Manipulating Reaction Rates of Metal-Oxide Heterogeneous Catalysts

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Manipulating Reaction Rates of Metal-Oxide Heterogeneous Catalysts via Semiconductor Heterojunctions Navaneetha K. Nandakumar† and Edmund G. Seebauer*

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Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana, Illinois 61801, United States ABSTRACT: Heterojunctions of metal oxide semiconductors enable the manipulation of surface chemistry for heterogeneous catalysts or sensors without introducing dopants and their attendant complications. If one of the semiconductors is sufficiently thin, charge exchange between the two semiconductors leads to charge buildup at the free surface. The excess charge influences the Lewis acid−base character of the surface and propagates into properties such as catalytic activity. Although the available literature offers evidence for such effects, published work does not outline a quantitative framework that links heterojunction behavior to catalytic activity. The present work develops and demonstrates such a framework for the oxidation of methanol to formaldehyde with a heterojunction of thin polycrystalline V2O5 grown on polycrystalline anatase TiO2. The framework accurately reproduces activity changes by a factor of 20 in response to V2O5 thickness and TiO2 donor concentration.

1. INTRODUCTION Heterojunctions composed entirely of metal oxide semiconductors have been investigated for applications involving surface chemistry such as gas sensors,1,2 photocatalysts,3−5 and other catalysts.6−8 Such structures enable the manipulation of surface chemistry without introducing dopants and their attendant complications. If one of the semiconductors is sufficiently thin, charge exchange between the two semiconductors leads to charge buildup at the free surface. Figure 1 shows such a case schematically for thin vanadia (V2O5) overlying TiO2.

activity. Although the available literature offers evidence for such effects, published work does not outline a quantitative framework that links heterojunction behavior to catalytic activity. The present work conceptualizes a supported catalyst as a semiconductor heterojunction device, develops a theoretical framework for manipulating reaction rates, and demonstrates its effectiveness for the oxidation of methanol on V2O5/TiO2 thin film catalysts. The framework consists of two primary elements: (1) a semiempirical correlation between the surface Fermi energy of d0 metal oxides and their catalytic activity,13 and (2) an electronic model for estimating the surface Fermi energy of a thin-film semiconductor heterojunction in terms of known material parameters.11 The semiempirical correlation was developed based upon a “collective” approach to catalytic rates that focuses upon a solid’s continuum properties rather than detailed atomic-scale interactions with adsorbates. For reactions whose rates depend upon surface acidity, the correlation rests upon a series of relations connecting a semiconducting oxide’s surface Fermi level to its activity through the point of zero charge and overall Hammett acidity. In short, the rates for a given reaction vary exponentially with the catalyst’s work function, which may be manipulated in principle by doping or (in the present case) a heterojunction configuration. The electronic model was developed for a semiconducting heterojunction wherein an oxide substrate with controlled carrier concentration supports a much thinner layer that cannot absorb all the charge that would normally transfer. Some of the excess charge therefore propagates to the

Figure 1. Schematic of V2O5/TiO2 heterojunction, showing charge transfer at the interface and accumulation of charges at the surface for a thin overlayer.

A related phenomenon occurs for Pt supported on TiO29 that can affect reaction rates.10 For metal oxide heterojunctions, this phenomenon occurs for overlayers thicker than those for metals, and existing models can be adapted to estimate the magnitude of the effect11 whenever the ambient fluid medium is a gas or a liquid of low ionic strength. The excess charge influences the Lewis acid−base character of the surface12 and propagates into properties such as catalytic © XXXX American Chemical Society

Received: January 21, 2018 Revised: July 1, 2018 Published: July 3, 2018 A

DOI: 10.1021/acs.jpcc.8b00712 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

depletion region in TiO2 and an accumulation region in V2O5. Ef depends upon the thickness of the V2O5 layer and varies by about 0.2 eV for thicknesses below about 30 nm. Partial oxidation of methanol to formaldehyde was chosen as a test reaction, with an overall reaction stoichiometry of

free surface and changes the surface potential and work function. The model employs a uniform-medium assumption for polycrystalline oxides, a standard Anderson description14 for interfacial band offsets, and an approximation to the solution of Poisson’s equation that truncates the bands at the free surface of the overlayer. Examined individually, both the semiempirical correlation and the electronic heterojunction model satisfactorily match the corresponding experimental results they seek to predict. However, the combined use of these tools to predict the variation of a catalytic reaction rate as a function of heterojunction variables such as overlayer thickness and support donor concentration has not yet been attempted. Methanol oxidation on TiO2-supported vanadia offers a test case, as the reaction follows a Mars−van Krevelen mechanism15,16 that is well understood and should respond to the position of the surface Fermi energy.

