Extended Donnan Model to Rationalize Equilibrium Ion Affinity and Preferential Transfer of Ions of Equal Charge in Ion-Exchange Membranes

In salt mixtures, ion-exchange membranes have different equilibrium affinities for various ions of the same charge (ion-exchange selectivity). Transport selectivity also occurs in salt mixtures with different ions of the same valence. These findings are usually attributed to the different affinities of assorted ions to ion-exchange groups. Nevertheless, specific interactions with ion-exchange groups suggest a localized binding/adsorption of ions, and bound ions may lose their mobility. Accordingly, it is not obvious that an increased equilibrium affinity should give rise to preferential ion transfer.

Ion diffusion coefficients in ion-exchange media are typically less than those in solution, and trends in the effective diffusion coefficients of various ions in the membrane phase are not always the same as the corresponding trends in bulk solutions. One proposed explanation for such differences is that partitioning into the membrane phase may include partial ion dehydration. This seems reasonable because water properties in the tight confinement and close vicinity of numerous ion-exchange groups may differ from those in free solutions. However, if partial dehydration is the explanation for trends in diffusion coefficients in the membrane, one should also take it into account when modelling partitioning between the solution and membrane phases.

This communication invokes an extended Donnan model that postulates differences in ion solvation energies in an ion-exchange membrane and in an equilibrium solution and, thus, takes into account the effect of possible partial ion dehydration. Because the dehydration does not imply localized specific interactions between ions and ion-exchange groups, this model easily explains how stronger equilibrium membrane affinity for a given ion may lead to higher transport selectivity for this ion.

We will briefly discuss the consequences of partial ion dehydration on the partitioning and transport of counterions and coions. We will also speculate on possible correlations between the excess solvation energy of an ion and the extent of its hydration in bulk water, namely, the stronger the hydration of an ion in solution the less it partitions into the membrane phase. This would give rise to a larger affinity for potassium over lithium, for example, which agrees with experiment. Finally, we will outline further studies that may better identify the mechanisms of ion transport and partitioning selectivity.