Ion transport in inhomogeneous ion exchange membranes

The effect on current efficiency produced by fluctuations in an ion-exchange membrane's fixed ion concentration (due to ion clustering) is determined by considering transport in several model membranes containing different fixed ion distributions. Electroneutrality is not assumed, so as to include nonlinear effects due to space charge in the clusters. The Nernst—Planck and Poisson equations are solved using perturbation theory, and the case of small fluctuations in fixed charge density is considered in order to obtain analytic solutions to the perturbation equations. Results show that an inhomogeneous distribution of fixed ions gives rise to increased current efficiency when the counterions and co-ions experience in the membrane unequal forces due to the potential produced by the fixed ions. The length scale over which the inhomogeneities occur is important in determining the current efficiency.