Quantitative relationship between nanotube length and anodizing current during constant current anodization

Highlights: • Ti anodization was performed by constant current rather than constant voltage. • The nanotube length was controlled by ionic current rather than dissolution current. • Electronic current can be estimated by the nanotube length and the anodizing current. • Dissolution reaction hardly contributes electric current across the barrier layer. - Abstract: The growth kinetics of anodic TiO₂ nanotubes (ATNTs) still remains unclear. ATNTs are generally fabricated under potentiostatic conditions rather than galvanostatic ones. The quantitative relationship between nanotube length and anodizing current (J_total) is difficult to determine, because the variable J_total includes ionic current (J_ion) (also called oxide growth current J_grow=J_ion) and electronic current (J_e), which cannot be separated from each other. One successful approach to achieve this objective is to use constant current anodization rather than constant voltage anodization, that is, through quantitative comparison between the nanotube length and the known J_total during constant current anodization, we can estimate the relative magnitudes of J_grow and J_e. The nanotubes with lengths of 1.24, 2.23, 3.51 and 4.70 μm, were formed under constant currents (J_total) of 15, 20, 25 and 30 mA, respectively. The relationship between nanotube length (y) and anodizing current (x =J_total=J_grow+J_e) can be expressed by a fitting equation: y=0.23(x-10.13), from which J_grow (J_grow = x -10.13) and J_e (∼10.13 mA) could be inferred under the present conditions. Meanwhile, the same conclusion could also be deduced from the oxide volume data. These results indicate that the nanotube growth is attributed to the oxide growth current rather than the dissolution current.