Mechanisms of Phase Transformations of TiO2 Nanotubes and

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Mechanisms of Phase Transformations of TiO2 Nanotubes and Nanorods Andrei Buin, Styliani Consta,* and Tsun-Kong Sham Department of Chemistry, The University of Western Ontario, London, Ontario, Canada N6A 5B7

bS Supporting Information ABSTRACT: Phase transformations of titanium dioxide (TiO2) nanotubes and nanorods at elevated temperatures are studied using molecular dynamics (MD) and replica exchange molecular dynamics (REMD) utilized here in the same way as simulated annealing. In the study, TiO2 nanotubes with amorphous (amT) and anatase structures (anT) as well as TiO2 amorphous nanorods (amR) that are amenable to experimental investigation are considered at various temperatures. It is found that amT and amR transform into a rutile rod, while anT transforms into a brookite nanotube. It is demonstrated that transformation of anT starts from TiO4 and TiO5 complexes found in the surfaces of the system, in contrast to amT and amR, where initial grains of the new phase may develop throughout the entire system starting from TiO5 and TiO6 complexes. The evolution of the number of TiOx (x = 4, 5, 6, 7) complexes indicates that the transformation of amT and amR occurs almost suddenly relative to the transformation of anT. The initial grains of transformation of amT have a structure close to rutile, while those of anT have brookite features. To our knowledge, we report the first simulations of phase transformations of TiO2 nanotubes and nanorods where simulations are performed beyond μs.

’ INTRODUCTION Synthesis and characterization of the various thermodynamic phases of TiO2 (titania) nanotubes have attracted considerable attention in the past decade because of the versatile properties of TiO2 nanotubes in photocatalysis, medicine, gas sensing, electrochemistry, and energy conversion.1 It is known that TiO2 can be found in nature in anatase, rutile, and brookite crystalline forms.26 The TiO2 polymorphs are composed of connected distorted octahedra with titanium at the center and one oxygen at every vertex. However, the octahedra are differently distorted in the various polymorphs and form distinct unit cells. Thermodynamically, rutile is the most stable of the three phases in bulk systems. In nanosystems, the three polymorphs are still prevalent but stability is size-dependent. It has been found experimentally7 and studied by simulations8 that, in nanoparticles, rutile is the most stable phase in sizes larger than 35 nm, brookite is stable from 14 to 35 nm, and anatase in smaller sizes. In TiO2 nanotube and nanorod systems, recent experiments detect the polymorphs and composition of their mixtures.9,10 However, molecular mechanisms of the phase transformations and the effect of the size of nanotubes and nanorods in stability have not yet been investigated. Knowledge of the transformation mechanism is needed in order to control the transformation and, thus, improve the performance of TiO2 nanotubes in photocatalysis, gas sensing, and gas separation as well as synthesize polymorphs with desirable properties. It has been found that performance in various applications depends on the composition of the TiO2 polymorphic mixtures. For instance, thermodynamically metastable states, such as anatase or mixtures of anataserutile, have r 2011 American Chemical Society

demonstrated better photocatalytic activity and antibacterial action at elevated temperature11 than rutile. Phase transformations of TiO2 are important not only in practical applications but also in the synthesis of nanotubes. Conversion of initial amorphous TiO2 nanotubes into crystalline phases by annealing between 500 and 700 C is an essential process in the last stage of synthetic routes that use anodic oxidation,1215 hydrothermal methods,16,17 and template methods.1820 Recently, phase transformations of TiO2 nanotubes produced by anodic oxidation at various calcination temperatures have been detected by X-ray absorption near-edge structure (XANES) and X-ray excited optical luminescence (XEOL).10 In computations, to date, there is limited study on the stability of TiO2 nanotubes and the related systems of nanoslabs. In these works, quantum density functional theory (DFT) and self-consistent-charge density functional tight binding (SCCDFTB)21 are used for thin nanotubes with small radii and up to a few hundreds of atoms in order to study their stability and formation.2226 In this paper, mechanisms of phase transformations of TiO2 nanotubes and nanorods at elevated temperatures are presented that are studied by molecular simulations. The systems that we study contain four to six unit cells of TiO2 between the surfaces. It has been demonstrated for nanoparticles that the stability of phases is size dependent;7 therefore, it is expected that the regime Received: August 11, 2011 Revised: October 2, 2011 Published: October 04, 2011 22257

