Analytical expression for Poisson’s equation in relation to a bispherical pore and examination of influence of the pore wall’s concave and convex structure on the EDL capacitance curve

Abstract

The effects of the convex and concave walls of a bispherical pore of a porous electrode of an EDL supercapacitor on the amount of capacitance have been investigated. The classical density functional theory in the framework of the primitive model, PM has been used. Also, the analytical solution for Poisson’s equation has been presented. The different accumulation of ions at the pore’s concave (outer) and convex (inner) walls leads to varying charge storage values and, consequently, the amount of EDL capacitance. The entropy effect causes the counterion accumulation at the concave wall to be greater than that at the convex wall; however, the energy effect, which is imposed by the electrode potential, effects on that. The amount of counterion adsorption directly affects the wall’s EDL capacitance, which has been thoroughly investigated for both concave and convex walls. Our results indicate that the concave wall’s capacitance is always larger than the convex wall’s. Finally, the effect of ion size and electrolyte concentration on the value of capacitance has also been studied; results show a camel-bell curve transition with concentration.