Reaction Kinetics of Water Molecules with Oxygen Vacancies on

Sep 16, 2015 - The formation of bridging hydroxyls (OHb) via reactions of water molecules with oxygen vacancies (VO) on reduced TiO2(110) surfaces is ...
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Reaction Kinetics of Water Molecules with Oxygen Vacancies on Rutile TiO2(110) Nikolay G. Petrik* and Greg A. Kimmel* Physical Sciences Division, Pacific Northwest National Laboratory, MSIN K8-88, P.O. Box 999, Richland, Washington 99352, United States S Supporting Information *

ABSTRACT: The formation of bridging hydroxyls (OHb) via reactions of water molecules with oxygen vacancies (VO) on reduced TiO2(110) surfaces is studied using polarized infrared reflection−absorption spectroscopy (IRAS), electron-stimulated desorption (ESD), and photon-stimulated desorption (PSD). Narrow IR peaks at 2737 and 3711 cm−1 are observed for the stretching vibrations of ODb and OHb, respectively. The IRAS spectra indicate that the bridging hydroxyls are oriented normal to the TiO2(110) surface. Using IRAS, we have studied the kinetics of water reacting with the vacancies by monitoring the formation of bridging hydroxyls as a function of the annealing temperature on the TiO2(110). Separate experiments have also monitored the loss of water molecules (using water ESD) and vacancies (using the CO photooxidation reaction) due to the reactions of water molecules with the vacancies. All three techniques show that the reaction rate becomes appreciable for T > 150 K and that the reactions are largely complete for T > 250 K. The temperature-dependent water−VO reaction kinetics are consistent with a Gaussian distribution of activation energies with Ea = 0.545 eV, ΔEa(fwhm) = 0.125 eV, and a “normal” prefactor, ν = 1012 s−1. In contrast, a single activation energy with a physically reasonable prefactor does not fit the data well. Our experimental activation energy is close to theoretical estimates for the diffusion of water molecules along the Ti5c rows on the reduced TiO2(110) surface, which suggests that the diffusion of water controls the water−VO reaction rate.

1. INTRODUCTION One of the most important issues driving interest in the photochemistry of titanium dioxide is related to the ongoing quest for an efficient technique for photocatalytic splitting of water to make hydrogen fuel.1−5 Here, a fundamental and indepth understanding of water’s interactions with the surfaces of TiO2 plays one of the key roles. The (110) surface of rutile TiO2 single crystals is one of the most common and stable surfaces of this material, and it is a model system for fundamental studies.6 Despite extensive investigations, there are numerous areas where our understanding of water’s interactions with the TiO2(110) surface is inadequate.4,7−10 It is well-known that water molecules react with bridging oxygen vacancies (VO) on the reduced TiO2(110) surface via dissociation and creation of a pair of bridging hydroxyls (OHb) according to the net reaction:11−16 H 2OTi + VO + Ob → 2OHb

Figure 1. Schematic of the reactions of H2O on reduced TiO2(110). (1) H2O adsorbs preferentially on the Ti5c sites at submonolayer coverage. (2) H2O diffusion along a Ti row. (3) An H2O molecule approaches an oxygen vacancy (VO). (4) H2O adsorbed in a VO. (5) H2O dissociates in a vacancy creating a pair of bridging hydroxyls (OHb). (6) H2O dissociation on a Ti5c site creating one OHb and one terminal hydroxyl (OHt). (7) H2O dimer, which diffuses along the Ti row faster than the monomer.

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This reaction proceeds through a sequence of elementary steps depicted schematically in Figure 1. First, water adsorbs on TiO2(110) via a precursor-mediated mechanism.17 After accommodation to the surface temperature, the H2O molecules adsorb on the 5-fold coordinated titanium (Ti5c) sites and bridging oxygen (Ob) sites with adsorption energies of ∼0.89 and ∼0.61 eV, respectively, as determined from temperatureprogrammed desorption (TPD) data.18 These experimental © XXXX American Chemical Society

