Curvature dependence of the camel-bell curve transition on the capacitance curve of spherical electric double-layer in porous electrodes: Density Functional Theory

Abstract

Using the Modified Fundamental Measure Theory as the theoretical framework, we investigate the effect of curvature on camel-bell curve transition on the capacitance curve of a super-capacitor formed inside the spherical cavity of a porous electrode. The results show that at a constant concentration, the capacitance curve has a camel shape for large enough cavities, while a transition is observed from camel to bell shape with increasing curvature. In fact, at constant concentration this transition happened with decreasing the cavity size while at constant cavity size it occurs with concentration. Although concentration of transition decreases with curvature, the packing parameter for the fluid in the cavity is about to 0.2, irrespective of the curvature. Also, the potential at which the saturation phenomenon happens increases with cavity size. Despite the increased capacitance with increasing cavity size, there is an optimum size beyond which capacitance shows no remarkable increase. Investigation of the effect of ion charge on capacitance shows that the position of maximum capacitance shifts toward lower electric potentials with increasing ion charge. Finally, it is found that, at high electric potentials and at constant concentrations, electrolytes with the same counter ions exhibit capacitances which is independent of co-ion charge due to saturation.