Nanoscale pore formation dynamics during aluminum anodization

A theoretical analysis of nanoscale pore formation during anodization reveals its fundamental instability mechanism to be a field focusing phenomenon when perturbations on the minima of the two oxide interfaces are in phase. Lateral leakage of the layer potential at high wave number introduces a layer tension effect that balances the previous destabilizing effect to produce a long-wave instability and a selected pore separation that scales linearly with respect to voltage. At pH higher than 1.77, pores do not form due to a very thick barrier layer. A weakly nonlinear theory based on long-wave expansion of double free surface problem yields two coupled interface evolution equations that can be reduced to one without altering the dispersion relationship by assuming an equal and in-phase amplitude for the two interfaces. This interface evolution equation faithfully reproduces the initial pore ordering and their dynamics. A hodograph transformation technique is then used to determine the interior dimension of the well-developed pores in two dimensions. The ratio of pore diameter to pore separation is found to be a factor independent of voltage but varies with the pH of the electrolyte. Both the predicted pH range where pores are formed and the predicted pore dimensions are favorably compared to experimental data. (c) 2002 American Institute of Physics.