Effect of ion migration on the self-assembly of porous nanostructures in anodic oxides

The self-organization of porous nanostructures in anodic oxide is considered. A mathematical model which incorporates the electrochemical transport of oxygen ions within the oxide layer and the chemical reactions at the metal-oxide and oxide-electrolyte interfaces is developed. It is shown through linear stability analysis that a short-wave instability exists in certain parameter ranges which can lead to the formation of hexagonally ordered pores observed in anodized aluminum oxide. Numerical simulations validate these results.