dx.doi.org/10.1021/jp2077006 | J. Phys. Chem. C 2011, 115, 22257–22264

The Journal of Physical Chemistry C of sizes that we study may exhibit different phase stability from very thin nanotubes or nanoslabs. However, the systems are still thin enough so as surface effects are important. The reported simulations do not consider impurities or interstitial defects, besides the obvious defects that arise from the surfaces themselves. Elevated temperatures were chosen because phase transformations in experiments take place at high temperatures and certain applications of titania nanotubes operate at elevated temperature. Our findings provide insight in the mechanisms of transformation that may take place in the calcination stage of production of TiO2 nanotubes by anodic oxidation, hydrothermal, and template methods. Since the experimental conditions are way more variable and less controlled than one may prepare in simulations, the similarities between experimental findings and simulations are at generic features of the transformations. Moreover, the simulations provide molecular details about the nucleation that cannot be readily detected in the experiments. Undesirable impurities is an important issue in experiments, such as residual Li+ or Na+ impurities in the last stage of hydrothermal methods.12 More usually than not, the TiO2 nanotubes are found at ambient conditions that involve humidity. Humidity may cause the formation of titanium hydroxy compounds on the surface of the tubes. Furthermore, in certain experimental methods that produce TiO2 nanotubes, the nanotubes are attached on Ti foil,10 and as a result, the connection of nanotube to the foil is also a source of impurity or defect. Oxygen defects on the surface and interior are also common. Understanding the role of defects and impurities in phase transformations deserves its own experimental and computational study. One of the advantages of computations in this investigation is that one can achieve better control of conditions, locations, and concentrations of defects. A complete computational study of the topic has to be comparative, between the realizations without and with defects or impurities. In this regard, understanding of the phase behavior of systems without impurities is the first step in the study of phase transformations in TiO2 nanotubes. Regarding the size of the nanotubes, it is noted that the atomic layer deposition method20 using organic template nanowire, which can be easily removed after TiO2 nanotubes are formed, can better control thickness and uniformity. The template method may produce TiO2 nanotubes with an external diameter as low as 40 nm with a thickness as low as 5 nm, which are within the range of sizes that is investigated by our simulations. In our simulations, we mimic to some extent what happens in the phase transformations in experiments closer than has been done so far. The potential energy surface of the TiO2 nanotubes and nanorods is interspersed by deep energy basins of metastable states that may be polycrystalline phases and stable states. Direct molecular dynamics (MD) was used in order to monitor the initial formation of nuclei and their growth during the transformation. However, direct MD is not sufficient to identify longliving metastable states in the time of simulations. Basins in the potential energy surface of TiO2 nanotubes and nanorods were identified by replica exchange MD (REMD)2730 used here in the same spirit as simulated annealing. It is found that amT and amR transform into rutile rod, following a transformation path that depends on temperature. anT transforms gradually into brookite tube. The transformations of amT and amR occur more rapidly than those of anT. Analysis of the initial grains in the formation of the new phase reveal that the transformation in anT starts mainly from the surface, while in amT and amR it may start

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Table 1. Parameters for the MA Potential Function ij

Aij (kcal/mol)

Fij (Å)

C (kcal Å6/mol)

TiTi

717654

0.154

120.997

TiO

391053

0.194

290.392

OO

271719

0.234

696.941

from the surface or interior. It is found that in anT the formation of grains initiates from TiO4 and TiO5 complexes that likely transform into brookite grains. In amT and amR, TiO5 and TiO6 complexes play a role in the transformation and the grains that develop have a structure close to rutile.

