Energy minimization of single-walled titanium oxide nanotubes

Different crystal structures have been proposed as a basis for titanium oxide nanotubes. We have used atomistic simulation techniques to calculate the relative stability of nanotubes with these different crystal structures. Our approach is to use energy minimization, where the total interaction energy is calculated with interatomic potentials based on the Born model of solids. The results reveal nanotubes with the trititanate structure to be the most stable (at unit activity for water). Indeed, nanotubes with the trititanate structure were found to be thermodynamically more favorable than bulk trititanate for nanotube diameters greater than approximately 8 nm. However, the formation of cross-linking bonds between layers of the trititanate structure occurred frequently; this problem was eliminated by replacing two out of three Ti(4+) ions with Ti(3+) ions, although this resulted in a higher energy. Of the structures that do not contain hydrogen, chiral nanotubes made from (101) sheets of anatase are the lowest in energy, suggesting that this is the most likely structure for nanotubes synthesized at low water chemical potential. In general, the stability of the nanotubes increased as the nanotube diameter increased.