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J. Phys. Chem. C 2009, 113, 13610–13615
Layered Titanium Oxide Nanosheet and Ultrathin Nanotubes: A First-Principles Prediction Tao He,† Mingwen Zhao,*,†,‡ Xuejuan Zhang,† Hongyu Zhang,† Zhenhai Wang,† Zexiao Xi,† Xiangdong Liu,†,‡ Shishen Yan,†,‡ Yueyuan Xia,† and Liangmo Mei†,‡ School of Physics and State Key Laboratory of Crystal Materials, Shandong UniVersity, Jinan 250100, Shandong, China ReceiVed: April 7, 2009; ReVised Manuscript ReceiVed: May 31, 2009
We propose stable layered structures and ultrathin tubular configurations of titanium oxide (TiO2) nanomaterials on the basis of first-principles calculations within density functional theory. The thinnest TiO2 nanosheet is characterized by a reconstructed (001) bilayer of rutile TiO2, while ultrathin TiO2 nanotubes can be built by rolling up a TiO2NS. These nanotubes are predicted to have high stability, large Young’s modulus, and tunable electronic properties. A possible synthetic route toward these nanostructures is also presented. Introduction Since the report of photoelectrochemical characteristics of titania (TiO2) in water-splitting and hydrogen production,1 considerable efforts have been focused on this clean, cheap, and versatile material, because of its potential applications in catalyst,1 photocatalyst,2,4 chemical gas sensor,3 self-cleaning and antiseptic coatings,4 dye-sensitized solar cells (DSSCs),5,13 and spintronic devices.6 Numerous experimental and theoretical investigations were paid on enhancing its photoelectric efficiency to satisfy the requirement of energy industry. One of the major attempts is to manufacture low-dimension TiO2, gifting them much higher surface-to-bulk ratio, which benefits them capturing more photons, broadening the contact surface with adsorbates or water molecules, and easily being functionalized by high dose doping. Low-dimensional TiO2 with different kinds of morphologies have been produced, such as thin film,7,8 nanotubes,8-12 nanowires,13-15 and nanoparticles.13,16-18 Theoretical studies focused on their geometries,19-25 electronic properties,19,21,24,25 and light absorption capability.22 Among these TiO2 nanomaterials, TiO2 nanotubes (TiO2NTs) are of particular interest, because of their endurance, strong oxidizing power, large surface area, high photocatalytic activity, nontoxicity, and low production cost.8,21 Their hollow structures with naturally open-ends8,9,12 make them suitable for chemical reaction and molecule transport. Recently, TiO2 film composed of nanotubes was used in quantum dot solar cells possessing high photo-to-charge carrier generation efficiency (IPCE).26 The already-synthesized TiO2NTs always have diameters as thin as several nanometers and lengths up to several micrometers.27,29 To the best of our knowledge, the thinnest TiO2NTs synthesized in experiments are about 5 nm wide, with interlayer spacing of 7-8 Å in their crystallized walls.8,28,29 The structures of the walls remain unclear. Wang et al.8 claimed that TiO2NTs have an anatase structure. Viriya-empikul et al.29 used raw anatase TiO2 to compose TiO2NTs, but the anatase signals disappeared in all produced TiO2NTs. Maiyalagan et al.27 characterized the walls of TiO2NTs synthesized in their experiments as a mixture of anatase and rutile. Meanwhile, kinds of single-walled inorganic nanotubes (INTs), such as BN,30 WS2,31 and MoS232,33 nanotubes, ac* Corresponding author. E-mail:
[email protected]. † School of Physics. ‡ State Key Laboratory of Crystal Materials.