’ MODEL AND COMPUTATIONAL METHODS The systems were modeled by the MatsuiAkaogi (MA) allatom force field.31 In the MA model, the potential energy function between any two atomic sites i and j is given by ! rij Cij qi qj ð1Þ 6 þ Uðrij Þ ¼ Aij exp Fij rij rij where the charge of the oxygen site is qO = 1.098e and that of the titanium site is qTi = +2.196e. Additional parameters are presented in Table 1. Regarding simulations of bulk TiO2 comparisons performed by Collins et al.32 for different force fields of titania, it was found that the MA force field for bulk TiO2 reproduces a range of properties of the brookite, anatase, and rutile TiO2 bulk crystals, such as crystal structures, volume compressibility, and volume thermal expansivity. Van Hoang33 did extensive testing of amorphous TiO2 structures and found MA to reproduce the distorted octahedral network structure with the mean coordination numbers of TiO and OTi like those observed in experiments. Swamy et al.34,35 did a comparison between MA force field and more sophisticated variable-charge method for bulk TiO2 and concluded that the MA force field performs better than the variable-charge method. Regarding surfaces, quantummechanical investigation for surfaces by Bandura et al.36 led to the conclusion that the MA force field is comparable to superior quantum mechanical methods. In several computational works8,3741 on nanosized systems, the surface plays a major role and the MA force field has been successfully applied. For instance, Naicker et al.8 predicted the correct trend in stability of different phases of nanoparticles, and Koparde et al.40,41 studied nanoparticle sintering modeled by the MA force field. We tested the validity of MA in modeling nanoslabs of various thicknesses against the SCC-DFTB method. The SCC-DFTB method was used as implemented in the program DFTB+21 with the SlaterKoster parameters for OO interactions taken from the mio parameter set42 and TiO and TiTi interactions taken from the trans3d43 parameter set. To measure the quality of the force field, we used the vibrational density of states (VDOS), which is expressed by VDOSðωÞ ∼

Z ∞ ∞

expðiωtÞÆvð0ÞvðtÞæ dt

ð2Þ

where v is the 3N-dimensional velocity vector. Comparison of VDOS for rutile monolayer and nanoslab thickness of five unit cells (2.3 nm) using MA and SCC-DFTB is shown in Figure 1. Figure 1 demonstrates that nanoslab MA gives comparable VDOS to SCC-DFTB VDOS, but the spectra become considerably 22258

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Table 2. Parameters for the System and Methods Used in the Simulationsa S

D (nm) L (nm) number of atoms T (K) range of REMD NR

amT

13.2

2.85

31392

14502000

32

amR anT

5.5 9.3

4.45 3.81

10620 19392

15202370 15502300

32 42

a

System (S), outer diameter (D), box size along the tube axis (L), temperature (T), and number of replicas (NR).

Figure 1. Vibrational density of states of rutile monolayer (upper panel) and nanoslab with a thickness of 5 unit cells (2.3 nm) (lower panel) modeled by SCC-DFTB and MA force field.

Figure 2. Examples of potential energy relaxation of amT trajectories at 1525 and 1650 K using direct MD and REMD. The inset magnifies the long time relaxation. The steps in the potential energy vs time arise because of the replica exchanges.

different at monolayer and thickness much less than 2.3 nm. The wall thickness of anT and amT was set to 3.0 and 2.7 nm, respectively, which is slightly larger than the minimum size that can be modeled by MA. The outer diameter of anT and amT was set to 9.3 and 13.2 nm, respectively, which is close to experimentally synthesized4446 TiO2 nanotubes with diameters in the range 415 nm. The smallest number of atomic sites simulated is 10620, and the largest is 31392. The study took place at elevated temperatures of T = 14502800 K. For systems of this size and rigidity, direct MD is not expected to be efficient even at the equilibration stage. On the other hand, REMD is a Monte Carlo scheme that allows for dramatic configurational changes in the system by exploiting configurations at elevated temperatures. REMD by construction cannot be used for sampling the coexistence of phases in first-order phase transitions (see the Supporting Information). However, it can be used to locate metastable states with better performance than simulated annealing, as shown by Deem et al.47 Efficiency of REMD vs direct MD is demonstrated in the examples presented in Figure 2. Evolution of the potential energy shows that for amT the short time relaxation is achieved within 20 ns with REMD vs

