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J. Phys. Chem. C 2007, 111, 9652-9657
First-Principles Design of Well-Ordered Silica Nanotubes from Silica Monolayers and Nanorings Mingwen Zhao,*,†,‡ Z. H. Zhu,‡ J. D. Gale,§ Yueyuan Xia,† and G. Q. Lu‡ School of Physics and Microelectronics, Shandong UniVersity, Jinan 250100, People’s Republic of China, ARC Centre of Functional Nanomaterials, School of Engineering, UniVersity of Queensland, Brisbane 4072, Australia, and Department of Applied Chemistry, Nanochemistry Research Institute, Curtin UniVersity of Technology, GPO Box U1987, Perth 6845, Western Australia ReceiVed: January 3, 2007; In Final Form: March 14, 2007
The structural characters and the possible synthetic routes of the hypothetical silica nanotubes (NTs) have been explored by using first-principles calculations. Silica nanorings (NRs) based on linked three-membered rings (3MRs) and silica monolayers (MLs) consisting of hybrid two- and six-membered rings (2-6MRs) or pure four-membered rings (4MRs) are presented as promising precursors for the fabrication of well-ordered silica NTs. Three kinds of silica NTs, namely, 2-3MR-NTs, 2-6MR-NTs, and 4MR-NTs, built from NRs and MLs are predicted to have lower strain energies than the edge-sharing silica fiber, among which the 4MRNTs are energetically most favorable. The electronic structures of these silica nanomaterials are also discussed to promote the potential applications in nanoscience and nanotechnology.
Introduction Materials with reduced dimensions have been attracting much attention due to their unique properties that differ from those of the bulk material. Silica nanoclusters and nanotubes (NTs) are of particular interest for biocatalysis, bioseparation,1 nanoscale electronic devices,2 nanoscale reactors,3 and protection of environmentally sensitive species.4 Low-dimensional silica nanostructures differ from bulk silica in that they possess diverse metastable building blocks with chain, ring, cage, and tubular configurations that are formed by assembling two-, three-, and four-membered rings (2MRs, 3MRs, 4MRs).5-11 This enriches the database of silica nanostructures and provides vital information for understanding the growth mechanisms of silica nanomaterials. The hypothetical nanostructures proposed from theoretical studies offer great opportunities for the experimental works that are seeking to realize them. So far, quasi-onedimensional (Q1D) silica NTs with thick walls (tens of nanometers) have been synthesized via various methods,12 but the atomic arrangement in the amorphous walls bears no resemblance to that of the well-ordered silica nanostructures modeled by first-principles calculations.11 Exploring Q1D ordered silica NTs remains a challenge. To the best of our knowledge, the possible synthetic pathway toward a family of well-ordered Q1D silica NTs is still far from being established, either experimentally or theoretically. An effective way to design a synthetic route toward tubular materials is to start from a precursor structure. In the case of silica NTs, we focus on two types of precursors. One is silica monolayers (MLs) built on the base of the two-dimensional (2D) network of SiO4 tetrahedra grown on a Mo substrate.13,14 Wellordered silica NTs can be formed by rolling the MLs in an analogue of the relationship between a single graphene sheet and carbon nanotubes (CNTs). Another is silica nanorings (NRs) †
Shandong University. University of Queensland. § Curtin University of Technology. ‡
