Correlation of H Adsorption Energy and Nanoscale Elastic Surface

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Correlation of H Adsorption Energy and Nanoscale Elastic Surface Strain on Rutile TiO(110). 2

Denis V Potapenko, Gisele T Gomes, and Richard M. Osgood J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05129 • Publication Date (Web): 01 Sep 2016 Downloaded from http://pubs.acs.org on September 2, 2016

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The Journal of Physical Chemistry

Correlation of H Adsorption Energy and Nanoscale Elastic Surface Strain on Rutile TiO2(110) Denis V. Potapenko, Gisele T. Gomes, and Richard M. Osgood, Jr.* Laboratory for Light-Surface Interactions, Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10025, USA

ABSTRACT:

Scanning tunneling microscopy (STM) has been used to obtain the aerial distribution of bridge-bonded hydroxyl groups (HOb) on a rutile TiO2(110) surface, modified with a well defined nanoscale strain field. Our study makes use of earlier findings that 5 – 30 nmwide locally strained areas of the surface can be formed via low-energy Ar-ion bombardment combined with a thermal treatment. These strained areas appear as protrusions in the STM images, resulting from subsurface argon-filled cavities. Our STM images show that the local surface concentration of OHb groups is lower on the protrusions. This lowering of concentration has been interpreted as a reduction in the local H absorption energy, ∆E, a result similar to that observed on metals. In this paper,

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analysis of the reduction in this O-H bond energy across the surface shows a strong correlation between ∆EOH and the characteristic surface strain value, S. The ∆EOH values have been calculated through a subtraction of the contribution of the repulsive dipoledipole interaction between OHb groups. This interaction has been estimated from an analysis of the radial distribution of OHb pairs in the STM images. The measured linear relation between the reduction in O-H bond energy and the surface strain has been estimated to be ∆EOH (meV) ≈ 11 · S (%).

1. INTRODUCTION Mechanical strain has been shown to alter the chemical and physical properties of solid surfaces; such strained surfaces are encountered, for instance, in supported catalysts,1 thin films, and nanostructured materials.2,3 Thus, charge-carrier mobility in semiconductors is strongly affected by lattice strain.4,5 In addition, adsorption and dissociation of adsorbates on single-crystal metal surfaces are also known to be significantly modulated by the surface strain.6-9 In particular, the pioneering work of Gsell, et al. used nanostrain fields, similar to those used in this work, to observe changes in surface chemistry.7 Thus potentially, engineered elastic deformation of solids may be used in catalyst design or for surface nanopatterning applications. An important basic question that arises in this regard is “How does surface strain alter adsorption of atoms and molecules?” Thus far, however, systematic large-dynamic-range studies of the influence of strain on adsorption properties have been limited due to the technical difficulties in achieving high levels of elastic strain in typically macroscopic samples. This paper is concerned with hydrogen on bridge-bonded oxygen atoms on a rutile (110) surface – a basic and simple adsorbate system on TiO2. Titanium dioxide is a


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technologically

important

semiconducting

oxide,

which

is

widely

used

in

photocatalysis,10 gas sensors,11 solar cells,12,13 and a multiplicity of other applications.14 In several of these applications, such as in production of hydrogenated black TiO2, the mechanical strain is known to play a direct role.15,16 Recently our laboratory has shown that local strain fields on a TiO2(110) surface are created by low energy argon-ion implantation combined with thermal treatment.17 This procedure is known to lead to the formation of subsurface Ar clusters with a highly strained surface layer of TiO2 above the clusters.17 We point out that significant strain has been directly measured in rare-gas implanted metal oxide films.18,19 These studies, using transmission electron microscopy and small spot X-ray diffraction, show that rare gas cavites are formed by ion implantion and that the values of strain are commensurate with finite-element modeling.19 Please note however, that the present paper is not intended to focus on rare-gas strain mechanisms but rather on chemcial effects of surface strain. Our method of surface patterning of oxides has yielded surface protrusions of 5 – 30 nm in width and up to 1 nm in height with calculated tensile strain values of up to 4%. In an earlier study, the authors had noted that the surface protrusion apparently show a local reduction in the surface concentration of bridge-bonded hydroxyl groups (OHb).20 An important issue that has arisen in relation to interpretation of the bright extended features in the STM images of TiO2(111) surface is the physical origin of these objects. One important group of studies has focused on the role of buried charged defects such as those due to interstitial metal ions.21-24 In these references, the apparent protrusions in the STM images were attributed to local band bending around a positively charged subsurface defect due to partially screened Coulomb potential.24 These seminal studies



