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J. Phys. Chem. C 2008, 112, 13204–13214
A Theoretical Investigation of the Selective Oxidation of Methanol to Formaldehyde on Isolated Vanadate Species Supported on Titania Anthony Goodrow and Alexis T. Bell* Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720-1462 ReceiVed: February 14, 2008; ReVised Manuscript ReceiVed: April 18, 2008
The selective oxidation of methanol to formaldehyde occurring on titania-supported vanadate species has been analyzed theoretically with the aim of understanding why the activity of VOx/TiO2 is ∼103 faster than that of VOx/SiO2. The active site was represented by a [(O)3VdO] group located at the corner of a cubic TiOx cluster, a model similar to that used successfully to describe the oxidation of methanol on isolated vanadate species supported on silica. Density functional theory was used to calculate the geometry, vibrational frequencies, and energy of all ground state and transition state structures. The equilibrium constants and rate coefficients for each elementary reaction step were calculated using statistical mechanics and absolute rate theory. Methanol oxidation to formaldehyde was taken to proceed via two key steps: the reversible adsorption of methanol across a V-O-Ti bond followed by the transfer of a hydrogen atom from an adsorbed methoxy group to a vanadyl O atom. The rate parameters and the apparent first-order rate coefficient determined for VOx/TiO2 were found to be very similar to those reported earlier in a theoretical analysis of VOx/SiO2 [J. Phys. Chem. C 2007, 111, 14753], indicating that the significantly higher rate of reaction seen experimentally for VOx/TiO2 is not due to an intrinsic electronic effect of the support on the catalytic properties of the active center. Introduction of an O-vacancy adjacent to the vanadate species results in a reduction in the activation barrier for the rate-limiting step and to close agreement between the rate parameters predicted and those found experimentally. The effect of O-vacancies in the support on the rate of methanol on metal oxidesupported vanadate species is further evidenced by a strong correlation between the turnover frequency for methanol oxidation and the energy required to form an O-atom defect on metal oxide supports. Introduction The selective oxidation of methanol to formaldehyde catalyzed by supported vanadia has been the subject of numerous investigations.1–11 For submonolayer coverages of vanadia, support composition has been observed to have a large effect on the specific activity of vanadium. The general consensus is that activity per vanadium atom decreases with support composition in the order SiO2 , Al2O3 , TiO2 < ZrO2 < CeO2 and that under identical reaction conditions the turnover frequency (TOF) for VOx/CeO2 is roughly 3 orders of magnitude higher than that that for VOx/SiO2.1,3,8–11 This trend has been attributed to the effect of the support on the electronic properties of the supported vanadate species based on the observation that the TOF for formaldehyde formation decreases with increasing Sanderson electronegativity of the support cation.3,8,9 Studies of the reaction kinetics have shown that at low conversions the rate of formaldehyde formation is first-order in the partial pressure of methanol and zero-order in the partial pressure of oxygen, independent of the support composition. Mechanistic investigations suggest that the reaction occurs in two steps.3,8,10,11 The first is the reversible adsorption of methanol, which occurs by methanol addition across one of the V-O-M bonds anchoring V to the support. The second, ratelimiting step is the transfer of a hydrogen atom from the resulting V-OCH3 species to an O atom associated with the active center.10 In the limit of low conversion, the overall rate expression for the formation of formaldehyde can then be written * Author to whom correspondence should be addressed: alexbell@ berkeley.edu.
as the product of the equilibrium constant for methanol adsorption, Kads, and the rate constant for the rate-limiting step, krls, as shown in eq 1
RCH2O ) KadskrlsPMeOH
(1)
On the basis of the observed decrease in TOF with increasing Sanderson electronegativity of the support cation, it has been proposed that the electronegativity of the support cation and, hence, reducibility of the support affects the equilibrium adsorption of methanol and the rate-limiting step in which an H atom is abstracted from an adsorbed methoxy group.3,8,9 The mechanism and kinetics of methanol oxidation on isolated vanadate species supported on different metal oxides have been investigated theoretically by several groups. Khaliullin and Bell12 have analyzed the energetics and kinetics of this reaction on isolated vanadate species supported on SiO2, TiO2, and ZrO2, using a small cluster model comprising a V)O group and three metal support atoms terminated by hydroxyl groups. The calculated TOF was found to be essentially independent of support composition in contradiction to what is observed experimentally. Zhanpeisov13 has carried out a similar analysis, using a more realistic representation for isolated vanadate species supported on rutile. The calculated bond lengths and vibrational frequencies for methanol adsorption on VOx/TiO2 were found to be in close agreement with those reported in previous experimental11 and theoretical studies.12 Using a large cluster model of VOx on SiO2, Sauer and co-workers14 have carried out a detailed analysis of the reaction mechanism for the oxidation of methanol to formaldehyde. These authors reported an apparent activation energy of 27 kcal/mol, in reasonable
10.1021/jp801339q CCC: $40.75 2008 American Chemical Society Published on Web 08/01/2008