consisting of linked 3MRs. The stability of these NRs and the possible synthetic routes toward them have been proposed by theoretical efforts.5e,8,9 The growth of silica NTs may also be achieved via the combination reaction of these NRs. In this work, we designed the synthetic routes from silica MLs and NRs toward well-ordered silica NTs on the basis of these precursors via first-principles calculations. The manufacturability of these NTs has been evaluated from the point of view of the energetic advantage over the real silica fiber combined with potential energy profile calculations along the designed reaction pathway. The structural characteristics and electronic properties are also predicted to promote potential applications in nanoscience and nanotechnology. Methods and Computational Details We have performed first-principles calculations based on density functional theory (DFT) by utilizing the SIESTA code,15 where the exchange-correlation potential is a generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE).16 Nonlocal pseudopotentials constructed using the Trouiller and Martins scheme17 were employed for the atomic core, while a linear combination of numerical pseudized atomic orbitals was adopted as a basis set for the description of the valence electrons. The atomic orbital basis set was of double-ζ quality with inclusion of polarization functions (DZP), with a split-norm value for partitioning of the zetas into inner and outer regions of 0.25. The basis functions were strictly localized within radii that corresponded to a confinement energy of 0.01 Ry, with the exception of the polarization functions where a fixed radius of 6.0 Bohr was specified. An auxiliary basis set of a real-space grid was used to expand the electron density for numerical integration. A kinetic energy cutoff of 250 Ry was employed to control the fineness of this mesh. A one-dimensional periodic boundary condition, along the axial direction, was applied to the silica NTs, while a vacuum region of up to 15 Å along the radial direction was specified to
10.1021/jp070032+ CCC: $37.00 © 2007 American Chemical Society Published on Web 06/13/2007
Well-Ordered Silica NTs from Silica MLs and NRs
J. Phys. Chem. C, Vol. 111, No. 27, 2007 9653
Figure 1. The schematic representation of the formation of silica NTs from silica MLs and NRs. (a) 2-6MR-ML(I), (b) (7,0) 2-6MR-NT, (c) 4MR-ML, (d) (9,0) 4MR-NT, (e) (SiO2)16 3MR-NR, (f) (SiO2)32 cluster, and (g) 2-3MR-NT(III). The dotted rectangles indicate the size of the supercells.
ensure that isolated Q1D silica NTs were considered. The Brillouin zone of the silica NTs was sampled with a k-point grid of (1 × 1 × 8), where the z axis is the repeat direction, according to the Monkhorst-Pack scheme.18 This k-point grid was converged within 0.1 meV/SiO2 against a 1 × 1 × 16 k-point grid for these tubes. For the silica MLs, a 2D periodic boundary condition along the x and y directions and a vacuum region of up to 15 Å along z direction were specified. A 16 × 16 × 1 k-point grid was employed for the silica MLs. Atomic coordinates were first annealed at 600 K for 1.0 ps using NVT dynamics with a Nose´ thermostat in order to remove any soft unstable modes and then subsequently optimized using a conjugate gradient (CG) algorithm until the maximal atomic force was below 0.01 eV/Å. The lattice vectors were also
optimized simultaneously, with each component of the stress tensor below 0.02 GPa. The strain energy (Es) was calculated as the difference between the total energy per SiO2 unit of silica NTs and that of R quartz. This scheme reproduces the structural properties of R quartz well, with the lattice constants of a ) 4.88 Å and c ) 5.41 Å, in good agreement with the experimental data, a ) 4.92 Å and c ) 5.40 Å. Note that the underestimation of the unit cell here, in contrast to the usual overestimation by GGAs, is due to partial cancellation with the effect of the basis set confinement, which tends to lower the volume. The Si-O bond length and O-Si-O bong angle of the atomic chain consisting of 2MRs of silica fiber are 1.68 Å and 90.9° from our calculations, comparable to the values from the B3LYP hybrid functional, 1.68 Å and 89.8°.6
