Counter-ion driven loss of freezable water weakens donnan exclusion in a cation-exchange membrane

Abstract

Ion-exchange membranes are defined by their permselectivity, which arises from their ability to exclude co-ions through Donnan exclusion. Yet, the factors limiting the predictability of co-ion exclusion are not fully understood. Here, we show that the identity of the counter-ion alone can weaken Donnan exclusion in a commercial cation-exchange membrane (Fumasep FKS-50) which is not captured by current thermodynamic models. Equilibrating the membranes with NaCl, KCl, and CsCl solutions progressively reduces the water content. Differential scanning calorimetry reveals that this reduction occurs almost entirely from the freezable water population, while the bound water remains sufficient to satisfy the effective hydration of the counter-ions and fixed sulfonate charges. Comparison of our experimental data with thermodynamic models shows that the Donnan-Manning model substantially improves agreement with experiment over the ideal-Donnan model and describes co-ion partitioning reasonably well for the NaCl- and KCl-equilibrated membranes, although small deviations remain at low salt concentrations. In contrast, it systematically under-predicts co-ion uptake in the Cs+ form across the entire concentration range, despite the integration of the experimentally determined differences in the membrane water content. Together with the retention of strongly associated hydration water, this finding indicates that the larger deviations for the Cs+ form cannot be explained by differences in membrane hydration alone. We instead attribute them to the redistribution of water within the membrane. Accordingly, the depletion of bulk-like water lowers the effective dielectric constant, while the accompanying loss of weakly associated water allows Cs+ to approach closer toward the fixed sulfonate groups. Both effects strengthen the Coulombic interaction between the counter-ion and the fixed charges, screening the effective fixed charge concentration and weakening Donnan exclusion. These results identify counter-ion driven loss of freezable water as a mechanism that limits the predictive capability of conventional thermodynamic models of co-ion partitioning, with direct implications for membrane permselectivity under the mixed-cation conditions encountered in practical separations.