CH3OH +

(2)

Over V2O5, the reaction is highly selective toward the formaldehyde and water products, with minimal side reactions and simple first-order kinetics.16,17 The mechanism and ratedetermining step are well understood. Reaction conditions are mild with relatively safe, easy-to-detect reactants and products. The reaction proceeds according to the well-known Mars− van Krevelen mechanism,15,18 with a lattice O ion being consumed for the dehydrogenation of methanol and the lattice being reoxidized by atmospheric O2. The reaction begins with the dissociative adsorption of methanol as a methoxy species adsorbed to V atoms. Rate limitation occurs in the next step wherein hydrogen abstraction by a lattice oxygen atom occurs, forming an adsorbed formaldehyde species.17 This conversion to and subsequent desorption of formaldehyde requires redox sites. Acidic sites can lead to products of dehydration such as dimethyl ether and dimethoxy methane. Strong basic sites cause further oxidation of the adsorbed formaldehyde, leading to formic acid, methyl formate, and carbon oxides. In the ratelimiting step for formaldehyde formation, the abstraction of H from the adsorbed methoxy species can occur as a proton transfer from methoxy19,20 and an electron transfer to the catalyst, or it can occur as a hydride transfer from methoxy21 and an electron transfer from the catalyst. Thus, both acidity and basicity of the catalyst are important in either of the proposed mechanisms. However, experimental data from the literature show unambiguously that a basic surface enhances the oxidation of methanol to formaldehyde.22,23 For low conversions in excess oxygen, the kinetics are firstorder in methanol and zero-order in oxygen, with an activation energy of 19.6 kcal/mol (82 kJ/mol) at atmospheric pressure set by the C−H bond within the adsorbed methoxy group.24 The rate expression is generally written as16

2. CONCEPTUAL BACKGROUND The semiempirical correlation relating surface Fermi energy Ef and catalytic rate constant k takes the following form ij k yz lnjjj 2 zzz = 5.3λ(Ef 1 − Ef 2) jk z k 1{ = 5.3λ(ϕ2 − ϕ1)

1 O2 → HCHO + H 2O 2

(1)

,where the numerical subscripts denote two different donor or acceptor concentrations, and ϕ denotes the work function. The parameter λ is a proportionality constant that depends upon the specific type of active oxide and reaction. Equation 1 predicts an exponential dependence of rate constant upon surface Fermi level, and implicitly embeds the Hammett acidity of the surface. Acid-catalyzed reactions (with positive values of λ) will have higher rates for n-type oxides that are induced to become more p-typevia doping or the presence of a nearby heterojunction interface. The electronic model for surface Fermi energy in terms of material parameters11 treats both sides of the heterojunction as uniform media. The effects of polycrystallinity, porosity, grain boundaries, and localized deviations in charged defect concentrations are all neglected. For semi-infinite media on each side of the junction interface, the spatial distribution of the electric potential can be obtained from the solution of Poisson’s equation. The simplest (Anderson) form of the boundary conditions at the interface assume continuity of electric displacement and the equating of the total band bending to the built-in potential between the semiconductors. This approach idealizes the semiconductors as though they were still far-separated and neglects chemical bonding effects and other perturbations at the interface. The truncation approximation at the free surface takes Ef to lie (with respect to the band edges) at the energy position given by the semiinfinite solution to Poisson’s equation. This approximation works best for free surfaces having densities of intragap surface states that are either small or uniformly distributed in energy, and seems experimentally to be adequate for V2O5. The V2O5/TiO2 heterojunction is a Type II “staggered gap” structure, wherein the band gaps of the two semiconductors partially overlap each other. Undoped polycrystalline anatase TiO2 and V2O5 are both intrinsically n-type materials due to excess native donor defects. Upon the formation of the junction, electrons flow from TiO2 into V2O5, creating a

r = kPCH3OH = K ads × k rds × PCH3OH

(3)

where Kads incorporates CH3OH adsorption, krds accounts for the rate-determining step, and PCH3OH denotes the partial pressure of methanol.

