A Quantum Chemical Study of the Decomposition of Keggin

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A Quantum Chemical Study of the Decomposition of Keggin-Structured Heteropolyacids Michael J. Janik,† Billy B. Bardin,‡ Robert J. Davis,*,† and Matthew Neurock*,† UniVersity of Virginia, 102 Engineers’ Way, CharlottesVille, Virginia 22904, The Dow Chemical Company, Midland, Michigan 48674 ReceiVed: September 19, 2005; In Final Form: January 3, 2006

Heterpolyacids (HPAs) demonstrate catalytic activity for oxidative and acid-catalyzed hydrocarbon conversion processes. Deactivation and thermal instability, however, have prevented their widespread use. Herein, ab initio density functional theory is used to study the thermal decomposition of the Keggin molecular HPA structure through the desorption of constitutional water molecules. The overall reaction energy and activation barrier are computed for the overall reaction HnXM12O40 f Hn-2XM12O39 + H2O. and subsequently used to predict the effect of HPA composition on thermal stability. For example, the desorption of a constitutional water molecule is found to be increasingly endothermic in the order silicomolybdic acid (H4SiMo12O40) < phosphomolybdic acid (H3PMo12O40) < silicotungstic acid (H4SiW12O40) < phosphotungstic acid (H3PW12O40), in agreement with the experimental ordering of their thermal stability. The presence of an adjacent Keggin unit may stabilize the structural defect created by the water desorption, thus suggesting that constitutional water loss is an initial step toward the decomposition into a bulk mixed oxide. The equilibrium concentration of defective Keggin units is determined as a function of temperature and water partial pressure. It is concluded that the loss of constitutional water molecules is a plausible deactivation mechanism of the acid catalyst. The intermediate structures along the decomposition path are proposed as possible active sites for oxidation catalysis. The results presented herein provide molecular level insight into the dynamic nature of the heteropolyacid catalyst structure.

Introduction Heteropolyacids (HPAs) demonstrate a unique coupling of acid1-3 and redox4-7 properties that enable them to catalyze industrially important hydrocarbon conversion processes. For example, HPAs have been shown to catalyze the alkylation of isobutane and butene,8,9 providing a green alternative to the homogeneous catalysts currently used. Deactivation and thermal stability of the supported HPAs, however, have prevented their widespread use.10 Furthermore, it is proposed that the active sites for heteropolyacid-catalyzed selective oxidation reactions involve partial decomposition of the molecular structure.11 Previous experimental12-19 and computational20-22 studies have examined thermal decomposition and the effect of HPA composition on stability. The impact of the composition on stability is not clear, however, and the use of different experimental methods or conditions makes comparison between studies difficult. In this study, ab initio quantum chemical calculations are utilized to determine the mechanism of thermal decomposition and provide a systematic ranking of the thermal stability of different HPAs of the Keggin structure. Heteropolyanions comprised of the Keggin structure (chemical formula XM12O40n-) are the most often studied due to their favorable acid and redox characteristics, greater stability, and availability.2,23,24 Many types of atoms have been employed as central atoms, including phosphorus, silicon, aluminum, and various transition metals. The addenda atoms typically used are tungsten and molybdenum; vanadium or other transition metal atoms can also be substituted into one or more addenda positions * Corresponding authors: e-mail, [email protected]; [email protected]. † University of Virginia. ‡ The Dow Chemical Company.

