Development of a space-charge transport model for ion-exchange membranes



A two-dimensional, electrokinetic transport model that incorporates ionic hydration, orientation of solvent molecules by an applied electric field, and solvent dipole-dipole interactions is developed. The model is used to simulate equilibrium and transport experiments for perfluorosulfonic acid membranes containing aqueous alkali metal sulfate solutions. The membrane is modeled as an array of cylindrical pores. Solution of the mathematical model requires that the membrane porosity, water partition coefficient, coion partition coefficient, water diffusion coefficients, and coion and counterion diffusion coefficients be known. Membrane coion and counterion diffusion coefficients were determined from free solution equivalent conductance data. All other parameters were determined experimentally for a Nafion (of E. I. du Pont de Nemours Inc.) cation-exchange membrane and five 0.1 M alkali metal sulfate solutions. Experimental radiotracer data for coion absorption as well as for coion and water transport are compared with theoretical predictions to test the accuracy of the model.