Article pubs.acs.org/JPCC
Theoretical and Experimental Study of Anatase Nanotube Formation via Sodium Titanate Intermediates Marie-Christine Runkel,† Olga Wittich,‡ Armin Feldhoff,† Michael Wark,¶ and Thomas Bredow*,† †
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, University Bonn, Bonn, Germany Institute for Physical Chemistry and Electrochemistry, Leibniz University Hanover, Hanover, Germany ¶ Technical Chemistry, Carl von Ossietzky University Oldenburg, Oldenburg, Germany ‡
S Supporting Information *
ABSTRACT: The initial stages of the formation of anatase nanotubes starting from TiO2 microparticles are studied theoretically at density-functional theory (DFT) level. Several formation mechanisms proposed in the literature are discussed. In the present study a mechanism is adapted that starts with NaOH adsorption on the anatase (101) surface. A phase transition from NaOH:anatase to sodium titanate is thermodynamically favorable but does not lead to the formation of sodium titanate nanotubes. Instead it is shown that anatase nanotubes with NaOH adsorbed on the inner surface are stabilized with respect to the unmodified 2D-periodic anatase surface structure. The structure and stability of selected intermediates of the nanotube formation process are investigated. In the experimental part we investigated the initial step of the nanotube formation and characterized the crystal structure of the as prepared titanate nanotubes.
■
INTRODUCTION The intense research on nanostructured materials began after fullerenes were discovered by Kroto et al. and the structure of carbon nanotubes was solved by Iijima et al.1 Soon afterward several well-known inorganic substances were also shown to form graphite-like layered structures and already in the late 1970s disulfide compounds consisting of a few atomic layers were obtained. In the following years, inorganic nanoframeworks could be systematically synthesized.1 Titanium dioxide nanotubes, obtained without templates, were first published by Kasuga et al. in 1998.2 Their synthesis route based on a hydrothermal reaction of concentrated sodium hydroxide with microcrystalline titanium dioxide powder is now well-established. As a result of the increased specific surface area and high surface tension of nanotubes their physical and chemical properties are significantly modified compared to the single crystal. The potential for applications of nanotubes in catalysis due to these modifications and possible customization by doping with different elements was already pointed out by Kasuga and Tenne.1,2 Over the last 20 years the use of TiO2 nanomaterials has dramatically increased. Besides the well-known nanoparticles also titanium dioxide nanotubes find applications in numerous © XXXX American Chemical Society
optical and catalytic processes. They are suitable for biochemical coatings, as carriers for pharmaceuticals or self-cleaning surfaces and consequently they became part of everyday life.3 Titanium dioxide is the subject of many general theoretical studies,4−6 in this respect it is quite surprising that despite the large number of theoretical7−10 and experimental studies11−17 dealing with titania-based nanomaterials and their synthesis,18 to our knowledge there is not yet a consensus on the formation mechanism. In their experimental studies Yang et al. proposed the dissolution of linear titania fragments which are aligned by O− Na−O interactions to form nanotubes.11 Kukovecz et al. suggested the existence of TiO6 octahedra in solution as they found that Na2Ti3O7 does not serve as a precursor for hydrothermal synthesis.12 In a recent publication Li et al. presented a mechanism that was induced by OH−TiO2 interaction, accompanied by Na+ intercalation, followed by epitaxial growth of thin layers and the final roll-up to nanotubes.13 Tsai et al. found the roll-up process of Na2Ti3O7 Received: April 22, 2014 Revised: February 12, 2015
A
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
package20,21 where a symmetry-based construction of nanotubes is implemented.22 A preliminary performance test of selected GGA density functionals23−25 and their corresponding hybrid functionals26,27 was performed (see Figure 1). The functionals were chosen due to their reported performance in solid-state calculations (e.g. refs 28−30).