to alter the redox properties. Heteropolyacids crystallize with a large number of hydration water molecules. The hydration level is a function of temperature and relative humidity, with dehydration under dry conditions complete at 473 K.25,26 The loss of the waters of hydration is represented by an endothermic peak in the differential thermal analysis (DTA) curve.12-17 A second endothermic peak occurs at higher temperatures (above 543 K) due to the loss of constitutional water, water composed of the acidic protons and structural oxygen atoms of the Keggin unit. Thermogravimetric analysis (TGA) confirms that this second peak represents the loss of all acidic protons as water.14-17 The weight of the material remains constant with further heating. DTA shows an exothermic peak at high temperature (above 640 K) due to the crystallization of the bulk oxides from the decomposed Keggin unit.12-17 Treatment of partially decomposed HPAs (heated to 463 and 593 K) with water vapor regenerates the Keggin structure and produces a sample with a temperature programmed desorption (TPD) pattern identical to a fresh sample.14 In addition, in-situ X-ray diffraction (XRD),16,18 infrared spectroscopy,18,27 and 31P MAS NMR18 studies confirm that partial decomposition is reversed or suppressed by water vapor.16,18 As the loss of constitutional water represents a desorption process, including gas phase water in a thermal experiment shifts the relative concentrations of decomposed Keggin units at adsorption/ desorption equilibrium. The loss of constitutional water may be linked to the deactivation of HPAs as acid catalysts. Phosphotungstic acid deactivates with high pretreatment temperatures and with time on stream for reactions such as pentane skeletal isomerization and butene double bond isomerization. Subsequent treatment with water vapor has been shown to partially reactivate the catalyst.28 Kim et al. also showed that

10.1021/jp0553176 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/07/2006

Decomposition of Keggin-Structured Heteropolyacids the addition of water to the butene feed enhanced the activity of phosphomolybdic acid for butene double bond isomerization.29 Water vapor also impacts the performance of HPAs as oxidation catalysts, although a detailed analysis is complicated by the possible involvement of water in the reaction cycle.29-31 Recent studies have speculated that the Keggin-structured HPA is only a molecular precursor of the active catalyst, and the active site for oxidation catalysis involves partial decomposition of the HPA into a metastable defective structure.11,32 Slow heating limits the amount of water still present in the gas phase during dehydration, which stabilizes the intermediate defective structure.11 A better understanding of the mechanism of decomposition and the effect of water on the intermediate structures is necessary to characterize the active site for oxidation catalysis. Though results from DTA and TGA provide rankings of thermal stability for HPAs of a few compositions, comparison between studies is difficult due to differences in the experimental parameters. These methods, however, provide little insight into the mechanism of decomposition and the factors that affect thermal stability. Furthermore, experimental studies concentrate on HPAs that are easy to synthesize or that are useful for a particular reaction. In this study, theoretical methods are used to explore the mechanism of thermal decomposition through the loss of constitutional water. As the loss of constitutional water represents the first step in decomposition of the HPA, the energetics of this step are used to determine the effect of composition on thermal stability. Ab initio density functional theoretical calculations are used to investigate a wide range of HPA compositions that would take considerable time to evaluate experimentally. The central atoms considered here include B, Al, Ga, C, Si, Ge, P, As, S, Se, and Te. In addition, tungsten and molybdenum are considered as addenda atoms, and the effect of substituting vanadium is also considered. It should be noted that some of these compositions have not yet been synthesized in acid form. Throughout the text, the composition of the HPA is given in the abbreviated form HXM, where X refers to the central atom and M to the addenda atom. The detailed mechanistic steps of constitutional water loss are considered for phosphotungstic acid, HPW, as this composition has been shown to produce the strongest acid.23,33,34 Computational Methods Quantum-chemical calculations were performed using gradient-corrected density functional theory as implemented in the Vienna ab initio Simulation Package (VASP) using plane-wave basis sets.35-37 Ultrasoft pseudopotentials were used to describe electron-ion interactions.38 The Perdew-Wang (PW91) form of the generalized gradient approximation was used to calculate the exchange and correlation energies.39 A cutoff energy of 396.0 eV for the plane-wave basis set was used in all calculations. A 1 × 1 × 1 Monkhorst-Pack mesh was used to sample the first Brillouin zone.40 A small subset of calculations were performed using the Amsterdam Density Functional (ADF) code.41-43 These calculations employed the Vosko-WilkNusair (VWN) exchange-correlation potential44 with Becke45 and Perdew46 nonlocal gradient corrections for the correlation and exchange energies, respectively. Triple-ζ basis sets with polarization functions were used for all atoms. The core electrons up to and including the 1s, 2p, and 4d shells were frozen for oxygen, phosphorus, and tungsten atoms, respectively. Scalar relativistic corrections were explicitly included via the frozen-core potential. Both the VASP and ADF methods have

