14834
J. Phys. Chem. C 2009, 113, 14834–14837
Energetic Minimum Structures of Imogolite Nanotubes: A First-Principles Prediction Mingwen Zhao,*,†,‡ Yueyuan Xia,† and Liangmo Mei† School of Physics and State Key Laboratory of Crystal Materials, Shandong UniVersity, Jinan 250100, Shandong, China ReceiVed: June 15, 2009
We perform first-principles calculations to study the stable configurations and electronic structures of imogolite nanotubes. Two energetic minimum structures (Nµ ) 9, 12) are predicted and correlated to the natural and synthetic imogolite nanotubes. The electronic structures of both nanotubes are quite similar with a band gap of 5.2-5.3 eV. The conduction band minimum (CBM) mainly arises from the states of the hydroxyls on the outer wall, whereas the valence band maximum (VBM) is contributed from the O(2p) states of the SiO4 tetrahedrons located on the inner wall. These features are consistent with the asymmetric charge distribution in the outer and inner regions of the tubes and responsible for electronic modifications in response to surface defects or decorations. Introduction Imogolite, a hydrous aluminosilicate with a composition of Al2(OH)3SiO3OH in tubular form, has attracted considerable attention, because of its potential applications, e.g., as a catalyst support,1,2 molecular sieve, gas storage device,1,3,4 proton conductor, and ion retention and channel devices.5 Imogolite nanotubes were first discovered in volcanic deposits (natural imogolite),6 and then synthesized using different approaches (synthetic imogolite).7-9 The structures of these nanotubes are modeled by a curved gibbsite sheet, and orthosilicate anions associate to each vacant octahedral site of the gibbsite sheet. The Si-OH group that is one corner of a SiO4 tetrahedron is pointing toward the inside of the tube, and the other three O atoms are shared with Al octahedra in the gibbsite sheet (see Figure 1). It is generally accepted that synthetic imogolite nanotubes are highly monodisperse in diameter, irrespective of synthesis conditions. The external diameter of an isolated synthetic tube is ∼22 Å.9-12 Experimental measurements showed that the natural and synthetic imogolite nanotubes may have different diameters. The center-to-center spacing between the tubes is ∼22.7 Å for natural imogolite nanotubes,7,8 which is shorter than that for synthetic ones, 26-28 Å.9,12 The following question naturally arises: Are such differences due to the intrinsic disorder of the tubes in the bundles or different number of gibbsite units around the circumference of the natural and synthetic imogolite nanotubes? The structural monodispersity of imogolite nanotubes is related to the energy minimum of these nanotubes. For carbon nanotubes, the strain energy required to roll up a graphene into a tube decreases monotonically with the increase of tube diameter. Therefore, no suitable energy minimum is available to produce nanotubes with a desired diameter. The tubular structure of imogolite, however, was attributed to a shortening of Al-O distances of vacant octahedral sites that arise from size misfit caused by bonding of orthosilicate anion with gibbsite sheet. The synthetic imogolite nanotubes were determined to have a circumference composed of 12 gibbsite units (Nµ) 12), i.e., 24 Al atoms around the circumference.4,13 This is further supported by the recent theoretical calculations using the densityfunctional-tight-binding method (DFTB),14 where the imogolite † ‡
School of Physics. State Key Laboratory of Crystal Materials.
