Simulations of Anodic Nanopore Growth Using the Smoothed Boundary and Level Set Methods

Self-ordered nanostructured films can be fabricated through an electrochemical oxidation process called anodization. These films, with features on the order of tens of nanometers, have potential applications ranging from solar cells to medical devices. The most widely examined anodic nanostructured film is nanoporous anodic alumina. Although several models have been developed to describe the growth and self-organization of nanoporous anodic alumina, none have captured the full range of observed behavior. Here, we present a multidimensional extension of a one-dimensional model of anodization, and its implementation utilizing the smoothed boundary and level set methods, which permit the simulation of a growing pore on a fixed, regular computational grid. The simulations capture much of the experimental behavior for a range of applied potentials and electrolyte pH values. Most importantly, the simulated pore geometry is shown to be insensitive to the electrolyte pH, as is observed experimentally but had not been captured in previous models. This improvement stems from the shift in the equilibrium concentration of adsorbed O^2- and OH^- species as the electrolyte pH changes. The absence of plastic flow in the model has been identified as a likely source of two primary differences between the simulation results and the experimental data.