Theoretical calculation on the membrane potential of charged porous membranes in 1-1, 1-2, 2-1 and 2-2 electrolyte solutions

The space-charge (SC) model and the Teorell–Meyer–Sievers (TMS) model are widely employed to calculate the membrane potential of charged porous membranes in 1-1 electrolyte solutions, but few works with the other kinds of electrolyte solutions have been reported. In this article, membrane potentials for 1-1, 1-2, 2-1 and 2-2 electrolyte solutions have been calculated numerically based on the two models using parameters of concentration, pore radius and surface charge density. The results suggest that equivalent electrolyte concentration is more suitable to characterize the membrane potential in different kinds of electrolyte solutions than electrolyte concentration. Membrane potential approaches to the Nernst potential in the low concentration region, which indicates membrane potential in monovalent cation electrolyte solution is twice as large as that in divalent cation electrolyte solution. In the high concentration region, membrane potential is close to the diffusion potential, which implies membrane potential would be reversed if the diffusion coefficient ratio of coion and counterion is larger than 1.0. While in the intermediate concentration region, membrane potential as a function of electrolyte concentration is almost linear. In the comparison of the SC and TMS models, theoretical predictions by the two models for 1-2, 2-1 and 2-2 electrolyte solutions appear to be similar to those for 1-1 electrolyte solutions reported earlier by Westermann-Clark and Christoforou . The two models coincide with each other when the radius, rp, is less than 5.0 nm and the dimensionless charge density in the pore wall, q0 is less than 1.0. Otherwise, the TMS model would overestimate the membrane potential. Furthermore, the membrane potential shows dependence on the ratio of the volume charge density to equivalent electrolyte concentration, ξf, q0 and rp by the SC model, but only varies with ξf irrespective of q0 and rp by the TMS model. These findings have a significant influence on the establishment of an appropriate theory to evaluate membrane potentials in different electrolyte solutions.