A mean spherical approximation study of the capacitance of an electric double layer formed by a high density electrolyte

In a recent grand canonical Monte Carlo simulation and modified Poisson–Boltzmann (MPB) theoretical study of the differential capacitance of a restricted primitive model double layer at high electrolyte densities, Lamperski, Outhwaite and Bhuiyan (J. Phys. Chem. B 2009, 113, 8925) have reported a maximum in the differential capacitance as a function of electrode charge, in contrast to that seen in double layers at lower ionic densities. The venerable Gouy–Chapman–Stern (GCS) theory always yields a minimum and gives values for the capacitance that tend to be too small at these higher densities. In contrast, the mean spherical approximation (MSA) leads to better agreement with the simulation results than does the GCS approximation at higher densities but the agreement is not quite as good as for the MPB approximation. Since the MSA is a linear response theory, it gives predictions only for small electrode charge. Nonetheless, the MSA is of value since it leads to analytic results. A simple extension of the MSA to higher electrode charges would be valuable.