Selective Oxidation of Methanol to Formaldehyde agreement with that determined from experiments;1,8,10 however, the apparent rate constant was 4 orders of magnitude smaller than that observed. More recently, Goodrow and Bell15 have reported an analysis of the mechanism and kinetics of methanol oxidation occurring on silica-supported vanadate species, in which not only was the pathway to methanol oxidation examined but also the pathway for catalyst reoxidation. The equilibrium constant for methanol adsorption and the apparent first-order rate coefficient for the reaction determined from first principles were found to be in very close agreement with the experimental values for these parameters. It was also concluded that reoxidation of the catalytically active centers is approximately 4 orders of magnitude faster than their rate of reduction, a result which is also in agreement with experimental observation. The purpose of the present study was to carry out a detailed theoretical investigation of the mechanism and kinetics of methanol oxidation on isolated vanadate species supported on the anatase phase of TiO2 with the aim of explaining why the rate of this reaction is significantly higher on VOx/TiO2 than on VOx/SiO2. The emphasis on isolated vanadate species was made for two reasons. The first is that experimental studies conducted by Bell and co-workers suggest that the mechanism of methanol oxidation to formaldehyde is the same for isolated vanadate species supported on silica and titania.10,11 Second, and as noted above, Goodrow and Bell15 have demonstrated that the kinetics for methanol oxidation on VOx/SiO2 are represented with reasonable accuracy by theoretical analysis. These results motivate us to ask whether the higher rate of methanol oxidation observed for VOx/TiO2 is due to the effects of the support on the electronic properties of the supported vanadate species or to some other cause. The results of the present study suggest that the difference in activity of VOx supported on TiO2 and SiO2 can be attributed to the effects of O-atom defects present on the surface of TiO2 in proximity to the active site but is not likely due to effects of the support on the electronic and, hence, catalytic properties of the supported vanadate species. Theoretical Methods Density functional theory (DFT) was used to compute optimized geometries, vibrational frequencies, and thermodynamic properties for all species involved in the reaction mechanism. As discussed below, the active center was described by a cluster that included a single vanadate species and a part of the support. In geometry optimization calculations, all atoms of the cluster were allowed to relax. The B3LYP functional was used to describe effects of electron exchange and correlation, and the 6-31G* basis set was used for all nonmetal atoms. Both V and Ti atoms were treated using the LANL2DZ basis set within Gaussian 03.16 The calculated frequencies were multiplied by 0.9614 to compensate for the overestimation of vibrational frequencies at the B3LYP/6-31G* level of DFT.17 The growing string method18 was used to find an initial estimate of the transition-state geometry, which was then refined by performing a transition-state search in Gaussian 03. The broken symmetry approach19,20 was used to calculate the activation energy for reactions involving multiple spin states, as described in previous studies.14,15 A more accurate estimate of the energy was obtained by performing single-point calculations on all optimized ground-state and transition-state structures using the 6-311++G** basis set for all nonmetal atoms and augmenting the LANL2DZ basis set with diffuse and polarization functions (triple-ζ effective core potential basis sets) for V and Ti. The Gibbs free energy for all structures was calculated using the standard equations of statistical mechanics.21–25 In the
J. Phys. Chem. C, Vol. 112, No. 34, 2008 13205
Figure 1. (a) Model A: a cubic model of TiO2, analogous to a silsesquioxane model of SiO2. The Ti atoms are terminated with H atoms. (b) Model B: a cluster representation of the (101) surface of anatase. The structure is terminated with point charges (where O atoms would be located) and pseudopotentials (where Ti atoms would be located).
determination of rate parameters, the partition functions for translation, rotation, and vibration were computed explicitly.15 Appropriate assumptions were made for all species involving the catalyst. For example, adsorbed species were assumed to have zero degrees of translational and bulk rotational freedom. Scaled frequencies (see above) were used to compute the vibrational partition function for all species. The standard state for all reported Gibbs free energies, at 450 K, the temperature at which the selective oxidation reaction was studied experimentally,11 is denoted as ∆G °(450). The standard state used for gas-phase species was taken to be 1 atm, and a mole fraction of 1 was used for all species involving the active site. Results and Discussion Representation of the Support and the Catalytically Active Site. Since our experimental studies of methanol oxidation catalyzed by titania-supported vanadia11 have used the anatase phase of titania as the support, the first objective of the present work was to find a suitable representation for the surface of anatase. The two models shown in Figure 1 were considered. The first of these, model A, is formed by replacing each of the Si atoms in silsesquioxane (Si8O12H8), the model used previously to represent silica,14,15 by a Ti atom. The core of this cluster (Ti8O12)isidenticaltothatfoundincrystalline[Ti8O12(H2O)24]8+.26–28 In this model, Ti has a coordination of 4 and O has a coordination of 2. Model B is formed by taking a cluster from the energetically preferred (101) surface of anatase.29,30 This cluster is terminated by point charges of -2 for O atoms and pseudopotentials for Ti atoms placed at their crystallographic positions, a method used in previous studies.31,32 In contrast to model A, model B exhibits the coordination of Ti and O present at the surface of anatase: 5-fold coordination for Ti and 2- or 3-fold coordination for O. However, while model B is a more realistic representation of the surface of anatase, the computational cost associated with this model is considerably higher than that associated with model A. For example, convergence of geometry optimizations and frequency calculations for model B (100-125 h of CPU time) took almost five times longer than for model A (24-36 h of CPU time). Consequently, it is important to establish whether the surface of anatase could be represented adequately using model A. To address this issue, the geometry, vibrational bands, and heats of adsorption for
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TABLE 1: Geometry of Models A and B Compared to Experiment
Model A r(Ti-O) r(Ti-Ti)
1.81 Å 3.44 Å
Ti-O-Ti 110.2° angle a
Model B
[Ti8O12(H2O)24]8+a
1.90 Å, 2.00 Å 1.82 Å 3.09 Å, 3.23 Å, 3.44 Å 3.80 Å 102.5-109.2° 97.5-102.4°
TABLE 3: Heats of Molecular and Dissociative Adsorption for H2O and CH3OH Calculated for Models A and B Compared with Calculated Values Determined for a Slab Model of TiO2 (A) and Experimental Values for TiO2 (A)a
TiO2(A)b
Model A
Model B
H2O (molec. ads.)