3. EXPERIMENT Heterojunction structures were synthesized on Si(100) substrates of approximate dimensions 2 cm × 2 cm. Anatase TiO2 was grown in amorphous form by atomic layer deposition according to protocols described previously.25 Subsequent annealing at 550 °C yielded polycrystalline anatase whose detailed characterization has also been described. The crystalline films were 100 nm thick, and capacitance−voltage measurements yielded a carrier concentration of 8.3 × 1016 cm−3.25 Polycrystalline V2O5 films of various thicknesses were grown atop the anatase by chemical vapor deposition at 200 °C according to methods detailed elsewhere.13 Additionally, some V2O5 films were grown directly on n-type silicon (100) substrates (with native oxide). Single-wavelength ellipsometry yielded film thicknesses for each specimen by measurements at B


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The Journal of Physical Chemistry C five distinct locations and averaging, using a measured refractive index of 2.3 for V2O5. The range of nonuniformity for each specimen was typically 99.8% pure, Sigma-Aldrich) was dispensed from a small glass bottle after multiple freeze− pump−thaw cycles to remove contaminants. Reaction kinetics were measured by analyzing gas samples from the reactor at specified time intervals in the quadrupole mass spectrometer. Gas samples from the reactor were continuously sent through a leak valve into the sampling chamber of the mass spectrometer and spectra were collected. The change in the signal intensity ratio of methanol to argon was used to calculate the reaction rate. Calibration curves (for signal intensity ratio) were generated with methanol−argon mixtures of known compositions. These calibrations were used together with known pressures of argon admitted during reaction to quantify the evolution of the methanol partial pressure. Due to interference in the mass spectrometer from other species participating in the reaction, the disappearance of reactant O2 could not be tracked quantitatively in a similar fashion. Products of the reaction were monitored as well during kinetic measurements, but only qualitatively. Only HCHO and trace amounts of CO2 could be observed throughout the course of the reaction. Other possible products such as formic acid, methyl formate, dimethyl ether, and others were sought but not observed. CO2 appeared in trace amounts that were scarcely visible above background and did not vary with time during the reaction. By contrast, HCHO was clearly visible and increased in proportion to the decrease in methanol. The reactor was loaded with an initial charge of the reactant gases (methanol vapor, oxygen) and the internal standard (Ar). Pressures of 1−2 Torr (133−267 Pa) were typically employed. Due to the continuous sampling, the system was modeled as a semibatch reactor.

X-ray measurements revealed that the vanadia was reduced chemically over time during the course of the measurements despite the presence of excess oxygen. This reduction results from the combination of rather low pressures and high temperatures, which favors oxide phases containing less oxygen than V2O5.27,28 To mitigate the slow drift in composition, specimens were reoxidized just before and after each reaction run by heating in 10 psig O2 at 350 °C for 30 min.

4. RESULTS 4.1. Material Characterization. Characterization of the TiO2 and V2O5 has been reported extensively elsewhere.11,25,29 Briefly, the heterojunctions consisted of crystalline anatase TiO2 with a [101] orientation and crystalline V2O5 with a [001] orientation and ∼50 nm grain size. Vanadia thicker than about 40 nm covered the titania entirely after deposition, but below this thickness, the films were usually not fully continuous and exposed the underlying anatase. In the case of very thin vanadia films, grains of the underlying anatase film could be easily seen (Figure 2).

Figure 2. (a)−(d) SEM images of ∼5 nm thin films of V2O5 on TiO2. (e) Top-view and (f) side-view SEM images of bare TiO2 films used for V2O5 deposition. Crevices in the TiO2 films are clearly visible in the images, especially (e) and (f).

