Ab initio study of ice nanotubes in isolation or inside single-walled carbon nanotubes

The results of an ab initio study of the properties of the ice nanotubes in isolation or inside the single-walled carbon nanotubes (SWCNTs) are reported. We consider both the van der Waals (vdW) interactions and the atomic vibrational entropy effects and find that all the ice nanotubes having different $m$-polygonal $(m=4–8)$ cross sections either in isolation or lying inside the (10,10) SWCNTs are stable. The octagonal ice nanotube is the most stable one followed by the hexagonal ice nanotube, a result in disagreement with the earlier workers. Thus, striking differences between the results of an ab initio and the empirical potential studies are observed. The ice nanotubes are coupled to the carbon nanotube only by the vdW interactions. Our analysis of the computed binding energy and the structural parameters shows that the ice tube inside the wide carbon nanotube experimentally observed by Maniwa et al. [J. Phys. Soc. Jpn. 71, 2863 (2002)] has a hexagonal structure. The electron energy gap for the ice nanotubes lie in the ultraviolet in the energy range, $3.32–3.92\mathrm{eV}$. The optical absorption for the isolated hexagonal and octagonal ice nanotubes appears in the ultraviolet region in the energy range, $3.7–4.0\mathrm{eV}$. The optical absorption of the (10,10) carbon nanotube is not affected significantly by the encapsulated hexagonal and octagonal ice nanotubes with the exception that all the absorption peaks are displaced toward the low-energy side by about $0.1–0.2\mathrm{eV}$.

Figure 1

(Color online) (a) The actually calculated minimum-energy atomic configuration of a part of an ice nanotube having hexagonal cross section. (b) The atomic configuration of a part of the optimized (10,10) carbon nanotube encapsulating the hexagonal cross-sectional ice nanotube. In both the figures, the dark(red) circles represent the O atoms whereas the small open circles show the H atoms. In (b), the shaded big circles denote the C atoms of the host carbon nanotube.

Figure 2

Electronic structure and the density of electron states (DOS) in the vicinity of the Fermi level for the isolated ice tubes: (a) hexagonal and (b) octagonal.

Figure 3

Same as Fig. 2 but for the two unit cells of the (10,10) carbon nanotube (a) pristine and (b) that with an encapsulated hexagonal ice nanotube.

Figure 4

Optical-absorption spectra for the hexagonal and octagonal ice tubes (a) isolated and (b) encapsulated inside (10,10) carbon nanotube.