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have used STM imaging of 2 – 13 nm wide bright features that are typically present on cleaned TiO2(111) surfaces to demonstrate the absence of bridge-bonded oxygen vacancies on these areas. The nanoscale modulation of surface chemical reactivity in these and other21,22 studies provides an additional strong motivation for examining other possible physical origins of altered surface reactivity in TiO2. The goal of the present work, was to determine if the presence of large surface strain on 0.1 – 0.4 nm high elastically deformed areas of the TiO2(110) surface modifies the H adsorption energy. For this purpose, we have employed a scanning tunneling microscopy (STM) study and have statistically analyzed OHb distributions over a large number of protrusions with different dimensions and then compared and correlated the change of the O-H bond-energy, ∆EOH, with different individual geometrical parameters and calculated strain values. We show that among these parameters, surface strain value is well correlated with our experimental values of ∆EOH. In addition, we used a statistical analysis of our STM images to estimate the pair-interaction potential for OHb species that is necessary to calculate the values of ∆EOH.

2. EXPERIMENTAL METHODS The experiments were conducted in an UHV chamber, with a base pressure of 4 × 10-11 Torr, equipped with an Omicron VT-STM, a combined in situ LEED/Auger probe, and an Ar-ion flood ion gun. A single-crystal 5 × 5 × 1 mm, TiO2 rutile(110) sample was mounted inside the commercial Omicron sample holder. A custom-built button heater with Mo surface served as the sample support, to which the sample was attached with Ta wires. Silver powder was used as a heat-conducting spacer between the sample and the


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heater. A K-type thermocouple was mounted at the edge of the sample to monitor the sample temperature. The surface of the sample was first cleaned by repeated cycles of Ar-ion sputtering at 2 keV incident ion energy using 20 min of 10 µA ion current, and annealing at 950 K for 5 min. Subsequently to generate stressed surface protrusions, the sample was bombarded with 1 keV argon ions at an elevated temperature of 900 K for 10 min. At this ion energy, the ion-gun produced argon-ion currents of ~5 µA. After ion irradiation, the sample was exposed to water vapor from an aperture-based gas system, consisting of a gas chamber (reservoir) with a 5 µm-diameter dosing aperture. To dose a sample, the reservoir was filled with water vapor at 3 mTorr pressure and dosing was accomplished by varying the exposure time. To insure uniformity of dose, the other side of this aperture opened to a 4 mm diameter tube directed at the sample; the latter faced the UHV-side opening of this tube at a ~5 mm distance. The values of surface strain in the protrusions and the geometrical parameters of the subsurface Ar-filled cavities were derived from computer simulations based on a continuum-mechanics model.25 The details of this calculation are provided in our previous publication.17 We note that despite the nanoscale size of our protrusions much prior work has established the validity of continuum mechanics modeling for features of these dimensions (including the presence of elastic deformation);19 we also note that prior electron microscopy studies have shown the formation of rare-gas-filled nanocavities in implanted samples.18

3. RESULTS AND DISCUSSION 3.1. STM data acquisition. After the initial surface cleaning, our TiO2 rutile(110) surface was examined via STM imaging. The STM images showed a low impurity adatom level of < 0.002 ML and a bridge-bonded oxygen vacancy (BBOv) concentration



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of ~0.10 ML. Throughout this paper, a monolayer is defined as the surface concentration of 5-coordinated Ti ions of 1 ML ≡ 5.2 · 10-14 cm-2. Subsequently the surface was bombarded with 1 keV Ar ions for 20 min. while the sample was kept at 900 K. After the ion gun was switched off and the vacuum in the chamber restored, the sample was annealed for an additional 3 min. at 950 K and then cooled down. This room temperature sample was then exposed to a saturation dose of water vapor.