J. Phys. Chem. B, Vol. 110, No. 9, 2006 4171 previously been shown to determine an equilibrium Keggin structure in reliable agreement with experiment.47 The calculations reported herein used either a one or two Keggin unit basis, as detailed in the text. The single Keggin unit molecular system was represented within the periodic code by using a 20 × 20 × 20 Å3 unit cell with 8 Å of vacuum space between Keggin units in adjacent supercells. Calculations involving two Keggin units utilized a 28 × 20 × 20 Å3 unit cell, where the extended lattice vector is in the direction of the vector linking the two central atoms. A minimum of 7 Å of vacuum space is maintained between Keggin units in adjacent unit cells. Optimized geometries were located using a quasiNewton minimization algorithm. The nudged elastic band transition-state search method was used within VASP to isolate transition states.48 A transition state was identified as the image with a maximum in energy and a tangential force less than 0.08 eV Å-1. This image was then separately optimized to remove any artificial forces introduced by the constraints of the elastic band method. Transition states were confirmed to have a single imaginary vibrational frequency along the reaction coordinate mode. The harmonic vibrational modes were determined for a subset of the structures presented to determine zero-point vibrational energy (ZPVE) corrections and vibrational partition functions. Positive and negative displacements of 0.01 Å in each of the Cartesian coordinates were used to determine the Hessian matrix. The use of “constrained” vibrational calculations was employed, in which the Hessian matrix is determined for a subset of atoms in the structure. The ZPVE corrections and partition functions presented are approximated by including only vibrational modes associated with the protons and oxygen atoms involved in the process considered. Results and Discussion Effect of Composition on the Defect Formation Energy. The decomposition of the anhydrous Keggin unit initiates through desorption of two protons and a structural oxygen atom as water. This loss of constitutional water creates a defect in the Keggin unit structure. The energy of defect formation, ∆Edef, is defined as the energy for the reaction

HnXM12O40 f Hn-2XM12O39 + H2O ∆Edef

(1)

The intact and defect Keggin units are both neutral species, and the addenda atoms adjacent to the defect site are not formally reduced during defect formation as the electrons involved in the M-O bond remain with the oxygen atom as a lone pair in the water molecule (see Supporting Information for charge analysis). The number of protons on the intact Keggin unit may differ with heteroatom type or because substitution of vanadium for tungsten or molybdenum can change the charge on the Keggin unit. The energy associated with the loss of the first constitutional water molecule for each structure is reported for different HPA compositions. In calculating the total energy of defect formation, the initial structure was assumed to be that with the protons in their optimal locations as previously determined for the three protons of HPW (two Oc, one Ob).47 For species with a 4th proton, an Od oxygen atom is the optimal position. The defect formation energy at each of the exterior oxygen positions of HPW is reported in Table 1. The removal of a bridging oxygen atom as water is substantially lower in energy than a terminal oxygen atom, with the Ob bridging oxygen defect lowest in energy, which is consistent with the computational

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Figure 1. Structures of (a) intact HPW with the four types of oxygen atoms in the Keggin structure labeled. Ob, Oc, and Od atoms are at the exterior of the structure and may associate with protons. (b-d) HPW with a single constitutional water removed. (b) structure with an Ob defect. (c) structure with an Oc defect. (d) structure with an Od defect. Interatomic distances and angles are given in Table 2.

TABLE 1: Energy of Defect Formation (∆EDef) of HPW in KJ Mol-1 VASP

ADF

defect position

∆Edef

ZPVE corrected

∆Edef

Ob Oc Od

161.1 185.9 306.8

146.2 170.3 289.2

165.8 176.0 307.1

study of Paul and Fournier.22 The remaining proton generally prefers to locate at an oxygen site furthest from the defect. The values in Table 1 indicate agreement between the periodic planewave basis set and atomic orbital-based code. All subsequent results reported in this work are taken from calculations using VASP. Zero-point vibrational energy corrections reduce the defect formation energy by approximately 15 kJ mol-1. These corrections, however, were calculated only for the HPW species. The defect HPW structures are illustrated in Figure 1, and relevant interatomic distances and angles within the intact and defect structures are given in Table 2. Following the loss of constitutional water, the tungsten atoms adjacent to the defect site move closer to the remaining bridging oxygen atoms. The removal of a bridging oxygen atom as water results in restructuring of the remaining oxygen atoms to form a tetrahedral arrangement about the tungsten atom. For example, in the Ob defect structure, the Ob-W-Oc angle across the defect site contracts from 155° in the intact structure to 127° following defect formation. The Wdef-Oa distances increase by ap-

