Diffuse double layer interaction between two parallel plates with constant surface charge density in an electrolyte solution III. Potential energy of double layer interaction

Abstract

By using the non-linearPoisson-Boltzmann equation, the potential energy of the diffuse double layer interaction between two parallel plates with constant surface charge density in a symmetrical electrolyte solution is calculated from the free energy of the double layers. The two plates may have unequal surface charge densities, dielectric constants and thicknesses. For very small plate separations, where the influence of the electric field which is induced within the plates by the overlapping of the double layers becomes important, the free energy is calculated by considering a charging process in which all the surface charges are increased at the same rate. For separations where the influence of the field within the plates may be neglected, a discharging process is used in which all the charges in the system are decreased at the same rate, and the potential energy of the double layer interaction is expressed in terms of elliptic integrals.