Characterization of Surface Defect Sites on Bulk and Nanophase

Feb 14, 2013 - Characterization of Surface Defect Sites on Bulk and Nanophase Anatase and Rutile TiO2 by Low-Temperature Specific Heat. Juliana Boerio...
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Characterization of Surface Defect Sites on Bulk and Nanophase Anatase and Rutile TiO2 by Low-Temperature Specific Heat Juliana Boerio-Goates, Stacey J. Smith, Shengfeng Liu, Brian E. Lang, Guangshe Li, and Brian F. Woodfield* Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, United States

Alexandra Navrotsky Peter A. Rock Thermochemistry Laboratory and NEAT ORU, University of California, Davis, Davis, California 95616, United States ABSTRACT: The specific heats of highly hydrated 7 nm nanoparticles and lightly hydrated 200 nm particles of rutile and anatase show a small, broad maximum below 5 K. The excess heat capacity can be modeled with a twolevel system having very small molar weighting factors (∼10−3 for nanoparticles, ∼10−5 for bulk) and energy separations of approximately (4.88 ± 0.06) K (7 nm particles) and (2.5 ± 0.3) K (200 nm particles). The weighting factors correspond to the number of very high-energy surface sites identified by adsorption calorimetry and to the number of isolated 3coordinate Ti defects observed on models built to the nanoparticle morphologies. We attribute the features to water adsorbed at defect sites on the particle surfaces. The very low energies associated with the Schottkytype heat capacity maxima are consistent with tunnel splittings of the ground state of a multiple-well potential. A double-well potential model for the hydrogen bonding of an OH group associated with the defects is consistent with the maxima observed for both the 7 and 200 nm particles.

1. INTRODUCTION The commonly occurring polymorphs of TiO2, rutile, and anatase find applications in numerous technical domains ranging from the use of rutile as the pigment in paints to the use of anatase in solar cells and as surfaces for photocatalysis and decomposition of water.1 There has been growing interest in using nanoparticles (NPs) of these materials because of the increased surface area of NPs and because of the potential to fine-tune desired properties such as the optical bandgap.2 Numerous studies have characterized the surface structure and reactivity of various rutile and anatase planar surfaces using ultrahigh vacuum (UHV) techniques.3,4 Relatively few other studies have considered fully hydrated NPs grown hydrothermally or in aqueous solutions.5−7 On the basis of this joint body of work, there is increasing certainty that surface defects are intimately related to the chemical reactivity of TiO2 surfaces. Most commonly the behavior of water near oxygen vacancies on planar surfaces has been studied,8−11 but recently it has been recognized that step edges are likely to play a substantial role in NP properties because of the greater dominance of the surfaces as particle size decreases. For example, Gong et al.12 estimated that 15% of surface atoms are located at step edges in a 3 nm particle. Water, which is almost always present on NP surfaces, has been used extensively as a model adsorbent on TiO2 surfaces because of its amenability for molecular modeling and because © 2013 American Chemical Society

it has important practical applications, e.g., electrochemical photolysis of water and more generally in the realm of catalysis, coatings, and corrosion.3,13 In addition, environmental scientists have interest in the structure of water at the interface of TiO2 particles because of the potential to use these materials in wastewater remediation, while geochemists are interested in the fundamentals of structure and reactivity at the mineral− water interface. Of particular interest to many is whether water dissociates when adsorbed on various surfaces or remains as an intact molecule. While there is agreement that dissociation occurs at defect sites and at low water coverage, there is some conflict between experimental results and computations about what happens when water coverage increases substantially.10,14,15 Using a suite of calorimetric techniques, we have studied the energetics of water on well-characterized NPs of TiO2 prepared using sol−gel techniques and washed extensively to remove surface impurities.16−18 In a previous publication19 we reported differences in the heat capacity of layers of water on the surfaces of 7 nm anatase and rutile NPs between 30 and 300 K; our results support observations concerning the layered structure and dynamics of adsorbed water obtained from quasielastic Received: November 7, 2012 Revised: February 14, 2013 Published: February 14, 2013 4544