TABLE 2: DFT-optimized Interatomic Distances and Angles of the Intact HPW Structure and Structures with One Constitutional Water Molecule Removed intacta

Ob defb

Oc defb

Od defb

P-Oa (Å) W-Oa (Å) W-Ob (Å)

1.55 2.50 1.93

1.54 2.61 1.85

1.62 1.93 1.86

W-Oc (Å)

1.95

W-Od (Å) Ob1-W-Oc1 (deg)

1.71 155

1.85 1.82 1.71 127

1.53 2.75 (1) 1.85 (2) 1.81 1.86 1.71 130

176

1.89

a Values averaged across entire Keggin unit. b Values given are the average over the octahedra that contain the defect. Multiple values are given when oxygen atoms become inequivalent following defect formation, as labeled in Figure 1.

proximately 0.1 Å as the central oxygen atom shifts away. In the case of terminal defect formation, the octahedral structure about the tungsten atom from which the Od atom is removed becomes square pyramidal, with the tungsten atom crossing the plane of the remaining bridging oxygen atoms toward the center of the Keggin unit. The O-W-O angles move closer to 90° while the Wdef-Oa distance decreases by over 0.5 Å. The proton affinity, the energy required to heterolytically cleave the H-O bond of the heteropolyacid, of the remaining proton was calculated to determine whether defect formation alters the acid strength. Following the formation of an Ob defect,

Decomposition of Keggin-Structured Heteropolyacids

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TABLE 3: Energy of Defect Formation for Various HPA Compositions in KJ Mol-1

a

species/defect site

Ob

Oc

Od

HPW HSiW HPMo HSiMo HPV1W11a HPV1Mo11a

161.1 152.9 125.4 101.4 106.2 80.4

185.9 208.1 148.7 133.2 132.3 105.5

306.8 236.4 282.6 183.3 159.9 142.4

Defect site is adjacent to the V atom.

TABLE 4: The Defect Formation Energy (∆EDef for Ob Position in KJ Mol-1) for Structures Substituted with Vanadium species

Ob position

∆Edef

HPW12 HPV1W11 HPV1W11 HPMo12 HPV1Mo11 HPV1Mo11 HPV2Mo10 HPV2Mo10

between 2 W between 2 W between W and V between 2 Mo between 2 Mo between Mo and V between Mo and V between 2 V

161.1 133.3 106.2 125.4 86.9 80.4 82.1 69.6

the remaining proton is preferentially located on an Oc atom. The proton affinity for this site is 1072 kJ mol-1, compared to 1079 kJ mol-1 for a single proton on an Oc atom of the intact structure.47 Therefore, it is concluded that defect formation removes two Brønsted acid sites without substantially affecting the acid strength of the remaining proton. The defect formation energies of HPAs for four of the most commonly studied HPAs are given in Table 3 for each of the three exterior oxygen types. The Ob atom defect is lowest in energy for all of the compositions examined. The Keggin unit stability, for the nonsubstituted HPAs, is ranked based on the Ob defect formation energy HPW > HSiW > HPMo > HSiMo. This ranking agrees with the ranking of structural stability based on their decomposition temperatures determined from DTA and TGA.12,17,34 The effect of the central atom is substantially less than the influence of the addenda atom. For example, changing the central atom from phosphorus to silicon reduces the defect formation energy by 8.2 kJ mol-1, while changing the addenda atoms from tungsten to molybdenum reduces the defect formation energy by 35.7 kJ mol-1. Substitution of Vanadium. Substitution of vanadium as an addenda atom produces a more favorable oxidation potential for catalyzing oxidation reactions.23 The highest oxidation potentials occur for HPAs with both molybdenum and vanadium as addenda atoms.33 To understand the effect of vanadium on the thermal stability, the defect formation energy was calculated for vanadium-substituted Keggin units. The substitution of a single vanadium atom substantially decreases the defect formation energy of HPW and HPMo. The defect formation energy calculated for each of the three oxygen positions adjacent to the substituted vanadium atom is given in Table 3. The formation of an Ob defect results in the lowest energy. The twelve Ob atoms are no longer equivalent when vanadium is substituted into the structure. The energy of forming an Ob defect at different positions (removal of an Ob atom between 2 molybdenums versus between a molybdenum and a vanadium) are given in Table 4. The formation of a defect adjacent to the substituted vanadium atom was found to be less endothermic. The defect formation energy for HPMo12 is 125.4 kJ mol-1 whereas that for a defect adjacent to a vanadium atom in HPV1Mo11 is 80.4 kJ mol-1. However, the substitution of vanadium also decreases the energy to form

