Diffuse and Stern capacitances at the concave wall of spherical cavities by density functional theory

Abstract

Abstract The dependence of Stern and diffuse capacitances on curvature for the electric double layer at the concave wall of spherical cavities is investigated using modified fundamental measure theory within the framework of restricted primitive model. As expected, both Stern and diffuse capacitances are found to increase with size. Moreover, the diffuse capacitance curve assumes a bell shape for small enough cavities while it exhibits a bell-camel transition with size. The Stern capacitance is observed to have a greater contribution to the total capacitance curve than does the diffuse one at low EPs for a (+1:−1) electrolyte irrespective of cavity size. At high electric potentials, the contributions of Stern and diffuse capacitances depend on cavity size. The diffuse potential is strongly affected by ion charge that, in turn, determines the shape of the capacitance curve. The sign of diffuse potential changes with electric potential depending on concentration for electrolytes with divalent counter ions. It causes that the diffuse potential passes from zero which leads to an infinite value for diffuse capacitances. Such a behavior has been observed with concentration for asymmetric electrolytes with divalent co ions. Finally, it is found that the diffuse potential can be used to predict the shape of the capacitance curve for symmetrical electrolytes.