Theoretical derivation of anodizing current and comparison between fitted curves and measured curves under different conditions.

Anodic TiO2 nanotubes have been studied extensively for many years. However, the growth kinetics still remains unclear. The systematic study of the current transient under constant anodizing voltage has not been mentioned in the original literature. Here, a derivation and its corresponding theoretical formula are proposed to overcome this challenge. In this paper, the theoretical expressions for the time dependent ionic current and electronic current are derived to explore the anodizing process of Ti. The anodizing current-time curves under different anodizing voltages and different temperatures are experimentally investigated in the anodization of Ti. Furthermore, the quantitative relationship between the thickness of the barrier layer and anodizing time, and the relationships between the ionic/electronic current and temperatures are proposed in this paper. All of the current-transient plots can be fitted consistently by the proposed theoretical expressions. Additionally, it is the first time that the coefficient A of the exponential relationship (ionic current j(ion) = A exp(BE)) has been determined under various temperatures and voltages. And the results indicate that as temperature and voltage increase, ionic current and electronic current both increase. The temperature has a larger effect on electronic current than ionic current. These results can promote the research of kinetics from a qualitative to quantitative level.