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TABLE 1: Structural Parameters and Strain Energies (Es) of Selected Silica Nanotubes (NTs) and Monolayers (MLs) with Different Morphologiesa configurations
2-6MR-NT
4MR-NT
2-3MR-NT
2-6MR-ML
∆(O-Si-O) (°)
dSi-O (Å) (5,0) (6,0) (7,0) (4,4) (5,5) (6,6) (5,0) (9,0) (12,0) (I)
1.68,1.63 1.68,1.63 1.68,1.62 1.68,1.63 1.68,1.63 1.68,1.63 1.66,1.63 1.66,1.64 1.66,1.64 1.69,1.65
(II)
1.68,1.64
(III)
1.67,1.64
(IV)
1.68,1.64
(I) (II)
1.68,1.62 1.68,1.64 1.66 1.68 1.68
4MR-ML isolated 2MR chain fiber (silica-w)
5.7 6.0 5.7 6.3 8.7 7.5 5.6 5.6 5.5 9.8 -0.1 6.3 -0.1 5.6 1.4 6.9 -0.1 4.7 6.2 6.1 10.0 10.0
5.5 5.3 5.5 5.7 3.2 6.2 -0.8 -0.5 -0.7 6.0 -1.7 6.0 -0.1 5.6 1.4 4.5 -0.9 4.6 5.8 6.1 10.0 10.0
4.1 4.1 4.1 5.0 1.7 4.0 -0.8 -0.5 -0.7 6.0 -2.1 3.3 -1.2 3.9 0.2 4.4 -1.2 4.4 4.9 -3.0 10.0 10.0
2.8 2.8 3.0 2.3 -2.0 2.0 -1.0 -0.5 -0.9 2.4 -3.1 2.9 -1.3 3.9 -0.7 3.0 -1.3 4.4 4.3 -3.0 10.0 10.0
-1.0 -1.0 -1.5 -1.8 -2.7 -1.8 -1.1 -0.6 -1.8 2.4 -3.3 2.4 -1.3 -1.7 -1.2 1.9 -1.5 -0.8 -3.1 -3.0 -18.6 -18.6
-18.0 -18.0 -18.0 -18.2 -18.3 -18.5 -2.3 -4.2 -1.8 0.1 -18.1 0.2 -18.2 -18.4 -1.3 1.3 -18.1 -18.1 -18.3 -3.0 -18.6 -18.6
RMS(∆)
Es
8.3 8.3 8.3 8.5 8.5 8.7 2.6 2.9 2.5
0.80 0.81 0.81 0.81 0.79 0.78 0.42 0.39 0.39
6.7
0.78
5.9
0.62
6.7
0.59
6.0
0.58
8.3 8.7 4.3 13.5 13.5
0.83 0.76 0.76 1.48 1.25
a
The dSi-O is the bond length of Si-O bonds. The ∆(O-Si-O) represents the deviation of O-Si-O bond angles of these configurations from the value of 109.5° for R quartz. The RMS(∆) is the root-mean-square of the ∆(O-Si-O). The strain energies are in eV/SiO2.
Results and Discussion By analogy with the formation of CNTs from graphite, one can naturally hypothesize that silica NTs can be built from silica MLs. However, stable layered structures, such as graphite, have not been synthesized for silica so far. Recently, an ultrathin silica film consisting of a 2D network of a corner-sharing SiO4 tetrahedron was grown on a Mo(112) surface.13 One oxygen atom (O′) of each SiO4 tetrahedra binds to the protruding Mo atoms of the Mo surface, while other oxygen atoms (O) are connected with two Si atoms in the 6MRs. Starting from this film, we designed a pristine silica ML excluding Mo atoms. The structural relationship between the hypothetical silica ML and the real film can be characterized by removing all of the Mo atoms and half of the O′ atoms from the Mo-SiO4 film, followed by the formation of parallel 2MRs through joining the residual O′ atoms to the adjacent 3-fold-coordinated Si atoms (Figure 1a). This ML has a hybrid 2D network with an equal number of 2MRs and 6MRs (2-6MR-ML), with each atom being fully coordinated. The Si-O distances and O-Si-O angles in the 2MRs are 1.68 Å and 90.1°, close to those of silica fiber, while the bond lengths of other Si-O bonds are about 1.62 Å, which are comparable to that of R quartz, 1.61 Å (Table 1). The arrangement of Si atoms exhibits a graphitic-like feature, except that the Si-Si distance in the 2MRs is 2.34 Å, which is shorter than that with a single O atom bridging between the two Si atoms (3.24 Å). The Es of this ML (2-6MR-ML(I)) with respect to R quartz is 0.83 eV/SiO2. Additionally, we also calculated the distorted isomeric structure (2-6MR-ML(II)) of the 2-6MR-ML reported by Bromely et al.9 Different from the 2-6MR-ML(I), the 2MRs in the supercell of the 2-6MR-ML(II) are no longer parallel, and the bond angles of the Si-O-Si bonds that join two 2MRs also deviate from the 180° of the 2-6MR-ML(I) configuration (Figure 2). The Es of the 2-6MRML(II) is lower than that of the 2-6MR-ML(I) by about 0.07 eV/SiO2 (Table 1). The plausibility of these MLs can be indicated by their stability relative to the isolated 2MR chain and already-synthesized silica fiber (silica-w), whose Es values are 1.48 eV/SiO2 and 1.25 eV/SiO2, respectively, based on the present calculations.
