The effect of the pH on electrolyte transport through microporous membranes bearing either weakly or strongly dissociating acid groups. A theoretical analysis using the space-charge model for a cylindrical capillary

Abstract

In this paper a theoretical study has been made of the pH dependence of 1-1 electrolyte transport through charged microcapillaries bearing either strong acid groups or weak acid groups ( K a = 1.8 × 10 −8 mol cm −3). Under the conditions of zero electrical current, and zero pressure and pH differences across the membrane, a set of three coupled differential (transport) equations has been solved numerically, which predict the cation flux, the proton flux, the barycentric velocity and the membrane potential over a wide range of external salt concentration ratios. The transport coefficients appearing in these equations were obtained by considering in the solution of the Poisson-Boltzmann equation two types of cations (the cation of the salt and the proton) and by incorporating a dissociation equilibrium for the proton at the pore wall. In this way the variation of the fixed charge concentration in the pore, induced by the salt concentration difference across the membrane, could be taken into account in the case of weakly ionizing acid groups. The theoretical results predict a marked difference in transport behavior between membranes with strong and weak acid groups as far as it is influenced by the pH.