The methanol oxidation reaction often promoted film agglomeration−manifesting as either discontinuities in initially continuous films (especially thinner ones) or exaggeration of existing discontinuities. Figures 2 and 3 show examples akin to those in ref 11. However, detailed investigation with SEM showed that the agglomeration took place on a time scale that was short compared to each kinetic experiment, so that agglomeration kinetics did not distort the rate measurements significantly. The kinetic results and micrographs presented here all reflect fully developed agglomeration. Characterization done in conjunction with the present work demonstrated analogous behavior occurs for V2O5 on Si. XRD showed that the vanadia films were crystalline with a preferred C


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Figure 3. SEM images of an ∼9 nm thin film of V2O5 on TiO2.

(001) orientation. Figure 4 shows SEM images indicating that the V2O5 is not fully continuous. Extensive imaging showed that the coverage generally increases with nominal thickness until full continuity at roughly 40 nm. However, the coverage was not entirely predictable; minor variations in synthesis details sometimes allowed for full continuity even below 40 nm. Figure 4 shows a relatively low-coverage film at 20 nm and a nearly continuous film at 23 nm. 4.2. Kinetic Measurements: V2O5/Si. Equation 1 implies that enhancements in rate depend on the identities of the oxide and reaction, and not on the identity of the support. To verify this behavior, kinetic experiments were performed with V2O5 grown to various thicknesses on silicon covered with native oxide SiO2. Figure 5 shows the first-order reaction rate constant k, normalized by unit area, at 300 °C as a function of nominal thickness. For discontinuous films, the exposed V2O5 surface area was estimated visually from electron micrographs such as those in Figure 4. The rate constant increases with nominal thickness by about a factor of 2 before leveling off above 30−40 nm (Figure 5). The reaction activation energy was also measured between 275 and 350 °C as a function of thickness. Figure 6a shows the value remained constant at 33 ± 4 kcal/mol (138 ± 17 kJ/mol). Figure 6b shows that the preexponential factor (calculated using rate constant per unit estimated area of the catalyst) remains mostly constant with V2O5 thickness. These plots show that the reaction mechanism and energetics are unchanged by V2O5 thickness. The reported TOF for bulk V2O5 (atmospheric conditions) at 230 °C is 0.022 s−1.24,30 From a reported activation energy of 19.6 kcal/mol,24 the TOF at 300 °C would be 0.22 s−1. However, a wide range of TOF values at 300 °C have also been reported by the same laboratory on bulk vanadia at atmospheric pressure, including (in s−1 units) 1.1,31 2.2,32 and 9.8.33 The reason for this wide variation (and the significant activity in some cases) was not noted by the authors

Figure 4. SEM images of V2O5 on silicon of nominal thickness 23 nm (a, b) and 20 nm (c, d).

Figure 5. Variation of the rate constant at 300 °C with nominal thickness for V2O5 on Si. Line represents a guide to the eye.

and is unknown, although methanol adsorbs primarily on the edges of anisotropic vanadia platelets rather than on basal planes.31−33 Active site densities present significant challenges for measurement despite significant improvements over time.32 We speculate that such challenges, together with variations in the synthesis procedure leading to different degrees of crystallite texturing in bulk vanadia, could account for the D


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as described above. The TOF rises to 5.1 s−1 for 4.5 nm V2O5/ TiO2. In contrast with Si substrates, the activation energy varies with the V2O5 thickness. Figure 8 shows that the activation

Figure 6. Variation of (a) the activation energy and (b) the preexponential factor with nominal thickness for V2O5 on Si. Lines represent guides to the eye.

difference. The present work assumes a vanadium reactive site density of 10 sites/nm2 (compared with a literature range of 8−1324,34−36). The TOFs at 300 °C calculated here at 1−2 Torr for bulk V2O5 (i.e., >30 nm thick) and for V2O5/Si vary between 0.5 and 1 s−1. 4.3. Kinetic Measurements: V2O5/TiO2. Kinetic measurements were performed in which V2O5 thickness was varied on TiO2 that was consistently 100 nm thick, as TiO2 thickness changes the donor concentration of TiO2 deposited by the methods employed here25,37 due to the effects of medium atomic-scale order. Figure 7 shows the results.