-15.8
-14.9
H2O (diss.ads.) MeOH (molec. ads.)
-7.25 -24.4
-7.35 -20.9
MeOH (diss. ads.)
-10.9
-10.1
1.94 Å, 1.97 Å 3.04 Å, 3.79 Å 102.6°, 154.8°
Ref.28 b Anatase.
TABLE 2: Calculated Vibrational Frequencies for Models A and B Compared with Those for TiO2 (A)
a
Experiment, TiO2 (A)
Slab -17.3b -18.0c -17.1d -6.92b -27.7c -19.4e -17.3f -11.1f b
-16.6 to -17.0g -15.0 to -15.9g -16.0h -7.93i -21.9j, -27.9k 34 c
Adsorption energies are in kcal/mol. Ref. Ref.35 d Ref.36 Ref37 (for partially and fully hydrated TiO2 (001) anatase). f Ref.38 g Ref39 (varies with coverage, second set of numbers obtained from Redhead analysis). h Ref.40 i Ref.41 j Ref42 (determined by Redhead analysis of the TPD peak at 350 K). k Ref11 (determined by Redhead analysis of the TPD peak at 400 K). e
Model A ν (cm-1)
Model B ν (cm-1)
TiO2 (A) ν (cm-1)
133 197 401 – – 646
160 177 390 – 527 639
144a, 146b 197a,b 397b, 399a 515a, 516b 519a 639a, 640b
a
Ref.33 b Ref.11
water and methanol were computed for models A and B, and the results compared with each other and with experimental values. Table 1 shows that the Ti-O bond length and Ti-Ti distance calculated for model A agree very closely with the experimental values for [Ti8O12(H2O)24]8+,28 but do not agree with the corresponding values for bulk anatase. The calculated Ti-O-Ti bond angle is larger than that seen experimentally in the cubic titania complex due to the absence of water coordination in model A. The calculated geometry of model B agrees much more closely with that of crystalline anatase. The two Ti-O bond distances listed for model B are for O atoms that have a coordination to Ti of 2 or 3, respectively, and the three Ti-Ti distances reflect whether each of the Ti atoms is 5- or 6-fold coordinated to O. (On the surface, O has a coordination of 2 or 3 and Ti has a coordination of 5, whereas in the bulk, O has a coordination of 3 and Ti has a coordination of 6.) The vibrational frequencies calculated for models A and B are listed in Table 2 together with the experimental values for anatase.11,33 Both models produce vibrational features that agree reasonably well with those observed for anatase, with the possible exception of the lowest frequency band. Closer inspection reveals that the calculated frequencies for model A are in somewhat better agreement with the experimental values than those calculated for model B. Calculated energies for molecular and dissociative adsorption of water and methanol obtained for models A and B are shown in Table 3. Adsorption energies based on slab calculations for the (101) surface of anatase34–38 and those obtained experimentally are also reported in this table.11,39–42 As can be seen, all of the theoretically calculated values agree reasonably well with
each other and with the experimentally reported values. It is also noted that on average the adsorption energies calculated for models A and B tend to be closer to those observed experimentally than those obtained from slab calculations. This difference between the cluster and slab calculations may be a consequence of the level of theory used for the two types of calculations. The cluster calculations were carried out at the B3LYP/6-311++G** level, whereas the slab calculations used the GGA method43,44 and plane-wave basis sets with ultrasoft pseudopotentials45,46 for Ti and O. While model A does not represent the geometry of the (101) surface of anatase, the calculated vibrational frequencies for this structure and the heats of adsorption of water and methanol agree well with those observed experimentally for anatase. For these reasons, it was decided to carry all further calculations out using model A to represent the support. It is also noted that the use of model B for these calculations was not an option because of the exceptionally high computational cost. Moreover, the actual surface of the anatase particles used in experimental work may not be represented well by any surface of a perfect crystal of anatase, since upon contact with the vanadia precursor, the surface of the support can become amorphous. An isolated vanadate group supported on titania was represented by replacing one of the Ti-H groups in model A with a vanadyl group, VdO. The resulting structure is shown in Figure 2. Table 4 shows that the geometry of the VO4 species in the optimized representation of VOx/TiO2 agrees very well with that seen experimentally, as do the vibrational frequencies for the VdO and V-O-Ti bonds. These bond distances are also in good agreement with recent slab calculations for isolated vanadate species supported on the (100) surface of rutile.47 Methanol Adsorption. Methanol adsorption can occur in four different ways, as shown in Figure 3. On isolated vanadate sites (species 1), the adsorption involves cleavage of a V-O-Ti bond to form either a V-OCH3/Ti-OH pair (species 2 and 2a) or a V-OH/Ti-OCH3 pair (species 2b). When methanol adsorbs to form a V-OCH3/Ti-OH species, hydrogen-bonding can occur between the methoxy and hydroxyl groups (species 2) or between the methoxy and vanadyl groups (species 2a). Methanol
Selective Oxidation of Methanol to Formaldehyde
Figure 2. Model of an isolated vanadate species supported on TiO2.
