Differential capacitance of the electric double layer: mean-field modeling approaches

Electrolytes screen the charges carried by an electrode through the formation of a diffuse double layer. The corresponding differential capacitance reflects the change of the surface charge density with the applied surface potential. Mean-field modeling of the differential capacitance is an attempt to qualitatively explain experimental findings such as the camel-to-bell shape transition in terms of physical factors including the ion size and concentration, nonelectrostatic ion–ion interactions, electrostatic ion–ion correlations, and the influence of the electrode curvature. We highlight the central role of the lattice gas model as a conceptual tool to describe concentrated electrolytes and ionic liquids, and we briefly summarize how extensions and generalizations of this model give rise to concepts known as ‘overscreening’ and ‘underscreening’.