Figure 8. Variation of (a) the activation energy and (b) the preexponential factor with nominal thickness for V2O5 on TiO2. Lines represent guides to the eye.

energy rises from roughly 15 kcal/mol (63 kJ/mol) below 10 nm to about 30 kcal/mol (126 kJ/mol) above 20 nm. Figure 8b shows a similar trend in the pre-exponential factor with V2O5 thickness.

5. DISCUSSION 5.1. Determination of λ. Figure 9 shows eq 1 plotted using a TiO2 donor concentration of 8.3 × 1016 cm−3, which is

Figure 7. Variation of the rate constant at 300 °C with nominal thickness for V2O5 on TiO2. Line represents a guide to the eye. Figure 9. Comparison of experimental data of relative reaction rates on V2O5/TiO2 as a function of V2O5 thickness, with model predictions.

For discontinuous films, the exposed V2O5 surface area was estimated visually from electron micrographs such as those in Figure 3. Use of TiO2 substrates prompted the reaction rate to vary much more dramatically with V2O5 thickness. After accounting for film discontinuity, the rate decreased monotonically with thickness by about a factor of 20 between 5 and roughly 40 nm. Similar to the case of V2O5/Si, the reaction rate constant value saturates beyond a V2O5 thickness of 40 μm, indicating the formation of a continuous “bulk” film where the free surface is not coupled to the V2O5/TiO2 interface. The TOF on “bulk” V2O5/TiO2 (∼60 nm V2O5 thickness) is ∼0.23 s−1 at 300 °C, which is quite close to the corresponding value of 0.22 s−1 estimated from the literature

characteristic of 100 nm TiO2 films. The parameter λ was permitted to vary as a free phenomenological parameter, and a least-squares fit to the experimental data yields λ = −6.0. The quality of the fit over the entire range of V2O5 thicknesses is good, giving evidence that the functional form of eq 1 is appropriate. The quality of the fit is remarkable, considering that eq 1 represents an exponential function of highly nonlinear changes in several variables−most notably the freesurface potential of the vanadia. That potential varies quite substantially with V2O5 thickness, as the potential reflects the E


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nm, the typical fraction of the surface occupied by bulk vanadia at 5 nm is about 0.3, which at 20 nm the fraction is 0.9. The ratio of reaction rates at 5 nm vs 20 nm V2O5 based upon a linear combination would be (0.3 × 1 + 0.7 × 2)/(0.9 × 1 + 0.1 × 2) = 1.55. Yet the observed ratio lies much higher at 7. Likely errors in either the area-based rates or the estimated fractional surface occupation by the bulk form are not sufficiently large to affect the disparity. The net contribution of active sites increases as the vanadia on TiO2 gets thinner. Within that increasing net contribution, the TOF of individual sites actually decreases, but the concentration of active sites increases in a way that more than compensates. The functional form of these variations with thickness is not known, and in any case, our data are not sufficiently precise to discriminate with precision among possible functional forms. Furthermore, direct comparison with the case of a Si support does not resolve the question, as we have measured neither the TOF nor the active site concentration for V2O5 monolayers on Si. So it is conceivable that a portion of the rate variation we observe for V2O5/TiO2 results simply from changes in the relative contributions of the monolayer sites and bulk edge sites. However, the decreased activation energy we observe as the proportion of monolayer sites rises seems inconsistent with the order-of-magnitude lower TOF comparted to bulk edge sites (ref 31, which did not report activation energies). The monolayer sites would need to have not only a smaller activation energy but also a much smaller pre-exponential factor whose decrease compared to edge sites more than compensates. Hence, the contribution monolayer sites may account for a small fraction (1.55/7) of the rate increase for the thinnest V2O5, but that even this small fraction seems unlikely due to the concomitant decline in activation energy. Direct consideration of activation energy also rules out the linear combination approach. The activation energy reported in the literature for this reaction of methanol oxidation on vanadia for both the bulk and various oxide-supported forms lies in the range 16−23 kcal/mol (67−96 kJ/mol).17,24,32 In the case of a TiO2 support, the activation energy is about 20 kcal/mol (84 kJ/mol) for both the bulk and supported forms of vanadia at atmospheric pressure. Yet in the present work, the activation energy declines from roughly 30 to 15 kcal/mol, which encompasses a much larger range than the entire literature for oxide-supported vanadia. Even allowing for differences among laboratories in pressure (a factor of 1000 lower here) and catalyst synthesis methods, it seems unlikely that the range of change observed here can be explained entirely by differing proportions of monolayer vs bulk vanadia covering the TiO2 support. Figure 10 provides important insights into the effects of V2O5 thickness in this work by showing estimates from eq 1 of the relative reaction rate (compared to bulk V2O5) as a function of V2O5 thickness for several values of donor concentration Nd in the underlying TiO2. The curves in Figure 10 were generated using λ = −6 together with conduction band profiles computed according to the methods of ref 11. The predicted rate increases as the vanadia films become thinner and less able to accommodate charge injected from the underlying TiO2, with the largest variation occurring for vanadia thicknesses < 5 nm. Greater donor concentrations in the TiO2 lead to increased charge injection into the V2O5,

