Differential capacitance of the solvent primitive model diffuse layer using the inhomogeneous Poisson–Boltzmann theory with an exclusion volume term

The solvent primitive model diffuse double layer capacitance is analysed using a Poisson–Boltzmann theory which incorporates the exclusion volume term in the Boltzmann distribution. Unequal ion and solvent sizes are considered and the differential capacitance calculated for 1:1 electrolytes at different electrolyte and solvent concentrations. The unequal ion sizes cause an asymmetry in the capacity curves while the solvent can radically influence its overall shape. At low electrolyte concentrations and small surface charge, the capacitance has a minimum which changes to a maximum as the electrolyte concentration increases. At the higher surface charge densities the capacity curve approaches limiting values, these values depending on the relative counterion size.