A mathematical model for initiation and growth of anodic titania nanotube embryos under compact oxide layer

The kinetics for initiation and growth of anodic titania nanotubes is not clear yet, because nanotubes are usually formed rapidly and initiation of nanotube embryos cannot be observed. By decoupling oxide growth and dissolution, nanotube embryos are fabricated beneath a pre-formed compact layer. Based on theories of ionic and electronic current, as well as the oxygen bubble mould effect, a mathematical model is developed for embryo initiation. The model exhibits high fidelity to measured current-time transients. Based on this model, the mechanism of nanotube embryo growth under different thickness of pre-formed layers is quantitatively explained. The embryos initiate without exposure to electrolyte, which is evidence against the traditional field-assisted dissolution theory.