Thermodynamic modeling of polyelectrolyte solutions and the application in phase equilibrium analysis of ion exchange membrane systems




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The investigations on the properties of polyelectrolyte solutions are essential for the design and simulation of industrial processes with polyelectrolytes, including but not limited to industrial pharmaceutical process, water treatment process with ion exchange membranes (IEMs), fuel cell with IEMs, and biomacromolecule studies, such as nuclei acids and proteins. Therefore, an accurate and reliable modeling approach with a rigorous thermodynamic framework is demanded to model the polyelectrolyte systems. This model should be reliable over a wide concentration range with a variety of ionic species and be flexible to extend to more complicated circumstances such as polyelectrolyte with mixed solvent. The focus of this dissertation is to establish a reliable and robust model to correlate and predict the polyelectrolyte solutions with various mobile ions. The model is gradually built up. Chapter I introduces the definition of polyelectrolyte and the corresponding thermodynamic properties. In addition, a brief literature survey is included to summarize the research and advances on polyelectrolyte solution within past few decades. Chapter II shows the polyelectrolyte NRTL model development for the polyelectrolyte solutions with single counterion species. In Chapter III, the model is generalized for polyelectrolyte solutions with mixed counterion species. Chapter IV shows one of the potential model application in ion-exchange membranes. Among all the modeling studies for polyelectrolyte solutions, the Manning’s limiting law is the most popular one. The model describes the nonideality of the polyelectrolyte solution by considering the electrostatic interaction between a polyion backbone chain and mobile ions. The activity coefficient expression is derived from the linearized Poisson-Boltzmann equation with the cylindrical coordinate. The model suggests that the counterions condense when the charge density of polyion backbone chain is greater than a critical value to avoid divergence of electrostatic energy. The Manning’s limiting law has been successfully applied in dilute aqueous polyelectrolyte solutions with added salt. However, it fails in a wide concentration range. The deficiency of the Manning’s limiting law motivates the author to develop a comprehensive model for polyelectrolyte solutions – polyelectrolyte NRTL model, which explicitly accounts the electrostatic polyion-ion interactions, ion-ion interactions and short-range interactions. Compared to Manning’s limiting law, those two additional terms for ion-ion and short-range interactions significantly contribute to the nonideality of polyelectrolyte solutions at high concentrations. The polyelectrolyte NRTL model successfully represents the experimental data, such as activity coefficient, osmotic coefficient, and the condensation fraction, for polyelectrolyte with single counterion in Chapter II. The tested polyions include polystyrene sulfonate (PSS), polyvinyl sulfate (PVS) and copolymer of polyvinyl sulfate and polyvinyl alcohol (PVAS), carboxymethylcellulose (CMC), and polymethyl acrylate (PMA). The counterions species include monovalent and multivalent counterions such as H+, Li+, Na+, Ti+, Ag+, Ba2+, Ca2+, Cd2+, Cu2+, Pb2+, Ni2+, Mg2+ and Zn2+. Then, the author generalizes the polyelectrolyte NRTL model for polyelectrolyte solutions with mixed counterions in Chapter III. In addition, to determine the condensation fraction for counterions in the polyelectrolyte system, a modified Two-Variable Theory is developed. It is a theoretically consistent counterion condensation theory to incorporate to the polyelectrolyte NRTL model framework. The Modified Two-Variable Theory is a Gibbs energy minimization approach for the system to calculate the optimized condensation fraction value for each counterion. The Gibbs energy of the system consists of three portions of contribution: the electrostatic potential between polyion and mobile ion, electrostatic potential between uncondensed ionic species, and the entropy of mixing. The polyelectrolyte NRTL model is tested and validated with various polyelectrolyte solutions with mixed counterions. The experimental data include counterion condensation fractions and counterion activity coefficient for various polyion solutions such as PSS, PMA, and dextran sulfate (DS). The mixed counterions are monovalent and divalent counterion mixtures like Na+ and Mg2+, Na+ and Ca2+, K+ and Mg2+, K+ and Ca2+, H+ and Pb2+, and Na+ and Pb2+. In addition, the polyelectrolyte NRTL model incorporated with the modified Two-Variable Theory is applied in the modeling framework of IEMs equilibria with mixed salt to represent the activity coefficient of mobile ions in the membrane phase. While the ionic activity coefficients in the bulk phase are calculated by the electrolyte non-random two-liquid (eNRTL) model. The experimental data including ion-exchange isotherms, counterion and/or coion concentrations in the membrane phase are successfully corelated by our model. In addition, our model is capable to predict the mobile ion partitioning and counterion selectivity for IEMs with mixed salts using the corresponding parameters regressed from IEM systems with single counterion. The tested IEM are commercially available, including CMV, CMS, CDS XL8, CSV Nafion, CSE, and ASE. In summary, this dissertation provides a fundamental approach for the modeling of polyelectrolyte solutions with various counterion species. Moreover, it suggests a guideline for the potential model applications in industrial processes such as IEMs.

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Polyelectrolytes, Counterion Condensation, Thermodynamic Properties, Ion Exchange Membranes