Figure 2. Two possible configurations of the 2-6MR-ML. The dotted rectangles indicate the size of the supercells.
A new family of silica NTs can be built by rolling a silica 2-6MR-ML(I) sheet in an analogous fashion to that for the formation of CNTs from a graphitic sheet (Figure 1a,b). We focus on two kinds of NTs with the axial orientation parallel and perpendicular to the 2MRs, respectively, which are labeled as (m,0) and (n,n) 2-6MR-NTs, analogously to zigzag and
Well-Ordered Silica NTs from Silica MLs and NRs
J. Phys. Chem. C, Vol. 111, No. 27, 2007 9655
Figure 3. The strain energy (Es) of silica 2-6MR-NTs (up- and down-triangles), 2-6MR-NTs (solid circles), and 4MR-NTs (diamonds). The dashed lines indicate the Es of silica MLs. The top views of the silica NTs are also presented as insets of this figure.
armchair CNTs. We relaxed the 2-6MR-NTs with m ) 5, 6, and 7 and n ) 4, 5, and 6 and found a narrow range of Es values, 0.78-0.81 eV/SiO2, which are slightly lower than that of the 2-6MR-ML(I) but a bit higher than that of the 2-6MRML(II) (Figure 3 and Table 1). The Si-O distances and the O-Si-O bond angles are also close to those of the 2-6MRML (Table 1). This is related to the feature of Si-O-Si angles that can vary widely in different silica materials to release the strain energy in SiO4 tetrahedra that counteracts the curvature effects of these 2-6MR-NTs. It is noteworthy that the 2MRs in the equilibrium configurations of (5,5) and (6,6) 2-6MR-NTs are no longer perpendicular to the tube axis, exhibiting a similar distortion of the 2-6MR-ML(II). Apart from the 2-6MR-ML, a silica ML with a square network has also been designed on the basis of the silica stripe grown on the Mo(112) surface.14 This ML purely consists of 4MRs with the O atoms placed alternatively on two planes parallel to the ML (4MR-ML), as shown in Figure 1c. The Si-O distance in this 4MR-ML is 1.66 Å, in between the values for 2MRs and R quartz. The largest deviation of an O-Si-O bond angle from that of R quartz is less than 6.1°. The 4MR-ML is energetically comparable to the 2-6MR-ML(II). The silica 4MRNTs with corner-sharing SiO4 tetrahedra can be built by rolling up the 4MR-ML. We calculated three 4MR-NTs with the axes perpendicular to the edges of the 4MRs and denoted them as (5,0), (9,0), and (12,0), analogous to CNTs (Figures 1c,d and the insets of Figure 3). These silica NTs have been revealed as the most stable configurations of the zigzag 4MR-NTs.11 The Es values are only 0.39-0.42 eV/SiO2, much lower than those of 2-6MR-NTs. The energetic favorability of the 4MR-NTs over the 2-6MR-NTs is also consistent with the small deviation of the O-Si-O angles from those of R quartz (Table 1). Moreover, the 4MR-NTs are more stable than the 4MR-ML by about 0.37 eV/SiO2. This indicates that strain energy is further released in the rolling of the 4MRs of the NTs, which is confirmed by the decrease of the deviation of O-Si-O angles from the optimal state (Table 1).