Received: August 3, 2015 Revised: September 10, 2015

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molecules dissociating in the bridging oxygen vacancies. In separate experiments, we also measured the loss of molecular water and the bridging oxygen vacancies versus the annealing temperature. The electron-stimulated desorption (ESD) of water and the photooxidation of CO were used to monitor the water and vacancy concentrations, respectively. All three techniques (ODb IRAS, water ESD, and CO photooxidation) showed that the water−vacancy reaction rate is low for T < 150 K, while the reactions proceed quickly for T > 250 K. The ratelimiting step for the reaction has a distribution of activation energies (centered around ∼0.55 eV) that is consistent with previous measurements and calculations of the diffusion barrier for water monomers along the Ti5c rows of TiO2(110).

adsorption energies are quite close to theoretical estimates.8,19−21 At submonolayer coverages, water adsorbs predominantly on the Ti5c sites (Figure 1(1)) and the binding energy decreases with increasing coverage.17,18,22,23 After adsorption, water can diffuse along the Ti rows (Figure 1(2)) with a diffusion barrier of ∼0.5 eV according to STM data and theory.8,24 While diffusing, the H2O molecule can be trapped by an oxygen vacancy (Figure 1(3,4)). Theory suggests a very small gain in binding energy, 0.01−0.14 eV,8,21 for water in a vacancy relative to the Ti5c sites. In the vacancy, the H2O molecule further lowers its energy by 0.41−0.59 eV upon dissociation into 2OHb (Figure 1(5)). However, DFT calculations indicate that there is a barrier for dissociation of 0.45−0.49 eV.8,21 As result, nondissociated water (Figure 1(4)) can be observed in vacancies with STM at low temperature (80 K).25 On hydroxylated TiO2(110), water molecules tend to form stable dimers (Figure 1(7)) that diffuse faster than the monomers along the Ti rows.24 With dimers, the total binding energy of water on TiO2(110) increases by 0.18 eV according to the DFT calculations.8 Larger water clusters (trimers, tetramers) are also observed, but they are not stable.24 The observed activation energy for dimer diffusion is in the range 0.23−0.35 eV,24 which is close to the theoretical estimate of 0.38 eV.8 While it is known that water monomers react with bridging oxygen vacancies, we are unaware of any published results on dimer−vacancy interactions.8,24 The cluster size distribution (monomers versus dimers) has not been reported, and there is a need for such data to understand the total diffusivity of water on the TiO2(110) surface and to compare STM data with the ensemble-averaged measurements. One of the biggest and ongoing controversies concerns the extent of dissociation of water molecules on Ti5c sites on a vacancy-free surface. Dissociation would create an OHb + OHt pair (Figure 1(6)), where OHt is a terminal hydroxyl located on top of a Ti5c site. Many theoretical calculations suggest that water adsorbs almost exclusively in molecular (not dissociated) form,8,21,26−29 while the others suggest a mixed molecular/ dissociative adsorption where the molecular form dominates.19,20,30,31 Most of the experimental studies (including STM) do not see dissociation of water molecules on regular Ti5c sites,8,13−15,22,25,32,33 while the X-ray photoemission experiments support a mixed molecular/dissociative adsorption state for water.34−37 Both isolated OHb and OHt are practically immobile on TiO2(110) at temperatures below 300 K.16,38,39 Therefore, dissociation would be self-trapping for the diffusing water molecule. The diversity of water’s reactions on the TiO2(110) surface complicates the understanding and description of the overall molecular dynamics and kinetics. Depending on the conditions (temperature, H2O coverage, defect density, etc.), different steps may become rate limiting. In the current work, we investigate the reactions of water molecules with bridging oxygen vacancies on reduced TiO 2 (110) at low coverages. First, we use infrared reflection−absorption spectroscopy (IRAS) to obtain the characteristic IR spectrum of the bridging hydroxyl with narrow peaks at ∼2737 (3711) cm−1 for stretching vibrations of ODb (OHb). IR measurements with polarized light demonstrate that the OD (OH) bond of the bridging hydroxyls is normal to the (110) surface. IRAS measurements of the ODb peak versus the annealing temperature of a small amount of D2O on TiO2(110) are used to investigate the kinetics of water

