(609e) Ion Diffusion Coefficients in Ion-Exchange Membranes: Significance of Counter-Ion Condensation

Despite the long history of literature on ion exchange membranes and their industrial importance, fundamental understanding of ion transport in such materials remains incomplete. Experimental techniques for characterizing ion sorption and transport in charged membranes have been firmly established, but a simple, unifying theoretical framework for interpreting, and ultimately predicting, the experimental results is missing. Such understanding would facilitate rational design of charged membranes with transport properties specifically tailored for a given application. Recently, we have proposed a theoretical framework to describe ion partitioning and diffusion in charged membranes using concepts from Manning’s counter-ion condensation theory for polyelectrolyte solutions. The framework accurately predicted equilibrium ion partitioning and salt permeability coefficients of homogeneous ion exchange membranes for various single electrolytes over a broad salt concentration range. This presentation will focus primarily on the impact of counter-ion condensation on ion diffusion in charged membranes. Counter-ion and co-ion diffusion coefficients in a series of commercial and synthesized ion exchange membranes were extracted from experimental ion sorption, salt permeability, and ionic conductivity results. For the membranes in which counter-ion condensation occurred, counter-ion diffusion coefficients were systematically greater than co-ion diffusion coefficients even after accounting for differences in ion mobilities due to differences in ionic hydrated radii. This observation was rationalized within the framework of the proposed model by assuming that condensed counter-ions migrate along the polymer backbone and contribute to the total measured counter-ion mobility. Diffusion coefficients of the condensed counter-ions were approximately two times greater than those of the uncondensed counter-ions. Interestingly, for membranes in which counter-ion condensation did not occur, the ratio of counter-ion to co-ion diffusion coefficients in the membrane was similar to that in aqueous solutions, in accordance with predictions from the model.