nanotubes as reversible, depending on the pH of the aqueous solution.14 Wu et al. described surface corrugation followed by the splitting of lamellar structures along the (100) plane in H2 Ti3 O 7. After a variation of experimental conditions, particularly the precursor size, nanowires or -belts were obtained.16 A similar sequence is described by Ren et al.17 They found the concentration of the sodium hydroxide solution to play a significant role: the nanotubes could not be formed if the NaOH concentration was too low. They proposed that the lack of Na+ in the solution made the intercalation process impossible, apart from that they suggest the formation of nanotubes from sheets induced by proton exchange. In a theoretical study by Zhang et al. finite clusters (curved surface sections with defined radii) were used as model systems for the formation of H2Ti3O7 nanotubes. The authors identified the change of Na+ content on the surface as the roll-up driving force19 To shed light on the titanate nanotube formation mechanism we performed a combined experimental and theoretical study of the early stages of anatase nanotube formation. In the experimental part we investigated the initial step of the formation by conducting the hydrothermal reaction at 80 °C. Furthermore, we characterized the final product after synthesis at 150 °C. This is consistent with the experimental conditions for a hydrothermal reaction described in various references.11,13,14,17 Since the process of nanotube formation cannot be observed in situ we used DFT and hybrid calculations in this study as a complementary method to investigate the possible intermediate structures. The initial step of the mechanism was modeled taking experimental findings into account. In our theoretical models a mechanism was adapted that starts with NaOH adsorption on the anatase (101) surface. A possible phase transition to sodium titanate was studied by calculating the relative stability of anatase:NaOH and modified Na2Ti3O7 slabs. The subsequent formation of anatase:NaOH and sodium titanate nanotubes was investigated.
Figure 1. Performance of GGA and hybrid functionals for the calculation of Na2Ti3O7 lattice parameters (aexp = 8.571 Å, bexp = 3.805 Å, cexp = 9.135 Å, and βexp = 101.57°31).
The evaluation criteria were the compliance between the experimental and calculated structure parameters of Na2Ti3O731 and its atomization energy.32 In Figure 1 the mean percental error for the lattice parameters a, b, c, and β obtained in the solidstate calculations of Na2Ti3O7 is displayed. In general the largest errors in absolute values occurred for the lattice parameters b and c. The smallest mean error was obtained with the hybrid method PW1PW.26 Also best agreement of the calculated reaction enthalpy ΔRH for the solid state reaction Na2O + 3TiO2 → Na2Ti3O7 (exp.: −225 kJ/mol32,33) was obtained with PW1PW: −217 kJ/mol. As can be seen the results provided by the hybrid functional PW1PW were in best agreement with experimental references; however, the application of hybrid functionals is computationally significantly more demanding compared to GGA functionals. Thus, as a compromise between the best agreement and computational efficiency, PBESOL,23 which was the most accurate among the GGA functionals, was used for structure relaxations. Single-point calculations with the more accurate hybrid functional PW1PW were performed to obtain energetic properties. The tolerances for Coulomb and exchange sums21 were set to 10−7 and 10−14 Hartree, respectively. The kpoint Monkhorst−Pack shrinking factor was found to be converged with a value of 4. We used hydrogen, oxygen, sodium, and titanium basis sets of valence triple-ζ quality, as developed previously by our group.34 Slab Models. To predict a possible pathway for the nanotube formation anatase and sodium titanate, slab models were compared to the corresponding nanotube models in their relative stability. In the first step two-dimensionally periodic slabs were constructed from the relaxed bulk structures. The atomic positions were fully optimized within the symmetry restrictions of the surface. The surface cell parameters were fixed to the corresponding optimized bulk values. The same slab models were also used to form nanotubes with different radii. In the structure optimization of the nanotubes only the cell parameter along the tube axis was fixed. We focus on the comparison of 2D
■
EXPERIMENTAL METHODS TiO2 nanotubes have been prepared by hydrothermal synthesis starting from anatase microparticles, which were dispersed in 10 M NaOH solution and kept in an autoclave at elevated temperatures (130−150 °C) for 48 h. Afterward the precipitates were centrifuged, then washed with water and 0.1 M HCl solution for ion exchange of sodium ions. Finally the powders were dried in air or at an elevated temperature of 80 °C. A JEOL2100F-UHR transmission electron microscope (TEM) with a Schottky field-emitter and a Gatan Imaging Filter (GIF 2001) was used for TEM micrographs and Selected Area Electron Diffraction (SAED). For these purposes the dried samples were dispersed in ethanol by sonication, dropped on an holey carbon grid, and dried under infrared light. For the study of initial dissolution of microparticles in hot NaOH solution the anatase precursor was dispersed in 10 M NaOH solution and kept at 80 °C for 48 h. Subsequently the white precipitate was washed with water and dried in air. The dried powder was spread on a graphite carrier for Scanning Electron Microscopy (SEM). SEM pictures were acquired with a JEOL JSM-6700F microscope.