a defect between two molybdenum atoms (125.4 kJ mol-1 in HPMo12, 86.9 kJ mol-1 in HPV1Mo11). The replacement of two of the molybdenum atoms with vanadium into the HPMo structure further reduces the defect formation energy to 69.6 kJ mol-1 (for a defect between two vanadium atoms). It should be noted that the intact di-substituted structure with two vanadium atoms sharing an Ob atom is energetically favored by 4.8 kJ mol-1 over that with the vanadium atoms far apart. TGA and DTA results indicate that the substitution of vanadium into HPMo lowers the temperature at which the loss of constitutional water begins,49 in agreement with the computational result that vanadium reduces the defect formation energy. Interestingly, the substitution of vanadium increases the temperature at which transformation into the bulk oxide occurs (as measured by the exothermic DTA peak).49,50 Substitution of multiple vanadium atoms in the Keggin unit virtually eliminates the plateau in temperature at which the anhydrous species is stable, and the removal of constitutional water molecules occurs concurrently with the desorption of the waters of hydration.49 The lower defect formation energy of vanadium substituted HPAs suggests that the active catalyst for high temperature (523-573 K) oxidation reactions likely contains partially decomposed Keggin units. The geometry of the defective Keggin unit is also altered by the inclusion of vanadium. For example, the Mo-Mo distance across an Ob defect in HPMo is 4.79 Å, while the V-V distance across an Ob defect in HPV2Mo10 is 5.06 Å. The inclusion of vanadium leads to a more open defect structure, with the central tetrahedron better exposed. The results from solid state 51V NMR studies indicate that vanadium occupies a tetrahedral arrangement following dehydration at 593 K.51,52 The appearance of the tetrahedral signal in the NMR spectrum correlates with catalytic activity for oxidative dehydrogenation of isobutyric acid.52 Following the formation of an Ob defect between Mo and V atoms in HPV1Mo11, the Mo-Oa distance is 2.63 Å and the V-Oa distance is 2.76 Å. The structure around the vanadium atom following Ob defect formation is tetrahedral, with little association of the vanadium atom with the central oxygen atom. Taouk et al. use the 51V NMR results to suggest that there is an expulsion of vanadium from the Keggin unit.52 We believe, however, that the NMR spectroscopy confirms the presence of a tetrahedral defect structure. These authors also reported that treatment with water vapor partially converted the NMR signal from tetrahedral vanadium to one from octahedral vanadium. This may be easier explained as the healing of structural defects rather than the return of an expelled vanadium atom. Further dehydration at 773 K returned the vanadium atoms to an octahedral position,52 indicating the conversion of defective Keggin units into a mixed oxide. The transformation of defective Keggin units is discussed below for the HPW structure, in which the octahedral geometry of the tungsten is reformed. Cohesive Energy and Defect Formation as Measurements of Stability. The energy required to form a defect is expected to correctly predict the relative solid state thermal stability of HPAs as it is a direct measurement of the energy required for the first step in the decomposition of the Keggin unit. Previous studies have proposed the “binding energy”, or what is referred to here as the cohesive energy, as a measurement of stability.20,21 The cohesive energy, ∆ECE, is defined as the reaction energy to construct the Keggin unit from the protonated central tetrahedral core (HnXO4) and the empty metal oxide outer Keggin unit shell (M12O36):

HnXO4 + M12O36 f HnXM12O40 ∆ECE

(2)