Figure 1: STM images of a rutile(110) surface in the vicinity of a surface protrusion. The surface concentration of hydroxyl groups OHb is determined by imaging to be ~0.2 ML. (a) A 21 × 16 nm image with a OHb-covered protrusion. (b) A 14 × 14 nm image with a OHb-free protrusion. (c) A sketch of the atomic structure of TiO2 rutile(110) surface with surface OHb groups. Following each water vapor dosing, the sample surface was explored using STM imaging. Atomic-resolution images were recorded for a total of 30 protrusions. Two such images are shown in Fig. 1(a, b). Both Fig. 1(a) and (b) show a TiO2(110) surface with a saturation coverage of bridge-bonded-hydroxyl groups OHb that appear as small bright spots in the images; for reference, a cartoon image of surface that explains the features in the image, is shown in Fig. 1(c). On a reduced TiO2(110) surface, deposited water


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molecules interact with BBOv’s, filling the defects with oxygen atoms from H2O and depositing two hydroxyl groups OHb.26 Hence the total concentration of OHb on flat areas of the surface is equal to 2 times the initial total oxygen-vacancy concentration, i.e. ~0.20 ML. Figures 1(a, b) also show the elliptical elevated surface regions or “protrusions”. In our earlier work we had shown that these protrusions exhibit elastic deformation above subsurface Ar clusters and thus when argon from a cluster is released the surface relaxes to its normal planar state.17 In our earlier work, we have shown that, prior to their reaction with water vapor, the deformed surfaces of the protrusions do not have BBOv’s, which are ubiquitous on the flat area of the TiO2 surface.17 This result can only be accounted for if, when the surface is exposed to H2O, OH groups form only on the flat areas as a result of water molecules reacting with the BBOv’s. Then the OHb groups on the protrusion areas, such as seen in Fig. 1(a), are the result of hydrogen species diffusing across the surface from the flat to the protruded areas.20 There are two mechanisms of hydrogen diffusion on TiO2(110) surface that have been reported as a result of extensive studies in literature: intrinsic along-the-row diffusion27 and water-assisted across-the-row diffusion mechanism.28 In order to determine which of these two mechanisms of hydrogen diffusion are applicable in our experiments, we have analyzed time-lapse STM images in our experiments of TiO2(110) surfaces containing OHb groups. From these experiments, we have found that both along- and across-the-row diffusion mechanisms are active under the conditions of our experiments (see Supplemental Figure S1 and the following discussion in the Supplemental Materials).



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3.2. Data analysis. For the purposes of analyzing our experimental data, each of the imaged protrusions has been characterized using STM data by their height h and width d (see Fig. 2(a)), the latter being the average of the protrusion’s in-plane dimensions along mutually orthogonal [001] and [1-10] directions. Also two derived values, the maximum surface strain S and the Ar-filled cavity depth H, have been calculated from h and d, using an elastic continuum model derived and described earlier.17 Note, that this model neglects any anisotropy of the TiO2 strain field and uses instead average values of the rutile elastic parameters.17 Our continuum mechanics calculations show that the strain components vary smoothly over the surface of the protrusion; the vertical component εzz of strain is negative (i.e. compressive) in the center and becomes weakly positive at the perimeter, the radial component εrr is positive in the center and becomes negative at the perimeter, and the tangential component εθθ is positive across the entire surface of the protrusion. All components of strain reach their maximum values in the center, where εxx = εyy = εrr = εθθ; i.e. all horizontal components for this central element are equal. We denote this maximum value of tensile strain in the horizontal plane by the symbol S in the present work, as illustrated by Fig. 2 (b). Although the elastic strain varies across the surface of a protrusion, its values at any given location scales with the value of S. Therefore, we use S as a representative value that shows how elastically deformed the material is at a given protrusion. Note that our data indicates that a simplified empirical relationship S(%) = 160 · h / d agrees to within 15 % of the exact S value calculated from the model, i.e. S is roughly proportional to h and 1/d.


