Some Analytic Expressions for the Capacitance and Profiles of the Electric Double Layer Formed by Ions Near an Electrode

Abstract

The electric double layer, which is of practical importance, is described. Two theories that yield analytic results, the venerable Poisson-Boltzmann or Gouy-Chapman-Stern theory and the more recent mean spherical approximation, are discussed. The Gouy-Chapman-Stern theory fails to account for the size of the ions nor for correlations amoung the ions. The mean spherical approximation overcomes, to some extent, these deficiencies but is applicable only for small electrode charge. A hybrid description that overcomes some of these problems is presented. While not perfect, it gives results for the differential capacitance that are typical of those of an ionic liquid. In particular, the differential capacitance can pass from having a double hump at low concentrations to a single hump at high concentrations.