Nanotubes from Rutile TiO2 (110) Sheets: Formation and Properties

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J. Phys. Chem. C 2010, 114, 9251–9256

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Nanotubes from Rutile TiO2 (110) Sheets: Formation and Properties Qiang-qiang Meng, Jian-guo Wang,* Qin Xie, and Xiao-nian Li College of Chemical Engineering and Materials Science, Zhejiang UniVersity of Technology, Hangzhou 310032, China ReceiVed: January 14, 2010; ReVised Manuscript ReceiVed: April 3, 2010

In this study, we proposed a general method for the formation of TiO2 nanotubes from the pristine or reconstructed single trilayer rutile TiO2 (110) thin sheets, which is similar to the formation of carbon nanotubes from a graphene sheet. The geometric and electronic properties of armchair and zigzag type TiO2 nanotubes have been investigated. We found that the electronic properties of TiO2 nantubes are dependent on the chirality, coordination environment, and so on. The stability of these nanotubes is evaluated by means of molecular dynamics simulation. The results show that several stable structures, identified from the density functional theory calculations, can exist in single or mixed phases depending on the temperature. Introduction As an important wide-band gap versatile semiconductor, TiO2 has been widely applied in a lot of research fields.1-27 Stimulated by the discovery of carbon nanotubes, a series of low dimensional TiO2 nanoarchitectures have been prepared with the development of synthesis technology on nanomaterials. Among them, TiO2 nanotubes have attracted more attention during the past decade28-30 due to the combination of semiconducting, photoelectrochemical properties of bulk TiO2 and the structural characters of nanotubes. A number of methods,28-30 including nanoporous alumina as the template, sol-gel, hydrothermal techniques, and the anodization of titanium in the electrolyte have been used to prepare TiO2 naotubes and arrays. Among these methods, the anodization of titanium in the electrolyte can control the nanotube dimensions and other structural paramers of TiO2 nanotubes. During the past decade, four generations of synthesis strategies28-30 of anodization of titanium in the electrolyte from fluoride-based to nonfluoridebased have been developed to prepare TiO2 nanotubes or arrays. Due to the outstanding charge transport and carrier lifetime properties, TiO2 nanotube arrays have been applied in sensors,31,32 dye zensitized solar cells,14,33-37 hydrogen generation from water photoelectrolysis,38-40 and photoreduction of CO2 under outdoor sunlight.41 In addition, they can also be applied to biomedical fields, such as biosensors,42 molecular filtration and drug delivery,43 and tissue engineering. The performances of TiO2 nanotubes38-40 in these applications are strongly dependent on their structural properties, including the crystallographic phases, the length, wall thickness, and pore size. Especially the nanotubes in different crystallographic phases show different properties. It is well-known that the as-fabricated nanotube arrays have an amorphous crystallographic structure. The amorphous nanotubes can transform into polycrystalline or anatse or rutile phases with annealing at elevated temperatures in an oxygen atmosphere. And the study of (glancing-angle) X-ray diffraction patterns29,44-46 and high-resolution transmission electron microscopy47 of the nanotubes shows the dominant peaks of anatase and rutile nanotubes are (101) and (110).44-46 Therefore, it is necessary to investigate the TiO2 nanotubes constructed by wrapping an anatase (101) and rutile (110) sheet. * Corresponding author. E-mail: [email protected].