TABLE 4: Comparison of the Geometry and Vibrational Frequencies for [(O)3VdO] Species Supported on TiO2 (A) Calculated for Species 1 and Observed Experimentally Theory r(VdO) r(V-O) ν(VdO) ν(V-O-Ti) a
1.57 Å 1.77 Å 1035 cm-1 977 cm-1
Experiment, TiO2 (A)a 1.58 Å 1.79 Å 1026 cm-1 980 cm-1
Ref.11
can also adsorb on the titania support to form Ti-OCH3/Ti-OH groups (species 2c). Figure 3 shows the adsorption energies and Gibbs free energies for these four scenarios. The most energetically preferred adsorbed species is species 2a, as this structure allows for the strongest H-bonding. This conclusion is supported by previous experimental studies, which have shown that V-OCH3 groups, as shown in species 2a, are necessary for the formation of formaldehyde.1,7,8,10 TPD and TPRx experiments reported by Bronkema et al.11 show that Ti-OCH3 groups do form formaldehyde but to a significantly lesser extent than do V-OCH3 groups. The results presented in Figure 3 also demonstrate that methanol reacts preferentially with V-O-Ti bonds than Ti-O-Ti bonds, in agreement with experimental observations.11 The calculated and observed frequencies for the bending and stretching modes of CH3 groups in Ti-OCH3 (in species 2c) and V-OCH3 (in species 2a) are shown in Table 5. The calculated frequencies for the C-H bending vibration and those for symmetric and asymmetric C-H stretching vibrations associated with Ti-OCH3 and V-OCH3 species agree with those observed experimentally, which further supports the choice of model A to represent the support.6,11,48,49 Mechanism and Kinetics of Methanol Oxidation. Experimental studies suggest that the oxidation of methanol to formaldehyde involves the dissociative adsorption of methanol, followed by the transfer of an H atom from the adsorbed methoxy group to the vanadyl O of the active site in the ratelimiting step, as illustrated in Figure 4.3,8,10 The reversible adsorption of methanol by 1 is characterized by ∆E ) -15.7 kcal/mol and ∆G °(450) ) -2.7 kcal/mol, and this process is assumed to be quasi-equilibrated. Transfer of one of the three methoxy H atoms in 2a to form 3 occurs with ∆E ) 36.7 kcal/ mol and a ∆G°(450) ) 39.0 kcal/mol. The calculated activation energy for this step is ∆E‡ ) 38.5 kcal/mol. The broken symmetry approach was used to determine the activation energy for this step because the electronic structure of V changes from a singlet in the reactant 2a (formally V5+ with no unpaired d
J. Phys. Chem. C, Vol. 112, No. 34, 2008 13207 electrons) to a triplet in the product 3 (formally V3+ with two unpaired d electrons). The weakly bound formaldehyde species in 3 desorbs with ∆E ) 16.3 kcal/mol and ∆G °(450) ) -0.6 kcal/mol, leaving behind two hydroxyl groups on the surface in species 4. These groups then react to form water with ∆E ) -9.6 kcal/mol and ∆G°(450) ) -24.8 kcal/mol. The activation energy for the reaction of 4 to 5 is ∆E‡ ) 9.7 kcal/mol. In the course of the reaction sequence shown in Figure 4, the V atom is reduced from the +5 oxidation state in 1 to the +3 oxidation state in 5. To complete the catalytic cycle, the V atom in species 5 must be reoxidized. It has been seen experimentally11 that V remains in the +5 oxidation state under reaction conditions, suggesting that the reoxidation process is very rapid. Figure 5 shows a possible mechanism for the reoxidation starting from species 5′, which consists of two reduced V3+ cations in opposite corners of the cubic model. This scheme is identical to that described in a theoretical study of methanol oxidation on VOx/SiO2.15 In the first step, a peroxide species is formed by the adsorption of O2 onto species 5′ with ∆E ) -44.8 kcal/mol. An O atom in the resulting peroxide then migrates through the support until both V atoms are reoxidized to V5+ in species 1′. The largest activation barrier in the reoxidation pathway is ∆E‡ ) 16.2 kcal/mol for the reaction of 7 to 8, which is similar to the barrier for O2 migration on the surface of anatase, 11.3 kcal/mol.50 The kinetics of methanol oxidation can be represented by eq 1 and the apparent first-order rate coefficient can then be expressed as
(
kapp ) Kadskrls ) k0app exp
-∆Eapp RT
)
(2)
‡ ∆Eapp ) ∆Eads + ∆Erls
(3)
k0app
where is the apparent pre-exponential factor, ∆Eapp is the apparent activation energy, ∆Eads is the energy change for ‡ methanol adsorption, and ∆Erls is the activation energy for the rate-limiting step. The equilibrium constant for methanol adsorption, Kads, is defined as
Kads ) σads
( ) (
qMeOH•S -∆Eads PV exp exp qMeOHqS RT RT
)
(4)
where σads is the symmetry factor for the adsorption of methanol and qi is the partition function for state i (S ) active site). Methanol was treated as an ideal gas. The rate constant krls for the rate-limiting step is defined as
(
‡ kBT q‡ -∆Erls krls ) σrlsκ(T) exp h qi RT
)
(5)
where σrls is the symmetry factor for the rate-limiting step and qi and q‡ refer to the partition functions for the reactant and transition state structures, respectively. The activation energy ‡ is denoted by ∆Erls . The transmission coefficient for tunneling, κ, is a function of temperature and is included because the transition state involves the transfer of an H atom. The value of κ at 450 K was determined to be 1.4 using Wigner’s approximation.51 The rate parameters determined for the oxidation of methanol to formaldehyde on the basis of the mechanism shown in Figure 4 for VOx/TiO2 are listed in Table 6 and compared with similar values reported earlier for VOx/SiO2.15 The adsorption energy for methanol, ∆Eads, and the activation energy for the rate‡ limiting step, ∆Erls , are essentially the same on both supports.
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Figure 3. Possible structures for methanol adsorption onto species 1 (left) or TiO2 (right). Values of ∆E and ∆G °(450) are in kcal/mol.
