A SIMPLE STATISTICAL-MECHANICAL APPROACH TO THE FREE-ENERGY OF THE ELECTRIC DOUBLE-LAYER INCLUDING THE EXCLUDED-VOLUME EFFECT

A simple analytic statistical mechanical approach is applied to derive an expression for the free energy of a single electric double layer. Electrostatic interactions are considered by means of the mean electro static field while the finite size of particles constituting the elect rolyte solution is considered by including the excluded volume effect. The calculated free energy of an univalent electrolyte is compared to the corresponding free energy obtained by the Poisson-Boltzmann theor y. It is shown that the excluded volume effect considerably increases the energy of the electrostatic field while the corresponding decrease of the entropic contribution is less pronounced. As the entropic cont ribution is larger than the energy of the electrostatic field and as t he effects on both contributions partially cancel, the free energy obt ained by the Poisson-Boltzmann theory is an excellent approximation re garding to the excluded volume effect.