2. EXPERIMENTAL PROCEDURE The experiments were performed in two UHV systems that have been described previously.40−42 Both systems consisted of a closed-cycle helium cryostat, a molecular beamline for adsorbate deposition, a quadrupole mass spectrometer (QMS), a UV photon source, and surface diagnostic equipment. The typical base pressure was less than 1 × 10−10 Torr. Additionally, one of the systems was equipped with a Fourier transform infrared spectrometer (Bruker Vertex 70), while the other has a rotating QMS stage for angle-resolved desorption experiments. The 10 × 10 × 1 mm rutile TiO2(110) crystals (CrysTec GmbH) were mounted on a resistively heated tantalum base plate. For temperature monitoring and control, a K-type thermocouple was spot-welded to the base plate. The base temperature for the samples was typically between 25 and 30 K. The TiO2 samples were prepared by sputtering with 2 keV Ne+ ions and then annealing for between 2 and 10 min in vacuum at 950 K. Multiple ion sputtering/annealing cycles resulted in reduced TiO2 samples.6 On the ion sputtered and annealed surfaces, θ(VO) was ∼0.05 ML based on the magnitude of the high temperature OH recombination peak during water temperature-programmed desorption (TPD).12,32 Photon irradiations were performed using a 100 W Hg lamp (Oriel #6281). The output of the lamp was focused onto a fiber optic cable that was used to introduce the light into the vacuum chamber. The infrared portion of the output was blocked using a water filter. The light was incident at 45° with respect to the surface normal. The distance of the fiber optic cable from the sample was chosen such that the illuminated spot on the sample was centered on, and somewhat larger than, the molecular beam spot on the sample. The entire UV portion of the lamp’s spectrum was used during photon irradiation. For the experiments reported here, all UV irradiations were performed at the base temperature (25−30 K). During photon irradiation, the increase in the sample temperature was 3 eV was ∼3 × 1015 photons/cm2·s. During ESD experiments, the electron beam was oriented 35° to the sample normal. For the results presented here, the incident electron energy was 100 eV. Typical instantaneous current densities in the electron beam were ∼3 × 1015 e−/cm2·s with a beam diameter of ∼1.5 mm. The sample surface was uniformly irradiated by repeatedly scanning the electron beam over a square area that was slightly larger than the film. Each individual scan of the sample was typically 1.1 s in duration and delivered a fluence of ∼9 × 1013 e−/cm2. When measuring ESD of water molecules, we always see an increase of the background signal due to electrons scattered from the sample B

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Figure 2. Differential absorbance IRAS spectra for p- and s-polarized light (a and b) on TiO2(110). The red and blue lines show the spectra for hydroxylated TiO2(110) produced by dosing 1 ML of H2O or D2O on reduced surface at 350 K, respectively. The green lines show the spectra for 1 ML D2O dosed on hydroxylated TiO2(110) at 210 K, and the light blue lines are for 100 ML of D2O dosed at 50 K. Dangling ODd groups on the surface of the 100 ML D2O film are shown magnified. The IR beam is parallel to the [001] azimuth (s-vector is across the Ti and O rows).

respectively (Figure 2a). The peaks are quite narrow with a fwhm of ∼4.7 cm−1 as measured with the spectrometer resolution set at 1 cm−1. As expected, these peaks are in the range of the stretching ν(OD) and ν(OH) vibrations.10,49 The absence of the vibrations for s-polarized light and the lack of the positive absorption peaks for p-polarized light indicate that the OHb (ODb) orientation is normal to the (110) surface of the TiO2. The bridging hydroxyl spectra are very different from the IRAS spectra of the molecular water on the TiO2(110). The green and light blue traces in Figure 2 show spectra of 1 and 100 ML of D2O dosed on hydroxylated TiO2(110) at 210 and 50 K, respectively. These spectra are similar to our previous data obtained on the same system.10 However, the 1 ML spectra presented here are averaged from more scans and, therefore, are less noisy. At 1 ML coverage, D2O molecules form chains along the Ti rows with hydrogen-bonded OD groups laying mostly parallel to the surface.10 As result, the peaks are broader than the ODb peak and significant absorption is observed in the s-polarized spectra (the positive absorption peak in the p-polarized spectrum in Figure 2a is also due to vibrations parallel to the surface as was described in the Experimental Procedure). For 1 ML of water on TiO2(110), there are two major types of hydrogen bonds determining the spectra:10 bonds between the adjacent D2OTi molecules (2609/ 2602 cm−1) and bonds between the D2OTi molecules and Ob atoms (∼2310 cm−1). Note that the ODb disappeared after the 1 ML D2O dose most likely because of hydrogen bond created between the D2O and ODb. For multilayer water coverages, broad ν(OD) bands are observed for the hydrogen-bonded water molecules in both polarization modes: ∼ 2360−2660 cm−1 for p-polarized light and ∼2250−2630 cm−1 for s-polarized light (Figure 2a and b, the lowest light blue traces). Small peaks due to “dangling” OD bonds (i.e., non- hydrogen bonded) at the water/vacuum