Compared with lots of experimental studies on the preparation and application of TiO2 nanotube arrays, few theoretical studies have been conducted on the structures and properties of TiO2 nanotubes. The formation mechanism and various properties of titanate nanotubes (H2TinO2n+1 (n ) 2, 3, and 4)) have been investigated by several research groups.48-52 TiO2 nanotubes formed from the anatase (101) surface53 or the anatase TiO2 monolayer55,56 and the application in hydrogen sensors54 have been investigated by means of density functional theory (DFT) calculations. Recently, the electronic properties of TiO2 nanotubes built by a reconstructed (001) bilayer of rutile55 or these nanotubes with hexagonal ABC PtO2 structure,56 with and without doping, have been studied.48,49 In this study, we presented a general mechanism for the formation of nanotubes from the pristine or reconstructed single trilayer rutile TiO2 (110) thin sheets, the same way as for the formation of carbon nanotubes from graphene sheets. They may serve as simplified models of experimentally observed rutile TiO2 nanotubes since they are all formed from various TiO2 (110) sheets. The geometric and electronic properties of TiO2 nanotubes have been investigated by means of density functional theory calculations. And the stability is evaluated by first principle molecular dynamics simulations at different temperatures. Method The first principles density functional theory (DFT) calculations were performed using the PWSCF package in Quantum ESPRESSO.57 The generalized gradient approximation (GGA) with the PBE58 functional was used to describe the exchangecorrelation (XC) effects. Ultrasoft pseudopotentials59 were used to describe electron-ion interactions. The plane-wave basis set cutoffs for the smooth part of the wave function and the augmented density were 25 and 200 Ry, respectively. For the pristine and reconstructed TiO2 (110) sheet, the Monkhorst-Pack k-point sampling is 8 × 4 × 1. For the investigated nanotubes in this study, the Monkhorst-Pack k-point sampling is 1 × 1 × 4. All of the atoms involved in calculations were fully relaxed until each component of the residual force on each atom was smaller than 0.03 eV/Å. First principles density functional theory molecular dynamics calculations were performed60,61 under the constant volume and constant temperature conditions (NVT). The temperature was

10.1021/jp100389f  2010 American Chemical Society Published on Web 05/04/2010

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Figure 1. (a) Formation energies of pristine and various reconstructed rutile (110) single trilayer thin sheets. (b) Optimized geometries of the rutile TiO2 (110) sheet with different b values and constant a (a ) 2.97 Å): (1) b ) 6.56 Å; (2) b ) 5.46 Å; (3) b ) 5.36 Å; (4) b ) 5.16 Å; (5) b ) 5.06 Å.

set from 300 to 2000 K with an interval of 100 K. The simulation times are 1.0, 3.0, and 5.0 ps dependent on the particular systems with a time step 5.0 fs. Results and Discussion 1. Formation of TiO2 Nanotubes from Rutile (110) Sheet. We first investigated the geometries and formation energies of single trilayer rutile TiO2 (110) (1 × 1) sheets with different unit cell parameters. The formation energies are defined as Eform ) E(sheet or NT) - E(bulk), where E(sheet or NT) and E(bulk) are the total energy per TiO2 subunit in the sheets or nanotubes and bulk. The parameters of a and b in the pristine sheet (structure 1) are 2.97 and 6.56 Å, respectively, taken from bulk rutile TiO2. The formation energy of a pristine single trilayer rutile TiO2 (110) (1 × 1) sheet is 2.05 eV, which indicates it is a very unstable structure. Indeed, in one unit cell, the coordination number of half of the oxygen and titanium atoms is three (O3f) and six (Ti6f), respectively. The coordination number of the other half of the oxygen and titanium atoms is two (O2f) and four (Ti4f), respectively. It is well-known that all oxygen and titanium atoms in bulk TiO2 are O3f and Ti6f. Even for the multi trilayer TiO2 (110) (1 × 1) surface, there are only two oxygen and titanium atoms that are two (O2f) and five (Ti5f) coordinated. The larger percentage of low-coordinated oxygen (O2f) and titanium (Ti4f) causes the instability of the pristine TiO2 (110) sheet. In other words, to get the stable TiO2 (110) sheet, the percentage of O2f and Ti4f should be reduced. It can be seen that the O3f and Ti6f can be obtained by moving two O2f atoms to Ti4f atoms of the pristine TiO2 (110) sheet in opposite directions, respectively. This transformation can be realized by changing the parameter b, while keeping a constant. Figure 1a shows the formation energies of TiO2 under different b values. We found that the formation energy of a thin rutile sheet gradually increases with b decreasing from 6.56 (structure 1) to 5.46 Å (structure 2), which indicates that the structure does not change so much. Indeed, the coordination environments of oxygen and titanium are the same in two kinds of structures (1 and 2). The only difference is the distance between O2f and Ti4f changing from 3.50 to 3.02 Å and the thickness from 2.45 to 2.56 Å. However, a stable structure 3 is obtained when the length of b is 5.36 Å. The formation energy is 0.34 eV per TiO2, which is much smaller than that of the pristine rutile TiO2 (110) sheet. It should be noted that all oxygen and titanium atoms in 3 are O3f and Ti6f, which are the same as those

Meng et al.

