Modeling the Growth Kinetics of Anodic TiO2 Nanotubes.

The fundamental understanding of the barrier layer (δ(b)) growth in TiO2 nanotubes (NTs) is here established and compared with the classical metal oxidation theory from Mott and Cabrera. The role of δ(b) in the anodization of TiO2 NTs under different applied potentials and times was analyzed using scanning transmission electron microscopy (STEM). Contrary to the well-known case of anodic aluminum oxide, we found that δ(b) of TiO2 NTs progressively grows over time due to the nonsteady anodization regime. We then establish a relation between the phenomenological growth of the barrier layer with time and applied voltage, δ(b)(V,t) using the high-field Mott and Cabrera conduction theory. The developed model was found to be in excellent agreement with the experimental data from both STEM and anodization curves. On the basis of these results, the relationship between δ(b) and the anodization time and potential can now be quantitatively understood.