that subsequently induce water desorption from other surfaces within the vacuum chamber. We show it with dashed lines marked “bare TiO2” on our ESD plots. The infrared light was incident on the TiO2(110) single crystals at grazing incidence (∼84° with respect to normal) and detected in the specular direction. Here, we use IRAS with sand p-polarized light incident along the [001] azimuth (Figure S1). Note that for s-polarized light on a dielectric substrate the absorbance peaks are negative, while for p-polarized light the absorbance peaks can be negative or positive depending on a variety of factors.10,42−46 For the chosen direction and the IR incidence angle, the s-polarized spectra are sensitive to vibrations that are parallel to the surface and perpendicular to the BBO rows (negative peaks), and the p-polarized spectra reflect a combination of vibrations normal to the surface (negative peaks) and parallel to the surface along the BBO rows (positive peaks). IRAS spectra were obtained using resolutions of 1 or 4 cm−1 as noted. Absorbances are defined as A(ν) ≡ log10[R0(ν)/R(ν)], where R(ν) and R0(ν) are the reflected signals from the TiO2(110) with and without adsorbed molecules. All IRAS spectra were measured at T ≈ 30 K. The total number of spectrometer scans varied from 20 000 to 60 000 depending on the size of the signal and the noise level.

3. RESULTS AND DISCUSSION Figure 2 shows the IRAS spectra taken with p- and s-polarized light from a TiO2(110) surface after hydroxylation by exposing to H2O (upper blue traces) or D2O (red traces below) at 350− 400 K. Only bridging hydroxyls, that is, the dissociated form of water on reduced TiO2(110), are expected to remain on this surface at these deposition temperatures.12,32,47,48 There is no absorbance observed in the s-polarized spectra (Figure 2b), but negative peaks at ∼2737 and ∼3711 cm−1 are detected in ppolarized spectra for the stretching vibrations of ODb and OHb, C

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spectra were measured at 30 K. The water dose was chosen because it is close to the coverage of oxygen vacancies on this surface. The integrated absorbance of the ODb peak, which is proportional to the coverage of bridging hydroxyls on the surface, is shown in Figure 3 versus the annealing temperature, Tann. At 110 K, water diffusion is minimal so very few bridging hydroxyls are formed and their IRAS signal is small. A distinct ODb peak becomes observable above 150 K; it grows with annealing temperature and saturates above ∼250 K. As was mentioned above, annealing to temperatures greater than 400 K leads to the disappearance of the ODb peak due to recombinative desorption of D2O (Figure S2). The data indicate that water reacts with the vacancies and produces bridging hydroxyls in the temperature range between 150 and 250 K, which is consistent with the earlier STM reports. Note that the temperature range over which the ODb signal increases depends upon the annealing time; for longer annealing times, the transition occurs at lower temperatures. Thornton et al.13 observed creation of OHb from H2O on TiO2(110) after annealing at 290 K, but no dissociation was seen at 150 K, and the OHb disappeared at temperatures above 500 K. Besenbacher et al.15 observed both H2O and OHb features when dosing water at 180 K, while at 290 K only OHb was seen on the surface. They disappeared recombinatively above 490 K recreating the oxygen vacancies. Unfortunately, no more systematic temperature-dependent measurements were reported. A noteworthy feature in Figure 3 is the relatively broad range of temperatures (∼150−250 K) over which the ODb signal increases. Below, we propose that this width arises from a distribution of activations energies for the reaction of water with the bridging oxygen vacancies. To further investigate this observation, we used two other experiments to probe the reaction of water with the bridging oxygen vacancies as a function of the temperature. The first of these experiments measured the electron-stimulated desorption (ESD) of molecular water to track the disappearance of water from the surface versus annealing temperature (Figure 4), while the second tracks the loss of the bridging oxygen vacancies through its influence on the photooxidation of CO (Figure 5). Therefore, these experiments complement the results in Figure 3, which monitored the appearance of the bridging hydroxyls. Previously, we have used the ESD of water from TiO2(110) surfaces at temperatures below the onset for appreciable thermal desorption to investigate diffusion and chemical reactions.48,62 Here, we utilize it to gauge the amount of nondissociated water molecules on the surface. Figure 4a shows a typical ESD signal of molecular water measured at ∼55 K from the sample dosed with 0.05 ML H218O at 70 K. The signal is maximal when the 100 eV electron beam is turned on and it decays with irradiation time. The integrated ESD signal, which is proportional to the coverage of water remaining on the surface, is shown in Figure 4b as a function of Tann. The ESD signal is largest at low temperatures, where no water has reacted with the vacancies. The H218O ESD signal starts decreasing at Tann ≈ 150 K and is gone by Tann ≈ 250 K, indicating there is no molecular water left on the surface at this point. The range of temperature over which the water ESD signal decreases (Figure 4b) is the same temperature range where the bridging hydroxyls are growing according to the IRAS data (Figure 3), and both data sets match well (Figure S4). The temperature range for the water−vacancy reaction is similar for different water isotopomers: D2O, H2O, and H218O (Figure S5). Note

