Exchange diffusion in one dimension: Liquid electrolytes and mixed conductor membranes

Abstract

The concurrent diffusion of redox ions and electrons is analyzed statistically. For point charge ion jumps with second order collision electron transfer, intrinsic ion D's show no effect of electron transfer. For ion jumps and electron jumps across space an enhancement of ion D's is predicted, but with a different form from that of Dahms and Ruff to allow for a decreased probability of ion jumps when electron hopping can also occur. Corrections are made in the Dahms and Ruff analysis by deriving the apparent electron D ϵ, from the gradient of the electron chemical potential. Generalization using the electron electrochemical potential gives Levich's result for the electric field-enhanced migration term and the numerically corrected Dahms-Ruff “diffusion” coefficient. The analysis applies to electrolytes and to redox polymer membranes. Crossed flux conditions and counterion motions are described. A form for the high field electron flux is also postulated.