What is the impact of ion aggregation and counterion condensation on salt transport in ion exchange membranes?

Ion exchange membranes are widely used in water purification and energy storage applications to selectively and efficiently regulate salt transport. However, concerted motions of ions arising due to ion aggregation and counterion condensation are often neglected when interpreting salt transport. In this study, we apply the Onsager transport framework to atomistic molecular dynamics simulations to study the impact of such physics on salt transport properties in a model cation exchange membrane. Cations and anions, distinct cations, and distinct anions tend to move in the same direction due to the formation and resulting motion of ionic aggregates. Such motions, in general, increase the salt diffusion coefficient and decrease the conductivity relative to "ideal" values which envision the ions to move independently of each other. In contrast, condensation-induced slowdown inhibits the motion of ionic aggregates since the condensed counterions serve as a connection between aggregates and the immobile polymer matrix. Such effects decrease deviations of salt transport properties from the ideal assumption.