Finite ion size effect on the force and energy of the double-layer interaction between two parallel similar plates at arbitrary separations in an electrolyte solution

Expressions are derived for the force and energy of the double-layer interaction between two parallel similar plates with arbitrary surface charge densities or surface potentials at arbitrary separations in an electrolyte solution, by taking into account the finite ion size effect on the basis of the full expression of the activity coefficients of electrolyte ions derived by Carnahan and Starling. The results for two models of the double-layer interaction, that is, the constant surface potential and constant surface charge density models, are given. It is shown that in the constant surface potential model, at large plate separations, the magnitudes of the double-layer interaction force and energy increase as the total ion volume fraction increases but this tendency reverses at small plate separations, while in the constant surface charge density model, they always increase as the total ion volume fraction increases.