Stability criteria for charged interfaces and their role in double-layer theory

Abstract

The thermodynamic criteria for interfacial stability with respect to separation into two coexistent surface phases are reviewed. Attention is focussed on systems containing electrolytes. The necessary conditions stated by Gibbs apply strictly only to components confined to the interfacial region. However, if specifically adsorbed ions or molecules and their bulk counterparts are considered as distinct species the stability criteria can be applied to systems in which there is specific adsorption from dilute solution. This is done by regarding equilibrium states as a subset of partial equilibrium states for which the electrochemical potentials of specifically adsorbed and bulk species differ, and by arguing that the stability criteria appropriate for partial equilibrium states apply. According to this viewpoint specifically adsorbed ions or molecules are by definition species confined to the interface.

The application considered in this paper is to the electrical double layer, which is assumed to consist of inner and diffuse regions. It is shown that the repulsion between identical double layers may be lower than that given by the constant potential boundary condition without violation of the necessary conditions referred to above, and that systems of this kind are prone to separation into two coexistent surface phases at high electrolyte concentrations.

When there is at least one ionic species in the system (usually an indifferent coion) which is not specifically adsorbed it is shown that if the solution composition is varied in an appropriate way, as described in the text, the outer Stern potential, ϕ_d, for an isolated surface will show super-Nernstein behaviour for ‘lower than constant potential’ interactions and vice versa. Such behaviour can be investigated experimentally when ϕ_d can be identified with the zeta potential.

The only assumption made concerning the nature of the double layer is that the split into inner and diffuse regions is legitimate. The additional assumption that ion distributions in the diffuse region conform to the Poisson–Boltzmann equation is not required.