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As shown in Figure S2a, the OD peak at ∼2737 cm−1 also disappears after annealing in the temperature range 400−600 K, which correlates well with the high temperature OH b recombination peak in the water TPD spectrum (Figure S2b). The OD peak is also suppressed after exposure to O2 (Figure S3)59 as expected for the bridging hydroxyls:38,60,61 ODb + O2 → Ob + DO2Ti

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These features are very specific for the bridging hydroxyls, but they are different from the properties of terminal hydroxyls. Therefore, these results confirm the assignment of the observed IR peaks in Figure 2 to the bridging hydroxyls on TiO2(110). To the best of our knowledge, these are the first reported IR spectra of the bridging hydroxyls on the TiO2(110) surface. As described in the Introduction, diffusing water molecules on a reduced TiO2(110) surface will react with bridging oxygen vacancies to create bridging hydroxyls. Figure 2 shows that, once formed, the OHb (or ODb) are readily distinguished in IRAS. As a result, IRAS provides a sensitive tool to investigate the reactions of water molecules with the bridging oxygen vacancies. For the results shown in Figure 3, a small amount of D2O, 0.04 ML, was dosed on the TiO2(110) surface at 110 K, then annealed for 60 s at various temperatures before the IRAS

Figure 3. Integrated absorbance of the ODb IRAS peak at 2737 cm−1 versus annealing temperature for 0.04 ML D2O dosed on TiO2(110) surface at 110 K and annealed for 60 s at Tann. D

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Figure 4. (a) H218O ESD signal at 55 K versus time for 0.05 ML H218O dosed on TiO2(110) at 70 K. (b) Integrated H218O ESD signal (for 0 ≤ t ≤ 28 s) versus annealing temperature for 0.05 ML H218O dosed on TiO2(110) surface at 70 K and annealed for 60 s at Tann.

Figure 5. (a) CO2 PSD signal at 30 K versus time from reduced (blue trace) and hydroxylated (red trace) TiO2(110) dosed with θ(O2) = θsat at 30 K, annealed at 100 K, and dosed with θ(CO) ≈ 1 ML at 30 K. To hydroxylate TiO2(110), 1 ML H2O was dosed at 400 K. (b) Integrated CO2 PSD signal versus annealing temperature for 0.1 ML H2O dosed on TiO2(110) surface at 30 K and annealed for 60 s at Tann. After the water was annealed, the sample was dosed with θ(O2) = θsat and then with θ(CO) ≈ 1 ML at 30 K. The lines are model fits to the data with different parameters (see text).

