Ionic diffusion and migration fluxes in passive film formation under mixed kinetic control

The elementary processes common to all electrochemical systems are electrical conduction and the transfer of charge across the interface between two different phases. In many practically-important situations, the chemical species generated by these interfacial charge transfers can subsequently react to form poorly-conducting or insulating substances, thereby increasing the resistance and decreasing the amount of electrical energy available for reaction. This self-limiting phenomenon is commonly referred to as passivation, and is of great importance in the study of corrosion and the behavior of porous battery electrodes. Electrochemical passivation is almost always a multistep process, involving transfer of charge across at least two interfaces and conduction phenomena taking place in the solid state and/or the electrolyte solution. It is well known that the rates of interfacial charge transfers are highly nonlinear functions of the overpotential, which is the departure of the potential difference from its equilibrium value. The transport processes may also involve nonlinearities resulting from coupling between diffusion and migration of charged species. When solid, electrically resistive reaction products are generated, the interfacial and transport phenomena are inextricably linked; there is at present no general basis on which their relative importance to the overall kinetics can be assessed. Existing treatments, based on the assumption that either process is rate-controlling, are not suitable for this purpose, since they imply that the other process is infinitely fast. What is required is a more general model allowing for mixed kinetic control, where both processes are assumed to occur at finite rates. In this paper, the interaction between the two elementary processes identified above is explored by considering a passivation process involving deposition of a porous layer of an otherwise insulating substance. The potential and ionic concentrations within the pore electrolyte are calculated by exact solution of the steady Nernst-Planck equations, eliminating the need for the approximations inherent in existing treatments. The contributions of diffusion and ionic migration to the species fluxes are thereby determined self-consistently as a function of current density. Calculations of the electrochemical kinetic characteristics of the process lead to the conclusion that, in the presence of excess inert electrolyte, the potential drop associated with ionic conduction through the pore electrolyte makes a small contribution to the total polarization. In contrast, the surface overpotential (associated with the finite rate of interfacial charge transfer) exerts the dominant influence in the early stages of passivation, while the concentration overpotential (resulting from concentration variations within the pore electrolyte) is predominant in the later stages.