The influence of excluded volume and excess ion polarizability on the capacitance of the electric double layer

We apply a modified Poisson-Boltzmann theory which permits ions of different sizes and excess polarizabilities to the study of these properties' effects on the differential capacitance of the electric double layer. For a planar electrode, we find an analytical expression for the differential capacitance, which is examined in the limits of low and high applied potential. In the low potential limit, a reduction of the solution relative permittivity caused by the ion polarizability causes the differential capacitance to decrease above a certain concentration, relative to the Gouy-Chapman-Stern theory. A similar effect is observed for the excluded volume, but only if the ions are of different sizes. In the high potential limit, the differential capacitance decreases inversely with the square root of the applied voltage. In a mixed electrolyte, asymmetries in both ion size and excess polarizability alter the surface adsorption of species: at high potentials, smaller ions displace larger ions and less polarizable ions displace more polarizable ions. The extent of the displacement agrees favorably with experimental data. A further consequence of this displacement is the appearance of a second peak in the differential capacitance, which is enhanced by excess ion polarizability.