Electrostatic interaction of ion-penetrable membranes. Effects of ionic solubility

An analytic, approximate expression for the electrostatic interaction between two membranes immersed in an electrolyte solution is derived on the basis of a simple membrane model. This model assumes that the membrane has a surface layer in which charged groups are uniformly distributed and that electrolyte ions can penetrate into the surface layer. The partition coefficients of cations and anions between the solution and the surface layer, which are related to their solubilities in the surface layer, may be different from unity.The electrostatic interaction depends on the ionic partition coefficients between the solution and the surface layer, and the relative permittivity of the surface layer, as well as on the membrane-fixed charges, the electrolyte concentration in the solution, and the surface layer thickness. It is shown, in particular, that even where the charge layer has no fixed charges, the electrostatic interaction force can be produced if the solubilities of cations and anions are different in the surface layer.