■
COMPUTATIONAL METHODS Periodic density functional theory (DFT) calculations were performed with the CRYSTAL09 crystalline-orbital program B
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Nanotube Models. For rectangular slab models there are two possible axes s1⃗ and s2⃗ along which the surface unit cell can be rolled up to a nanotube. The translation vector of the 1D unit cell L⃗ is orthogonal to R⃗ . The circumference |R⃗| is in general determined by the parameters N1 and N2 for each of the two different axes:21
periodic, relaxed slabs with their corresponding 1D periodic, likewise relaxed nanotube models. Titanates of the structurally related Na2TinO2n+1 type are confirmed intermediates during the hydrothermal synthesis of TiO2 nanotubes. Since Na2Ti3O7 approaches the stoichiometry of this intermediate as close as possible, and also some of the previous studies using the hydrothermal synthesis route found Na2Ti3O7 as an intermediate phase,12,14 we focused on Na2Ti3O7 as a model compound in the present theoretical study. A further advantage is that its full structural information was available, contrary to Na2Ti2O5·H2O and Na2Ti4O9. The conventional unit cell of Na2Ti3O7 contains 24 atoms (Z = 2). The Na2Ti3O7 structure is classified by the monoclinic space group P21/m with lattice parameters aexp = 8.571 Å, bexp = 3.805 Å, cexp = 9.135 Å, and βexp = 101.57°.31 Anionic titanate strings are separated by sodium cation layers along the x axis. Experimental anatase lattice parameters for the tetragonal structure with space group I41/amd are aexp = 3.875 Å and cexp = 9.512 Å,35 its conventional cell contains 12 atoms (Z = 4). With CRYSTAL the models used for the surface calculations are truly 2D periodic and have been constructed in a symmetrical way so that they have no dipole moment in the direction of the surface normal without adsorbates. Based on previous studies7,17 we used the slab resulting from a cut along the (100) sodium layers in the Na2Ti3O7 structure (see Figure 2). We took the most stable (101) surface of anatase microparticles36 (see Figure 2) as a basis for the construction of the titania nanotubes in our calculations.
R⃗ = N1 s1⃗ + N 2 s2⃗
(1)
We only used the longer axis s1⃗ as roll-up direction producing a shorter 1D periodic translative unit cell and allowing a wider variety of possible radii (see Figure 2). N2 is in all cases set to zero, therefore the 1D lattice vector is L⃗ = s2⃗
(2)
and the circumference |R⃗| is directly determined by the multiplication of the first lattice vector s1⃗ with N1
R⃗ = N1 s1⃗
(3)
Most of the nanotube calculations are performed with oneand two-layer models due to the increased computational costs compared to the calculation of their corresponding 2D slab model. A schematic diagram of the automatic construction can be found in the Supporting Information.
