Solution of the Poisson-Boltzmann equation for surface excesses of ions in the diffuse layer at the oxide-electrolyte interface

Abstract

Models of the electrode-electrolyte interface must include some description of physical structure at the interface and some description of energetics of adsorption. Traditional Gouy-Chapman-Stern models have been developed for interfaces charged by adsorption of a potential-determining ion or by an extermally applied potential. Thus the primary independent variable in the model is the surface potential. In contrast, oxide surfaces are charged as a result of specific chemical affinity of the surface for charged ions in the bulk of solution, species which are not part of the oxide lattice. Thus neither the potential-determining ion nor the external applied potential paradigm is appropriate for the oxide surface. The basis for the model must be the fixed chemical affinity of surface hydroxyl groups for charged species in solution. A mathematical approach to modeling the oxide-electrolyte interface in terms of a Gouy-Chapman-Stern (GCS) structure has been developed which includes consideration of electrostatic and chemical energy of adsorption at the surface and inner Helmholtz planes, and solution of the Poisson-Boltmann equation for concentration of ions in the diffuse layer. Whereas the roughness of oxide surfaces at an atomic level precludes strict interpretation of the oxide-electrolyte interface in terms of a GCS structure, the interface does exhibit average properties describable in terms of a GCS structure. In contrast to previous models the approach presented here allows consideration of any number and kind of ions in solution and at the surface, and is applicable to multi-component equilibria in membranes as well as at charged interfaces. For colloidal suspensions of oxides in dilute electrolytes, it is shown that a significant fraction of electrolyte ions can be attracted to or repelied from the diffuse layer. The diffuse layer concentrations must be taken into account when computing mass balances and considering evidence for specific adsorption of Particular ions