60 ns with direct MD at T = 1525 K. It is noted here that in REMD, which is an MC method, the reported time is the accumulated time of the short MD trajectories that take place between the swapping of the configurations. In the long time, the energy of the direct MD indicates that the trajectory has been trapped in local minima that are at higher energy than the minima detected by REMD. As expected the efficiency of REMD is more significant at lower temperatures than higher. In these calculations, direct MD runs were performed using 1664 8-core Intel Xeon E5540 cpu's and REMD runs using 2561024 cpu's. Simulations were performed with GROMACS version 4.5.1,48 where the MA potential function was implemented. GROMACS simulations of TiO2 nanotubes were also tested against DL_POLY v.4,4951 and it was found that GROMACS outperformed DL_POLY in speed, which allowed us to study large systems efficiently. Three systems were studied: amorphous tube (amT), amorphous rod (amR), and anatase tube (anT). The lowest lying replica was used in the analysis of the data. Details of the structure and methods are presented in Table 2. All tubes were cut directly from bulk anatase structure in the plane orthogonal to the tube axis being along the [001] direction. In order to maintain charge neutrality, some oxygen atoms have been removed from the surface; hence, Ti sites closer to the surface have coordination number 4 or 5. Surface reconstruction has not been considered, where coordination number can be the same as in the bulk.23 Amorphous structures were prepared by annealing the anatase phase from 300 K up to 2700 K for 28 ps, followed by rapid quenching to 1230 K for 4 ps. Periodic boundary conditions were applied in all three directions x, y, z. The distance between the periodic images in the plane orthogonal to the tube axis was set to 80 Å in order to diminish the electrostatic interactions between images. The cutoff distance for short-range interactions was set to 10 Å, and the electrostatic interactions were treated with particle-mesh Ewald (PME).52 For all the representative systems, direct MD in the NVT ensemble was performed for 1.0 μs, and REMD for 100 ns per replica (3.24.2 μs total time). The MD integrator was leapfrog with a time step of 3 fs (see the Supporting Information). Swaps of configurations were attempted every 5 ps. All calculations were performed in the canonical (NVT) ensemble using a NoseHoover thermostat with a coupling constant of 0.7 ps. After an initial run for 100 ns of direct MD, sample structures were used as initial structures for REMD calculations. Subsequently, these structures were run for 150 ps in the various replicas before starting the exchange of configurations in REMD. The analysis of the structures was done by comparing with simulated powder X-ray diffraction (XRD) patterns, as described in ref 6.8 The reference structures were generated by replicating the unit cell of the corresponding phases in three dimensions so as sufficiently large systems were created to represent the XRD spectrum. 22259



Figure 3. Snapshots53 of the initial and final states of the systems described in Table 2 taken from REMD simulations. The red color represents the oxygen site and the green titanium. (a) initial amT that transforms into (b) rutile rod; (c) initial amR that transforms into (d) rutile rod; (e) initial anT that transforms into (f) brookite tube.

In our calculations, the temperature range for REMD was determined by testing various temperature ranges both with direct MD and REMD. The aim was to include replicas at temperatures slightly beyond the melting temperature. Trial and error showed that for anatase tube temperature close to 2300 K, was slightly beyond the melting temperature, which in the right range based on the finding of Koparde et al. for melting of nanoparticles.40 In the same way, the melting temperature of brookite was found to be ∼2800 K. Rutile did not melt up to 2820 K. Low temperature for the REMD was chosen according to the highest temperature and reasonable number of replicas that maintain initial overlap.