Figure 2. Formation of various TiO2 nanotubes from the most stable reconstructed rutile (110) sheet (β-PtO2 type). The unit cell of the β-PtO2 type rutile (110) sheet highlighted in blue is defined by the primitive lattice vectors R1 and R2. The same scheme as carbon nanotubes is used with zigzag nanotubes defined by rollup vectors along the (n, 0) direction and armchair nanotubes defined by rollup vectors along the (n, n) direction.

Figure 3. Several typical TiO2 (8, 8) nanotubes that formed from the rutile (110) sheet: (a) pristine (TiO2 (8, 8)a); (b) β-PtO2 structure (TiO2 (8, 8)b); (c) reconstructed (TiO2 (8, 8)c); (d) reconstructed (TiO2 (8, 8)d). The inset presents the top view of the nanotube.

of bulk TiO2. In particular, we found that this structure is very similar to that of the single layer of β-PtO2.56 The structure with saturated coordination oxygen and titanium is very stable within the range of b value from 5.36 to 5.16 Å. Once the saturated coordination environments of oxygen or titanium are changed, the structure of the thin rutile sheet becomes unstable again. For example, the formation energy of structure 5 is 1.63 eV per TiO2, which is much higher than that of structure 3 and 4. Due to the very short b value (5.06 Å), half of the four oxygens and all of the titanium oxygens are O1f and Ti5f. The stable single trilayer rutile (110) sheets (structure 3 and 4) can be obtained by choosing the suitable length of b, which

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is highlighted in Figure 2. We found the structure shown in Figure 2 is same as that of a single layer of β-PtO2.62 The hexagonal ring of the most stable TiO2 sheet is very similar to that of graphene (Figure 2) although they have three or one layers, respectively. Therefore, we can define various TiO2 nanotubes with the same rules of the carbon nanotubes (CNTs) by rolling the graphene sheet.63 According to CNTs, two primitive lattice vectors R1, R2 are defined in Figure 2. A pair of integers (n1, n2) can define a vector R:

r)

a |R| n 2 + n22 + n1n2 ) 2Π 2Π √ 1

Each R within this wedge defines a different TiO2 NT, and all unique NTs can be defined by this set of R, which referred to the SWCNTs. So the TiO2 NTs can be classified to armchair (n1 ) n2), zigzag (n1 * 0, n2 ) 0), and chiral (n1 * n2). Of course, TiO2 nanotubes can also be formed by pristine or other reconstructed rutile (110) sheets. 2. Geometric and Electronic Properties of Rutile TiO2 Nanotubes. 2.1. Armchair TiO2 NTs. After the determination of the nomenclature of TiO2 nanotubes, the geometric and electronic properties of armchair and zigzag nanotubes have been investigated. In this study, as the representative armchair and zigzag type TiO2 NTs, (8, 8) and (8, 0) are chosen, which have 48 atoms in one unit cell. The optimized geometries of several typical TiO2 (8, 8) nanotubes formed from pristine and reconstructed (including β-PtO2 type) rutile (110) sheets are shown in Figure 3. The TiO2 (8, 8)a NT formed from a pristine single trilayer rutile TiO2 (110) sheet (Figure 2a) is very unstable; half of the oxygen and titanium atoms are O2f and Ti4f (Table 1). The formation energy of the (8, 8)a NT per TiO2 is 1.99 eV. All oxygens and titaniums of the TiO2 (8, 8)b, formed from the β-PtO2 type rutile (110) sheet, are O3f and Ti6f (Table 1). The average Ti-O distance of

R ) n1R1 + n2R2 Basis vectors are defined as

R1 ) aiˆ a a√3 ˆ R2 ) ˆi + j 2 2 where a ) 31/2d (d is the average Ti-O bond distance), and ˆı and ˆj denote the usual unit vectors along the x and y axes, respectively. The radius for a (n1, n2) nanotube is defined by

