The Electric Double-Layer Differential Capacitance at and near Zero Surface Charge for a Restricted Primitive Model Electrolyte

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Abstract
The behavior of the differential capacitance of a planar electric double layer containing a restricted primitive model electrolyte in the neighborhood of zero surface charge is investigated by theory and simulation. Previous work has demonstrated that at zero surface charge the differential capacitance has a minimum for aqueous electrolytes at room temperature but can have a maximum for molten salts and ionic liquids. The transition envelope separating the two situations is found for a modified Poisson−Boltzmann theory and a Poisson−Boltzmann equation corrected for the exclusion volume term. Good agreement is found between simulation and the modified Poisson−Boltzmann theory in the neighborhood of the envelope at the reduced temperature of 0.8, while the exclusion volume corrected Poisson−Boltzmann theory shows correct qualitative trends.