■
RESULTS AND DISCUSSION Experimental Section. Our experimental results point toward a three-step reaction (see Table 1), that was already described by Ren et al.17
Table 1. Three-Step Reaction toward TiO2 Nanotubes (with n = 2, 3, 4) (1)
nTiO2(anatasemicro) + 2NaOH
Δt
→
Na2TinO2n+1(nanotube) + H2O
t
(2) (3)
Na2TinO2n+1(nanotube) + 2HCl H2TinO2n+1(nanotube)
→ ΔT
→
H2TinO2n+1(nanotube) + 2NaCl nTiO2anatase(nanotube) + H2O
In agreement with other publications,11,13,16,17 we found titanate nanotube structures after reaction 1 in Table 1. The bright-field TEM picture in Figure 3 displays cluster-assembled
Figure 2. Surface unit cells with s1⃗ and s2⃗ to construct the nanotube models with hydrogen (turquoise), oxygen (red), sodium (blue), and titanium (gray).
In the following we distinguish between atomic layers and stoichiometric layers of the slab models. An atomic layer consists of all atoms having the same z coordinate. In the coordinate system of a given surface the z-direction is parallel to the surface normal. A stoichiometric layer is an assembly of atomic layers that contains an integer number of formula units of the system. Due to the low symmetry of Na2Ti3O7 each atomic layer of a (100) slab contains only one atom. The minimum unit of a slab model therefore consists of 12 atomic or one stoichiometric layer. For anatase the conventional bulk unit cell was used to construct the slabs. Here one stoichiometric layer consists of six atomic layers each containing two atoms. In the following a layer will denote the minimum amount of atomic layers that forms a stoichiometric and symmetric arrangement and has no dipole moment in the z-direction. Subsequently all slab models mentioned correspond to these stoichiometric, symmetric layers, unless otherwise specified.
Figure 3. Bright field TEM picture of titanate nanotubes. C
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C titanate nanotubes after hydrothermal reaction and washing procedure. The corresponding SAED data are shown in Figure 4,
Figure 6. Dissolution of anatase layers.
cell, A is the area of the surface unit cell, and n is the number of formula units in the slab model. ESurface was calculated as a function of the slab thickness in order to investigate the convergence behavior. We calculated up to four layers and the converged (100) surface energy of Na2Ti3O7 was low, 0.48 J/m2, which can be explained by the weak interactions between the layers.
Figure 4. SAED of titanate nanotubes.
which display d-spacings being in rough agreement with data reported by Chen et al. for H2Ti3O7 nanotubes.37 In their study they found d-spacings at 7.80, 3.68, and 1.88 Å resulting from (200), (211), and (020) planes, respectively. These values fit quite reasonably to H2Ti3O7 with a monoclinic unit cell with a = 16.03 Å, b = 3.75 Å, c = 9.19 Å, and β = 101.45° as reported by Feist and Davies.38 In Figure 5 the SEM picture of the anatase precursor is shown. After hydrothermal reaction at 80 °C the formerly smooth
E(n) − nE bulk (4) 2A The surface energy of anatase(101) is known to be strongly dependent on the number of layers, convergence is only reached with values of n > 10.30 The two-layer slab which is the basis for the nanotube models has a surface energy of 0.84 J/m2, 0.1−0.2 J/m2 larger than reference values from experiment and previous theoretical work.10,39,40 This difference has to be kept in mind in the following, but will not change the conclusions of the present study. Based on experimental findings we developed theoretical models to explain the possible reaction mechanisms (see Figure 7). The principal question to answer is the order of nanotube formation and phase transition during reaction 1 (see Table 1). The possibilities are: (Mechanism 1) dissolved anatase layers could form nanostructures initiating the phase transition to titanate or (Mechanism 2) the phase transition to titanate is induced during the dissolution of stripes from the anatase surface before nanotubes are formed. Anatase and trititanate were compared in their relative stability for the stoichiometry Na2Ti3O7, matching a product of reaction 1 (see Table 1). We used surface unit cells containing 48 atoms, corresponding to four formula units of Na2Ti3O7 or 12 formula units of TiO2 with four Na2O formula units (see eq 5). At first sight the phase transformation has to follow the dissolution of anatase stripes from the precursor surface (Mechanism 2) since the titanate structure is energetically favorable for the 2Dperiodic case. ESurface(n) =
Figure 5. Anatase precursor particles.
