Counterion Mobility in Ion-Exchange Membranes: Spatial Effect and Valency-Dependent Electrostatic Interaction

Enhancing the selectivity of ion-exchange membranes (IEMs) is an important need for environmental separations but is hindered by insufficient understanding of the fundamental transport phenomena. Specifically, existing models do not adequately explain the order of magnitude disparity in diffusivities of mono-, di-, and trivalent ions within the membranes. In this study, a transport framework is presented to describe counterion migration mobility using an analytical expression based on first-principles. The two governing mechanisms are spatial effect of available fractional volume for ion transport and electrostatic interaction between mobile ions and fixed charges. Mobilities of counterions with different valencies were experimentally characterized and shown to have high R2s in regression analyses with the proposed transport model. The influence of membrane swelling caused by different counterions was further accounted for to better model the spatial effect. The frictional effect of electrostatic interaction was quantitatively linked to the membrane structural and electrical properties of fixed charged density and dielectric constant. Additionally, the anion-exchange membrane exhibited a weaker electrostatic effect compared to cation-exchange membranes, which was attributed to steric hindrance caused by hydrocarbon chains of the quaternary amine functional groups. The insights offered in this study can inform the rational development of IEMs and membrane processes for ion-specific separations.