Thickness Dependence of Size and Arrangement in Anodic TiO₂ Nanotubes

The degree of self-assembly and the size variation of nanotubular structures in anodic titanium oxide prepared by the anodization of titanium in ethylene glycol containing 0.25 wt % $NH_4F$ at 40 V were investigated as a function of anodization time. We found that the degree of self-assembly and the size of the nanotubes were strongly dependent on thickness deviation and thus indirectly on anodization time, as the thickness deviation was caused by the dissolution of the topmost tubular structures at local areas during long anodization. A large deviation in thickness led to a large deviation in the size and number of nanotubes per unit area. The dissolution primarily occurred at the bottoms of the nanotubes ($D_{bottom}$) in the initial stage of anodization (up to 6 h), which led to the growth of nanotubes. Dissolution at the tops ($D_{top}$) was accompanied by $D_{bottom}$ after the formed structures contacted the electrolyte after 12 h, generating the thickness deviation. After extremely long anodization (here, 70 h), $D_{top}$ was the dominant mode due to increase in pH, meaning that there was insufficient driving force to overcome the size distribution of nanotubes at the bottom. Thus, the nanotube array became disorder in this regime.