Investigation of ion concentration and electric potential distributions in charged membrane/electrolyte systems

The ion concentration, electrical potential and current distributions of a membrane/electrolyte system under equilibrium conditions are investigated numerically. The membrane is modeled as an array of finite-length charged pores with uniform distributed surface charge density and in contact with single- or multi-component electrolytes in both sides of the membrane. The numerical model is verified using the theoretical results from Donnan, Nernst and the surface potentials. For cases involving equal electrolyte bulk concentrations in both sides of the membrane, it is found that the dimensionless Debye length and surface charge density characterize the ion concentration and potential distributions in the system. The electrical potential difference between the membrane and external bulk electrolyte depends on the degree of increase in counter-ion concentration inside the pore relative to the bulk electrolyte. Higher potential difference can be resulted as the dimensionless Debye length decreases or the surface charge density increases. In a membrane/multi-component system, the resulting potential difference between the membrane and external bulk electrolyte is smaller as compared with the membrane/single-component electrolyte system due to the increase in dimensionless Debye length. For systems with unequal electrolyte bulk concentrations in contact with the membrane, current flow appears in the system due to the establishment of concentration and potential gradients in the system. The current flow increases with the increase in the bulk electrolyte concentration difference. The current flow in the multi-component electrolyte system is found to be smaller than that for the single-component system due to the increase in dimensionless Debye length.