Multicomponent space-charge transport model for ion-exchange membranes

A multicomponent space‐charge transport model for ion‐exchange membranes was developed, where the membrane structure was modeled as an array of cylindrical pores with a uniform distribution of fixed‐charge sites on the pore walls. Ion/fixed‐charge site electrostatic interactions, electric‐field‐induced water dipole orientation, ion‐hydration free‐energy changes during ion partitioning, and concentration‐dependent transport parameters were considered in the analysis. The model predicted experimental concentration vs. time data accurately for Donnan dialysis separations with a DuPont Nafion 117 cation‐exchange membrane, where the membrane separated a dilute H2SO4 solution from an aqueous mixture of either Cs2SO4 + Li2SO4 or Cs2SO4 + Na2SO4. Both computer predictions and experimental measurements showed that the alkali metal cation with the larger hard‐sphere radius (lower surface charge density) was selectively absorbed in and transported across the membrane during a multicomponent separation. The cation/cation transport permselectivity was less than the selectivity for equilibrium uptake due to slow ion transport near the pore wall, where discrimination between like‐charge cations was greatest.