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Table 1. Water Stoichiometry, Schottky Parameters, and Debye theta (θD) Values for all TiO2 Samples 7 nm particles

bulk

anatase

TiO2·0.677H2O

TiO2·0.532H2O

TiO2·0.379H2O

TiO2·0.023H2O

n/10−3 θS/K θD/K rutile

2.424 4.804 367 TiO2·0.361H2O

0.860 5.006 402 TiO2·0.296H2O

2.308 4.817 363 TiO2·0.244 H2O

0.044 2.781 782 TiO2·0.005H2O

n/10−3 θS/K θD/K

0.637 4.882 421

0.672 4.875 445

0.804 4.890 434

0.056 2.254 781

neutron scattering on nanorutile.20 In a second publication, we studied the enthalpy and entropy of adsorption of water onto the surface of those same particles21 and concluded that extensive dissociation of water took place on both rutile and anatase NPs. The conclusion is based on a large exothermic enthalpy and large negative entropy of adsorption regardless of surface coverage. These latter results disagree with the conclusions drawn from the UHV experiments cited above. An important outcome of our calorimetric experiments is the realization that adsorbed water plays an essential role in stabilizing the energetic surfaces of NPs. This observation has critical implications for the dispersion of NPs. Agglomeration is widely observed with NPs and limits their implementation in applications where increased surface area is critical. In this paper, we exploit the high sensitivity of the specific heat at very low temperatures (T < 10 K) to characterize a lowenergy phenomenon associated with defect sites on these same NPs. Calorimetrically obtained heat capacities of 7 nm particles of anatase and rutile with variable water contents show small rounded maxima below 2 K that are consistent with Schottkytype anomalies. Measurements on much larger (>200 nm diameter) and much less hydrated anatase and rutile particles (henceforth referred to as bulk samples) revealed similar features, but with a much diminished intensity and maxima shifted to lower temperatures (1 K). The statistical weights obtained from fitting the low-temperature specific heat maxima correlate with the number of very high-energy surface sites identified by the adsorption calorimetry. On the basis of human-sized mock-ups (ball and stick physical models) of the NP surfaces, we offer an identification of the plausible nature of the energetic structural features and attribute them to corner and edge effects.

following removal of the samples from the calorimeter. These same NP samples were used in the variable water content experiments reported earlier.19 The new heat capacity measurements reported here were made following gentle heating and evacuation to remove loosely bound water without affecting particle size. NP sizes were determined by line-broadening of the principal XRD lines, by transmission electron microscopy (TEM), and surface areas were determined by Brunauer− Emmett−Teller (BET) measurements. There is general agreement among the results of a NP diameter of 7−9 nm. The bulk samples showed a greater dispersion in particle size, with grains generally >200 nm in diameter as determined from TEM observations. The bulk anatase sample was contaminated with a few percent of rutile; corrections to the anatase heat capacity have been made using our heat capacity results on bulk rutile. The heat capacities of these samples were measured in the temperature range 0.5−30 K using a semiadiabatic calorimeter described by Lashley et al.23 Each sample was approximately 0.2 g in mass and wrapped in approximately 0.08 g of copper foil (99.999% pure) to provide greater thermal conductivity. Each nanopowder sample was compressed into a pellet of 3/8” diameter and 1/8” thickness which was then attached to the sample platform of the apparatus using Apiezon N grease. The contributions of the copper, grease, and addenda were subtracted to obtain the molar heat capacity of nanocrystalline samples. The thermometry for the semiadiabatic instrument has been calibrated on the ITS-90 temperature scale, and the accuracy was generally found to be better than 0.25% and a resolution of 0.1% based on the measurement of pure copper.

3. RESULTS AND DISCUSSION 3.1. Schottky Anomalies. In analyzing the specific heats below 5 K, we found that a function consisting of a series expansion in odd powers of temperature to model the lattice contribution24 and a two-level Schottky function, CSchottky

2. EXPERIMENTAL METHODS The anatase and rutile NP samples were prepared from different starting materials and using different techniques. These samples have been used for a variety of measurements, and substantial synthetic and characterization details are available elsewhere for these samples.17,18 The bulk sample of anatase was obtained commercially from Alfa-Aesar,22 and bulk rutile was prepared by heating the bulk anatase at 600 °C until complete phase conversion occurred. All samples were bright white, indicating stoichiometric TiO2 with no significant oxygen deficiencies. All materials were carefully characterized for chemical and phase purity using powder X-ray diffraction (XRD), inductively coupled plasma (ICP), thermogravimetry/ differential thermal analysis (TGA/DTA), and chemical analysis for trace metals and C, H, N, and Cl.17,18 The only significant impurity found in all materials at greater than a few parts per million was water. Table 1 shows the water stoichiometry determined by TGA experiments immediately