’ RESULTS AND DISCUSSION Transformation of amT and amR. REMD-based search of the potential energy surface showed transformation of amT and amR into rutile rod and captured distinct intermediate states. Typical snapshots53 of the initial amT and final state within the simulation time are shown in Figure 3a and b, respectively. The simulated XRD pattern of the final structure is shown in Figure 4A. The final state of amT has peak locations that almost coincide with the reference structure, which suggests a nearly perfect monocrystalline rutile phase. Direct visual inspection of Figure 3b also confirms the XRD result. We selected two typical examples of direct MD to present here, that demonstrate the manner that temperature may affect the transformation path.

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Figure 4. XRD spectra of reference (ref.) structures of anatase, rutile, and brookite, as well as final configurations in the lowest lying replica. (A) Final configurations starting from amR and amT depicted in Figure 3b and d, respectively. (B) Final configurations starting from anT depicted in Figure 3f. The inset in part B shows the XRD pattern of an anT intermediate in the course of the transformation and comparison with the reference and final anT structures. The anT intermediate shows the presence of an anatase phase.

At 1525 K, amT transforms into a shrunk rutile tube within 73 ns. Most likely, the system will eventually evolve into a rutile rod based on the energetics (3.979 107 kJ mol1 for shrunk rutile tube vs 3.983 107 kJ mol1 for rutile rod averaged over 1 ns). The transformation is initiated by grains formed in the inner and outer surface that evolve into initial crystalline rutile within 2.5 ns. At 1650 K, the amT goes initially into amorphous rod and then to rutile rod by formation of grains into the bulk and surface regions. An example of grain formation inside and on the surface of the rutile rod is shown in Figure 5. In order to characterize the structure of the initial interior nucleus (central highlighted region in Figure 5a), lattice periodicity was identified in three orthogonal directions. Lattice parameters, as indicated in Figure 5b, were found to be a = b = 4.56 Å and c = 3.12 Å on average in a single time frame, which is in close agreement with the rutile parameters (a = b = 4.59 Å and c = 2.959 Å). The c length of the new grain is 5% higher than the rutile possibly because of residual stress. The facile formation of grains throughout the nanorod may be attributed to the distorted TiO2 octahedral network (point defects such as TiO4, TiO5, and TiO7 structural units) and vacancy-like defects in the amorphous rod.54 Characterization of 22260



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Figure 5. (a) Grain formation inside amT within 10 ns for the same trajectory in the course of direct MD at T = 1550 K. (b) Magnification of the details in the interior grain with lattice parameters shown. Average lattice parameters are a = b = 4.56 Å, c = 3.12 Å.

Figure 6. (a) Segment of an anatase tube in the course of direct MD at T = 1840 K that shows the initial stage of the transformation of anT. (b) Close-up of the newly formed phase. The arrows point toward the periodicity along the y-axis. The newly formed structure has brookite features.

the structure of the amT and its later form was performed by radial distribution profiles of the average coordination numbers of Ti averaged over the tube axis (see the Supporting Information). The closest coordination number of Ti sites was determined by the oxygen sites within a sphere of 2.4 Å . The profiles show that the average coordination number of Ti in amorphous bulk deviates from 6, which is due to the presence of a non-negligible amount of TiO5 (found in the surface and bulk) and TiO7 (found in bulk). TiO4 is also present, which is mainly found in the surface. In a layer of 8 Å in the proximity of the inner and outer surfaces, the coordination number falls off from bulk value to average values of 4 and 5. The role of TiO5 and TiO6 in the transformation of amT as time progresses is shown in Figure 7a and b, respectively. As Figure 7a,b indicates, TiO6 is formed at the expense of TiO5, while TiO4 and TiO7 play a minor role. Figure 7c depicts the rate (dN/dt) of formation or depletion of TiOx (x = 4, 5, 6, 7) units, where one can see that, once a grain is formed, the growth of the new phase happens within 20 ns. One also expects the time to form a grain is temperature dependent. Since the amorphous rod was identified as a distinct intermediate of amT, it was selected for further investigation by simulating a new NVT ensemble of the rod (Figure 3c,d). The XRD pattern of the final configuration of amR (Figure 4A) reveals a bimodal (110) peak and shifted (101) peak, which can be attributed to the existence of the polycrystalline rutile phase and residual stress within the tube, respectively. Even though the