TABLE 5: Comparison of the Vibrational Frequencies Calculated for Ti-OCH3 (2c) and V-OCH3 (2a) with Those Observed Experimentally Adsorbed Species Ti-OCH3 V-OCH3
a
Vibrational Mode
Theory (cm-1)
Experiment (cm-1)a
C-H Bend Symmetric C-H Asymmetric C-H C-H Bend Symmetric C-H Asymmetric C-H
1432 2832 2919 1421 2838 2929
1440-1443 2819-2833 2921-2932 1435-1436 2832 2929-2939
Ref.11
TABLE 6: Comparison of the Energetics and Apparent First-Order Rate Coefficient for Methanol Oxidation on Isolated VOx Species Supported on SiO2 and TiO2 ∆Eads (kcal/mol) ∆E‡rls (kcal/mol) ∆E‡reox (kcal/mol) ∆Eapp (kcal/mol) kapp (1/atm · s) a
VOx/SiO2a
VOx/TiO2
-15.5 39.8 28.1 24.3 3.99 × 10-5
-15.7 38.5 16.2 22.8 9.35 × 10-5
Ref.15
The apparent activation energy on both supports differ by only 1.5 kcal/mol and the apparent first-order rate constant is less than a factor of 3 larger on TiO2 than SiO2. These results suggest that the much higher methanol oxidation activity observed for titania-supported vanadia relative to silica-supported vanadia is not due to an intrinsic difference in the electronic properties of the support, in agreement with the results reported earlier by Khaliullin and Bell.12 Therefore, another explanation must be sought for the strong enhancement in the rate of methanol oxidation observed for vanadate species supported on titania. Titania and silica differ in the concentration of O-vacancies and their effect on the oxide. These O-vacancies or defects occur in much higher concentration on the surface of titania than that
of silica.52–55 Moreover, the O-atom defects in titania differ from those in silica.56 When an O-vacancy is formed in silica by removal of an O atom from a Si-O-Si bond, the distance between the Si atoms decreases. Excess electron density on the Si atoms is localized and leads to the formation of a Si-Si bond. However, when an O-vacancy is formed in titania, the Ti atoms become formally Ti3+ and the distance between the Ti atoms increases. The excess electron density carried on the pair of Ti atoms associated with the O-vacancy shifts to the 3d orbitals and causes even more electron delocalization in the neighboring atoms.56 A density of states analysis shows that the band gap is decreased when there is an O-vacancy, making the unoccupied orbitals in Ti more reactive. In most studies of O-atom defect formation in titania, defects are produced by heating the oxide in vacuum. An interesting finding of such work is that surface O-vacancies are energetically favored compared to those in the bulk.57 This conclusion is supported by theoretical work demonstrating that the diffusion of an O-vacancy from the bulk to the surface of titania is significantly faster than the reverse process.58 Quantification of the surface concentration of O-atom defects is rare; however, STM studies show that upon heating rutile in vacuum to 700-1100 K, the (110) surface of rutile can contain 2-10% O-vacancies.42,59–61 An important question is whether O-vacancies can be sustained at elevated temperatures when titania is heated in oxygen. Since the energy for O-atom defect formation is 4.0 eV for rutile (110) and 4.3 eV for anatase (101),62 O-vacancies would not be expected to be present on the surface or in the bulk of titania if the process of defect formation and annihilation were controlled by thermodynamics. However, recent work by Sekiya and co-workers has shown that O-atom defects can be sustained in anatase at temperatures up to 873 K in the presence of 1 MPa of O2.63–66 These authors observed the presence of O-atom defects by polarized absorption spectroscopy and EPR. When an as-grown anatase crystal was heated in O2, a band developed at about 3 eV, which grew in intensity as the
Selective Oxidation of Methanol to Formaldehyde
J. Phys. Chem. C, Vol. 112, No. 34, 2008 13209
Figure 4. Pathway for the selective oxidation of methanol to formaldehyde on isolated vanadate species supported on titania. Values of ∆E, ∆E†, and ∆G°(450) are in kcal/mol.
Figure 5. Pathway for the reoxidation of V from V3+ to V5+ on titania via oxygen migration. Values of ∆E, ∆E†, and ∆G°(450) are in kcal/mol.
temperature was raised from 473 to 873 K, and the crystal changed its color from pale blue to yellow.63,65 The EPR signal of the yellow crystal indicated the absence of paramagnetic spin associated with the conduction band, suggesting that the O traps two electrons to form a relatively deep level. When the yellow crystal was heated in O2 at 1073 K for 60 h the band at 3.0 eV disappeared completely and the crystal became clear. The stability of the defects up to 873 K when the yellow crystal was heated in 1 MPa of O2 led to the conclusion that O-atom defects in anatase are not in thermodynamic equilibrium with the gas phase.
