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 electrostatic field while the finite size of particles constituting the electrolyte 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 theory. 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 contribution is larger than the energy of the electrostatic field and as the effects on both contributions partially cancel, the free energy obtained by the Poisson-Boltzmann theory is an excellent approximation regarding to the excluded volume effect.