Ion Activity Coefficients in Ion Exchange Polymers: Applicability of Manning’s Counterion Condensation Theory

Manning’s counterion condensation theory, originally developed for polyelectrolyte solutions, was used to predict ion activity coefficients in charged (i.e., ion exchange) membranes with no adjustable parameters. Equilibrium sodium and chloride ion concentrations in negatively and positively charged membranes were determined experimentally as a function of external NaCl concentration, and ion activity coefficients in the membranes were obtained via a thermodynamic treatment. Theoretical values for membrane ion activity coefficients obtained via Manning’s model were compared with those obtained experimentally. Good agreement was observed between the experimental and theoretical values for membrane ion activity coefficients, especially at higher external NaCl concentrations. However, some deviation between experimental and theoretical values was observed in the dilute regime. Manning’s model was also used to obtain activity coefficients for various electrolytes in ion exchange resins using ion sorption data from the literature, and these values were compared to those obtained experimentally.