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Figure 2: (a) 3D cross-sectional schematic combining a portion of the same STM image as in Fig. 1(a) with the sketch of a buried Ar cluster. (b) A drawing that illustrates the origin of elastic surface strain field and shows different components of elastic strain of a portion of the solid at the center of a protrusion. It is evident from Fig. 1(a) that the local concentration of OHb groups on the protrusion area is lower than that on the flat areas. Our earlier work paper.20 made the basic observation that the OHb concentration varied across the protrusion. However, our present more extensive experiments have yielded an empirical relationship between the adsorption properties for H of the elastically deformed rutile(110) surface and the geometrical parameters of the protrusions. To determine this relationship, STM images of an ensemble of protrusions with different geometries were analyzed. Each protrusion was characterized by the average value of OHb concentration, thus averaging over any



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possible variations in the concentration across the surface of a given protrusion. To obtain this quantity, the total number of OHb species on the elliptical area of a protrusion was counted and then this quantity was normalized by the area of this protrusion to thus obtain the value of Cbump. This value is then normalized again using the concentration Cflat of OHb groups on flat areas of the same surface terrace that contained the protrusion to obtain the quantity Cbump/Cflat.

This quantity is plotted in Fig. 3(a) versus the

maximum strain value S for each protrusion. The use of S as the x-axis here will be justified below.

Figure 3: (a) Distribution of OHb concentration on protrusions, normalized to that on flat surface, as a function of the maximum strain value S. (b) Distribution of the calculated total OHb energy shift on the protrusions ∆E as a function of surface strain S. As mentioned above hydrogen atoms are sufficiently mobile under the conditions of our experiments such that their average surface distribution is that resulting from thermal


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equilibrium. Therefore, the surface concentration of OHb has a Boltzmann distribution, which in our case can be expressed by the formula: Cbump/Cflat = exp(∆E/kT)

(1)

where k is Boltzmann’s constant, T is the temperature (room temperature in our case) and ∆E is the difference between the total potential energy of a hydrogen located at the surface of a protrusion or on a flat area. Note that this approach has been used in the pioneering work by Menzel group to treat a similar problem.7 Using Eqn. (1), the values of ∆E are calculated for each protrusion using the non-zero Cbump/Cflat values found from the STM images. A plot of the values of ∆E as a function of the maximum strain S for the analyzed protrusions is shown in Fig. 3(b). The data points follow an approximately linear dependence, thus the protrusions with higher strain have lower OHb concentration. In a minority of cases, that correspond to the extreme values of strain S > 3 %, hydrogen-free protrusions, such as the one shown in Fig. 1(b), were observed. In these cases, the condition Cbump/Cflat = 0 holds and the corresponding data points are marked with a red oval in Fig. 3(a). For these minority cases, Eqn. 1 yields an unphysical infinite solution for ∆E. The existence of the hydrogen-free protrusions may be explained on the basis of the two following observations: First, our group had previously shown that OHb can be formed only on flat areas of a surface as a result of the reaction of H2O with bridging oxygen vacancies.20 Thus hydroxyl groups are found in all protrusion areas only as a result of diffusing from the flat regions of the surface. Second, in this same work, it was shown that the lowest OHb concentration is observed along the perimeter of a protrusion rather than in the center.20 These two observations allow for the possibility that in a minority of cases (e.g. 4 cases in Fig. 3(a)) of H-free protrusions, an energy barrier



