Differential capacitance of the diffuse double layer at electrode-electrolyte interfaces considering ions as dielectric spheres: Part I. Binary electrolyte solutions.

A full theoretical account of the differential capacitance of the diffuse part of the electric double layer at electrode-electrolyte solution interfaces is presented. It builds upon the standard electrokinetic model adding all the additional effects related to the finite ionic size. This includes steric interactions among ions by means of either the Bikerman or Carnahan-Starling expressions and all the permittivity related effects that arise when ions are represented as dielectric spheres. These include the solution permittivity dependence on the local ionic concentration, calculated by means of the Maxwell mixture formula, and two additional forces acting on the ions, namely the Born and the dielectrophoretic forces that depend on the permittivity and the electric field gradients, respectively. The obtained results show that the diffuse double layer behavior is sufficient to qualitatively account for the observed differential capacitance dependence on the electrode voltage. Moreover, when combined with an inner layer capacitance and using the Carnahan-Starling expression, a remarkably good quantitative agreement is achieved.