When vanadia is supported on titania other changes can occur in addition to the formation of O-vacancies in titania. A number of authors have shown EPR evidence for the formation of isolated V4+ cations for vanadia supported on either rutile or a mixture of rutile and anatase.67–74 Since g| > g⊥ and A| > A⊥, V4+ cations are presumed to have octahedral symmetry and to be located at the positions of Ti4+ cations in the rutile phase of the matrix.70,74 However, estimates of the fraction of the supported V converted to V4+ for VOx/TiO2 samples containing predominantly isolated vanadate species show that only about 1% of the V is present as V4+.70,74 The incorporation of V4+
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TABLE 7: Comparison of Theoretical and Experimental Values for the Energetics and Rate Parameters for Methanol Oxidation on VOx/TiO2a Theory (450 K) Theory (450 K) Theory (450 K) with 1%, No Defect Defect 2% Defectsb Adsorption Step (1,2a), (1d,2ad)
Rate-Limiting Step (2a,3), (2ad, 3d)
Apparent Kinetics
∆Eads (kcal/mol) Kads0 (1/atm) Kads (1/atm) ∆Erls‡ (kcal/mol) krls0 (1/s) krls (1/s) ∆Eapp (kcal/mol) kapp0 (1/atm · s) kapp (1/atm · s)
-15.7 4.21 × 178 38.5 2.63 × 5.26 × 22.8 1.11 × 9.35 ×
10-6
1012 10-7 107 10-5
-15.9 6.17 × 337 31.8 1.75 × 6.34 × 15.9 1.08 × 2.14 ×
10-6
1012 10-4 107 10-1
-15.9 6.17 × 337 31.8 4.03 × 1.46 × 15.9 2.48 × 4.92 ×
10-6
1011, 6.48 × 1011 10-4 Å, 2.35 × 10-4 106, 4.00 × 106 10-2, 7.92 × 10-2
Experiment (450 K) -14.5c, -13.0d 3.36 × 10-5c, 3.44 × 10-6e 371c, 301d 30.5c, 30.7e 1.57 × 1011 c, 2.54 × 1012 e 2.41 × 10-4 c, 3.10 × 10-3 e 16c, 15.93d 5.30 × 106 c, 2.38 × 106 d 8.96 × 10-2 c, 4.37 × 10-2 d
The apparent rate constants are defined on a per active site basis. b Corresponding value in previous column multiplied by 23% (for 1% surface O vacancies) and 37% (for 2% surface O vacancies). Refer to Figure 8. c Ref.11 d Ref.8 e Ref.3 a
Figure 6. Model of a VOx/TiO2 active site with a defect. The location of the O-vacancy is circled.
cations into anatase was not considered, since in this case g| < g⊥.74 For these reasons, it is unlikely that V4+ cations would have an effect on the catalytic activity of isolated vanadate species supported on titania. Direct evidence for the formation of O-vacancies in TiO2 have been obtained recently by high-field (14.9 T) EPR carried out on VOx/TiO2 (containing exclusively isolated vanadate species). The catalyst was used for methanol oxidation (T ) 450 K, P ) 1 atm, MeOH/O2 ) 1: 2), rapidly quenched, and then sealed.75 As shown in the Supporting Information, a sharp peak is observed at g ) 2.00, corresponding to electrons trapped at the O-vacancies, and a broad peak is observed at g ) 1.96, corresponding to Ti3+. The latter peak is not observed in the sample prior to reaction. Thus, EPR spectroscopy suggests that during methanol oxidation O-vacancies are created in the support, and that the electrons thus released can form two Ti3+ cations per O-vacancy. O-vacancies present on the surface of VOx/TiO2 can be associated with either a V or a Ti atom. Previous research has shown that the migration of surface defects is facilitated in the presence of gas-phase O2;76 hence, it is reasonable to assume that the distribution of vacancies is determined by thermodynamics. Equilibrium can be established between an active site with an O-vacancy, represented as [V-D] (where V stands for a V atom and D stands for an O-vacancy) and without an O-vacancy, represented as [V-ND] (where ND stands for no O-vacancy). Calculations performed with species 1 show that the energetically preferred location for an O-vacancy is next to the vanadate species, as shown in Figure 6. The stability of an O-vacancy in the vicinity of a vanadate is further supported by the fact that removal of an O atom from a V-O-Ti bond is
almost 35 kcal/mol higher than removal from a Ti-O-Ti bond. The equilibrium constant for the migration of an O-vacancy from titania to a position adjacent to an isolated vanadate species can be determined on the basis of the scheme shown in Figure 7. Using this scheme, the equilibrium constant for the exchange of an O-vacancy in titania with an O atom near an isolated vanadate species (1) is calculated to be 2.65 at 450 K, from which it is concluded that O-vacancies present on the surface of VOx/TiO2 prefer to be near vanadate species. Figure 8 shows the relationship between the fraction of isolated vanadate species containing an adjacent O-vacancy and the fraction of Ovacancies in the titania for the conditions of the experiments reported by Bronkema et al.11 The change in energy and Gibbs free energy for the reaction mechanism involving an active site with an O-vacancy is shown in Figure 9. This mechanism is analogous to the mechanism in Figure 4 for an active site without an O-vacancy. The adsorption of methanol onto a defect site, the reaction of 1d to 2ad, occurs with ∆E ) -15.9 kcal/mol and ∆G °(450) ) -2.4 kcal/mol. Both of these values are similar to the energetics seen for methanol adsorption on a site without an O-vacancy, suggesting that methanol adsorption on VOx/TiO2 is essentially the same for active sites with and without an O-vacancy. The values for the change in energy and Gibbs free energy for the rate-limiting step, the transfer of an H atom from an adsorbed methoxy group, are ∆E ) 19.5 kcal/mol and ∆G°(450) ) 24.7 kcal/mol, respectively. These values are considerably smaller than those determined for the same reaction in the absence of a defect. A plot of the energy profile as a function of reaction coordinate is shown in Figure 10 highlighting the difference between the H-abstraction step on an active site with and without an O-vacancy. The reason for the smaller energy of the reaction for 2ad to 3d is that the defect provides the active site with more flexibility thereby allowing for a larger degree of Hbonding in the product between Ti-OH and V-OH ligands. A Mulliken charge analysis shows that the oxidation state of V in this step is the same as when there is no O-vacancy present. The activation energy for 2ad to 3d is 31.8 kcal/mol, which is almost 7 kcal/mol lower than that calculated for the case of an active site without a defect. The decrease in activation energy is a result of H-bond stabilization in the transition state structure. The H-abstraction step is followed by desorption of formaldehyde from 3d to 4d, with ∆E ) 22.3 kcal/mol and ∆G°(450) ) 3.5 kcal/mol. The remaining two hydroxyl groups come together to form water and reform a V-O-Ti support bond in the reaction of 4d to 5d. For this reaction, ∆E ) -8.7 kcal/ mol, ∆G°(450) ) -25.0 kcal/mol, and ∆E‡ ) 12.1 kcal/mol.