The strong energetic preference for the 4MR-NTs facilitates the facile formation of the 4MR-NTs from the 4MR-ML, as revealed by molecular dynamic simulations. We heated a 4MRML with a finite width (∼14 Å) and infinite length (periodic) from 300 to 1000 K and then maintained the temperature at 1000 K for 5 ps, with a time step of 1.0 fs, and found that the planar sheet self-curved around the infinite repeat direction, thus displaying an obvious tendency to form a 4MR-NT. These 4MRNTs, especially the (12,0) 4MR-NT, have buckled surfaces caused by a surface reconstruction (the insets of Figure 3) due to the flexibility of the Si-O-Si angles. Another synthetic route toward silica NTs is via the assembly of silica NRs, which are the stable forms of small silica clusters. Differing from the bulk materials, small silica clusters always consist of 2-, 3-, 4- and 6MRs terminated by nonbridging oxygen atoms (NBOs), with the Es depending on the size of these Si-O polygons and the number of NBOs. Generally, a NBO has an associated high Es and is thus disadvantageous for the stabilization of these clusters. This is the main reason why the molecular rings (2MR-NRs) built by joining the NBOs of a 2MR chain have lower Es’s than that of the chain.6,7 In our previous work, we have presented a (SiO2)16 molecular ring (3MR-NR) with a linked 3MR configuration (Figure 1c) and showed that it has an Es comparable to that of the 2MR-NR with a similar diameter.7 The (SiO2)8 3MR-NR has also been predicted as a magic configuration of silica clusters and a possible nanoscale building block for super-(tris)tetrahedral materials.8 In contrast to the fully coordinated 2MR-NRs, it includes NBOs and undercoordinated Si atoms. The electronic structure calculations indicate that the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) mainly come from the states of NBOs and the undercoordinated Si atoms connected with the NBOs, respectively, making these regions possible reactive centers. If the 3MR-NR could be successfully synthesized, that is, through laser ablation experiments, the possibility of larger silica clusters via joining the NBOs of one 3MR-NR with the undercoordinated Si atoms of
9656 J. Phys. Chem. C, Vol. 111, No. 27, 2007
Figure 4. The band structures of (a) (7,0) 2-6MR-NT, (b) (9,0) 4MRNT, (c) 2-3MR-NT(III), and (d) R quartz along the Γ(0,0,0)2π/a A(0,0,0.5)2π/a direction. The energies at the Fermi level are set to zero. The vertical axes are broken from -2.0 to 2.0 eV.