strong and nonlinear spatial variation of band bending in an accumulation region. The parameter λ is analogous13 to the Bronsted coefficient defined for liquid-phase reactions. Its value should be positive for reactions catalyzed by acids, and negative for those catalyzed by bases. The negative sign for λ is expected for a base-catalyzed reaction of the kind described by the Mars−van Krevelen mechanism that is operative here. In liquids, the nominal absolute value of λ is unity for a fully ionic transition state. However, larger values as high as 1.638 have been reported for multifunctional acids or bases. For gasphase reactions, even larger values are possible. For example, λ = +6.1 has been computed13 for gaseous CO oxidation on doped NiO15 based on the variation of activation energy with work function. Very few measurements of λ exist for surface reactions, however, and most fall between 0.1 and 0.6.13,39 The theoretical interpretation of such cases remains unclear, and the present work treats λ simply as a phenomenological parameter. 5.2. Effect of V2O5 Thickness. For V2O5/Si, the rate constant decreases slightly below 30−40 nm where the films become discontinuous, but the activation energy remains constant throughout the entire range of thickness within the limits of experimental error. The variation appears to arise mainly from changes in the pre-exponential factor, although the data are sufficiently noisy to preclude determination of the functional form. Indeed, the Si substrate, with insulating native oxide, would not be expected to affect the reaction mechanism or energetics. We surmise the film discontinuity exposes crystal planes other than the dominant (001) orientation in continuous films. These other planes are not as active for methanol oxidation, leading to larger changes in the active area for reaction than accounted for by the coverage normalization procedure. The trend in rate constant reverses when TiO2 replaces Si as the support, clearly demonstrating the influence of the TiO2. For V2O5/TiO2, the rate constant increases as the films become thinner and rises more sharply for the thinnest layers. However, the variations begin to appear at about the same thickness that the films become discontinuous. In principle, the observed behavior could therefore result from higher reactivity for extremely thin (monolayer-level) supported vanadia due to atomic-scale effects rather than heterojunction effects that manifest through several nanometers of film depth. For some acid-catalyzed reactions on TiO2 such as selective catalytic reduction,40 the increase in overall surface reactivity for monolayer films of vanadia arises due to the TOF. For monolayer vanadia on TiO2, the most recent and comprehensive study involving methanol oxidation31 shows that the TOF actually falls below that for the bulk (by a factor of 10), but this decline is more than compensated by an increase in the density of active sites (by a factor of about 20). The areabased rate and reaction energetics could conceivably vary with film thickness according to a mathematical combination of distinct contributions from the monolayer and bulk forms of vanadia. Detailed consideration of the specific values of both the rate constant and the energetics appear to rule out this possibility, however. With respect to the rate constant, the sharp increase as the films become thinner is too large to explain via a simple linear combination. As suggested above, the area-based rate for monolayer vanadia lies about a factor of 2 above that for the bulk form. In an example case comparing the rates at 5 and 20 F