TABLE 1: Geometric (Number and Position of O2f, O3f, Ti4f, Ti5f and Ti6f in One Unit Cell, Unit Cell Length along the z Direction (Z) and Average Diameter) and Electronic (the Band Gap and Formation Energies) Properties of Various TiO2 Nanotubes Investigated in This Study NT

sheet

O2f

O3f

Ti4f

Ti5f

Ti6f

Z (Å)

diameter (Å)

Egap (eV)

Eform (eV/TiO2)

(8,8)a (8,8)b (8,8)c (8,8)d (8,0)a (8,0)b

pristine β-PtO2 reconstructed reconstructed β-PtO2 reconstructed

16a 0 16b 8 0 16c

16 32 16 24 32 16

8 0 0 0 0 0

0 0 16 8 0 16

8 16 0 8 16 0

2.96 3.01 2.93 2.97 5.17 5.10

18.96 15.20 17.54 17.10 10.11 10.71

0.93 2.71 3.61 3.35 2.62 3.08

1.99 0.56 0.50 0.40 0.95 0.88

a (8out, 8in). Out and in represent the O2f located on the outside and inside shell of TiO2 nanotubes. b (16out). Out represents the O2f located on the outside shell of TiO2 nanotubes. c (16out). Out represents the O2f located on the outside shell of TiO2 nanotubes.

Figure 4. Band structure, projected density of states, and the highest occupied and the lowest unoccupied molecular orbitals of (a) TiO2 (8, 8)a, (b) TiO2 (8, 8)b, (c) TiO2 (8, 8)c, and (d) TiO2 (8, 8)d nanotubes. The inset presents the magnified view of the atomic orbital.

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Figure 5. Kinds of zigzag TiO2 (8, 0) nanotubes (TiO2 (8, 0)a (a, c) and TiO2 (8, 0)b (b, d)) with top view in different angles.

the outer and inner shell of TiO2 (8, 8)b is 2.01 and 1.94 Å. The TiO2 (8, 8)b NT has been investigated in a recent DFT study by He et al.55 However, we found two other more stable structures, as shown in Figure 3c (TiO2 (8, 8)c) and Figure 3d (TiO2 (8, 8)d). The TiO2 (8, 8)c NT is obtained from the TiO2 (8, 8)b NT by breaking all of the O-Ti bonds in the outer shell of the TiO2 (8, 8)b NT and increasing the radius of the TiO2 (8, 8)b NT. After relaxation, the diameter of the TiO2 (8, 8)c NT is 17.54 Å, which is much larger than that of the TiO2 (8, 8)b NT.

Meng et al. The TiO2 (8, 8)c NTs have the same number of O2f and O3f as the TiO2 (8, 8)a NT, but all of the O2f are located on the outside shell of the nanotubes (Table 1). To our surprise, the most stable structure is TiO2 (8, 8)d, as shown in Figure 3d, which is obtained by breaking every other O-Ti bond in the outer shell of the TiO2 (8, 8)b NT and increasing the radius of the TiO2 (8, 8)b NT. In TiO2 (8, 8)d, a quarter of the oxygen atoms are O2f and half of the Ti atoms are Ti5f (Table 1). Due to these changes, the diameter of TiO2 (8, 8)d is 17.10 Å, which is larger than 15.20 Å of TiO2 (8, 8)b. The band structures of the four different configurations along the Γ-Z direction are shown in Figure 4. They all exhibit the semiconducting character whose direct band gaps are 2.71, 3.61, and 3.35 eV in TiO2 (8, 8)b, (8, 8)c, and (8, 8)d respectively. The band gap of (8, 8)a is only 0.93 eV, which is caused by the unsaturated oxygen and Ti.64 To analyze the contribution of each species, the projected density of states (PDOS) of oxygen and Ti in different coordination numbers, also the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of each structure are shown in Figure 4. We can see that the valence and conduction bands of TiO2 (8, 8) NTs are mainly contributed from oxygen and Ti. Indeed, the HOMO and LUMO orbitals of TiO2 (8, 8)a are contributed from O2f and Ti4f. Although TiO2 (8, 8)c has the same number of O2f with (8, 8)a, the band structure and PDOS are totally different. The position of lowest conduction band and highest valence band are +2.1 and -1.5 eV, which are contributed from Ti5f, O2f, and O3f (2p). These differences are probably caused by the different coordination between Ti and oxygen. The (8, 8)b NT, with the saturated coordinated oxygen and Ti, has very a band structure and PDOS similar to that of bulk TiO2.65 However, the valence band maximum of O3f is very close to the Fermi energy. When the valence band maximum moved away from