microcrystalline anatase precursor exhibits stepped notches, where the NaOH etched the surface (Figure 6). The size and shape of the precursor microparticles correspond to the resulting particles after hydrothermal reaction. In addition in some places the dissolution of stripes on the surface of the microcrystalline anatase powder clearly can be observed; in Figure 6 such regions are highlighted by arrows. Quantum-Chemical Calculations. The surface energy ESurface for the anatase as well as for the titanate slabs was calculated according to eq 4 where E(n) is the total energy of the slab model, Ebulk is the total energy per formula unit of the bulk
Anatase(101): NaOH → Na 2Ti3O7 (100) kJ ΔR E = − 630 /f.u. mol
(5)
But the second question is how much energy is required to roll up a certain amount of surface layers to form a nanotube. Therefore, further investigations of the corresponding nanotube structures were made and as a measure of the relative stability with respect to the planar surface the strain energies ΔE are used. D
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Figure 7. Complete reaction path with initial reaction 1 (see Table 1).
ΔE is defined by eq 6, similar to a former study,41 but with the surface unit cell as reference. Etot(nanotube) − Etot(slab) (6) N1 The strain energies ΔE were used to evaluate the energetic driving force for nanotube formation. The results for anatase:NaOH and Na2Ti3O7 are displayed in Figure 8, and ΔE =
Figure 9. Possible pathways for the initial step of the reaction mechanism with titanium (gray), oxygen (red), sodium (blue), and hydrogen (turquoise).
Figure 8. Strain energies of the anatase with ions adsorbed on the inner surface and sodium titanate with Na2O removed on both surfaces and Na+ and OH− on the inner surface (see eq 6).
and on top of an oxygen atom. As a result the stoichiometry is Na2H2Ti4O10 with 18 atoms in the surface unit cell (see Figure 9a). We found an NaOH adsorption energy of ca. −165 kJ/mol on the anatase surface with respect to one formula unit NaOH. The second model exhibits a titanate structure, but similar to the anatase adsorption model the Na+ and OH− ions are restricted to one side of the slab. To adjust the stoichiometry to that of the first model, Na2O is formally removed from the surfaces of the slab (see Figure 10a,b). On one of the surfaces NaOH is absorbed (see Figure 10b,c) so that the resulting composition is Na2H2Ti6O14 with 24 atoms in the surface unit cell (see Figure 9c). Due to the smaller area of the surface unit cell, the adsorption places are more restricted than on the anatase(101) surface. Ideally the stoichiometry of the two models should be identical for the nanotube models as well. As can be seen in the previous paragraph, the surface unit cell of NaHTi3O7 for both structures would have contained 48 atoms, this could not be achieved for the nanotubes in the present study
the data can be found in the Supporting Information. Etot is the calculated total energy of the fully relaxed 2D system with the same number of layers as the nanotubes. The variable N1 is the number of surface unit cells in the 1D periodic nanotube unit cell (see eq 1). The formation of nanotubes from single-crystal surfaces is energetically favored when ΔE is negative. In the following the strain energies are used as a measure for the relative stability of different nanotubes. To characterize the interactions between Na+, OH− and the surface and their influence on the formation of nanotubes in detail the ΔE of two different model structures was calculated. The first model is a two-layer anatase(101) slab with one-sided adsorption of two OH− anions and two Na+ cations to form a monolayer of sodium hydroxide (Figure 9a). The adsorption sites were chosen to saturate 5-fold coordinated Ti atoms with hydroxide groups. Na+ cations were placed on two oxygen atoms E
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
Figure 10. Composition of titanate model structure for reaction 1 (see Table 1).
