Ion Activity Coefficient of Sodium Halides in Anion-Exchange Polymers: Empirical Model Based on Manning’s Counterion Condensation Theory

The theory of electrolyte solution provides a precise description of the thermodynamic state and non-ideality of electrolyte solutions, allowing for the accurate prediction of the crystallization separation process of Salt Lake brine. Analogously, we attempt to describe the non-ideality of ions in ion-exchange polymers based on Manning’s Counterion Condensation Theory, which was originally used to describe the thermodynamics of polyelectrolyte solutions, has amply proven the potential to extend to ion-exchange polymers. In this article, equilibrium solvent and solute concentrations in aminated cross-linked polystyrene AEM were determined experimentally as a function of external NaCl concentration, and ion activity coefficients in the membranes were obtained via a thermodynamic treatment. With the recombination and empirical parameters added to Manning’s model, the ion activity coefficient of NaCl and NaBr in the aminated cross-linked polystyrene AEM can be accurately described in concentration ranges of 0.01 mol·kg−1~3 mol·kg−1. Compared with the original model, the Coefficient of Determination between the improved model and the experimental data was increased from 0.65 to 0.95. The Residual Sum of Squares is reduced by about one order of magnitude, significantly improving the Manning model’s adaptability when applied to AEM.