θ

CSchottky

( ) ⎞ ( )⎟⎠

exp TS ⎛ θS ⎞2 ⎛ g0 ⎞ = nR ⎜ ⎟ ⎜⎜ ⎟⎟ ⎝ T ⎠ ⎝ g ⎠⎛ ⎛g ⎞ 1 ⎜ 1 + ⎜ g0 ⎟exp ⎝ 1⎠ ⎝

θS T

2

(1)

was able to fit all the data sets quite well below 5 K. In eq 1, R is the molar ideal gas constant and θS is the energy difference between the two levels, expressed as a temperature; the degeneracy ratio (g0/g1) equals 1. The “n” coefficient measures the mole number of species responsible for the Schottky contribution. The high accuracy of the low-temperature calorimeter, described in detail elsewhere,25 makes it possible to determine absolute heat capacities with confidence so that comparisons can be made across the samples. 4545

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reasonably comparable within the bulk rutile and anatase particles, θS = 2.5 ± 0.3 K. Although the energies are different between the nanoparticles and the bulk particles, the similarity within each size regime suggests that the same species is responsible for the anomaly in all samples. The n values (Table 1) indicate that this species is present at the millimolar level in the NPs but is smaller by a factor of 100 in the bulk particles. These small concentrations immediately suggest the anomaly could be related to an impurity. This line of reasoning led Sandin and Keeson,26 who observed a similar bump in their Cp measurements on stoichiometric rutile, to attribute the anomaly to an iron impurity even though their n value was significantly lower than the iron impurity present in the sample. (Note that the (T < 50 K) heat capacity of bulk anatase has not been reported by others until now.) Attempts to fit the anomaly in our samples using the same spectroscopic energy levels27 for Fe3+ were not successful. More importantly, the levels of trace metal impurities in the four sample types in our study are quite comparable and so cannot explain the dramatic differences in both n and θS from the large particles to the small ones. Though the NPs show slightly different lattice parameters than the bulk materials,2,16,18 these changes are also not likely to be sufficient to influence the electronic levels of a transition metal ion enough to nearly double θS from 2.5 to 4.8 K. The peak’s origin thus does not appear to be due to iron or another metallic impurity. The only remaining “impurity” is the adsorbed surface water. The large water levels within the NP samples are not directly correlated with the small n values, yet the trend in n across the four sample types (bulk and nanometer anatase and bulk and nanometer rutile) does reflect the trend in the overall water concentration, suggesting some relationship between the Schottky anomaly and the water adsorbed at the TiO2 surface. 3.2. Structural Models and Defect Sites. To better envision interactions between adsorbed water and the TiO2 surface which might lead to a Schottky anomaly, we sought to model the TiO2 surface. TEM images17,18 show that the anatase particles are spherical, being roughly 7 nm in diameter, and that the rutile particles are rods, also being 7 nm in diameter but with lengths that are several times the diameter. While we could not distinguish well-defined faces on the NPs perhaps because of the extensive washing of the particles,6 the TEM images did show that the rutile rod axis was parallel to [001]. We built three-dimensional physical models of the NPs using Ti (octahedral) and O (trigonal planar) atoms (spheres with holes cut at appropriate angles) purchased from Darling Models. Lacking evidence for distinct facets on either sets of particles, we adopted a simple procedure to construct the surface shell of the NPs. Using a scale factor set by the dimensions of the atomic models, the 3.5 nm radius was transformed to a 1.2 m radius in the plastic models. Starting with a single unit cell and guided by a string cut to the 1.2 m radius, atoms were added vertically and horizontally to make 1/ 8 of a sphere for anatase and 1/8 of a sphere for rutile with an additional portion of the rod extending below the spherical cap. To a first approximation, the anatase sphere consists of (001) layers truncated at the edges to maintain the size constraint. The rutile rod cap was modeled as a quadrant of a hemisphere with (001) layers truncated as in the anatase structure. Twodimensional representations of these models are shown in Figures 2 and 3.