due to limitations of computational resources. For the nanotube models we rolled the surface in such a way that the NaOH is adsorbed on the inside of the nanotube. Since the nanotube walls found experimentally are thicker than the 1 to 3 atomic layers that have been used in other studies,28,29,41,42 we decided to specifically improve this aspect of our model. It was checked that the outside adsorption leads to less stable structures, according to larger distances between adsorbed Na+ and OH − and therefore decreased attractive Coulomb interaction. For anatase nanotubes with Na + and OH − adsorption on the outer face the calculated strain energies were between 23 and 31 kJ/mol. We assume that the attractive interaction between adsorbed Na+ and OH− on the inside of the nanotube is the driving force for the detachment of single titania layers from the microparticle surface and the formation of the observed stripes. This is similar to the study of Li et al., who found that the possible intercalation of Na+ into the surface structure may dissolve titania stripes.13 The two slabs with their corresponding nanotube models representing the two possible pathways are shown in Figure 9. (a) Anatase stripes (Figure 9a) are formed which could roll up into anatase nanotubes (Figure 9b) followed by a phase change to titanate nanotubes (Figure 9d). (b) The phase change from anatase to titanate on the anatase surface (Figure 9a and 9c) is the other possibility, titanate nanotubes (Figure 9d) are rolled up in the following. Our assumption of the mechanism is shown in Figure 7: Na+ diffusion to the kinks and edges of the microcrystalline TiO2 surface leads to intercalation of ions and induces the detachment of stripes (see Figure 6). Attractive interactions between the adsorbed Na+ and OH− ions on the nanotube inside lead to surface strain which is compensated by a curvature, completed by the nanotube formation of the anatase stripes. This is supported by the finding that the anatase nanotube models with sodium and hydroxide on their outside are less stable than the ones with adsorbed ions on the inside. Experimentally the average radius of the nanotubes was 20 nm (based on TEM pictures, not shown). Due to computational limitations, it was not possible to match the radii of theoretical nanotube models to these experimental findings. To associate experimental and theoretical results the data points were fitted to a 1/rn series. This is similar to a former study by Enyashin et al.,43 who found a 1/r2 dependence for their nanotubes. Based on the fit function we estimated the slope of the function. The energetic results reveal not only the attractive interaction between the anatase surface and the adsorbed ions but also the relaxed structures of the nanotube models. As a representative for the general trend during structure relaxations a cutout of the 14.5 Å nanotube model is shown in Figure 11. During relaxation, Na+ and OH− move closer to the surface layers so that a more regular
Figure 11. Frontal cutout of an anatase nanotube model with rstart = 14.5 Å.
structure is formed (see Figure 11b). The average distance change between unrelaxed and relaxed structure was 0.4 Å for oxygen and 0.8 Å for sodium. It can be concluded that the Na+ and OH− ions on the inner face of the nanotubes stabilize the curvature of the anatase stripes and can therefore induce the formation of nanotubes. Finally we compared the strain energy of the anatase model with adsorbed Na+ and OH− and the titanate model where Na2O was removed from both surfaces and sodium and hydroxide ions were put on the inner surface (see Figure 8). The data were fitted to a 1/rn series. The fit function of the modified titanate nanotubes converges at relatively small radii. In agreement with a former DFTB study by Enyashin et al.43 we found the TiO2 nanotubes to be more stable than the titanate species. Furthermore, the formation of modified sodium titanate nanotubes is endothermic with ΔE > 30 kJ/mol. Although sodium titanate is thermodynamically more stable than anatase, the titanate nanotubes cannot be formed directly starting from their corresponding slabs. On the contrary ΔE for anatase(101):NaOH is negative, converging to −40 to −50 kJ/mol. We therefore conclude that the formation of sodium titanate follows Mechanism 1 instead of Mechanism 2. From the two possible reactions following after NaOH adsorption on anatase nanoparticles, phase transition to modified sodium titanate is thermodynamically favorable but does not lead to nanotube formation. The metastable anatase(101):NaOH layers may roll up in a concave way as depicted in Figure 7 and later undergo a phase transition to sodium titanate nanotubes.
