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

Abstract

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.

Simulation of anodizing current-time curves and morphology evolution of TiO2 nanotubes anodized in electrolytes with different NH4F concentrations

“…Two theoretical formulas of the ionic current and the electronic current were derived from the general definitions of ionic conductivity and electronic conductivity [37]. The fitted curves deduced theoretically all show an excellent accordance with the measured curves under different temperatures and voltages [37]. Here, we focused on the effect of NH 4 F concentration on the morphological structure, length and porosity of TiO 2 nanotubes.…”

“…Herein, the three stages of the total anodizing current density-time curves can be elucidated by the electronic current and the 'oxygen bubble mold' [32][33][34][35][36][37]. When the constant voltage (60 V) is applied on the cell, the electric field is high, and the ionic current is the predominant mode of charge transport, the total anodizing current decreases with the increase of barrier oxide [34].…”

“…1(marked 0.2 wt%). According to the model of ionic and electronic current [34,37], it is because that the electronic current is too low when the amount of NH 4 F is small. For the three curves of different concentrations (0.2 wt%, 0.4 wt% and 0.6 wt% NH 4 F), the equilibrium current increases with the amount of NH 4 F and it is because ionic current and electronic current both increase with the amount of NH 4 F. The equilibrium current densities obtained at 300 s in the electrolytes with 0.2 wt%, 0.4 wt% and 0.6 wt% NH 4 F were ~2.20 mA·cm -2 , ~7.75 mA·cm -2 , ~10.35 mA·cm -2 , respectively.…”

“…However, as Hebert et al [5,31] Based on the 'plastic flow' model [16,17] rather than 'field-assisted dissolution', the 'oxygen bubble mold' and the electronic current model were proposed by Zhu and coworkers [21,22,32,33] to explain the formation of nanotube embryo and gaps around the nanotubes [34][35][36]. Two theoretical formulas of the ionic current and the electronic current were derived from the general definitions of ionic conductivity and electronic conductivity [37]. The fitted curves deduced theoretically all show an excellent accordance with the measured curves under different temperatures and voltages [37].…”

“…The present study takes into account the effect of different concentrations of NH 4 F and we associate the difference of fluoride content with the difference of the corresponding current density-time curves to find out the inherent reasons. By a theoretical formula [37], the total anodizing current density-time curve was separated into two parts: the ionic current density-time curve and the electronic current density-time curve. It shows that, when the NH 4 F concentration increases, the corresponding curves have obvious variation.…”