Modelling and simulation of self-ordering in anodic porous alumina

Real-time evolution of pre-textured anodic porous alumina growth during anodization is numerically simulated in two-dimensional cases based on a kinetic model involving the Laplacian electric field potential distribution and a continuity equation for current density within the oxide body. Ion current densities governed by the Cabrera–Mott equation in high electric field theory are formed by ion migration within the oxide as well as across the metal/oxide (m/o) and oxide/electrolyte (o/e) interfaces, and the movements of the m/o and o/e interfaces due to oxidation and electric field assisted oxide decomposition, respectively, are governed by Faraday's law. Typical experimental results, such as linear voltage dependence of the barrier layer thickness and pore diameter, time evolution of the current density, scalloped shape of the barrier layer, and the extreme difference in the reaction rates between pore bottoms and pore walls, are successfully predicted. Our simulations revealed the existence of a domain of model parameters within which pre-textured porous structures which do not satisfy self-ordering configurations are driven into self-ordering configurations through a self-adjustment process. Our experimental results also verify the existence of the self-adjustment process during anodization.