Effect of the Thickness of a Mesopore Containing Concentrated Ionic System on Capacitance

Concentrated ionic systems confined between parallel, oppositely or equally charged surfaces are studied using the mesoscopic density-functional theory recently developed for the electric double layer. We focus on the effect of the distance L between the confining surfaces on the capacitance C ( L ) in systems with oscillatory decay of the charge–charge correlation function in the bulk, with the period and range of charge oscillations 2π/α 1 and 1/α 0, respectively. Our analytical results show that, in the case of oppositely charged electrodes, the ratio C ( L )/ C H, where C H is the Helmholtz capacitance, can be strongly enhanced or somewhat reduced when the confinement induces compression or expansion of the charged layers, respectively. For equally charged electrodes, C ( L )/ C H takes a maximum or a minimum when the charges at the electrode and at the central layer have the same or opposite sign. In a porous capacitor with slit-like pores and low polydispersity, a significant increase in capacitance can be achieved when the average pore width is smaller than three periods of the charge density oscillations. Since, for systems with potential applications, the oscillatory decay lengths can be determined experimentally, our analytical expressions in terms of L, α 1 and α 0 may serve as a guide for an experimental search for optimal supercapacitors.