title: Predicting Salt Permeability Coefficients in Highly Swollen, Highly Charged Ion Exchange Membranes.
abstract: This study presents a framework for predicting salt permeability coefficients in ion exchange membranes in contact with an aqueous salt solution. The model, based on the solution-diffusion mechanism, was tested using experimental salt permeability data for a series of commercial ion exchange membranes. Equilibrium salt partition coefficients were calculated using a thermodynamic framework (i.e., Donnan theory), incorporating Manning's counterion condensation theory to calculate ion activity coefficients in the membrane phase and the Pitzer model to calculate ion activity coefficients in the solution phase. The model predicted NaCl partition coefficients in a cation exchange membrane and two anion exchange membranes, as well as MgCl2partition coefficients in a cation exchange membrane, remarkably well at higher external salt concentrations (>0.1 M) and reasonably well at lower external salt concentrations (<0.1 M) with no adjustable parameters. Membrane ion diffusion coefficients were calculated using a combination of the Mackie and Meares model, which assumes ion diffusion in water-swollen polymers is affected by a tortuosity factor, and a model developed by Manning to account for electrostatic effects. Agreement between experimental and predicted salt diffusion coefficients was good with no adjustable parameters. Calculated salt partition and diffusion coefficients were combined within the framework of the solution-diffusion model to predict salt permeability coefficients. Agreement between model and experimental data was remarkably good. Additionally, a simplified version of the model was used to elucidate connections between membrane structure (e.g., fixed charge group concentration) and salt transport properties.
authors.affiliation: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin , 10100 Burnet Road Building 133 (CEER), Austin, Texas 78758, United States.
authors.forename: Jovan
authors.initials: J
authors.lastname: Kamcev
authors.affiliation: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin , 10100 Burnet Road Building 133 (CEER), Austin, Texas 78758, United States.
authors.forename: Donald R
authors.initials: DR
authors.lastname: Paul
authors.affiliation: Department of Chemistry and Chemical Biology, Rutgers University , 610 Taylor Road, Piscataway, New Jersey 08854-8087, United States.
authors.forename: Gerald S
authors.initials: GS
authors.lastname: Manning
authors.affiliation: McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin , 10100 Burnet Road Building 133 (CEER), Austin, Texas 78758, United States.
authors.forename: Benny D
authors.identifier: http://orcid.org/0000-0003-2779-7788
authors.initials: BD
authors.lastname: Freeman
keywords: Donnan theory; counterion condensation; ion exchange membrane; salt diffusion; salt permeability; salt sorption; tortuosity