Abstrakt
Coupled diffusion of two counterions in a fixed-site, permselective, ion-exchange membrane is treated by the method of moments. Theoretical expressions are given for the evaluation of ion diffusion coefficients from the ion-exchange measurements.
They are used to analyze the transport properties of a Nafion membrane in the presence of proton and a univalent (Li+ Na+, K+, Rb+, or Cs+) or divalent (Ru(2,2'-bipyridine)(3)(2+)) cation. Diffusion coefficients of alkali metal cations, as calculated from ion-exchange rates when the hydrogen ion is initially present in the membrane (the forward process) or in the solution (the reverse process), differ significantly.
Moreover, only the latter parameters are comparable with the corresponding self-diffusion coefficients. These effects can be attributed to a different water content in Nafion prior to forward or reverse exchange measurements and to the cross effects arising from the simultaneous transport of the two counterions.
While the rates of Ru(2,2'-bipyridine)(3)(2+) exchange into the as-received Nafion and the Nafion cast films are about the same, the present analysis yields a much lower value of the diffusion coefficient.