Modeling the Growth Kinetics of Anodic TiO₂ Nanotubes

Abstract

The fundamental understanding of the barrier layer (δ b ) growth in TiO 2 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 TiO 2 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 TiO 2 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.Theory of the oxidation of metals goes back to the late 1940s, when Mott and Cabrera discussed the growth of oxide thin films formed by anodic oxidation under an applied electric field. 1 In the Mott−Cabrera picture, the oxide growth of Ti and other valve metals (Al, Hf, Ta, W, etc.) is governed by the high-field conduction mechanism. 1−3 Under higher fields, the entry of a cation across the metal/oxide interface into the oxide is the oxide growth ratedetermining step. Thus, during oxidation, both the rate of oxidation and the rate-limiting process depend on the thickness of the oxide. 1 According to the underlying theory, the growth kinetics of the passive film is described by the relation between current density (j) and the electric field strength (E = V/δ b , where V is the applied potential and δ b the oxide thickness)Under this approach, the electrochemical oxidation of metals can lead to (i) stable continuous oxide 2 films, if the oxide is insoluble to the electrolyte, or (ii) nanoporous oxide films if the oxide is fairly soluble in the presence of an acidic electrolyte. 4 Indeed, in past decades, Al and Ti electrochemical anodization together with other valve metals (Hf, Ta, W, etc.) has been widely studied because highly regular hexagonal arrangements of pores or nanotubes can be obtained. Both anodic aluminum oxide (AAO) nanoporous and anodic TiO 2 nanotubes (NTs) have stimulated considerable scientific and technological interest with extensive use in practical nanostructures. 5−9 In particular, the distinct properties of anodic TiO 2 NTs make it highly attractable for a wide range of applications, mainly in renewal energy sources such as H 2 generation by water photoelectrolysis and dye-sensitized solar cells (DSCs). 6,7Because Zwilling et al. first introduced the anodic oxidation of Ti using fluoride-based electrolytes, 10 anodization parameters such as electrolyte composition, applied potential, time, temperature, and Ti surface roughness were found to significantly influence the growth and morphology of TiO 2 NTs. This influence is seen in the crucial geo...

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

“…Until now, the growth kinetics and self-organizing process of ATNTs have been attracting a lot of attention [8][9][10]. As found in the previous studies, the nanotube growth was attributed to the field-assisted dissolution (TiO 2 +6F¯+4H + →[TiF 6 ] 2− +2H 2 O) process [11][12][13][14][15].…”

Tailoring the Anodic Hafnium Oxide Morphology Using Different Organic Solvent Electrolytes

“…The evaluation of the mechanisms that lead to the formation and growth of self-ordered HfO 2 nanoporous/nanotubes, can be studied using current density [j(t)] curves ( Figure 2) [23][24][25][26][27]. The evolution of the HfO 2 barrier layer thickness (δ b ) at the bottom of the NTs (Figure 1) was also estimated from the j(t) curves ( Figure 3) [27]. According to the high-field conduction theory [28], the current density (j) is related to the voltage (V) drop across the barrier layer as follows:…”

“…where α and β are electrolyte and material-dependent constants and the (V/δ b ) ratio is the effective electric-field across δ b [27,28]. From Equation (6) we obtain,…”

Defect creation and Diffusion under electric fields from first-principles: the prototypical case of silicon dioxide

“…In our work we use Density Functional Theory (DFT) as in implemented in Quantum Espresso [7], [8]). A Perdew-Zunger [9] exchange-correlation functional together with a Norm-conserving pseudo-potential from the original QE library 1 have been used. The valence wave functions are expanded into plane waves basis up to an energy cutoff of 80 Ry.…”

“…Resistive switching phenomena taking place under electric fields on oxide-based memories have attracted much attention in the last decade. Under the modelling view point, a number of investigations have exploited empirical kinetic Monte Carlo (kMC) approaches [1], [2], [3], [4], [5] to model ionic transport. In all these approaches, the effect of the electric field on the migration energy change is accounted by means of the classical electric work of a point charge, Q in vacuum, first proposed by Cabrera and Mott [6], as part of their Model of Oxidation of Metals.…”