Figure 6. Band structure, projected density of states, highest occupied and lowest unoccupied molecular orbitals of (a) TiO2 (8, 0)a and (b) TiO2 (8, 0)b nanotubes. The inset presents the magnified view of the atomic orbital.

Figure 7. Geometries of (8, 8)d NT at different temperatures with NVT molecular dynamics simulation for 3.0 ps: (a) 500 K; (b) 1000 K; (c) 2000 K.

Nanotubes from Rutile TiO2 (110) Sheets Fermi level, the most stable structure TiO2 (8, 8)d could be obtained. Moreover, we can see that the LUMO of (8, 8)b is from eg of the Ti states (dZ2), while (8, 8)a, (8, 8)c, and (8, 8)d are hybridizations of d states (t2g or dZ2) from the orbital. As we know that t2g is more stable than eg (E(eg) > E(t2g)66) in the positive octahedron crystalline field TiO2, which may lead to the conclusion that the (8, 8)d NT is more stable than the (8, 8)b NT. 2.2. Zigzag TiO2 NTs. To make a comparison with the armchair TiO2 (8, 8) NT, we built two kinds of zigzag TiO2 (8, 0) NTs (Figure 5). The TiO2 (8, 0)a NT is formed by rolling the β-PtO2 type rutile (110) sheet. Therefore, all of the oxygen and titanium atoms of the TiO2 (8, 0)a NT are O3f and Ti6f, and the distances between the oxygen and three bonded titanium in the outer shell of the nanotubes are nearly all 2.21 Å. The TiO2 (8, 0)b NT is obtained from the TiO2 (8, 0)a NT by breaking one of the O-Ti bonds in the outer shell of the TiO2 (8, 0)a NT and increasing the radius of the TiO2 (8, 0)a NT. The coordination environment of oxygen and titanium in TiO2 (8, 0)b is very similar to that in TiO2 (8, 8)c. The numbers of O2f and O3f in one unit cell of TiO2 (8, 0)b are both 16, which leads to 16 Ti5f. And all of O2f are located on the outside shell of nanotubes (Table 1). The distances between O2f and bonded titanium are 1.85 and 1.85 Å. Moreover, the band structure, PDOS, and molecular orbital are shown in Figure 6. The formation energies of TiO2 (8, 0)a and (8, 0)b are 0.95 and 0.88 eV per TiO2, which is much higher than those of (8, 8)b, (8, 8)c, and (8, 8)d. In other words, the zigzag TiO2 NTs are less stable than the armchair ones. The band gaps of TiO2 (8, 0)a and (8, 0)b are 2.62 and 3.08 eV, both belonging to the direct-band gap semiconductor55 (Figure 6). 3. Stability of Rutile TiO2 Nanotubes. In the above section, various TiO2 nanotubes formed from pristine and reconstructed rutile TiO2 (110) sheets (including β-PtO2 type) have been discussed. And we found that the armchair TiO2 nanotubes are more stable than the zigzag systems. So we preliminarily discussed the stability of armchair TiO2 (8, 8) nanotubes based on the first principles molecular dynamics simulations, which were performed under constant volume and constant temperature conditions (NVT). The temperature was set from 300 to 2000 K with an interval of 100 K. We found that below 500 K, TiO2 (8, 8)d does not change basically even after 5.0 ps molecular dynamics simulations (Figure 7). And TiO2 (8, 8)b and TiO2 (8, 8)c can easily change into the mixed structure (majority TiO2 (8, 8)d) at very short times (even less than 1.0 ps) below 500 K, which indicates the TiO2 (8, 8)d is the most stable structure among TiO2 (8, 8). But above 600 K and below 1500 K, the equilibrium structure is the mixed phase of TiO2 (8, 8)d, TiO2 (8, 8)b, and TiO2 (8, 8)c, in which the major phase is still TiO2 (8, 8)d. Of course, the composition of the mixed phase is determined by the particular temperature and time step. Above 1500 K, the structures are destroyed in different degrees due to the breaking of the Ti-O bond. Conclusions A general mechanism for nanotube formation from rutile TiO2 (110) sheets was proposed in this study, the same way as for the formation of CNTs by rolling the graphene sheets. They may serve as the simplified models of experimentally observed rutile TiO2 nanotubes, since they are all formed from pristine and reconstructed rutile (110) sheets. The band structures and electronic properties of TiO2 nantubes are dependent on the chirality, coordination environment, and so on. The stable structures identified from DFT are confirmed by the first principles molecular dynamics simulations.

