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On the Stability of Dititanate Nanotubes: A Density Functional Theory Study Anna M. Ferrari,* M. Lessio, D. Szieberth, and L. Maschio Dipartimento Chimica IFM, UniVersita` di Torino and NIS, Nanostructured Interfaces and Surfaces - Centre of Excellence, V. P. Giuria 7, 10125 Torino Italy ReceiVed: August 20, 2010; ReVised Manuscript ReceiVed: October 27, 2010
Nanotubes having the H2Ti2O5 stoichiometry have been studied by DFT methods in the diameter of ∼20-60 Å. Dititanate nanotubes have been found to be more stable than the dry lepidocrocite nanotubes and the tubes based on trititanate (H2Ti3O7) structures at all diameters investigated. At diameters 40 Å. It is characterized by the same stepped lepidocrocite structure of the flat surface as indicated by the Ti3-O9 distances (∼2.37 Å) close to the value of the reference film (2.31 Å); see
Figure 3. Strain energies ES and relative strain energies ERS of DT1 and DT2, trititanate, and lepidocrocite nanotubes. The infinity symbol marks the flat slab values.
DFT Study of the Stability of Dititanate Nanotubes
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Figure 4. PDOSs plots of DT1 and DT2 flat surfaces and (25,0) DT1 and DT2A nanotubes showing the top of the valence band. For comparison PDOSs of a dry lepidocrocite flat slab and of a lepidocrocite (n,0) nanotube of approximately the same size have been included. See Figure 1 for labeling of atoms. The labels “Oext” and “Oint” refer to all the oxygens located at the inner or at the outer surfaces of the tubes.
Figure 5. Schematic view of DT2A nanotubes.
Table 1 and Figure 5. At these D, the curvature is small and the tensile strain at the external surface can be sustained without the break of the bridge centered at the O2 oxygens. The related distances, Ti1-O2 and Ti3-O2, are only slightly elongated (1.96
and 2.14 Å, respectively, in the case of the (19,0) tube) with respect to the corresponding values for the flat surface (1.91 and 2.05 Å, respectively), to which the tubes smoothly approach by increasing D. At the inner wall, the compressive strain is still not negligible and some of the Ti-O distances are significantly shortened (see Ti7-O8 distances, Table 1). ES is quite small (0.04 eV/Ti atom) already for the (19,0) tube and exhibits a minimum at D ∼ 50 Å where ES becomes slightly negative (-0.01 eV); see Figure 3. A second structure, denominated DT2B, has been recognized in the region D < 35 Å. The morphology of DT2B is more similar to a hydrated lepidocrocite than to the stepped lepidocrocite typical of the dititanate slabs. In fact, the Ti3-O9 distances, 2.18 and 2.17 Å for (12,0) and (15,0)-DT2B, respectively, are very close to the corresponding values computed for the dry lepidocrocite (2.17 Å); even the bond distances related to O8 atoms, Ti5-O8 and Ti7-O8, (1.82 and 1.82 for (12,0)-DT2B; 1.83 and 1.84 for (15,0)-DT2B) match the corresponding values computed for the dry lepidocrocite (1.82 Å); see Table 1 and Figure 6. To sustain the tensile strain at the external surface, the bridges centered at the O2 oxygens are opened and replaced by hydrogen bonds HBs between adjacent hydroxyls. For smaller nanotubes (D < 40 Å), the geometry of the interacting hydroxyls (d(O · · · H) ) 1.7-1.5 Å) is effective to create stabilizing hydrogen contacts whereas at larger D, d(O · · · H) becomes too short and destabilizes the structure. At the inner wall, the compressive strain is more sustainable as indicated by the negligible deviations in the Ti5-O8 and Ti7-O8
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Figure 6. Schematic view of DT2B nanotubes.
(10,0) and (12,0)-DT2A) requires to be corrected for the extrastabilization from the intermolecular HBs (corrected ES ) 0.18 and 0.09 eV/Ti atom for (10,0) and (12,0)). Corrected ES values show a minimum around 40 Å, thus increase with D and do not approach the flat slab limit indicating the presence of a metastable morphology. The overall behavior of ES for DT2 nanotubes are summarized in Figure 3. We can notice that (i) all the three investigated DT2 structures exhibit a minimum value of ES providing the indication that asymmetric slab prefer to adopt a curved shape; (ii) at D > 40 Å, the DT2A is the less strained structure thus indicating that small diameter nanotubes reduce the strain expelling water from the inner wall; and (iii) DT2C nanotubes show the largest ES at all the investigated D. ERS values, as seen in Figure 3 and Table 1, show that irrespective to the value of D DT1 nanotubes are always the most stable structures. The band gap of DT2 tubes varies from 5.2 to 5.4 eV, very close to the value computed for the dry lepidocrocite. Computed PDOSs of DT2A nanotubes exhibit the presence of tails at the top of the valence states as observed for DT1 tubes; however this feature is less evident than in DT1 tubes and the upshift of the edge of the valence band is intermediate between dry lepidocrocite and DT1 tubes. This is the result of two contributions. First, the dehydration at one side of the nanosheet causes a shift of valence band edge toward higher energy in DT2 flat surface with respect to DT1 (-0.269 vs -0.285 hartree) with a high contribution from the oxygen atoms connecting the lepidocrocite-like segments (O8) and skeleton oxygens closer to the surfaces of the slabs (Figure 4a). The cause of the change in the electronic structure can be traced back to the change in the wall structure of the slab; one side of the Ti-O bridges between the “lepidocrocite” parts become longer (Ti7-O8 and Ti1-O4 distances) while the other part (Ti3-O4 and Ti5-O8 distances) shorter. Second, moving from the flat DT2 to the (25,0) DT2A the valence edge shifts to lower energies with the concomitant narrowing of the bands constituting the valence edge (Figure 4b). The shift of the bands corresponding to the oxygen atoms on the internal surface of the tube wall that was observed in case of the DT1 tubes is missing due to the dehydration that decreases the congestion on the internal surface.