■
CONCLUSIONS After complementary experimental and theoretical investigations we suggest a consistent mechanism for the initial step of the formation of titania nanotubes. We verified the hydrothermal F
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
(12) Kukovecz, A.; Hodos, M.; Horváth, E.; Radnóczi, G.; Kónya, Z.; Kiricsi, I. J. Phys. Chem. B 2005, 109, 17781−17783. (13) Li, M.-J.; Chi, Z.-Y.; Wu, Y.-C. J. Am. Ceram. Soc. 2012, 95, 3297− 3304. (14) Tsai, C.-C.; Teng, H. Chem. Mater. 2006, 18, 367−373. (15) Zhang, S.; Chen, Q.; Peng, L.-M. Phys. Rev. B 2005, 71, 014104− 1−014104−11. (16) Wu, D.; Liu, J.; Zhao, X.; Li, A.; Chen, Y.; Ming, N. Chem. Mater. 2006, 18, 547−553. (17) Ren, L.; Qi, X.; Liu, Y.; Zou, X.; Huang, Z.; Li, J.; Yang, J.; Zhong, L. Cryst. Res. Technol. 2012, 47, 738−745. (18) TiO2 Nanotube Arrays: Synthesis, Properties, and Applications; Springer: Berlin, Germany, 2014. (19) Zhang, S.; Peng, L.-M.; Chen, Q.; Du, G.; Dawson, G.; Zhou, W. Phys. Rev. Lett. 2003, 91, 256103−1−256103−4. (20) Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V. R.; Zicovich-Wilson, C. M. Z. Kristallografiya 2005, 220, 571−573. (21) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; DArco, P.; Llunell, M. CRYSTAL09 User’s Manual; University of Torino: Torino, Italy, 2009. (22) Noel, Y.; D’Arco, P.; Demichelis, R.; Zicovich-Wilson, C.; Dovesi, R. J. Comput. Chem. 2010, 31, 855−862. (23) Perdew, J.; Ruzsinszky, A.; Csonka, G.; Vydrov, O.; Scuseria, G.; Constantin, L.; Zhou, X.; Burke, K. Phys. Rev. Lett. 2008, 100, 136406− 1−136406−4. (24) Perdew, J. Electron. Struct. Solids 1991, 11. (25) Perdew, J.; Burke, K.; Ernzerhof, M. PRL 1996, 77, 3865−3868. (26) Bredow, T.; Gerson, A. R. Phys. Rev. B 2000, 61, 5194−5201. (27) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158−6170. (28) Szieberth, D.; Ferrari, A.; D’Arco, P.; Orlando, R. Nanoscale 2010, 3, 1113−1119. (29) Evarestov, R.; Zhukovskii, Y.; Bandura, A.; Piskunov, S. J. Phys. Chem. C 2010, 114, 21061−21069. (30) Esch, T.; Gadaczek, I.; Bredow, T. Appl. Surf. Sci. 2014, 288, 275− 287. (31) Andersson, S.; Wadsley, A. D. Acta Crystallogr. 1961, 14, 1245− 1249. (32) Holzinger, M.; Benisek, A.; Schnelle, W.; Gmelin, A.; Maier, J.; Sitte, W. J. Chem. Thermodyn. 2003, 35, 1469−1487. (33) Chase, M. J. J. Phys. Chem. Ref. Data, Monogr. 1998, 9, 1−1951. (34) Peintinger, M.; Oliveira, D. V.; Bredow, T. J. Comput. Chem. 2013, 34, 451−459. (35) Burdett, J.; Hughbanks, T.; Miller, G.; Richardson, J. W., Jr.; Smith, J. J. Am. Chem. Soc. 1987, 109, 3639−3646. (36) Herman, G.; Dohnalek, Z.; Ruzycki, N.; Diebold, U. J. Phys. Chem. B 2003, 107, 2788−2795. (37) Chen, Q.; Du, G.; Zhang, S.; Peng, L.-M. Acta Crystallogr. 2002, B58, 587−597. (38) Feist, T.; Davies, P. Solid State Chem. 1992, 101, 275−295. (39) Labat, F.; Baranek, P.; Adamo, C. J. Chem. Theory Comput. 2008, 4, 341−352. (40) Navrotsky, A. Chem. Phys. Chem. 2011, 12, 2207−2215. (41) Ferrari, A.; Szieberth, D.; Zicovich-Wilson, C.; Demichelis, R. J. Phys. Chem. Lett. 2010, 1, 2854−2857. (42) Ferrari, A.; Szieberth, D.; Noel, Y. J. Mater. Chem. 2011, 21, 4568. (43) Enyashin, A.; Ivanovskii, A. J. Phys. Chem. C 2009, 113, 20837− 20840. (44) Kokalj, A. J. Mol. Graphics Modell. 1999, 17, 176−179.