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TABLE 5: Defect Formation Energies (∆EDef for Ob Position) and Cohesive Energies (∆ECE) for Keggin Structured HPAs (HnXM12O40) of Different Compositions X

∆Edef M n (kJ mol-1)

∆ECE (eV)

X

M

∆Edef n (kJ mol-1)

∆ECE (eV)

B Al Ga As P C Ge Si Se Te S

W W W W W W W W W W W

-1.02 -2.72 -2.62 -2.90 -3.39 -1.77 -2.40 -2.52 -1.94 -1.11 +4.16

As P Te Se B Al Ga S Si Ge C

Mo Mo Mo Mo Mo Mo Mo Mo Mo Mo Mo

3 3 2 2 5 5 5 2 4 4 4

-2.55 -2.96 -1.16 -1.92 +0.11 -1.59 -1.55 +4.31 -1.60 -1.57 -0.76

5 5 5 3 3 4 4 4 2 2 2

187.8 184.3 182.2 162.1 161.1 157.1 155.2 152.9 151.6 146.3 141.2

125.8 125.4 119.0 118.2 110.4 108.7 106.5 101.5 101.4 100.2 93.0

This definition of the cohesive energy differs from that used by Jansen and co-workers.20,21 Their binding energy was computed using charged species without the neutralizing protons. Our results, however, indicate that binding energies computed by calculating the energy of placing the charged central tetrahedron into the empty shell scales with the charge on the anion. This method predicts an increasing binding energy with an increasing charge to be delocalized over the Keggin unit structure. A substantially greater binding energy is predicted for HSiW than HPW, in disagreement with experimental measurements of thermal stability. Furthermore, as the central tetrahedron is likely protonated and/or solvated during aqueous synthesis, the value of ∆ECE as defined above may be more indicative of the actual formation energy. The cohesive energy defined in eq 2 does not apply to a real process, as the M12O36 Keggin unit shell is not known to form without the central tetrahedron. However, the relative values of ∆ECE provide a second approach to compare the stability of HPAs of different compositions. The heteroatoms considered are known to form heteropolyanion structures, though the acid form of the Keggin structure has not been confirmed in all cases.23 The calculated defect formation energy (∆Edef) for the formation of an Ob atom defect and the cohesive energy (∆ECE) are presented in Table 5 for HPAs of different compositions. There appears to be no observable correlation between the two values. The defect formation energies indicate that HPAs with tungsten addenda atoms are more stable than those of molybdenum for all central atoms. This clearly indicates that the central atom is a relatively minor factor in determining the thermal stability of HPAs. The minor effect of the central atom differentiates the stability within addenda atom groups. The defect formation energies tend to group by the charge on the heteropolyanion (n), with generally little deviation within each group. This indicates that the effect of the central atom is determined by the charge it imparts on the overall Keggin unit. However, the ordering of stability with charge on the central atom is not monotonic, and differs between the W and Mo species. The defect formation energy does not scale with the size of the central tetrahedron nor with the electronegativity of the central atom. The cohesive energy values do not predict the solid thermal stability behavior. For example, the ∆ECE values predict the HPMo structure to be more stable than the HSiW structure. While the defect formation energy is dictated mainly by the addenda atoms, the central atom has a greater effect on the cohesive energy. The cohesive energy provides a good measure of the degree of binding of the central tetrahedron with the shell. Therefore, it may well predict the ability to form the HPA from the constituent parts in an acidic aqueous solution. For example, to our knowledge the acidic HSW and HSMo Keggin species,

Figure 2. Reaction energy diagram for the defect formation process at a bridging oxygen (Ob) atom position. Solid line represents the anhydrous process, with ZPVE-corrected energies given. The dashed line indicates the lower activation barriers for the proton hopping steps in the presence of adsorbed water. The relative energies given correspond to the anhydrous species only. (inset)sthe mobile proton location at each step is illustrated.