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The activation energies for bulk-like V2O5 films are consistently ∼30 kcal/mol, irrespective of the substrate. This value is significantly higher than the 19.6 kcal/mol reported in the literature. This divergence may be due to the present experiments being conducted at much lower pressures (1−2 Torr) compared to previous work at atmospheric pressure. Figure 8a shows the activation energy decreases by roughly a factor of 2 (to 15 kcal/mol) for very thin V2O5 on TiO2. We surmise this change occurs in response to the increase in basicity of the surface due to the injection of electrons from the TiO2 into the V2O5 as a result of Fermi level equalization between the two solids. Because the V2O5 is too thin to accommodate all the charge that would normally transfer, the surface becomes more electron-rich to a degree suggested by standard heterojunction analysis. The increased surface basicity lowers the barrier for the rate-determining step of H abstraction from the adsorbed methoxy group. The apparent activation energy almost certainly includes a contribution from the adsorption enthalpy of methanol. An increase in surface basicity of the catalyst would lead to a more facile adsorption of the slightly acidic methanol on the catalyst,21 thus leading to a lower apparent activation energy. Figure 8b shows an increase in and then saturation, of preexponential factor with V2O5 thickness. This means that the entropy change during the hydrogen abstraction increases with V2O5 thickness and then saturates. As V2O5 thickness increases, the surface basicity decreases and thus the adsorbed HCHO is less stabilized, Overall, Figure 8 shows that the rate enhancement for thinner V2O5 films is primarily due to a lowering of activation energy, and this offsets any reduction in rate caused by a lower pre-exponential factor The absolute magnitude of λ observed here is quite large. The heterojunction model does a remarkably good job in predicting surface potential,11 so an explanation for the large value of λ probably lies elsewhere. In addition, changes due to increased ionicity (and therefore basicity) of surface V−O bonds, which is known to increase activity of V2O5 in methanol oxidation, 22 should be already accounted for in the assumptions underlying eq 1. Several effects, tacitly lumped into λ, may influence the thickness dependence of the reaction rate. One effect is the exposure of new crystallographic orientations due to polycrystallinity and agglomeration. As the thickness decreases, spaces progressively open up between the grains, and new crystallographic orientations become exposed. A second possible effect originates from the donor concentration within the V2O5. We have assumed a best known value (1016 cm−3) from the literature, but the actual value for our films could differ and could even vary with thickness as it does for thin polycrystalline TiO2. A third possible effect is that of oxygen adsorption. O2 acts as an electron acceptor, and thereby changes the work function upon adsorption. Conversely, more electron-rich surfaces adsorb more oxygen. This synergy implies that the adsorption-induced change in surface potential may be greater for vanadia films that start more electron-rich. Such phenomena have already been described,41,42 in which case Poisson’s equation would need to be solved selfconsistently with the adsorption isotherm and reaction kinetics for O2 on the vanadia. 5.3. Effect of TiO2 Donor Concentration. Figure 10 shows that rate enhancements vary considerably with the TiO2 donor concentration. Figure 12 shows such enhancements plotted another wayas a function of Nd in the TiO2 for

Figure 10. (a) Rate predictions using the heterojunction model and with λ = −6, for various Nd values in TiO2. The rates are normalized by the value for bulk V2O5. (b) Same rate predictions zoomed in to the first few nanometers of the surface.

which boosts the rate by roughly 2 orders of magnitude for TiO2 donor concentrations near 1019 cm−3. The uniform-medium assumption that undergirds these computations does not account for many effects that may become important for very thin films. Examples include changes in effective area as the nominally uniform films agglomerate, corresponding exposure of different crystallographic orientations and the reactive sites they support, and changes in grain boundary structure that influence the effective donor concentration in the vanadia. Yet Figure 10 remains useful in gauging the general magnitude of the possible effects. These computations assume a donor concentration in the V2O5 of 1016 cm−3, which is consistent with the values reported in the scant literature. Larger donor concentrations in the vanadia would screen the free surface more effectively from the interface with TiO2, and shift the rate enhancements to smaller thicknesses. Conversely, smaller donor concentrations would stretch the region of rate enhancement to greater thicknesses, as shown in Figure 11.