synthesis route for titania nanotubes via microcrystalline TiO2 precursor and 10 M NaOH solution.2 Our theoretical results indicate that the adsorption of Na+ and OH− on the surface and the resulting concave curvature of the anatase stripes is a necessary requirement for the formation of the nanotubes. Attractive forces between the adsorbed anions and cations induce this curvature. Shortly after the hydrothermal synthesis is started and at the point where the surface stress exceeds a certain limit, the nanotubes are formed. The long reaction time of 48 h leads to a phase transition from anatase-like nanotubes into titanate nanotubes which can be further treated according to reactions 2 and 3 in Table 1. From the combined experimental and theoretical data we can reason that the phase transition to titanate is induced after nanotubes are formed from dissolved anatase stripes. Further studies are necessary to verify the complete mechanism.
■
ASSOCIATED CONTENT
* Supporting Information S
A schematic diagram of the automatic nanotube construction implemented in the CRYSTAL program package and a table containing the calculated surface energies of anatase and titanate as well as the calculated strain energies for the nanotubes. This material is available free of charge via the Internet at http://pubs. acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS Figures 2, 9, 10, and 11 have been created with the XCrysden program.44 This work was partially supported by BMBF (Bundesministerium für Bildung und Forschung - Federal Ministry of Education and Research). We acknowledge financial support by the DFG (Deutsche Forschungsgemeinschaft − German Science Foundation) within the research unit FOR 1277 (WA 1116/19).
■
REFERENCES
(1) Tenne, R.; Rao, C. Philos. Trans. R. Soc. London A 2004, 362, 2099− 2126. (2) Kasuga, T.; Hiramatsu, M.; Hoson, A.; Sekino, T.; Niihira, K. Langmuir 1998, 14, 3160−3163. (3) Roy, P.; Berger, S.; Schmuki, P. Angew. Chem. 2011, 123, 2956− 2995. (4) de Angelis, F.; di Valentin, C.; Fantacci, S.; Vittadini, A.; Selloni, A. Chem. Rev. 2014, 114, 9708−9753. (5) Yu, J.; Low, J.; Xiao, W.; Zhou, P.; Jaroniec, M. J. Am. Chem. Soc. 2014, 136, 8839−8842. (6) Galynska, M.; Persson, P. Int. J. Quantum Chem. 2013, 113, 2611− 2620. (7) Wang, Y.; Sun, T.; Yang, D.; Liu, H.; Zhang, H.; Yaob, X.; Zhao, H. Phys. Chem. Chem. Phys. 2012, 14, 2333−2338. (8) Wang, Y.; Liu, H.; Zhang, H.; Yao, X.; Zhao, H. Chem. Phys. Lett. 2011, 511, 82−86. (9) Enyashin, A.; Seifert, G. Phys. Status Solidi B 2005, 242, 1361− 1370. (10) Vittadini, A.; Casarin, M.; Selloni, A. Theor. Chem. Acc. 2007, 117, 663−671. (11) Yang, J.; Jin, Z.; Wang, X.; Li, W.; Zhang, J.; Zhang, S.; Guo, X.; Zhang, Z. Dalton Trans. 2003, 3898−3901. G
DOI: 10.1021/jp5110399 J. Phys. Chem. C XXXX, XXX, XXX−XXX