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along the perimeter of the protrusion may prevent the needed OHb diffusion into the protrusions; this phenomenon is currently not well understood and is the subject of additional studies. However, for the protrusions with surface hydrogen atoms it was assumed that any possible diffusion barrier is sufficiently low that the distribution of OHb groups is dictated only by thermodynamics, i.e. that in Eqn. 1. The ∆E data in Fig. 3(b) reflects the change in the total potential energy of a hydrogen atom on the surface (termed here “adsorption energy”) as a part of the ensemble of OHb’s under our specific experimental conditions. Our immediate goal is to relate the local shift in the binding energy to the local surface stress. However, this H adsorption energy obviously depends on another factor – local OHb concentration C, since each hydrogen atom has an overall positive charge in the adsorbed state29 and, therefore, experiences an electrostatic repulsive force from the other H atoms. Taking into account the small scale of ∆E in comparison with the absolute value of E (see the discussion section), these two factors may be separated using a standard multivariable calculus approach ∆E = ∆E (S, ∆C) = ∆EOH(S)|C = Co + ∆EH-H(∆C)|S = 0 ,

(2)

where ∆E is the change in the total potential energy of a H adsorbate on a given protrusion, S is the average value of strain and ∆C is the change of OHb concentration on the same protrusion, and C0 is the OHb concentration on flat surface areas. Equation (2) introduces two new functions. One is ∆EH-H, which reflects the change in the mutual interaction energy of the OHb groups solely due to the change in concentration, ∆C, a quantity which is not relevant to the strain in the substrate. The other, ∆EOH, that we will term “the O-H bond energy change”, represents the change in the H adsorption energy due to the surface strain in the hypothetical situation of a fixed OHb concentration. It is


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this quantity, ∆EOH = ∆E - ∆EH-H, that is a true representative of the influence of strain on adsorption and this value can be compared with ab initio theory. Therefore, in order to find ∆EOH from our data, it is necessary to find the general form of the concentration dependence of EH-H(C). Note that in our earlier work20 a first-order approximation was used, which considered only the simple nearest-neighbor Coulombic interaction between H atoms. In the present work, a more detailed approach is employed (see below), which allows us to estimate the energy of OHb pair interactions. 3.3. Estimation of the OHb mutual repulsion energy. In our analysis, the interaction potential between two isolated OHb groups on a flat TiO2(110) surface is first estimated. For this purpose, the radial distribution function for OHb groups on the surface is considered – an approach used in many problems in statistical physics for the many-body interactions of identical particles.30 To obtain the radial distribution function of surface hydroxyls, STM images of flat (protrusion-free), OHb-covered surfaces, a portion of such a surface is shown in Fig. 4(a), are analyzed. To analyze this image, the origin of the coordinate system was consecutively placed on each OHb in the image and the locations of the neighboring OHb groups were recorded. By averaging over the measured radial distributions of approximately 400 OH groups, the probability of surface-site occupancy, C(rx, ry) was found, where rx, and ry are the radial coordinates, expressed in units of the surface unit cell (0.30 and 0.65 nm), along the [001] and [1-10] directions respectively; see Fig 4(a). An example of C(rx, ry) for rx = 0, 1 and ry = 0, 1, … , 6 is shown in Fig. 4(b). Note that for each rx ≠ 0 and ry ≠ 0 there are 4 different actual surface sites corresponding to these (rx, ry) coordinates.



