469195 Thermodynamic Modeling of Polyelectrolyte Solutions with Electrolyte Nrtl Model

Monday, November 14, 2016
Grand Ballroom B (Hilton San Francisco Union Square)
Yue Yu, Yuan Li and Chau-Chyun Chen, Chemical Engineering, Texas Tech University, Lubbock, TX

Thermodynamic modeling of polyelectrolyte solutions with eNRTL model

Yue Yu, Yuan Li, Chau-Chyun Chen

Department of Chemical Engineering

Texas Tech University

Polyelectrolytes are polymers with charged functional groups along the backbone chains. The charged functional groups are electrostatically attached with counterions that carry opposite charges. The charged polymers are attractive to counterions and repulsive to coions. Such behavior makes polyelectrolytes applicable in processes of separation, purification, biomedical systems, and energy storage systems [1-3].

Thermodynamic description of the mobile ions including both counterions and coions in polymer and solution phases draws great interest of research. Early works proposed various excess Gibbs energy models [4-7]. There had been no limiting law for polyelectrolyte solutions like Debye-Hückel theory for simple electrolytes until Manning put forward his counterion condensation theory [8]. Manning defined a “dimensionless linear charge density” of polyelectrolytes as the Manning parameter and stated that counterions would condense on the charged functional groups of polyelectrolytes when charge density was larger than a critical value. Applying Manning’s model as the limiting law, Danner and his co-workers incorporated NRTL model for additional short-range interaction contribution and successfully calculated activity and osmotic coefficients [9-10]. Sadowski combined Manning’s limiting law and Perturbed-Chain Statistical Association Fluid Theory to describe vapor-liquid equilibrium and polymer swelling [11]. Recently, Manning et al. extended the counterion condensation theory to predict activity coefficients of mobile ions in cross-linked ion exchange membranes in equilibrium with simple electrolyte solutions [12].

This work presents a different approach to model polyelectrolytes. A new concept of an “effective charge number” is introduced for polyelectrolytes to account for the counterion condensation derived from the charge density of the polymer chains. While the real charge number of polyelectrolytes is related to the number of ionic sites or the capacity of attracting counterions, the “effective charge number” represents the electrostatic influence of charged functional groups in the solution. The very successful electrolyte Non-Random Two Liquid (eNRTL) model is then used to describe the excess Gibbs energy of the polyelectrolyte system with the “effective charge number”.

eNRTL model has been proven to be applicable to varieties of aqueous and mixed-solvent electrolyte solutions [13]. We show the eNRTL model is capable of systematically correlating and extrapolating thermodynamic properties for all components in polyelectrolyte solutions including osmotic coefficients, solvent activity, mobile ion activity coefficient, Gibbs free energy of the solution, etc. We further show successful modeling results for describing equilibrium of mobile ions in ion exchange polymers and external salt solutions,

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