On Capacitance and Energy Storage of Supercapacitor with Dielectric Constant Discontinuity

The classical density functional theory (CDFT) is applied to investigate influences of electrode dielectric constant on specific differential capacitance Cd and specific energy storage E of a cylindrical electrode pore electrical double layer. Throughout all calculations the electrode dielectric constant varies from 5, corresponding to a dielectric electrode, to εwr= 10⁸ corresponding to a metal electrode. Main findings are summarized as below. (i): By using a far smaller value of the solution relative dielectric constant εr=10, which matches with the reality of extremely narrow tube, one discloses that a rather high saturation voltage is needed to attain the saturation energy storage in the ultra-small pore. (ii): Use of a realistic low εr=10 value brings two obvious effects. First, influence of bulk electrolyte concentration on the Cd is rather small except when the electrode potential is around the zero charge potential; influence on the E curve is almost unobservable. Second, there remain the Cd and E enhancing effects caused by counter-ion valency rise, but strength of the effects reduces greatly with dropping of the εr value; in contrast, the Cd and E reducing effects coming from the counter-ion size enhancing remain significant enough for the low εr value. (iii) A large value of electrode relative dielectric constant εrw always reduces both the capacitance and energy storage; moreover, the effect of the εrw value gets eventually unobservable for small enough pore when the εrw value is beyond the scope corresponding to dielectric electrode. It is analyzed that the above effects take their rise in the repulsion and attraction on the counter-ions and co-ions caused by the electrode bound charges and a strengthened inter-counter-ion electrostatic repulsion originated in the low εr value.