Figure 1(a) shows the measured heat capacities for all samples with various symbols representing the experimental

Figure 1. (a) Heat capacity data for all rutile and anatase samples: Anatase bulk (black circle), Anatase 0.677·H2O (red down triangle), Anatase 0.532·H2O (green box), Anatase 0.379·H2O (yellow diamond), Rutile bulk (blue triangle), Rutile 0.361·H2O (pink circle), Rutile 0.296·H2O (teal circle), and Rutile 0.244·H2O (gray down triangle). The lines represent the Schottky fits. The inset highlights the anomaly in the bulk data. (b) Same heat capacity data and fits as in (a) except with the lattice contribution subtracted to more clearly show the Schottky anomalies. Note that the increased noise in the data on the high-temperature side of the Schottky anomaly is caused by the increased contribution from the lattice. Error bars have been added to both (a) and (b) to denote the uncertainty in the data, though the error bars in (a) are so small that they are not visible.

data and the smoothed lines giving the results of the theoretical fits to the data. Figure 1(b) shows the same results with the lattice contribution subtracted, and the n, θS, and Debye theta (θD) values are given in Table 1. As the figures show, the data are fit very well by the combination of the odd powers function and the two-level Schottky function. As shown in Table 1 using the Debye thetas for the six nanosamples, the lattice contribution is also reasonably consistent between the three anatase samples and the three rutile samples, thus providing further validity to the fitting model. It should also be noted that the Debye thetas for bulk anatase and rutile are also in agreement with accepted values.22 The ability to fit the low-temperature feature to a Schottky function and the magnitude of the fit parameters provide clues to the species and mechanism responsible for the heat capacity bump. The Schottky energies are remarkably similar across both rutile and anatase NPs, θS = 4.89 ± 0.06 K, and are 4546

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Table 2. (a) Total Percentages of Each Type of Ti and O Atom on the Surface of the Anatase Model and (b) Total Percentages of Each Type of Ti and O Atom on the Surface of the Rutile Model (a) anatase Ti

% of surface Ti atoms

5-coordinate 4-coordinate 3-coordinate isolated 3-coordinate O

46 35 19 1.1 % of total coverage

2-coordinate O 1-coordinate O total Ti (b)

50 14 36

rutile spherical ends

Figure 2. (a) Representation of the physical model of our anatase TiO2 nanoparticles. (b) Close-up view of a section of the anatase model with the various types of atoms found on the surface labeled as follows: (a) 5-coordinate Ti atoms, (b) 4-coordinate Ti atoms, (c) 3coordinate Ti atoms, (d) 2-coordinate O atoms, and (e) 1-coordinate O atoms.

Ti

% of surface Ti atoms

5-coordinate 4-coordinate 3-coordinate isolated 3-coordinate O

45 27 27 7.1 % of total coverage

2-coordinate O 1-coordinate O total Ti rutile rod

52 18 30 % of total coverage

2-coordinate O 1-coordinate O Ti (all 5-coord.)

50 27 23

a size constraint rather than the electron-counting rules used to govern stable surfaces28 undoubtedly resulted in models with overly energetic surfaces because simulations of stable planar surfaces do not tend to show 4- and 3-coordinate Ti atoms except at the corners of layer edges, though 1-coordinate O atoms (as titanyl groups TiO) have been observed on (011) rutile surfaces15,29 and on the corners of TiO2 nanoparticles.9,15,30,31 All of the 4-coordinate and the 3-coordinate Ti atoms could have their coordination number increased if the 1.2 m radius rule was relaxed and another O atom added. However, upon close inspection of the models we found a small number of 3-coordinate Ti atoms whose geometries were such that another O atom could not be accommodated between it and an adjacent Ti without a significant distortion of the bond lengths and bond angles. This phenomenon in our model is associated with the curvature of the surface, but the geometry of the resulting isolated 3-coordinate Ti atoms resembles the coordination at corners and edges of steps on dehydrated planar surfaces. From the number of isolated 3-coordinate Ti atoms on the surfaces of the rutile and anatase nanoparticle models and the particle densities and surfaces areas, we calculated n values for these isolated sites in a manner that would reflect their statistical weight on the nanoparticles. By adopting similar models for the bulk particles, we could also obtain n values for such sites on the bulk samples (see Table 3). The agreement between the Schottky fit n values and those calculated from the model is remarkably good, especially given the simplicity of our physical models of the structures. Also shown in Table 3 are the estimated n values that would arise from the number of high-

Figure 3. (a) Representation of the physical model of our rutile TiO2 nanoparticles. (b) Close-up view of a section of the rutile model with the various types of atoms found on the surface labeled as follows: (a) 5-coordinate Ti atoms, (b) 4-coordinate Ti atoms, (c) 3-coordinate Ti atoms, (d) 2-coordinate O atoms, and (e) 1-coordinate O atoms.