simulation of amR ended in the polycrystalline phase, it is very likely that it will proceed to the monocrystalline phase, since such polycrystalline intermediates were also observed in the amT simulation. Microscopic details of the transformation of amR's (initiated from amT and amR) reveal development of domains with crystalline features on the surface and bulk region. Direct MD at 1400 K shows initially the development of one domain that extends very slowly within 1.0 μs, while REMD identifies intermediates with a few crystalline-like domains that do not necessarily have the same orientation of crystalline planes. Combined MD and REMD data suggest that the crystalline domains may not necessarily start out simultaneously. REMD identified few exceptions of intermediates with grain formed inside the amorphous rod. Transformation of anT. REMD for anT (Figure 3e) shows formation of brookite tube (Figure 3f), which is characterized by an XRD pattern in Figure 4B. For the anT, one can see preferable orientation based on the relative intensity of the (121) peak with respect to the first peak. Initially, anT went into a distinct intermediate state, with the presence of anatase and brookite phases at approximately 1:2 ratio, which can also be tracked in the inset of Figure 4B. After subsequent restart of REMD from the intermediate state, the system did convert fully into monocrystalline brookite, which can also be seen in the inset of Figure 4B. The brookite structure was further investigated by starting several REMD simulations from the lowest temperature replica, 22261



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Figure 7. (a) Time dependence of radial distribution profiles of TiO5 units in amT at T = 1650 K. (b) The same but for TiO6. (c) Rate of formation or depletion of TiOx (x = 4, 5, 6, 7) units in amT. (d) Radial distribution profiles of TiO4 and TiO5 units in equilibrated anT at T = 1840 K. (e) Rate of formation or depletion of TiOx (x = 4, 5, 6) units in anT. We note that the radial distribution profiles have not been normalized in order to compare the absolute values.

1550 K, spanning different temperature ranges. No phase transformation of brookite was observed for 40 ns of REMD (1.4 μs total time) in the temperature range 16002787 K. The results presented here are in line with the observation of Koparde et al.,41 who observed sintering of anatase and amorphous nanoparticles into brookite structure. Direct MD at 1840 and 2100 K captures the initial stage of transformation, which starts from the surface. The initial formation of a region of the new phase is shown in Figure 6a, which depicts a segment of the tube. Figure 6b shows that the melted phase leaves one plane intact with an interplanar distance of 5.72 Å. This is an indirect indication that the new formed phase is brookite, as one of its lattice parameters is equal to 5.47 Å. Figure 7d shows that TiO4 and TiO5 were distributed in the surface layer, with a small concentration of TiO5 in the bulk region. TiO7 was not

statistically significant throughout the tube. The rate of growth of TiO4, TiO5, and TiO6 units is depicted in Figure 7e and shows that the rate of growth of TiO4 and TiO5 is negligible relative to those of the amT. It is also shown that TiO5 forms at the expense of TiO4. Since TiO4 and TiO5 are found simultaneously on the surface, the combination of data in Figure 7d,e suggests that surface reconstruction takes place. For anT, 1.2 μs was not sufficient for the complete transformation, which is expected, since in experiments time of the order of milliseconds and longer is used to ensure the transformation. REMD, on the other hand, did also show the growth of the new phase as a frontal propagation. A variety of intermediates arise because of the progressive formation of crystalline regions in the anatase tube. Analysis of direct MD runs of amR and anT at elevated temperatures suggests that initially the Ti and O atoms hop to 22262



Figure 8. Root mean square displacement vs time for amT and anT at various temperatures.

