Free Energy of Electric Double Layer. Effect of Ion Size

An expression for the free energy of an electric double layer is derived. A method of undetermined multipliers is applied within a simple statistical mechanical approach. The electrostatic interactions are described by the mean electrostatic field while the finite size of particles, constituting the electrolyte solution, is considered by the excluded volume effect. The particles in the solution are distributed over a lattice with an adjustable constant. The free energy is derived for any composition of ions and any ion valency allowing the mean electrostatic field to vanish far from the charged plane.