Analysis of the models revealed a mix of 5-, 4-, and 3coordinated Ti atoms with 2- and 1-coordinate O atoms (see Figures 2 and 3). The percentages of the various types of atoms on the model surfaces are shown in Table 2. Our application of 4547

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Table 3. Comparison of the n Values from the Schottky Fits with Those Predicted by the Concentration of the 3-Coordinate Surface Ti Atoms and Those Predicted by the Concentration of Sites on Nanoparticles with ΔadsH < −120 kJa average measured n n predicted by the # of 3-coordinate Ti atoms on model n predicted by the # of sites per particle with ΔadsH < −120 kJ a

anatase NPs

rutile NPs

anatase bulk

rutile bulk

1.9 × 10−3 1.5 × 10−3 7.2 × 10−3

7.0 × 10−3 9.9 × 10−4 9.5 × 10−3

4.4 × 10−5 5.2 × 10−5

5.6 × 10−5 2.9 × 10−4

Comparisons are made for both the bulk and nanoparticle (NP) samples of rutile and anatase.

energy water sites (ΔadsH < −120 kJ) found on the surfaces of the NPs in the adsorption enthalpy studies.21 The congruence of these three sets of numbers gives us confidence that the Schottky phenomenon arises from a Ti defect site, most likely at the corners of step edges on the nanoparticle surfaces. 3.3. Models for Low-Energy Phenomena. We have considered what possible phenomena involving a defect site could give rise to a set of Schottky levels with such a low-energy (2−5 K) split. Eliminating transition metal impurities as the source, three possible explanations present themselves. Sandin and Keeson26 saw a more pronounced bump in the heat capacity of vacuum-reduced rutile with significant amounts of O vacancies (separate from what they attributed to Fe3+). This feature was ascribed to thermal excitation arising from a set of impurity states lying just below a narrow conduction band gap. The excess heat capacity in their model levels off with increasing temperature, rather than falling to zero as does our excess heat capacity (see Figure 1(b)). While we associate our heat capacity features with defect sites, we dismiss the Keeson model as an explanation for our observations since the temperature dependence of the excess heat capacity is very different. Numerous experimental and theoretical studies of the reactivity of water on planar TiO2 surfaces show that dissociation takes place at or near oxygen vacancies and gives rise to a pair of OH groups.3,4 Recent experimental and theoretical studies show that the water and/or OH groups can be very mobile.29,32,33 Given the consensus that OH groups are found at defects, we have considered several models of OH group motions that could give rise to the low-energy states needed to explain a Schottky heat capacity. The first model is that of a hindered rotation of the OH group about an axis established by the Ti− O bond (Figure 4(a)). Di Valentin et al.29 in molecular dynamics simulations of water on reconstructed R(011)-(2 × 1) surfaces found evidence for such a hindered rotation with an energy barrier of approximately 1−2 kJ mol−1 (corresponding to a temperature of 100−200 K). The second model is that of a double-well hydrogen bond potential in which the H atom associated with a hydroxyl group forms a hydrogen bond with a nearby O atom (Figure 4(b)). Molecular simulations show that some H atoms existing on TiO2 surfaces in bonding situations like those shown on the left- and right-hand sides of Figure 4(b) can shuttle between the two orientations, either by tunneling or by hopping over the barrier separating them.34 Both model types invoke a multiwell potential energy. Under favorable circumstances, the energy states within individual wells can interact, giving rise to a splitting of individual well states. The interaction occurs when the individual well wave functions extend significantly beyond the classical turning points of the potential and overlap with each other. Parameters such as the barrier height V0, the barrier width, and the mass of the tunneling particle influence the magnitude of the energy splitting, Δ.

Figure 4. Two multiwell potentials and their molecular origins. (a) Two types of hindered rotation; the value of φ affects the moment of inertia, while θ is set by the site symmetry of the Ti atom. (b) A double-well O−H···O hydrogen bond. The solid line represents a chemical bond and the dotted line the hydrogen bond. In both figures, the ground states are shown with a small energy split (Δ) due to tunneling, and V0 is the barrier height separating the minima.

