Mean-Field Potential for Heterogeneous Electrical Double Layers, with Application to the Surface Pressure of Charged Monolayers

Abstract

In this paper expressions are derived for the electrostatic mean-field potential at a nonuniformly charged interface. Within the Gouy-Chapmann model of electrical double layers two levels of approximation are compared. In the first scheme, solution of the linearized Poisson-Boltzmann equation gives a generalization of the familiar Debye-Hückel formula. In the second, semi-nonlinear approach, the leading order term which describes the case of a uniform surface charge is retained at the nonlinear level of theory, while higher-order contributions associated with the charge heterogeneity are treated perturbatively, each term being governed by a linear differential equation having an explicit solution. As an application of the model, systems of charged heterogeneous monolayers at the air/water interface are considered. An analytic formula for the electrostatic contribution to the surface pressure of a heterogeneous film is given.