Model for anodic film growth on aluminum with coupled bulk transport and interfacial reactions

Films grown through the anodic oxidation of metal substrates are promising for applications ranging from solar cells to medical devices, but the underlying mechanisms of anodic growth are not fully understood. To provide a better understanding of these mechanisms, we present a new 1D model for the anodization of aluminum. In this model, a thin space charge region at the oxide/electrolyte interface couples the bulk ionic transport and the interfacial reactions. Charge builds up in this region, which alters the surface overpotential until the reaction and bulk fluxes are equal. The model reactions at the oxide/electrolyte interface are derived from the Våland-Heusler model, with modifications to allow for deviations from stoichiometry at the interface and the saturation of adsorption sites. The rate equations and equilibrium concentrations of adsorbed species at the oxide/electrolyte interface are obtained from the reactions using Butler-Volmer kinetics, whereas transport-limited reaction kinetics are utilized at the metal/oxide interface. The ionic transport through the bulk oxide is modeled using a newly proposed cooperative transport process, the counter-site defect mechanism. The model equations are evolved numerically. The model is parametrized and validated using experimental data in the literature for the rate of ejection of aluminum species into the electrolyte, embedded charge at the oxide/electrolyte interface, and the barrier thickness and growth rate of porous films. The parametrized model predicts that the embedded charge at the oxide/electrolyte interface decreases monotonically for increasing electrolyte pH at constant current density. The parametrized model also predicts that the embedded charge during potentiostatic anodization is at its steady-state value; the embedded charge at any given time is equal to the embedded charge during galvanostatic anodization at the same current. In addition to simulations of anodized barrier films, this model can be extended to multiple dimensions to simulate anodic nanostructure growth.