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 [Formula: see text] and specific energy storage [Formula: see text] of a cylindrical electrode pore electrical double layer. Throughout all calculations the electrode dielectric constant varies from 5, corresponding to a dielectric electrode, to [Formula: see text] 10(8) corresponding to a metal electrode. Main findings are summarized as below. (i): By using a far smaller value of the solution relative dielectric constant [Formula: see text] , 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 [Formula: see text] value brings two obvious effects. First, influence of bulk electrolyte concentration on the [Formula: see text] is rather small except when the electrode potential is around the zero charge potential; influence on the [Formula: see text] curve is almost unobservable. Second, there remain the [Formula: see text] and [Formula: see text] enhancing effects caused by counter-ion valency rise, but strength of the effects reduces greatly with dropping of the [Formula: see text] value; in contrast, the [Formula: see text] and [Formula: see text] reducing effects coming from the counter-ion size enhancing remain significant enough for the low [Formula: see text] value. (iii) A large value of electrode relative dielectric constant [Formula: see text] always reduces both the capacitance and energy storage; moreover, the effect of the [Formula: see text] value gets eventually unobservable for small enough pore when the [Formula: see text] 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 [Formula: see text] value.