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Figure 4: (a) STM image of a flat rutile(110) surface with OHb groups. The overlaid grid illustrates the collection of data for the OHb radial concentration distribution. (b) Two components of the radial concentration distribution function C(r). (c) A plot of the calculated OHb pair-interaction potential (black symbols). The red and blue symbols show the potentials of Coulomb and electric dipole-dipole interactions fitted to the experimental data. For the purposes of illustrating our data analysis let us, first, compare the C(rx, ry = 1) and C(rx, ry = 0) data sets that are shown with the blue and black symbols in Fig. 4(b). Note that the deviation of the C(rx, ry = 1) points from the average OHb surface coverage θOH = 0.20 ML is below the statistical error, as marked by the error bars. Values for C(rx, ry = 0), however, vary widely from 0 to 0.23. A comparison of the C(0,1) = 0.18 and C(2,0) = 0.08 data points is particularly illustrative. The values of average concentration for these two points are very different, while the physical distance of these two points from the central OHb group is almost identical, i.e., 0.65 and 0.60 nm, respectively. This result is most easily explained as a manifestation of an additional attractive force between adsorbates, that are located across the atomic rows on the TiO2 rutile(110) surface and that offsets the repulsive electrostatic force. A similar “across-the-rows” attraction, which


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often manifests itself in the lateral alignment of the surface-adsorbed molecules, has been observed for physisorbed polycyclic,31 chemisorbed organic molecules,26 and even metaloxide clusters on TiO2(110).32 In this paper, the interaction of OHb groups, located on different atomic rows are ignored, since their strength is small compared to the interaction of hydroxyls within the same row and because, in any case, this interaction is below the detection level of our experimental method. The interaction of the hydroxyl groups in the same atomic row of the TiO2(110) surface is statistically reflected in the data for C(rx, ry = 0) (black symbols in Fig. 4(b)). From the figure, it can be seen that next-site hydroxyl neighbors (rx = 1) are absent and the 2nd site occupancy (rx = 2) are significantly depleted. This observation indicates the pair-wise repulsive interactions between the OHb groups. However, since the average site occupancy is relatively high (0.2 ML), the overall radial distribution is also affected by the “indirect” interactions, for which, as an example, the central hydroxyl influences the position of another OHb group, which in turn acts on a third hydroxyl group. In order to deduce the OHb pair-interaction potential that is needed to estimate ∆EEL(S), we have used the Ornstein–Zernike equation-based approach. This O-Z equation is typically used in the theory of fluids, but formally it is also applicable for an interacting surface-adsorbate systems.30 A hypernetted-chain equation was used as the closure relation, since it approximates well long-range interaction potentials.30 Mathematical details are given in section S2 of the Supplemental Materials. The above approach can be used to determine the interaction potential of the OHb pairs. Thus the interaction potential u(r), calculated from the C(rx, ry = 0) data in Fig. 4(b), is shown via the black-filled symbols in Fig. 4(c). The data points begin with rx = 2, since



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for rx = 0 and 1, the site occupation, C, is zero, and the corresponding values of u(r) are indefinite. The calculated function can readily be fit with an electrical dipole-dipole interaction potential udip(r) = ke · p / r3, where ke is the Coulomb constant. Our best fit corresponds to a dipole moment of p = 0.095 e·nm = 1.5 · 10-29 C·m and is shown using the unfilled blue symbols. The results in Fig. 4(c) show clearly that the simulated function fits the experimental data u(r) well, particularly if this best fit is compared to that with a simple Coulomb-interaction potential uq(r) = ke · q / r, corresponding to a fractional charge of q = 0.11e. To the best of our knowledge, the results presented above are the first experimental estimates of OHb mutual interactions. From these estimates, it follows that the interaction energy of the two nearest-neighbor OHb groups is 0.49 eV. This number can be compared with the published results of DFT calculations. Thus, using the numbers from a DFT calculations on a 4 × 2 slab by Kowalski et al.,33 yields a nearest-neighbor interaction energy of 0.326 eV; while in a second example, Li, et al used a DFT calculation with a nonorthogonal unit cell to obtain 0.48 eV for the interaction energy.27 Note that the latter is close to our experimental value. However, note also that the Bader charge analysis in the same study provided a very different value of 0.21 eV for nearest-neighbor OHb repulsive energy.27 The knowledge of the value of the effective dipole moment p alone is not sufficient for an estimation of EEL(C). The reason is that (as mentioned above) two effects, cause the OHb concentration, C, to influence the total electrostatic interaction energy, EEL. One effect is related to the total number of interacting species; this channel alone would render EEL proportional to C. The second effect or channel arises from the variation of the


