Beyond Poisson–Boltzmann: Images and correlations in the electric double layer. I. Counterions only

Abstract

The general solution to the zero size mean spherical model is found for an inhomogeneous electrolyte (with specified profile) between charged planar surfaces. The analysis includes the effects of images and correlations. It provides the primary correction to the classical mean field theory of the double layer and allows the error in that theory to be easily estimated over experimental regimes. The relationship between Lifshitz theory and primitive model theories of electrolytes is made explicit. Results obtained for the one component double layer are accurate for systems with low coupling.