A theory of the spontaneous formation of spatially regular hexagonal arrays of nanopores in aluminum oxide film growing during aluminum anodization is presented. Linear stability analysis shows that, in certain ranges of the applied voltage and electrolyte pH, the oxide film is unstable with respect to perturbations with a well-defined wavelength. The instability is caused by a positive feedback between the oxidation-dissolution rates and variations of electric field caused by perturbations of the metal-oxide and oxide-electrolyte interfaces. The competition between this instability and the stabilizing effects of the Laplace pressure and elastic stress provides the wavelength selection mechanism. The hexagonal ordering of pores results from the resonant quadratic nonlinear interaction of unstable modes.
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Singh et al. (2005) studied this question.
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