J. Phys. Chem. C, Vol. 114, No. 20, 2010 9255 Acknowledgment. This work was supported by the National Natural Science Foundation of China (No. 20906081), the “Qianjiang Scholars” program of Zhejiang Province, the Key Projects of Science and Technology Research of the Ministry of Education of China (No. 209055), and the Scientific Research Foundation for Returned Scholars, Ministry of Human Resources and Social Security of China. References and Notes (1) Diebold, U. Surf. Sci. Rep. 2003, 48, 53. (2) Matthey, D.; Wang, J. G.; Wendt, S.; Matthiesen, J.; Schaub, R.; Laegsgaard, E.; Hammer, B.; Besenbacher, F. Science 2007, 315, 1692. (3) Matthiesen, J.; Hansen, J. O.; Wendt, S.; Lira, E.; Schaub, R.; Laegsgaard, E.; Besenbacher, F.; Hammer, B. Phys. ReV. Lett. 2009, 102. (4) Wendt, S.; Matthiesen, J.; Schaub, R.; Vestergaard, E. K.; Laegsgaard, E.; Besenbacher, F.; Hammer, B. Phys. ReV. Lett. 2006, 96. (5) Wendt, S.; Schaub, R.; Matthiesen, J.; Vestergaard, E. K.; Wahlstrom, E.; Rasmussen, M. D.; Thostrup, P.; Molina, L. M.; Laegsgaard, E.; Stensgaard, I.; Hammer, B.; Besenbacher, F. Surf. Sci. 2005, 598, 226. (6) He, Y. B.; Tilocca, A.; Dulub, O.; Selloni, A.; Diebold, U. Nat. Mater. 2009, 8, 585. (7) Tilocca, A.; Cormack, A. N. J. Phys. Chem. C 2008, 112, 11936. (8) Tilocca, A.; Di Valentin, C.; Selloni, A. J. Phys. Chem. B 2005, 109, 20963. (9) Tilocca, A.; Selloni, A. Chemphyschem 2005, 6, 1911. (10) Li, S. C.; Wang, J. G.; Jacobson, P.; Gong, X. Q.; Selloni, A.; Diebold, U. J. Am. Chem. Soc. 2009, 131, 980. (11) He, Y. B.; Li, W. K.; Gong, X. Q.; Dulub, O.; Selloni, A.; Diebold, U. J. Phys. Chem. C 2009, 113, 10329. (12) Ni, M.; Leung, M. K. H.; Leung, D. Y. C.; Sumathy, K. Renewable Sustainable Energy ReV. 2007, 11, 401. (13) De Angelis, F.; Fantacci, S.; Selloni, A.; Gratzel, M.; Nazeeruddin, M. K. Nano Lett. 2007, 7, 3189. (14) Kuang, D.; Brillet, J.; Chen, P.; Takata, M.; Uchida, S.; Miura, H.; Sumioka, K.; Zakeeruddin, S. M.; Gratzel, M. Acs Nano 2008, 2, 1113. (15) Bach, U.; Lupo, D.; Comte, P.; Moser, J. E.; Weissortel, F.; Salbeck, J.; Spreitzer, H.; Gratzel, M. Nature 1998, 395, 583. (16) Gao, F.; Wang, Y.; Shi, D.; Zhang, J.; Wang, M. K.; Jing, X. Y.; Humphry-Baker, R.; Wang, P.; Zakeeruddin, S. M.; Gratzel, M. J. Am. Chem. Soc. 2008, 130, 10720. (17) Macak, J. M.; Zlamal, M.; Krysa, J.; Schmuki, P. Small 2007, 3, 300. (18) Varghese, O. K.; Mor, G. K.; Grimes, C. A.; Paulose, M.; Mukherjee, N. J. Nanosci. Nanotechnol. 