Charging Dynamics of Electric Double-Layer Nanocapacitors in Mean Field

Abstract

An electric double-layer capacitor (EDLC) stores energy by modulating the spatial distribution of ions in the electrolytic solution that it contains. We determine the mean-field timescales for planar EDLC relaxation to equilibrium after a potential difference is applied. We tackle first the fully symmetric case, where positive and negative ionic species have the same valence and diffusivity, and then the general, more complex, asymmetric case. Depending on the applied voltage and salt concentration, different regimes appear, revealing a remarkably rich phenomenology relevant for nanocapacitors.