Diffusion Coefficients of Alkali Metal Cations in Nafion® from Ion‐Exchange Measurements: An Advanced Kinetic Model

Abstract

An advanced kinetic model of the coupled diffusion of two counterions in a fixed‐site ion‐exchange membrane is developed considering the effect of the varying ionic composition on the membrane water content. The transport problem is solved numerically for a set of ratios of the diffusion coefficients of the two counterions and 1:1 ion‐exchange stoichiometry. The model is used to evaluate the diffusion coefficients of alkali metal cations in the as‐received and expanded H‐ and M‐form Nafion® (M = Li, Na, K, Rb, Cs) from ion‐exchange measurements. Owing to a compensating effect of the electro‐osmotic pore fluid flow, the initial rates of ion exchange correspond to a fixed water content which, however, is different in H‐ and M‐form membranes. A strong correlation is revealed between the ratio of the membrane to aqueous ion diffusion coefficients and the polymer‐phase volume fraction. It is concluded that the polymer phase presents mainly a steric effect without significantly changing the mechanism of transport of alkali metal cations or protons, which resembles that in bulk water. The different behaviors of the as‐received and expanded Nafion® forms are probably associated with the prevailing cluster‐ or pore‐network morphology, respectively.