temperature, as shown in Figure 7.1. Typically, the molded polymer film inside the temperature-controlled chamber of the rheometer should remain colorless during the measurement to insure the reliability of the rheology data. This thermal degradation issue may be solved by introducing an antioxidant before the rheology measurements. Detailed procedures are unknown and more studies are needed for the selection of an antioxidant. Also it was difficult to measure the depression of the glass transition temperature of the polymer-solvent mixture at high solvent weight fractions with the differential scanning calorimeter due to the problem of sealing the pan. A better hermetically sealed pan should be used to make sure all the solvent is retained in the pan during the DSC measurements.

158 144 Figure 7.1 Thermal degradation of HPMCAS during rheological measurements For the infinitely dilute inverse gas chromatography results, the deviations for both the partition and diffusion coefficients due to the finite concentration effect shown in Figures 4.9 and 4.10 can be re-examined with data obtained from another newly made column. Littlewood 45 has recommended the film thickness of the stationary phase on the inside wall should be smaller than about 1/300 th of the inner diameter of the capillary column. In the current studies, the inner diameter of the capillary column was around cm. Using Littlewood s recommendation, a HPMCAS film thickness below 1.76 μm should be coated. Therefore, a new capillary column with 1.5 μm film thickness could be made, and the results compared with the regressed partition and diffusion coefficients from the previous columns. As for the finite concentration inverse gas chromatography experimental section, no experimental data were obtained above the glass transition temperature of the HPMCAS-acetone system since the weight fraction of acetone was not high enough to turn the glassy HPMCAS to its rubbery state. Theoretically, there should be an inflection point for the sorption isotherm and a diffusivity change at the isothermal glass transition