Selective Oxidation of Methanol to Formaldehyde
J. Phys. Chem. C, Vol. 112, No. 34, 2008 13211
Figure 7. Scheme for an O-vacancy in TiO2 (TiO2-D) exchanging with an O atom to form an active site with an O-vacancy (1d).
Figure 8. Dependence of the percent of V atoms with an associated O-vacancy on the percent of O sites with an O-vacancy on the surface of titania at 450 K.
The reoxidation mechanism of V on a site with an O-vacancy is achieved in the same manner as in Figure 5 for a site without an O-vacancy. Since the surface O-vacancies are mobile on the surface, an O-vacancy will be rapidly interchanged with an O in the active site (1 to 1d). The rate of vacancy diffusion has been estimated to be 10-2 to 10-1 s-1 at 250 K and to increase with temperature and exposure to O2.76 Assuming an Arrhenius temperature dependence and an activation barrier for O migration of 10.4 kcal/mol,77 the rate of vacancy diffusion at 450 K under would be 102-103 s-1, which is significantly faster than the rate-limiting step in the reaction mechanism, 2ad to 3d. Hence, the rate of reoxidation is rapid and not kinetically relevant. Comparison with Experimental Results. Table 7 lists the calculated rate parameters for methanol oxidation for an active site with and without an adjacent O-vacancy at 450 K and the experimental values reported by Burcham and Wachs3,8 and by Bronkema et al.11 The presence or absence an O-vacancy near the vanadate center has virtually no effect on the value of the adsorption energy. The calculated values of the adsorption energy are in good agreement with the experimental value reported by Bronkema and Bell11 but somewhat higher than that reported by Burcham and Wachs.3,8 The corresponding equilibrium adsorption constants at 450 K are K1,2a ) 178 atm-1 and K1d,2ad ) 337 atm-1. Both types of active site show reasonable agreement with experimental measurements of the equilibrium adsorption constant. The better agreement for the site containing an O-atom defect comes primarily from the higher pre-exponential factor. As mentioned previously, the rate-limiting step in the selective oxidation of methanol to formaldehyde is abstraction of an H atom from an adsorbed methoxy group to a vanadyl O. Table 7 shows that the difference in activation energy between sites with and without an O-vacancy is 6.7 kcal/mol. It is also evident
that the value of ∆E‡rls determined for the site with a O-vacancy agrees more closely to that seen experimentally by Bronkema and Bell,11 and Wachs and co-workers.3,8 The value of the preexponential factor determined for the site with an O-vacancy is very similar to that for the site without an O-vacancy. To compare the value of the pre-exponential factor observed experimentally with those determined from experiments, it is necessary to estimate the fraction of all vanadate sites that are adjacent to an O-vacancy. Unfortunately, this is difficult to do, since there are no experimental data on which to base this estimate, and there is insufficient knowledge of the kinetics of O-atom defect formation and annihilation to obtain a theoretical estimate. Therefore, we have assumed that 1-2% of the O atoms present at the surface of the support are absent, i.e., are O-atom defects, and have used Figure 8 to then determine the fraction of surface vanadate groups associated with an O-atom defect. On this basis, we project that 23-37% of the vanadate species are associated with an O-vacancy in the support (corresponding to 1-2% O sites with an O-vacancy). Since the pre-exponential factors determined from experimental data assume that all of the V sites are equally active, we have multiplied the values of 0 determined for vanadate sites associated with an O-vacancy krls 0 by 0.23-0.37. Table 7 shows that the corrected value of krls 0 agrees reasonably well with the values of krls reported experi0 mentally than does the value of krls determined for sites not associated with an O-vacancy. Likewise, it is seen that the value of krls determined for vanadate sites associated with O-vacancies and corrected for the fraction of such sites agrees much more closely with the experimentally reported values of this parameter. Table 7 also lists the apparent pre-exponential factor, apparent activation energy, and the first-order rate coefficient determined from eq 2 for the cases of isolated vanadate sites that are and are not next to an O-vacancy. The value of ∆E‡app determined for the site which contains an O-vacancy is 6.9 kcal/mol lower than that determined for the site that does not have a vacancy, and the value of ∆E‡app is in excellent agreement with the values observed experimentally. While the presence of O-vacancies has almost no effect on the calculated values of the apparent pre-exponential factor, k0app, the value of the apparent first-order rate coefficient, kapp, is roughly 3 orders of magnitude larger when an O-atom defect is present near a vanadate site, the principal cause of this difference being the lower value of ∆E‡app. When the values of k0app and kapp are corrected for the estimated fraction of vanadate species associated with O-vacancies, Table 7 shows that the experimental and theoretical values are in excellent agreement. The results presented in Tables 6 and 7 suggest that the higher activity of isolated vanadate species supported on titania relative to those supported on silica is not due to inherent differences in the electronic properties of vanadate species caused by the composition of the support. Instead, we propose that the significantly higher activity of VOx/TiO2 can be attributed to a reduction in the activation energy for the rate-limiting step
13212 J. Phys. Chem. C, Vol. 112, No. 34, 2008
Goodrow and Bell
Figure 9. Pathway for the selective oxidation of methanol to formaldehyde on isolated vanadate species supported on titania, with the active site containing an O-vacancy. Values of ∆E, ∆E†, and ∆G°(450) are in kcal/mol.
