Modeling the Potential Distribution in Porous Anodic Alumina Films during Steady-State Growth

Abstract

Porous anodic alumina (PAA) films, formed by anodic oxidation in acidic solutions, contain hexagonal arrays of parallel cylindrical pores, with pore diameter and spacing between ten and several hundred nanometers. Simulations were developed for the electrical potential distribution in the film during steady-state PAA growth, and used to calculate the rates of metal-film and film-solution interface motion. In particular, a model using the assumption of no space charge (Laplace’s equation) and one based on the current continuity equation, in each case coupled with high-field ionic conduction, were evaluated with respect to the requirement that the interface profiles are time invariant. Laplace’s equation, on which prior simulations of PAA growth were based, yielded unrealistic behavior with highly nonuniform interface motion, suggesting the presence of significant space charge. In contrast, interface motion predicted by the current continuity equation was uniform, except near convex ridges on the metal-film interface between pores. To fully rationalize the steady-state PAA geometry, phenomena other than conduction should be considered, which are able to provide inhibition of the oxidation rate on these ridges.