that for the water ESD experiments, it is important to set the water coverage close to the vacancy concentration because any unreacted water also desorbs between 250 and 300 K. As a result, water in excess of the vacancy concentration makes the whole transition broader (see Figures S6 and S7). CO on TiO2(110) can be photooxidized to CO2 by molecular oxygen chemisorbed in bridging oxygen vacancy,41,63−66 but the CO2 PSD yield is low on a hydroxylated surface (Figure 5a).41 This suggests that the CO2 PSD yield from the photooxidation of CO can also be used as a measure of the unoccupied bridging oxygen vacancy coverage on TiO2(110). For the experiment shown in Figure 5b, the integrated CO2 PSD signal was measured for a TiO2(110) surface initially dosed with ∼0.1 ML H2O at 30 K and then annealed at various temperatures for 60 s. After the annealing, the sample was dosed with a saturation coverage of oxygen (θ(O2) = θsat) at 30 K,67 annealed at 100 K (to chemisorb the oxygen), and then dosed with θ(CO) ≈ 1 ML at 30 K.41,66 Finally, the sample was exposed to the UV radiation and the CO2 PSD was measured. While previous research has shown that the kinetics of the photooxidation of CO on TiO2(110) are complicated,41,66 for this experiment the time-integrated CO2 PSD yield depends on the annealing temperature, but the kinetics do not (data not shown). This suggests that the reaction mechanism is not changing as the coverage of unoccupied vacancies decreases. For the annealing temper-

atures below 150 K, the time-integrated CO2 PSD yield (blue markers) is large and unchanging. This is consistent with the data presented in Figures 3 and 4, indicating that the water molecules have not reacted with the vacancies at these low temperatures. Above 150 K, the CO2 PSD yield decreases as water molecules hydroxylate the vacancies. By ∼250 K, the CO2 yield is nearly zero corresponding to a completely hydroxylated surface (i.e., without vacancies). The data shown in Figures 3, 4, and 5 clearly indicate that coverages of all three species, the unoccupied bridging oxygen vacancies, the nondissociated water molecules, and the bridging hydroxyls, change in a correlated fashion in the temperature range between 150 and 250 K. Experiments such as those shown in Figures 3, 4b, and 5b, provide valuable insights into the kinetics of the water−vacancy reaction on TiO2(110). Although there are several elementary steps involved in the reactions between water molecules and vacancies, it is instructive to consider the overall reaction as a k

bimolecular reaction: H 2O + VO → 2OHB, where k = ν· exp[−Ea/kBT]. In that case, we can solve for the coverages of the reacted H2O and VO as a function of time (i.e., ΔθH2O(t) = E

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The Journal of Physical Chemistry C ΔθV(t) = x(t)) and compare the solutions to the experimental results. Recall that after annealing at various temperatures for 60 s, the integrated CO2 PSD yield (Figure 5b) is proportional to coverage of vacancies that remain unoccupied, θV(t), and the water ESD yield (Figure 4b) is proportional to remaining water coverage, θH2O(t). For the initial coverage of water, θH2O0, and the initial vacancy coverage, θV0, we have

