Charge formation in microporous membranes by single-acid site dissociation

The electrolyte concentration and pH dependence of the effective charge density of weak ion exchange membranes have been studied by combining solutions of the Poisson-Boltzmann equation in cylindrical pores with a simple dissociation equilibrium of weakly acid groups attached to the pore walls. Analytical expressions for the effective charge density and wall potential are presented which describe these quantities in terms of pH, electrolyte (1 : 1) concentration, acid constant, density of acid groups and the pore size. The concentration dependence of the effective fixed charge density experimentally observed for cellulose membranes and NaCl-solutions agrees quantitatively with the theoretical predictions. For track-etched mica membranes and KCl-solutions the influence of pH and electrolyte concentration on the effective charge density can be qualitatively explained. Also an interpretation of electro-osmotic findings obtained with an asymmetric cellulose acetate membrane and NaCl-solutions is given.