companied by unique properties have been revealed in both theoretical and experimental works. Questions arise: (1) Can TiO2 form stoichiometric single-walled TiO2NTs? (2) What are the new properties involved in these new materials? The energetic stability of a hypothetic ultrathin TiO2 nanotube composed of TiO6 octahedra with an O-Ti-O sandwich-like structure has been studied using semiempirical tight-binding20 and density functional based tight-binding21 methods. However, the possible synthetic routes toward these TiO2NTs and the properties related to the applications in solar energy harvests have not yet been reported. In this work, we propose a possible synthetic route to ultrathin TiO2 nanosheet (TiO2NS) from rutile (001) surface and subsequently to nanotubes (UTiO2NTs), using first-principles calculations within density functional theory (DFT). The geometric, energetic, and electronic properties of TiO2 nanosheet and nanotubes are investigated. The electronic structure modifications of UTiO2NTs in response to the doping of nonmetal group and element (NH and C) are also predicted. This work is expected to promote the realization and applications of these novel structures in nanoscience and nanotechnology. Methods and Computational Details We utilized plane wave basis Vienna ab initio simulation package (VASP),34 implementing DFT and the projectoraugmented wave (PAW) method.35,36 The electron-electron interaction was treated within generalized gradient approximation (GGA) with PW91 exchange-correlation functional.37 Structural optimization was performed by employing conjugate gradient (CG) procedures to converge systems to their instantaneous ground states. Atomic forces were converged to 0.01 eV/Å, and 0.1 meV precision was gained for the total energies. Positions of atoms and the size of the unit cell were fully relaxed without any symmetric restrictions. The energy cutoffs used for plane-wave expansion of electron wave functions are 450 eV for all elements. The Brillouin zone was sampled on a grid of 8 × 8 × 1 k points for the TiO2NS and 1 × 1 × 8 k points for the UTiO2NTs. A vacuum space up to 30 Å was applied to exclude the lateral images interaction. The cell we adopted in calculation of UTiO2NTs contains 2n Ti atoms and 4n O atoms, for both armchair (n, n) tubes and zigzag (m, 0) tubes. The scheme can reproduce the equilibrium structure of rutile TiO2. The lattice constants a and c given by the present calculations are 4.651 and 2.964 Å, respectively, in good agreement with
10.1021/jp9032244 CCC: $40.75 2009 American Chemical Society Published on Web 07/01/2009
Layered TiO2 Nanosheet and Ultrathin Nanotubes
J. Phys. Chem. C, Vol. 113, No. 31, 2009 13611
TABLE 1: Lattice Constants a and c and Band Gap (Egap) Values for TiO2 Calculated from GGA-Form DFT Using Either PAW Method or Ultrasoft Pseudopotentials (US-PP)a structure rutile anatase
method
a (Å)
c (Å)
Egap (eV)
PAW US-PP experiment PAW US-PP experiment
4.651 4.655 4.594b 3.817 3.818 3.785c
2.964 2.975 2.959b 9.623 9.691 9.512c
1.65 (2.43) 1.73 3.0d 1.88 (2.71) 2.00 3.2d
a Experiment values are also presented. The values in the parentheses are from LDA+U calculations. b Reference 38. c Reference 39. d Reference 40.
the experiment results, 4.594 and 2.959 Å.38 The results obtained using ultrasoft pseudopotentials (US-PP) are also listed in Table 1. The energy band gap (Egap) values given by the PAW method are 1.65 and 1.88 eV for rutile and anatase, a bit smaller than those from US-PP method by about 0.1 eV, which are in good agreement with other theoretical works.41,42 It is noteworthy that present calculations underestimate the Egap values of rutile and anatase by about 45% and 41% compared to experimental results, due to the well-known errors of the DFT-GGA scheme. This can be partially overcome by considering on-site Coulomb repulsion U of the 3d orbital of Ti atoms. We employed local density approximation plus U (LDA+U) to calculate the Egap values of TiO2 crystals. The Egap values of rutile and anatase are 2.43 and 2.71 eV under the effective U of 5.8 eV,6,43 which are comparable to the experimental data. Another advantage of the LDA+U method lies in revealing more a realistic local band morphology around the gap, which is crucial for the study of gap excitation. Additionally, it is interesting to see that both GGA and LDA+U methods give close values of the band gap difference between anatase and rutile, ∼0.2 eV, which also agree well with experimental data (See Table 1). This implies that the variation tendency of Egap of TiO2 nanostructures predicted on the basis of DFT-GGA calculations is reliable. Results and Discussion It is a common sense that an isolated layered structure is a starting point for tubular forms, such as graphene for carbon nanotubes. However, there is no stable layered structure for bulk TiO2. The stable phases of TiO2 materials observed in nature are rutile, anatase, and brookite, among which the rutile is the most stable. It is noteworthy that the structures of ultrathin sheets may differ significantly from the bulk materials because of surface reconstructions, which makes the stable layered structures possible.44 We calculated the stable configurations of TiO2 sheet with (001) surface of rutile TiO2, showed in Figure 1. Our calculations show that with decreasing sheet thickness, the Ti-O distance between two adjacent (001) bilayers (Ti-Oout) increases, while the Ti-O distance in a (001) bilayer (Ti-Oin) decreases (as shown in Figure 2a). When the thickness of sheet is reduced to 16.64 Å, corresponding to that of six (001) bilayers of rutile, the average Ti-Oout is elongated to 2.135 Å, while the Ti-Oin is shortened to 1.922 Å, compared to the values of rutile phase, 1.961 and 1.985 Å.This indicates that the interaction between (001) bilayers is weakened while the interaction in a (001) bilayer is enhanced as the TiO2 sheet becomes thinner, which facilitates the formation of single (001) bilayer by exfoliating TiO2 sheets.45 More interestingly, when the sheets contain less than four (001) bilayers (