Matthiesen et al.24 reported similar activation energies for water monomers hopping on Ti5c rows of the TiO2(110) surface from analysis of STM data: Ea = 0.50 (0.46) eV with ν = 1011.9(1010.6) s−1 for fully hydroxylated samples (i.e., no vacancies) with θ(OHb) = 0.10 (0.06) ML. These numbers are close to the calculated barrier, ∼0.52 eV, for water molecules hopping between Ti5c sites8 and to the activation energy reported here for the water−vacancy reaction: ∼0.55 eV. Additionally, a water molecule in a vacancy has a barrier for dissociation, which theory estimates at 0.45−0.49 eV,8,21 that is quite close to the diffusion barrier. However, if dissociation in the vacancy was the rate-limiting step in the water−vacancy reaction, we would expect to have a significant fraction of the vacancies occupied with nondissociated water molecules. This is not consistent with the observed correlated change in coverage of all three species, VO, H2O, and OHb, in the temperature range between 150 and 250 K (see Figures 3−5). Therefore, the rate-limiting process in the reaction between water molecules and oxygen vacancies on TiO2(110) is most likely the thermally activated diffusion of the water molecules to the vacancy sites. This hypothesis is consistent with the results from the earlier STM studies suggesting that the mobility of water monomer is a “prerequisite for dissociation to occur”.15 The STM experiments also showed that the water dimers diffuse faster than the monomers along the Ti rows on TiO2(110) with Ea = 0.35 (0.23) eV and ν = 108.2(106) s−1 for θ(OHb) = 0.10 (0.06) ML. However, because the experiments were performed on hydroxylated surfaces, they did not provide any information on potential reactions between water dimers and bridging oxygen vacancies.24 In earlier STM experiments, only water monomers were observed to react and dissociate in the VO’s.15 The experiments reported here do not exclude reactions between water dimers and bridging oxygen vacancies. Because the initial water coverage is much less than 1 ML and because the water is deposited at temperatures where diffusion is limited, very few dimers are expected to be formed during dosing. For annealing above 150 K, monomer diffusion allows them to react with the vacancies or dimerize. Once formed, dimers could then rapidly diffuse (as compared to the monomers) and potentially react with water vacancies. However, because monomer diffusion is required to form the dimers, monomer diffusion would still be the rate-limiting step in the experiments reported here. It appears to be common for various processes on TiO2(110) to be governed by a distribution of activation energies instead of a single Arrhenius term. As was already mentioned, an energy distribution was also observed for the interlayer exchange of water molecules (or protons) with Ea(max) = 0.29 (0.26) eV and ΔEa(fwhm) = 0.07 eV in thin films of water on TiO2 (110) (Gaussian-type distribution with “normal” ν = 1012 s−1). Additionally, analysis of water TPD spectra for TiO2(110) (see ref 18 and Figures S10−S12) suggests that there is a distribution of activation energies for the thermal desorption of water molecules from the Ti5c sites. In the low coverage range, comparable with the water coverages used here, the molecular water binding energy increases by ∼0.14 eV (from ∼0.96 to 0.82 eV) with the θ(H2O) decreasing below ∼0.045 ML (Figure S12). Interactions between adsorbed molecules,68 or inhomogeneities on the TiO2(110) surface (such as steps, and local variations in the defect densities), and delocalization of the compensating negative charge around vacancies can lead to a distribution of interaction energies.6,47,69−72 The distribution of

⎧ ⎪ θ (θ V0 − x) θV = = V0 ·exp⎨ (θ V0 − θH2O0) · ⎪ θH2O θH2O0 (θH2O0 − x) ⎩ ⎛ ⎡ E ⎤⎞ ⎫ ⎪ ⎜⎜ν·exp⎢ − a ⎥⎟⎟ ·t ⎬ ⎪ ⎣ kBT ⎦⎠ ⎭ ⎝

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(See the Supporting Information for details.) By fitting eq 4 to the experimental results, values for ν and Ea can be obtained. For the CO2 PSD experiment, which monitors θV(t), the best fit is obtained with ν = 2 × 103 s−1 and Ea = 0.21 eV (Figure 5b, solid blue line). While the fit is good, such a low value for the prefactor, ν, is unphysical. Alternatively, a single activation energy with “normal” value of the prefactor (i.e., 1012±1 s−1) predicts a transition that is too abrupt (Figure 5b, dashed black line). A similar problem was encountered in our earlier studies of the H−D exchange and molecular mobility in 2 ML water films on TiO2(110).62 In that case, a combination of a “normal” prefactor and a distribution of the activation energies, P(Ea), was employed to fit the data. Here, the data in Figure 5b can also be fitted well using the “normal” prefactor, ν = 1012 s−1, and a Gaussian distribution of activation energies centered on 0.545 eV with ΔEa(fwhm) = 0.125 eV (Figure 5b, solid red line). The data in Figure 5b can also be fit using different distributions for the activation energy. For example, a “square” distribution with equal probabilities in the Ea range from 0.47 to 0.63 eV also fits the data well (not shown). The model fits to the reaction kinetics as a function of temperature using either a single activation energy (Figure 5b, solid blue line) or a distribution of activation energies (Figure 5b, solid red line) are nearly indistinguishable. However, for isothermal experiments where the reaction kinetics are measured versus the annealing time, a single activation energy and a distribution of activation energies predict different results.62 Figure S8 shows the CO2 PSD signal versus annealing time for several different temperatures. The procedure was similar to that used for the experiment shown in Figure 5b: 0.1 ML H2O was deposited at 40 K and annealed for the indicated time at Tann, O2 and CO were then dosed, and the CO2 PSD signal was measured. The decreases in the PSD signals versus time are not described by a simple exponential decay. For example, the dashed line shows the predicted vacancy hydroxylation kinetics at 185 K using the “best-fit” single activation energy and prefactor (i.e., Ea = 0.21 eV and ν ≈ 2 × 103 s−1; see Figure 5b (solid blue line)). In contrast, using a distribution of activation energies with a “normal” prefactor fits the reaction kinetics versus time (Figure S8, solid lines) and temperature (Figure 5b, red solid line) very well. According to the data in Figure S8, the overall temperature range of the experimentally observed water−vacancy reaction, presented in Figures 3, 4b, and 5b, will shift to higher temperatures with decreasing annealing time. We actually see such behavior experimentally (Figure S9a), and our model also tracks these changes (Figure S9b). F