Hindered rotations can contribute to the specific heat in two ways. Hindered rotations of ammonium ions and methane molecules in crystals are known to produce measurable tunnel splittings of the librational levels.35 Thermal occupation of these low-energy states gives rise to an excess heat capacity at low temperatures T for which kT ≈ Δ. Then, when kT exceeds V0, the excess heat capacity approaches a constant limiting value, 1/2R per degree of rotational freedom. Crystalline ethane and other methyl-group containing organic molecules show similar behavior.36−38 We have used the FGH1D program described in ref 37 to calculate the heat capacity due to a hindered rotation using the two geometries shown in Figure 4(a).39 Closed-form solutions for Δ cannot be obtained, but the splitting can be calculated for a given set of molecular parameters. We assumed a fixed Ti atom with a 3-fold rotational symmetry and V(θ) = V0 cos(3θ); bond lengths, bond angles, and barrier heights were allowed to vary over reasonable ranges using geometries reported on various surfaces.10,11,15,29,32,33,40,41 For no geometry were we able to obtain an energy splitting of the ground states small enough to provide the specific heats needed. Each geometry exhibited simple harmonic oscillator heat capacities at low temperatures, results that are inconsistent with the Schottky anomalies we observe at low temperatures. We must now consider the possibility that a double-well model of hydrogen bonding arises from the presence of O atoms in the vicinity of the OH group bonded at a defect site. Double-well hydrogen bonding potentials are very well established in crystals of organic acids where molecular dimers form six-membered rings involving the carboxylic acid groups. Tautomeric shifts can transform a carbonyl carbon into a hydroxyl-bonded carbon and vice versa. It has been proposed that this can occur in inorganic compounds as well;43,44 for 4548

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defect sites, most likely undercoordinated Ti atoms situated on the corners of step edges on the surfaces of nanoparticles. Similar features, but with a greatly reduced intensity and lowershifted maxima, are observed on bulk particles of these materials. The reduced intensity is consistent with the smaller fraction of corner sites on large particles. The maxima shift can be associated with either differences in the bond lengths and asymmetry of the O−H···O assemblage or the barrier height between the two potential wells on the surfaces of the large and small particles.

example, an excess heat capacity in crystalline NaOH (which does not appear in NaOD) is attributed to tunnel splitting.45 The details of the tunnel splitting depend upon the particulars of the double-well potential. For simplicity, we considered a quartic double-well potential for which V(x) is given by V (x) = V0

[x 2 − a 2]2 a4

(2)

where ±a locates the minima and V0 is the barrier height. The tunnel splitting, Δ, of the ground vibrational state is given by42 ⎡ ⎛ 16V0 ⎞⎤ ⎛ 16V0 ⎞1/2 ⎟ exp⎢ −⎜ ⎟⎥ Δ = 4ℏω⎜ ⎝ 2π ℏω ⎠ ⎣ ⎝ 3ℏω ⎠⎦

■

Corresponding Author

(3)

*E-mail: brian_woodfi[email protected].

and ω is given by

Notes

The authors declare no competing financial interest.

⎛ 8V ⎞1/2 ω = ⎜ 02 ⎟ ⎝ ma ⎠

■

(4)

ACKNOWLEDGMENTS This work was financially supported by a grant from the Department of Energy (USA) under contract number DEFG02-05ER15666.

We have calculated Δ for two masses, the reduced mass of the OH group and the mass of just the H atom at a range of minima separations and barrier heights. Unlike the hindered rotator model, we found that a double-well potential could produce tunnel splittings of both 2.5 and 4.8 K. Table 4 presents the

■

Table 4. Barrier Heights Required to Obtain the Observed Tunnel Splits for Representative Separations of the DoubleWell Minima4 H atom a/Å

V0/meV

a/Å

V0/meV

2.5

0.1 0.5 0.75 1.0 0.1 0.5 0.75 1.0

12450 384 136 63 10900 319 109 49

0.1 0.5 0.75 1.0 0.1 0.5 0.75 1.0

11700 360 127 59 10250 298 102 46

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OH group

Δ/K

4.9

AUTHOR INFORMATION

potentials and intermolecular separations ±a for which these tunnel splittings are obtained. The smallest separation in Table 4 corresponds to a geometry observed in a simulation of water dissociated on (001) anatase40 with −O−H = 1.12 Δ, H···O = 1.31 Δ. The other separations indicate a range of hydrogen bond geometries that have been reported. The barrier heights are generally within the range that has been calculated for proton transfers and motion of OH groups on TiO2 surfaces, e.g, barrier heights of 200−600 meV.11,32 Table 4 also shows that, for a given distance between the potential wells, a relatively small change in barrier height can explain the different maxima observed in the bulk particles versus the NP. While this double-well potential model does not provide definitive evidence for the origin of the low-temperature Schottky anomalies observed in our measurements, it certainly provides a plausible explanation.

4. CONCLUSION The temperature dependence of a small heat capacity maximum observed on the surface of nanoparticles of anatase and rutile TiO2 can be explained by invoking a double-well hydrogen bonding potential associated with OH groups attached to 4549

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The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp310993w | J. Phys. Chem. C 2013, 117, 4544−4550