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average distance between the hydroxyls. In order to estimate this second component, our STM images of the hydroxyl-covered protrusions, such as shown in Fig. 1(a), were used to identify the locations of the individual OHb groups on the surfaces of the protrusions and to calculate the radial concentration distribution for each protrusion in the same way as was done for flat areas on the TiO2 crystal; see Figs. 4(a, b). These radial concentration distributions, together with our dipole interaction potentials, udip(r), were employed to calculate the total electrostatic energy EEL for the individual protrusions. This value enables calculating ∆EOH = ∆E – ∆EEL; these values of the strain-induced variation of the O-H bond energy for individual protrusions are plotted in Fig. 5 as a function of three different geometric parameters of the protrusions and the calculated maximum strain values. In these calculations the assumption was made that the dipole moments of OHb groups are constant and are independent of the surface strain. This approach is used since the contribution of the variation in p is expected to be small compared to the calculated ∆EEL values, since other strain-related effects are generally small compared to the equilibrium values, e.g. < 4 % change in bond lengths (i.e. strain), < 2 % change in OH bond strength (see below). 3.4. Correlations of the O-H bond energy ∆EOH. As mentioned above, a statistical approach is used evaluate our data, in which the correlation between the values of ∆EOH and five measured parametric properties of the protrusions are determined. In particular, the data is quantified by the correlation factor R2, for plots of ∆EOH(x) versus x = h, d, H, 1/d, and S. The correlation factors were found to be 0.34, 0.05, 0.19, 0.08, and 0.69, respectively. Four of these dependencies: ∆EOH(h), ∆EOH(d), ∆EOH(1/d), and ∆EOH(S) are shown in Fig. 5. Of these factors, the value of maximum strain, S, showed by far the



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highest correlation with ∆EOH. Note that although S is approximately proportional to h / d, the correlation of ∆EOH with S is much higher than its correlation with h or 1/d separately.

Figure 5: Plots of calculated O-H bond energy as a function three geometrical factors, shown in label on each plot, and the maximum-strain value S. The red lines show the best linear fit to the data. The value of R2 is included in each plot. A linear fit to the data points of ∆EOH vs. S is shown in the plot in Fig. 5(d). This linear dependence follows the relation ∆EOH(meV) = 0.8 + 11.0 · S(%). Note, that the Yintercept of 0.8 is much closer to zero than the Y-intercept of –3.9 in the plot of ∆E vs. S shown in Fig. 3(b). By definition, ∆EOH(0) = 0. Therefore, the observation that the unconstrained linear fit to the ∆EOH(S) data falls very close to the origin, provides additional support to our model, in which ∆EOH is calculated from ∆E


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From the empirically determined linear dependence of ∆EOH(meV) ≈ 11 · S(%), and the maximum value of elastic strain of S = 4%, which has been observed in our experiments,17 the maximum value of the O-H bond weakening of ∆EOH = 0.044 eV is expected. To put this value into a perspective, we can compare it to the typical value of O-H bond strength of 2.82 eV; this number can be obtained from DFT calculations of H adsorption energy on a BBO of TiO2(110)33 and the known H-H bond strength.34 Thus the maximum achievable strain causes only a ~1.6 % change in the hydrogen binding energy. It is remarkable that such a small change manifests itself so clearly in our experiments. The comparison of correlation factors in the ∆EOH(x) dependencies shown in Fig. 5 indicates that, in our experiments, the distribution of OHb groups on the surfaces of the protrusions is well correlated to the values of elastic surface strain in the protrusion. However, the estimated statistical and methodological errors, indicated in Fig. 5(d) by the error bars, are apparently not sufficiently large to explain the deviation of some points from a linear dependence. This observation appears to suggest that factors other than surface strain apparently also influence the surface distribution of the hydroxyls. In this connection, as mentioned above, one group has discussed extensively the role of subsurface charged impurities in altering the distribution of the adsorbates on the protrusions.21-24 This intriguing idea has not been examined here due to our focus on strain, which is clearly present in the protrusions. Nonetheless it remains for future experiments to examine the joint effect of both of these quantities. Finally, the results of our study raise the question of the physical origin of the observed strain – chemistry relation. In the case of metals, such a relationship has received