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The Journal of Physical Chemistry C charge in the vicinity of vacancies has attracted considerable attention recently. STM experiments and DFT theory69,70 discovered a distribution of sites for the excess electrons surrounding vacancies (or bridging hydroxyls) that extends over more than 10 neighboring Ti5c sites. The excess electron density decreases the effective charge of the Ti4+ ions and presumably affects the binding energy of various adsorbates. It was suggested that such a charge distribution will repel the electron-donating H2O molecules from the defect sites.69 This hypothesis is consistent with the higher binding energy of H2O molecules on the oxidized TiO2(110) surface relative to the reduced one as evident in the water TPD spectra from these surfaces.32,73,74 Therefore, at any given instant, the random distribution of defect electrons in the vicinity of a water monomer could contribute to the observed distribution of activation energies for diffusion and reaction with the vacancies on the TiO2(110) surface.

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AUTHOR INFORMATION

Corresponding Authors

*Phone: (509) 371-6151. E-mail: [email protected]. *Phone: (509) 371-6134. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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4. CONCLUSION IRAS spectra of the bridging hydroxyl stretching vibration on TiO2(110) with narrow peaks at ∼2737 (3711) cm−1 are reported for of ODb (OHb). By dosing water at low temperature on a reduced TiO2(110) surface and annealing it, we monitored the temperature-dependent kinetics of the water−oxygen vacancy reaction yielding bridging hydroxyls. Coverages of bridging hydroxyls, water molecules, and unoccupied oxygen vacancies were monitored using IRAS, ESD, and PSD techniques, and they are found to be well correlated. For annealing times of ∼60 s, the reaction starts at Tann ≈ 150 K and is complete for Tann > 250 K. The data can be modeled by an Arrhenius process with a “normal” prefactor, ν = 1012 s−1, and a distribution of activation energies centered at 0.545 eV with ΔEa(fwhm) = 0.125 eV. In contrast, a single activation energy with a “normal” prefactor does not fit the data, yielding a temperature range between the onset and completion of the reaction that is too narrow. Our experimental activation energy is close to the STM data and theoretical estimates for the water monomer hopping on the Ti5c sites.8,24 These results suggest that diffusion limits the reaction rate of water molecules with the oxygen vacancies.

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reaction form the IRAS data and from the model calculations; Figure S10, coverage-dependent desorption energy obtained from inversion analysis of the 1.0 ML H2O TPD spectrum; Figure S11, the H2O desorption energy probability distribution obtained from the 1.0 ML H2O TPD spectrum; Figure S12, coverage-dependent desorption energy obtained from inversion analysis of the 0.12 ML H2O TPD spectrum; kinetic analysis of the bimolecular reaction between the water molecule and the oxygen vacancy (PDF)

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. The work was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for DOE by Battelle.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07526. Figure S1, a schematic for the IRAS geometry on TiO2(110); Figure S2, decomposition of bridging hydroxyls via recombination desorption around 500 K from IRAS and TPD spectra; Figure S3, reaction of bridging hydroxyls with O2 molecules from IRAS data; Figure S4, the correlated disappearance of molecular water and the appearance of bridging hydroxyls in the 150−250 K range from ESD and IRAS data; Figure S5, D2O, H2O, and H218O ESD yields versus annealing temperature; Figure S6, ESD yields from 0.05 and 0.1 ML H218O versus annealing temperature; Figure S7, ESD and PSD yields from H218O dosed on the annealed and hydroxylated TiO2(110) surfaces versus annealing temperature; Figure S8, CO 2 PSD yield from TiO2(110) predosed with H2O versus annealing time at various temperatures; Figure S9, the effect of annealing time on the temperature range of the water−vacancy G

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