The steady state properties of ion exchange membranes with fixed sites

Abstract

The properties of the steady states of a system composed of two solutions separated by a quite general type of ion exchange membrane having fixed sites are derived as functions of the compositions of the solutions and of the difference of electric potential between the two solutions. These properties are evaluated with the restraints that the membrane is solely permeable to cations or anions, no flow of solvent occurs, and the solutions contain no more than two permeant ionic species, which are monovalent. Under the assumptions that the difference of standard chemical potentials of the permeant species and the ratio of their mobilities are constant throughout the membrane, even when the spacing of sites is variable, explicit expressions are derived for the electric current, individual fluxes, and concentration profiles. An unexpectedly simple dependence of these expressions upon distribution of sites is found.