Figure 7. Schematic view of DT2C nanotubes.
Conclusions
distances with respect to the lepidocrocite slab; see Table 1. ES of DT2B shows a minimum close to D ) 33 Å followed by a diverging trend. Finally the third polymorph, denominated DT2C, is distinguished by a reconstruction to a more anatase-like morphology as also suggested by the long Ti3-O9 distances that changes from 3.36 to 3.06 Å for (10,0) and (25,0) tubes; see Figure 7. To sustain the tensile strain at the external surface, the bridges centered at the O2 oxygens are opened and replaced by hydrogen bonds HBs between adjacent hydroxyls. At small D, the geometry of the interacting hydroxyls (d(O · · · H) ) 1.7-1.6 Å) is effective to create stabilizing hydrogen contacts whereas at larger D, d(O · · · H) becomes too short and destabilizes the structure. The water molecules weakly bound to the nanotube inner side at small D lose any contact with the nanotube wall (d(Ti-Ow ) 5.96 Å) and prefer to rearrange to form intermolecular hydrogen bonds. The stabilizing effect induced by water HBs have been estimated to be 0.45 and 0.098 eV per water molecule for (10,0) and (12,0) DT2A nanotubes, respectively. Strain energies increase with the nanotube diameter, Table 1; however, a proper estimate of ES for small nanotubes (namely
Dititanate nanotubes have been investigated by means of accurate DFT calculations. Two different structures have been considered: DT1, in which water dissociates at both side of the slab; and DT2, in which dissociation occurs only at one side of the sheet, whereas at the other border water is molecularly weakly bound. The energy strain of DT2 nanotubes are in general smaller than those of DT1 and exhibit a minimum value indicating that asymmetric slab prefer to adopt a curved shape. However, the lower strain of the DT2 structure is overcompensated by the higher thermodynamic stability of the DT1 nanotubes. The stability of the dititanate tubes have been compared to the lepidocrocite-like and to trititanate tubes calculated in an earlier work,24,25 and the DT1 structure has been found to be more stable at all investigated diameters, indicating that (i) the lepidocrocite TiO2 nanotubes are susceptible to hydration, (ii) the hydration ratio of 1:2 of dititanates is favored with respect to the ratio of 1:3 of trititanates. However, it can be noticed that the energy difference is rather small and could be easily overcome by entropy effects. The band gaps of DT1 and DT2 nanotubes and nanosheets are considerable larger than bulk TiO2 (more than 1 eV) and
DFT Study of the Stability of Dititanate Nanotubes they change with the diameter of the tubes only in a relatively narrow energy range. The presence of hydroxyl groups in DT1 nanotubes produce tails in the density of the states at the top of the valence band that pushes the edge of the band up; however this feature is less evident in DT2 tubes. Acknowledgment. We acknowledge the CINECA award under the ISCRA initiative, for the availability of high performance computing resources and support and the CINECAINSTM agreement for cofinanced Key Project. References and Notes (1) Motonari, A.; Jinting, J.; Seiji, I. Curr. Nanosci. 2007, 3, 285– 295. (2) Bavykin, D. V.; Friedrich, J. M.; Walsh, F. C. AdV. Mater. 2006, 18, 2807–2824. (3) Fujishima, A.; Zhang, X.; Tryk, D. A. Surf. Sci. Rep. 2008, 63, 515–582. (4) Ni, M.; Leung, M. K. H.; Leung, D. Y. C. Renewable Sustainable Energy ReV. 2007, 11, 401–425. (5) Tang, Z.; Ji, Y.; Xu, Y.; Xu, R.; Zhang, Z.; Zhou, Z. Sens. Lett. 2008, 6, 933–937. (6) Deng, D.; Kim, M. G.; Lee, J. Y.; Cho, J. Energy EnViron. Sci. 2009, 2, 818–837. (7) Kasuga, T.; Hiramatsu, M.; Hoson, A.; Sekino, T.; Niihara, K. Langmuir 1998, 14, 3160–3163. (8) Wang, Y. Q.; Hu, G. Q.; Duan, X. F.; Sun, H. L.; Xue, Q. K. Chem. Phys. Lett. 2002, 365, 427–431. (9) Saponjic, Z. V.; Dimitrijevic, N. M.; Tiede, D. M.; Goshe, A. J.; Zuo, X.; Chen, X.; Barnard, A. S.; Zapol, P.; Curtiss, R.; Rajh, T. AdV. Mater. 2005, 17, 965–971. (10) Moglievsky, G.; Chen, Q.; Kulkarni, H.; Kleinhammes, A.; Mullins, W. M.; Wu, Y. J. Phys. Chem. C 2008, 112, 3239–3246. (11) Ferrari, A. M.; Szieberth, D.; Zicovich-Wilson, C. M.; Demichelis, R. J. Phys. Chem. Lett. 2010, 1, 2854–2857. (12) Akita, T.; Okumura, M.; Tanaka, K.; Ohkuma, K.; Kohyama, M.; Koyanagi, T.; Date, M.; Tsubota, S.; Haruta, M. Surf. Interface Anal. 2005, 37, 265–269.
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