Figure 11. Effect of V2O5 donor concentration on the variation of catalytic activity vs V2O5 thickness. Larger V2O5 donor concentrations screen the surface from the interface (such as electron transfer from TiO2) and shift the rate enhancements to lower thicknesses. G


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effects, if present, presumably affect all the rate measurements in a similar way, and mostly cancel out in the normalization of rates to those of thick films. The uniform-medium approximation for the polycrystalline films works remarkably well, as it does for thin-film photocatalysis by TiO2.43,44

6. CONCLUSION A quantitative framework for predictably tuning the catalytic activity of a supported oxide catalyst through heterojunction principles has been demonstrated. The framework accurately reproduces activity changes by a factor of 20 in response to V2O5 thickness and supporting TiO2 donor concentration. No dopants were employed in this case; only native defects were employed to control carrier concentration in the TiO2. This work illustrates an additional degree of freedom that a semiconducting support offers (in contrast to an insulator) for tuning the Lewis acid−base properties of a supported metal oxide surface. For such cases, native defects in the support may be employed directly to control the donor/acceptor concentration. Alternatively, if suitable electrically active dopants are known for the substrate, those dopants could be used to control donors or acceptors. In principle, direct manipulation of carrier concentration in the support oxide could be used to manipulate the surface electron richness and therefore the Lewis acid−base properties. However, for many metal oxides of technical importance, an adequate science base does not exist for controlling carrier concentration, or the available dopants are incompatible chemically or otherwise with the targeted surface chemistry. In such cases, and those wherein the support modulates the active surface properties by mechanisms in addition to providing charge carriers, welldesigned heterojunction structures may offer the best approach.

Figure 12. Predicted effect of carrier concentration in TiO2 on the activity of supported V2O5 films of various thicknesses. The available TiO2 thicknesses (25−200 nm) correspond to the donor concentration range of 1018 to 1016 cm−3.

various V2O5 thicknesses down to 2 nm, below which the continuum approximation for the solids probably breaks down. Again, the rates are referenced to that on bulk V2O5 with a donor concentration of 1016 cm−3, assuming λ = −6. Equation 1 predicts significant changes in the reaction rate for TiO2 for donor concentrations 1018−6 × 1015 cm−3, corresponding to a work function range of from 3.98 to 4.12 eV. For example, the reaction rate doubles by increasing the TiO2 carrier concentration from 6 × 1015 cm−3 to 1018 cm−3, with a 3 nm V2O5 overlayer. This method of reaction rate enhancement could prove particularly useful in cases where the science of defect engineering or doping is better developed for the substrate material than for the overlayer. Additionally, this method of tuning the catalytic activity also avoids possible side effects of directly manipulating the overlayer thickness or carrier concentration through doping. 5.4. General Commentary. It may seem surprising that eq 1 seems to fit the experimental data in Figure 9 so well with only a single adjustable parameter. With regard to the variation of reaction rate with overlayer thickness, eq 1 implicitly predicts a superexponential functional form that is the exponential of a nearly exponential function of thickness. The reason is that,11 for vanadia−titania heterojunctions like those used here, the Fermi energy at the free surface exhibits an approximately exponential variation with vanadia thickness due to the physics of charge exchange at heterojunctions. The behavior of the surface Fermi energy observed experimentally was reproduced remarkably accurately by a standard Anderson band-offset model with a truncated solution of the relevant Poisson equation, regardless of the polycrystallinity and occasional discontinuity of the vanadia. Yet the present work extends the physical observations of ref 11 to catalytic rate measurements as embodied in eq 1, whose applicability is supported by a rather sparse literature of directly relevant measurements.13 In principle, the functional form implied by eq 1 could fail for a number of reasons relating to issues with spatial nonuniformity of the vanadia, possible contamination, or the effects of surface or bulk defects. Indeed, section 5.2 points to a specific possible manifestation of film discontinuity in the magnitude of λ via exposure of different ratios of crystallographic orientations (and any surface defects they may contain). Yet the variation of relative rate predicted by eq 1 is so strong that it evidently persists in its superexponential form even despite complications that may arise due to film polycrystallinity and discontinuity. The numerical values of the constituent parameters may be affected, but the strong variation remains. Contamination

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1-217-244-9214. Fax: +1-217-333-5052. ORCID

Edmund G. Seebauer: 0000-0002-4722-3901 Present Address †

Maxim Integrated, Dallas, TX 75254, United States.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge funding from the National Science Foundation (DMR 07-04354, DMR 10-05720, and DMR 1306822). One of us (N.K.N.) was partially supported by a Drickamer Research Fellowship awarded by the University of Illinois.

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REFERENCES

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