Ion Diffusion Coefficients in Ion Exchange Membranes: Significance of Counterion Condensation

This study presents a new framework for extracting single ion diffusion coefficients in ion exchange membranes from experimental ion sorption, salt permeability, and ionic conductivity data. The framework was used to calculate cation and anion diffusion coefficients in a series of commercial ion exchange membranes contacted by aqueous NaCl solutions. Counterion diffusion coefficients were greater than co-ion diffusion coefficients for all membranes after accounting for inherent differences due to ion size. A model for ion diffusion coefficients in ion exchange membranes, incorporating ideas from counterion condensation theory, was proposed to interpret the experimental results. The model predicted co-ion diffusion coefficients reasonably well with no adjustable parameters, while a single adjustable parameter was required to accurately describe counterion diffusion coefficients. The results suggest that for cross-linked ion exchange membranes in which counterion condensation occurs condensed counterions migrate along the polymer backbone and contribute to a current in the presence of an externally applied electric field. Moreover, diffusion coefficients for condensed counterions were approximately 2-2.5 times greater than those for uncondensed counterions.