2004, 4, 733. (19) Yoriya, S.; Prakasam, H. E.; Varghese, O. K.; Shankar, K.; Paulose, M.; Mor, G. K.; Latempa, T. J.; Grimes, C. A. Sens. Lett. 2006, 4, 334. (20) Varghese, O. K.; Gong, D. W.; Paulose, M.; Ong, K. G.; Grimes, C. A. Sens. Actuators, B 2003, 93, 338. (21) Lu, H. F.; Li, F.; Liu, G.; Chen, Z. G.; Wang, D. W.; Fang, H. T.; Lu, G. Q.; Jiang, Z. H.; Cheng, H. M. Nanotechnology 2008, 19. (22) Cheng, H. Z.; Selloni, A. Phys. ReV. B 2009, 79. (23) Di Valentin, C.; Finazzi, E.; Pacchioni, G.; Selloni, A.; Livraghi, S.; Czoska, A. M.; Paganini, M. C.; Giamello, E. Chem. Mater. 2008, 20, 3706. (24) Finazzi, E.; Di Valentin, C.; Selloni, A.; Pacchioni, G. J. Phys. Chem. C 2007, 111, 9275. (25) Matthiesen, J.; Wendt, S.; Hansen, J. O.; Madsen, G. K. H.; Lira, E.; Galliker, P.; Vestergaard, E. K.; Schaub, R.; Laegsgaard, E.; Hammer, B.; Besenbacher, F. Acs Nano 2009, 3, 517. (26) Wang, J. G.; Hammer, B. Top. Catal. 2007, 44, 49. (27) Wang, J. G.; Hammer, B. Phys. ReV. Lett. 2006, 97. (28) Grimes, C. A. J. Mater. Chem. 2007, 17, 1451. (29) Mor, G. K.; Varghese, O. K.; Paulose, M.; Shankar, K.; Grimes, C. A. Sol. Energy Mater. Sol. Cells 2006, 90, 2011. (30) Shankar, K.; Basham, J. I.; Allam, N. K.; Varghese, O. K.; Mor, G. K.; Feng, X. J.; Paulose, M.; Seabold, J. A.; Choi, K. S.; Grimes, C. A. J. Phys. Chem. C 2009, 113, 6327. (31) Zheng, Q.; Zhou, B. X.; Bai, J.; Li, L. H.; Jin, Z. J.; Zhang, J. L.; Li, J. H.; Liu, Y. B.; Cai, W. M.; Zhu, X. Y. AdV. Mater. 2008, 20, 1044. (32) Zuruzi, A. S.; Kolmakov, A.; MacDonald, N. C.; Moskovits, M. Appl. Phys. Lett. 2006, 88. (33) Wang, D. A.; Liu, Y.; Wang, C. W.; Zhou, F.; Liu, W. M. Acs Nano 2009, 3, 1249. (34) Kang, T. S.; Smith, A. P.; Taylor, B. E.; Durstock, M. F. Nano Lett. 2009, 9, 601. (35) Mor, G. K.; Shankar, K.; Paulose, M.; Varghese, O. K.; Grimes, C. A. Nano Lett. 2006, 6, 215. (36) Shankar, K.; Bandara, J.; Paulose, M.; Wietasch, H.; Varghese, O. K.; Mor, G. K.; LaTempa, T. J.; Thelakkat, M.; Grimes, C. A. Nano Lett. 2008, 8, 1654.

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