Formation Mechanism of ${\mathrm{H}}_2{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ Nanotubes

Formation mechanism of ${\mathrm{H}}_2{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ nanotubes by single-step reaction of crystalline ${\mathrm{T}\mathrm{i}\mathrm{O}}_2$ and NaOH has been investigated via transmission electron microscopy examinations of series specimens with different reaction times and extensive ab initio calculations. It was found that the growth mechanism includes several steps. Crystalline ${\mathrm{T}\mathrm{i}\mathrm{O}}_2$ reacts with NaOH, forming a highly disordered phase, which recrystallized into some ${\mathrm{H}}_2{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ thin plates. H-deficiency on the top surface leads to an asymmetrical environment for the surface ${\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7^{2-}$ layer. The calculations of the surface tension, elastic strain energy, interlayer coupling energy, and Coulomb force indicated that the asymmetrical environment is the principal driving force of the cleavage of the single sheets of ${\mathrm{H}}_2{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ from the plates and the formation of the multiwall spiral nanotubes.

Figure 1

(a) HRTEM image showing ${\mathrm{H}}_2{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ plates coexist with nanotubes after reaction of ${\mathrm{T}\mathrm{i}\mathrm{O}}_2$ with NaOH for 24 h. The inset (b) shows a low-magnification TEM image of the nanotubes after the reaction for three days.

Figure 2

Schematic models showing the effect of the alkali environment and the cleavage of the surface layer due to hydrogen deficiency on the surface. White balls: H; black balls: O; gray balls: Na. (a) A near stoichiometric ${\mathrm{H}}_2{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ surface in contact with many ${\mathrm{O}\mathrm{H}}^{-}$ and ${\mathrm{N}\mathrm{a}}^{+}$ ions. (b) Many ${\mathrm{H}}^{+}$ on the surface have been carried away by ${\mathrm{O}\mathrm{H}}^{-}$, forming ${\mathrm{H}}_2\mathrm{O}$. (c) When the surface hydrogen loss exceeds a critical value the surface strain energy becomes so large that the surface layer may overcome the coupling with the beneath layer and peel off from the plate.

Figure 3

(a) A relaxed curved fragment of a layer of ${\mathrm{H}}_{2-\delta }{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ crystal with $\delta =1.0$. The radius of curvature of the ${\mathrm{H}}_{2-\delta }{\mathrm{T}\mathrm{i}}_3{\mathrm{O}}_7$ fragment is $R=4.16\mathrm{n}\mathrm{m}$. (b) First-principle calculations of different forms of energy (per molecule) contributing to the curvature of a single trititanate sheet.

Figure 4

(a) Structure model of a single trititanate sheet. (b) A nanotube formed by rolling the trititanate sheet along the [010] direction with a chiral vector along the [001] direction and a chiral angle $\theta =0$. (c) Two-dimensional map of the total energy surface $E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}(\theta ,R)$ as a function of the chiral angle $\theta$ and $1/R$.

Figure 5

Competing contributions of coupling energy and Coulomb energy to the total lattice energy as functions of the number of shells in a multiwall nanotube.