First-principles study of the nanotubes from the TiO₂ hexagonal sheet

Using the method based on the density functional theory, the geometric and electronic properties of the TiO₂ single-wall nanotubes, constructed by rolling the most stable nanosheet along the (n, 0) and (n, n) directions, have been investigated systematically. The nanotubes with size from n = 6 up to n = 20 have been modeled and studied. The strain energies of the nanotubes decrease monotonically as the radii of the nanotubes increase, regardless of the rolling direction. The band gaps of the nanotubes are increasing with the increase of the n value, approaching the value of the nanosheet. However, there is one nanotube significantly different from the others, i.e., the (6, 0) nanotube. The substantial structural change of (6, 0) nanotube causes a reduction of the band gap. Then, the isovalent sulfur (S) substitution and adsorption with the (6, 0) nanotube have been studied. Energetically, S adsorption at the inner surface is preferred. Electronically, the band gaps are further reduced by 35% for S substitution of oxygen and 22% for S adsorption, respectively, making the nanotube visible light-sensitive.