nanotube with Nµ ) 12 was revealed as an energy minimum structure. Electron diffraction measurements suggested that the most likely structure model of natural imogolite nanotubes contains 10 gibbsite units (Nµ ) 10) around the circumference corresponding to a tubular diameter of 21 ( 0.5 Å.12 However, no energy minimum was found at Nµ ) 10 from the previous theoretical investigations. On the other hand, Farmer and Fraser concluded that the natural imogolite is composed of 12 gibbsite units (Nµ ) 12).8 Molecular dynamics simulations showed the potential energies of imogolite nanotubes have a minimum at Nµ ) 14-16.15 Because imogolite nanotubes have large-size supercells (containing several hundreds of atoms), most of the present theoretical investigations are based on efficient empirical ´ lvaforce field13,16 or tight-binding methods.14 Very recently, A rez-Ramfrez first studied the structural and electronic properties of imogolite nanotubes using first-principles calculations within density functional theory (DFT).16 However, first-principles study of the energy minimum of imogolite nanotubes has not yet been reported. Moreover, in view of the potential device applications of imogolite nanotubes, detailed analysis of the electronic structures is desirable. In this contribution, we performed first-principles calculations within DFT to study the energetics of imogolite nanotubes as a function of tube diameter with Nµ ) 7-14. The electronic properties of imogolite nanotubes are addressed from the wave function analyses. We expect this work to provide vital information for the characterization and utilization of imogolite nanotubes. Computational Details All the calculations were performed using the SIESTA code.17-19 A localized linear combination of numerical atomicorbital basis sets was adopted for the valence electrons, and norm-conserving nonlocal pseudopotentials constructed using the Trouiller-Martins scheme20 were employed for the atomic core. The nonlocal components of the pseudopotentials were expressed in the fully separable form of Kleinman and Bylander.21,22 The Perdew-Burke-Ernzerhof (PBE) form generalized gradient approximation (GGA) corrections were used for the exchange-correlation potential.23 The atomic orbital basis set was of double-ζ quality with inclusion of polarization functions (DZP). An auxiliary basis set of a real-space grid was
10.1021/jp9056169 CCC: $40.75 2009 American Chemical Society Published on Web 07/09/2009
Energetic Minimum Structures of Imogolite Nanotubes
J. Phys. Chem. C, Vol. 113, No. 33, 2009 14835
Figure 1. Polyhedron representations (left panel) and atomic structures (right panel) of (a) imogolite sheet and (b) imogolite nanotube with Nµ ) 9. (c) The local map of atomic structure. Si, Al, O, and H atoms are represented by cyan, purple, red, and white balls, respectively. Some representative bonds are also indicated.
used to expand the electron density for numerical integration. A kinetic energy cutoff of 100 Ry was employed to control the fineness of this mesh. Imogolite nanotubes were placed in a supercell repeated along the z direction with a vacuum region of up to 10 Å along the x and y directions to exclude the mirror interactions. The Brillouin zone was sampled with a k-point grid of (1 × 1 × 6), according to the Monkhorst-Pack scheme.24 The atomic positions along with the lattice vectors were optimized by using a conjugate gradient (CG) algorithm, until each component of the stress tensors was reduced below 0.02 GPa and the maximum atomic forces were less than 0.01 eV/ Å. The total energy of the tubes was converged to within 0.01 eV, corresponding to an energy error of less than 0.003 kJ/mol of atoms. The electron density of states, D(E), was calculated using the Gaussian smear technique:
D(E) ) 1/N ×
∑(∆π1/2)-1 exp(-(Ebk /∆)2) b ki
i
ki point where Ebki is the energy of the ith electron band at the b in the Brillouin zone and N is the total number of k points. A smear parameter (∆) of 0.15 eV was adopted in these calculations. The optimized cell parameters of gibbsite crystal in the space group P21/n, a ) 8.84 Å, b ) 5.12 Å, c ) 9.69 Å, and β ) 95.79°, from the present calculations agree well with the experimental results, which are a ) 8.68 Å, b ) 5.09 Å, c ) 9.74 Å, and β ) 94.54°, and the results of other DFT calculations, a ) 8.74 Å, b ) 5.11 Å, and c ) 9.80 Å.25 The relaxed lattice parameters for R-silica are a ) 5.10 Å and c ) 5.56 Å, close to the experimental data a ) 4.92 Å and c ) 5.40 Å. We also calculated the electron density of states (DOS) of gibbsite crystal. The valence states of the gibbsite spread into two parts, one (-20 to -17 eV) originates from the O(2s) states, and another (-9 to 0 eV) comes from the O(2p), Al(3s, 3p), and H(1s) states. The relative positions of the upper valence band edge (set to 0 eV) and the O(2s) band agree well with the XPS study26 and other DFT calculations.27 All of these results
14836
J. Phys. Chem. C, Vol. 113, No. 33, 2009
Figure 2. Variation of the strain energy of imogolite nanotubes relative to imogolite sheet as a function of Nµ. The error bars (
