From ion partitioning to ion transport: Scaling invariance of the charged polymer network in ion exchange membrane

Abstract

This study probes ion transport in charged polymer networks of ion-exchange membranes (IEMs) via systematic conductivity measurements on commercial CR61 and CMI-7000S membranes equilibrated with solutions of alkali metal chlorides (0.003 mol/L to near saturation). Using an electrochemical impedance spectroscopy (EIS) based direct-contact cell modified to suppress water loss, reproducible data show that conductivity increases rapidly with increasing external salt concentration below 0.1 M. Comparisons with six homogeneous-theory models show that only the scaling-regular-solution (SRS) framework, which treats uncondensed counterion diffusion as electrostatically accelerated hopping (enhanced parameter α^SRS = 6–20), correlates the full dataset using the determined scaling factor from the ion partitioning equilibrium data, suggesting a scaling invariance of the charged polymer networks linking ion partitioning to conductivity. Intrinsic diffusion coefficients of uncondensed counterions exceed aqueous values by up to 20×, possibly suggesting “negative-friction” transport in low-tortuosity nanopores with high charge density. The findings suggest that the innovation of advanced IEMs should balance the topology of charged polymer networks, charge density, tortuosity, and the service aqueous solution.