another NR arises under certain condition. In the resultant (SiO2)32 cluster, half of the NBOs and the undercoordinated Si atoms are replaced by 2MRs which bridge the two NRs (Figure 1f). The reaction is exothermic, with the resultant configuration more stable than the reactants by about 0.64 eV/SiO2. We also scanned the potential energy profile of this combination reaction by calculating the total energy of the reactants (two parallel (SiO2)16 NRs shown in Figure 1e) at a set of reaction coordinates represented by the distance (dc-c) from the center of one NR to the center of another NR. In each step, the system was relaxed,
Zhao et al. with the atoms between the two silica NRs moving freely, whereas the atoms in other region were fixed. No energy barrier was found along the reaction path. This is also consistent with the results of molecular dynamics simulations. We heated two parallel (SiO2)16 NRs with dc-c ) 8.3 Å at 800 K for 2.0 ps, with a time step of 1.0 fs, and found that 2MRs were formed between them. All of these results indicate the combination tendency of these silica NRs. Moreover, the residual NBOs in the (SiO2)32 cluster led to a continuous growth by joining more NRs, until a Q1D NT was finally formed, with the diameter dependent on the size of the silica NRs (Figure 1e-g). We designed four silica NTs based on the (SiO2)8, (SiO2)12, (SiO2)16, and (SiO2)20 NRs, which are labeled as (I), (II), (III), and (IV), as shown in the insets of Figure 3. These NTs (23MR-NTs) have a 2-3MR hybrid network with a ratio of 2MRs to 3MRs of 1:2. The Es of the 2-3MR-NTs decreases with increasing tube diameter (Figure 3). The 2-3MR-NT(I) is energetically more favorable than the silica fiber by about 0.69 eV/SiO2 based on the present calculations, which is consistent with other DFT calculations.10 The Si-O distance and O-Si-O angle in the 2MRs of the 2-3MR-NT(III) are also close to the values of the silica fiber and 2-6MR-NTs (Table 1). The 2-3MRNTs are less stable than the 4MR-NTs but still more stable than the 2-6MR-NTs, owing to the lower ratio of 2MRs. The study of the electronic structure of these silica NTs is another interesting issue. The band gaps are approximately 9.2,
Figure 5. The isosurfaces of the Kohn-Sham states of the highest valence orbital (HVBO) and the lowest conduction band orbital (LCBO) at the Γ point of (a) (7,0) 2-6MR-NT, (b) (9,0) 4MR-NT, and (c) 2-3MR-NT(III).
Well-Ordered Silica NTs from Silica MLs and NRs 9.2, and 9.6 eV for the 2-6MR-, 4MR-, and 2-3MR-NTs, respectively,19 which are close to that of R quartz (9.2 eV).20 All of these silica NTs have direct band gaps at the Γ(0,0,0)2π/a point. The insulating character is related to the ionic-like Si-O bonding resulting from the electron transfer from Si to O atoms, which is ∼1.4 |e| per Si atom in these silica nanostructures. The highest valence band (HVB) and the lowest conduction band (LCB) mainly originate from the O(2p) and Si(sp3) orbitals, respectively (Figure 5), again consistent with the properties of the valence and conduction bands of R quartz. The Kohn-Sham states of the O(2p) orbitals are widely separated in these silica NTs, forming localized electronic states and, accordingly, flat valence bands near the Fermi level (Figure 4). For the 2-6MRand 2-3MR-NTs, the overlap between the Kohn-Sham states of the Si(sp3) orbitals is still very weak, and the LCBs are therefore flat with the band widths of 0.7 and 0.3 eV, which are narrower than that of R quartz (1.7 eV). However, the 4MR NTs have delocalized Si(sp3) orbitals and thus a dispersed LCB with a bandwidth of 2.7 eV. We should stress that the 2MRs that remained in the 2-6MRand 2-3MR-NTs may be chemically reactive because they still involve a high strain energy, and the frontier orbitals of these silica NTs mainly come from the contribution of the 2MRs. The stability of these silica NTs under aqueous conditions is crucial for potential applications in fields ranging from catalysis to drug release. The studies of hydrated silica NTs and the reaction between water molecules and these silica NTs are currently underway in our group and will be reported subsequently. Conclusions In summary, on the basis of a first-principles study of silica nanostructures, including MLs, NTs, and silica fiber, we predict synthetic routes toward a family of silica NTs. The silica NTs based on 2-6MRs and 4MRs may be synthesized from the silica MLs that have a close relationship with the ultrathin silica film and silica stripe grown on a Mo substrate. The 2-3MR-NTs, on the other hand, can be built via assembly of silica NRs consisting of linked 3MRs. The energetic order of these silica nanostructures is 4MR-NTs < 2-3MR-NTs < 4MR-ML ≈ 2-6MR-ML(II) < 2-6MR-NTs