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considerable attention in the literature. For example, seminal work by Mavrikakis et al.9 has shown that the reactivity of transition-metal surfaces generally increases with lattice expansion – this effect has been attributed to the upshift in energetic position of d bands. Strain effects in metal oxides often show a more complex nature. For example, in a theoretical study Kushima et al.35 has shown that oxygen adsorption on LaCoO3 is modulated by tensile strain through three competing mechanisms: elastic stretching of the Co-O bonds reducing the overlap of the Co d and O p bands, anisotropic local relaxations reforming the Co-O bonds and phase transitions in spin state. Influence of strain on electronic structure in semiconductors4 and 2D materials36 is well documented. Also, in the light of our Section 3.3 in the present manuscript, it can be suggested that the displacement of the Ti4+ and O2+ ions from their equilibrium positions may alter the local electrostatic fields near the surface that again would change the H adsorption energy. Each of these strain effects may be at play in our H/TiO2 system and it is clear that separate extensive theoretical work is required to understand these phenomena more completely.

4. CONCLUSION This paper analyzes the deviation of the surface concentration of adsorbed hydrogen atoms on bridge-bonded oxygen on a TiO2 (110) surface in the presence of elastic surface strain. The nanoscale strain fields used in the experiments were created by low-energy argon implantation so as to form nanometer protrusions and are thus analogous to reports of nanometer-scale surface strain in metal crystals and macroscopic metal oxide crystals. Our study was based on extensive statistical analysis of STM images and focused on


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determining the change in H adsorption energy, which was deduced from lowering of the local surface concentration of OHb on the protrusion surfaces. The additional interference of the mutual repulsion of the surface hydroxyl groups was estimated from the radial distribution of OHb groups on flat surface areas. The local strain values were calculated from the geometrical parameters of the protrusions. Our model shows a linear relationship between O-H bond energy and the maximum strain on the protrusion that can be expressed as ∆EOH(meV) ≈ 11 · S(%). Thus the surface strain causes a clear shift in the O-H bond energy on TiO2 surface. To the best of our knowledge this study is the first experimental work that establishes a numerical relation between surface strain and the chemical properties of this surface. Finally our discussion above notes important related works22,23 that aim to understand the effects of buried charged impurities on the same TiO2 surface adsorption properties.

ASSOCIATED CONTENT Supporting Information Time-lapse STM images of flat TiO2(110) surface with bridge-bonded hydroxyls OHb demonstrating different mechanisms of hydrogen diffusion followed by a short discussion of diffusion mechanisms; details of the mathematical calculations used in data analysis. These materials are available free of charge via Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author



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*E-mail: [email protected] (RMO), tel.: 1-914-806-3696. Notes The authors declare no competing financial interests

ACKNOWLEDGEMENTS The authors gratefully acknowledge support of this work by the U.S. Department of Energy, Basic Energy Science (Chemical Sciences Division), Contract No. DE-FG0290ER14104. We wish to thank Zhisheng Li for his contributions at the onset of the project, and Igor Lyubinetsky and Nikolay Petrik for their kind and extensive discussions of their experiments and our results. We also thank the unknown referees for their helpful critical comments on our model.

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Table of Contents graphics


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Correlation of H Adsorption Energy and Nanoscale Elastic Surface

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