local energy basins (see the Supporting Information) and their mobility decreases in time, leaving only small oscillations at equilibrium position. The collective mobility of the Ti and O sites is monitored by the root-mean-square displacement (rmsd) of their positions from their initial positions presented in Figure 8. Figure 8 shows that phase transformation of amorphous structure takes place much faster than the crystalline anatase phase transformation. The anatase phase transformation is gradual as opposed to amorphous into crystalline that occurs suddenly. The sudden changes are also reflected in the rate of formation/ depletion of TiOx (x = 4, 5, 6, 7), as shown in Figure 7. These features are in line with the MA force field, which is dissociative by nature. The hopping at the initial stage agrees with the reported reconstructive mechanism for bulk TiO2 anatase to rutile transformation. The features of transformations reported here are independent of initial conditions for the particular simulated systems, and this is supported by a number of runs that started from different initial conditions. However, in simulations and experiments, the path may be affected by temperature, imperfections, impurities, and environment.

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to a better understanding of how impurities affect the rate and transformation pathway. For the sizes of systems we investigated, long simulation times preclude DFT modeling of interactions from studying nucleation and growth events. It was demonstrated that transformation of anT starts from TiO4 and TiO5 complexes found in the surfaces of the system, in contrast to amT and amR, where initial grains of the new phase may develop throughout the entire system starting from TiO5 and TiO6 complexes. The mechanism of transformation of amT and amR supported by the simulations is that initially few grains form throughout the system that propagate until they have a common interface, and then long-time reorientation takes place. A side-result in utilizing REMD was the melting temperatures of anatase and brookite nanotubes that were found to be significantly different (2300 vs 2800 K, respectively). Rutile did not melt up to 2820 K, which suggests that brookite T rutile is very difficult to capture at lower temperatures by direct MD and Monte Carlo methods. For lower temperatures, the nuclei will form in a much longer time than nanoseconds. In this case, it would be impractical to collect nucleation events by direct MD. One then has to rely on definitions of order parameters to define the nuclei and sampling of the nuclei configurations by using methods for activated processes, such as umbrella sampling. A successful choice of order parameters should involve initial direct observations of nuclei, that will provide information on what features of the nuclei should be modeled in the order parameters. In relation to experiment, because of the variety of the experimental conditions, we look for generic similarities between experiments and computations. In this regard, we found that the transformation of anatase starts from the surface, and that amT shrinks to form a rutile rod in agreement with observations in experiments.10 The exact way that the transformation of amT into a rutile rod proceeds is temperature dependent. The study also demonstrated that large-scale calculations close to experimental sizes and long times are feasible, and therefore can be an important tool in understanding the formation of nanophase systems and their behavior, which is crucial to controlled synthesis and engineering of desired nanomaterials.

’ ASSOCIATED CONTENT ’ CONCLUSION In conclusion, we have investigated the phase transformations of amT, amR, and anT of TiO2 at elevated temperatures, as can be predicted by the MA model. It was found that MA captures all the phases (anatase, brookite, rutile, and amorphous) and can predict different pathways of transformation depending on temperature. Utilizing REMD and direct MD, it was found that amT and amR transform directly into rutile rod at elevated temperature while anT transforms first into brookite tube in the temperature range T = 15502100 K. The transformation path of brookite T rutile cannot be clarified in the present study. Experiments also show contradicting data regarding the transformation path in nanoparticles.7 Nucleation events and growth of the nuclei were observed that cannot be readily detected in experiments because the seeds of nucleation are only a few complexes of TiOx (x = 4, 5, 6, 7) and at the same time the nucleation happens within nanoseconds at elevated temperatures. The role of TiO5,7 is similar to donor acceptor relation, where one of the bonds breaks or is added. The way that the concentration of these complexes changes can lead

bS

Supporting Information. Additional computational details with emphasis on intermediate results of replica exchange molecular dynamics and additional details on the structure of TiO2 nanotubes. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT T.-K.S. wishes to acknowledge the support of CFI, CRC, and OIT. S.C. and T.-K.S. also thank the Discovery Grant and Accelerator Grant for Exceptional New Opportunities (AGENO) of Natural Sciences and Engineering Research Council of Canada (NSERC) for funding this research and SHARC-Net, RQCHP, Scinet, Westgrid, for providing the computing facilities to perform the simulations. 22263



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