TABLE 8: Sanderson Electronegativities and Energies for the Formation of O-Vacancies in Metal Oxide Supports Metal Oxide Support SiO2 R-Al2O3 TiO2 (A) m-ZrO2 CeO2
S (cation)a 2.138 1.714 1.5 0.9 0.9
Ef1/2O2 (eV)b 8.5c 6d 4.3e 4e 3.3e
Ref 78. b Ef1/2O2 is defined as the defect formation energy using half of the total energy of molecular oxygen; see ref 62. c Ref 80. d Ref 79. e Ref 62. a
Figure 10. Energy profile for the H-abstraction step on an active site with and without an O-vacancy adjacent to the active site. The reaction coordinate axis has been normalized.
caused by an O-vacancy adjacent to the active center. This interpretation differs from that given by Wachs and co-workers who proposed that the higher activity of VOx/TiO2 relative to VOx/SiO2 is due to the effect of support composition on the intrinsic electronic properties of the supported vanadate species. This conclusion was based on the observation that the specific activity of supported vanadate species for methanol oxidation to formaldehyde increases with a decrease in the Sanderson electronegativity of the metal cation in the support oxide. While the two interpretations for the effects of support composition appear to be in conflict, in fact, they are not. As noted in Table 8, the Sanderson electronegativity of the support cation78 exhibits a positive correlation with the energy to form an O-vacancy. The net result is a positive correlation between the turnover frequency for methanol oxidation to formaldehyde and the energy of O-vacancy formation. Figure 11 shows a strong inverse correlation between the turnover frequency for methanol oxidation and the energy of O-vacancy formation62,79,80 for data on different supports reported by Wachs and co-workers7 (R2 value of 0.9486) and Bell and co-workers10,11,81 (R2 value of
Figure 11. TOF per V atom for methanol oxidation versus the O-vacancy formation energy. a Ref 7. b Refs 10 (SiO2), 11 (TiO2), 81 (ZrO2).
0.8974). The lower TOFs reported by Bell and co-workers than those reported by Wachs and co-workers may be a consequence of the difference in the surface coverage of vanadia and, hence, the structure of the vanadate groups present on the support surface. In the work of Wachs and co-workers all samples had high vanadia surface coverages, resulting in the presence of polyvanadate as well as monovanadate species, whereas in the work of Bell and co-workers all of the sample were prepared
Selective Oxidation of Methanol to Formaldehyde with predominantly (>90%) monovanadate species. The results of the present investigation, therefore, have revealed a new and unexpected effect of O-atom defects on the activity of vanadate species for the oxidation of methanol. It is reasonable to anticipate that such defects may have similar effects on other reactions occurring on dispersed metal oxides. Conclusions The oxidation of methanol to formaldehyde catalyzed by isolated sites supported on titania has been examined theoretically. The properties of the active site are well represented by a model consisting of a [(O)3VdO] group positioned at the corner of a cubic TiOx cluster, a model similar to that used previously to model the oxidation of methanol on isolated vanadate species supported on silica. Each of the rate parameters, the apparent activation energy, and the apparent rate coefficient determined for VOx/TiO2 are very similar to those determined previously for VOx/SiO2.15 This finding indicates that the electronic properties of isolated vanadate species are not affected by the composition of the support and, hence, that the significantly higher activity of VOx/TiO2 seen experimentally cannot be explained by this means. In contrast to silica, O-vacancies can form on the surface of titania, and such defects can affect the catalytic properties of species supported on titania. Our calculations show that the introduction of an O-vacancy in the support at a point adjacent to a vanadate site reduces the apparent activation energy for methanol oxidation from 22.8 to 15.9 kcal/mol. If the concentration of O-atom defects on the surface of the support is taken to be 1-2% of all O atoms present at the surface, it is found that surface defects concentrate preferentially adjacent to the vanadate species. The preexponential factor and activation energy for the rate-limiting step determined for a model of the active site with an adjacent O-vacancy agree very well with those deduced from experiments, as does the apparent activation energy. The role of defects in facilitating the rate of methanol oxidation is further supported by the observation that the specific activity of vanadium centers increases with decreasing energy of defect formation. Acknowledgment. The authors acknowledge Andrzej Ozarowski and Klaus-Peter Dinse, who acquired the EPR data given in the Supporting Information. This work was supported by the Methane Conversion Cooperative funded by BP. Supporting Information Available: A zip archive contains minimum energy structures and transition state structures in XYZ format from Gaussian03. README.txt files are included within the archive to guide the reader. EPR spectra of VOx/ TiO2 recorded before and after use for methanol oxidation are also presented. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Deo, G.; Wachs, I. E. J. Catal. 1994, 146–323. (2) Deo, G.; Wachs, I. E. J. Catal. 1994, 146, 335. (3) Burcham, L. J.; Wachs, I. E. Catal. Today 1999, 49, 467. (4) Lim, S. Y.; Haller, G. L. Appl. Catal., A 1999, 188, 277. (5) Briand, L. E.; Farneth, W. E.; Wachs, I. E. Catal. Today 2000, 62, 219. (6) Baltes, M.; Cassiers, K.; Van Der Voort, P.; Weckhuysen, B. M.; Schoonheydt, R. A.; Vansant, E. F. J. Catal. 2001, 197, 160. (7) Burcham, L. J.; Briand, L. E.; Wachs, I. E. Langmuir 2001, 17, 6164. (8) Burcham, L. J.; Badlani, M.; Wachs, I. E. J. Catal. 2001, 203, 104. (9) Wachs, I. E. Catal. Today 2005, 100, 79. (10) Bronkema, J. L.; Bell, A. T. J. Phys. Chem. C 2007, 111, 420.
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