which have the most endothermic ∆ECE values, have not been previously synthesized, though the tetrabutylammonium salts of SW12O402- and SMo12O402- are known.53-55 HSW and HSMo are difficult to form due to the extremely small size of the tetrahedron and exceptional stability of the charged tetrahedron (HSO4-). However, if HSW were formed, the defect formation energy predicts the solid would be at least as stable to heating as HPMo. Mechanism of Defect Formation. The previous section examined the total energy for defect formation without regard for the mechanism and activation barriers to the process. In this section, the energies of the elementary steps that lead to defect formation are presented for HPW. The initial intact structure is assumed to begin with the three protons in their optimal locations. The protons may move between oxygen atoms on the exterior of the Keggin unit. A detailed computational study of the proton-hopping reaction along the exterior of the HPW Keggin unit has been previously published.56 The ZPVEcorrected activation barrier for anhydrous proton movement from a bridging oxygen atom to a terminal oxygen atom was calculated to be 103.3 kJ mol-1. The adsorption of water to a proton reduces the barrier by almost an order of magnitude to 11.2 kJ mol-1. The formation of a defect through the loss of constitutional water requires first the association of two protons with a single bridging or terminal oxygen atom followed by the desorption of the water molecule. The path to defect formation begins with a series of proton hops. The final protonhopping step requires a proton to move to an oxygen atom to which another proton is bound. Therefore, defect formation is directly linked to proton mobility. Following the association of two protons on the same oxygen atom, the final step to defect formation is the desorption of the water molecule from the Keggin unit structure. An energy diagram for the defect formation process is given in Figure 2. A series of proton-hopping steps can alter the structure such that a proton resides on an Od atom adjacent to an Ob atom to which a proton is already bound. This state is 27.6 kJ mol-1 (ZPVE corrected) higher in energy than that with the protons in their optimal location. The energetics of these proton-hopping steps are likely only slightly affected by the position of other protons, and the previously published activation barriers can be assumed.56 The ZPVE-corrected activation barrier for the final proton-hopping step, from a nearby terminal

Decomposition of Keggin-Structured Heteropolyacids

Figure 3. The transition state for the final proton-hopping step toward defect formation. A proton transfers from a terminal to a bridging oxygen atom to which another proton is bound. The ZPVE-corrected activation barrier for this step is 98.2 kJ mol-1. Distances are given in Å.

oxygen atom to a bridging oxygen atom already bound to a proton, was found to be 98.2 kJ mol-1. The transition state for this step, involving the localization of the hopping proton with a bridging hydroxyl species, is illustrated in Figure 3. In the transition state, the W-Od bond bends toward the bridging oxygen atom to decrease the distance over which the proton transfers. The transition state geometry differs only slightly from that previously determined for an Oc-Od proton-hopping reaction.56 The activation barrier for the Od to Oc proton hop is 7.3 kJ mol-1 higher with a second proton already on the bridging oxygen atom. The state with two protons bound to an Ob atom is 67.6 kJ mol-1 (ZPVE corrected) higher in energy than the optimal configuration of isolated protons on the Keggin structure. The presence of adsorbed water can greatly assist proton movement as H3O+. The activation barrier for the movement of H3O+ from an Od atom to an Ob atom with another proton bound is only 26.6 kJ mol-1, and the reaction energy for this step is reduced from 40.0 kJ mol-1 in the anhydrous case to 19.6 kJ mol-1. Water desorption must then precede the final step of defect formation. The desorption of the combined structural oxygen atom and two protons is the final step in the proposed defect formation mechanism. The energetics for this reaction step were determined by carrying out a series of constrained optimizations. The P-Ob-defect distance was constrained and the rest of the structure was optimized in each calculation. The energy monotonically increased toward the energy of the separated H2O and defect Keggin unit fragments. This final step is, therefore, not activated, which is common for a unimolecular desorption process. The ZPVE-corrected total energy for the desorption step is 78.6 kJ mol-1. The total energy for the defect formation process, which is the sum of the energy necessary to combine two protons on the same oxygen atom (67.6 kJ mol-1) and the energy of the desorption step, is 146.2 kJ mol-1. The total energy for the separated water molecule and defect Keggin structure is higher in energy than the transition state of the final protonhopping step. Assuming a Boltzmann population is reached for proton distribution along the path to defect formation, the rate of defect formation is determined by the overall energy difference between the optimal proton configuration and defect state. Therefore, defect formation proceeds with an activation

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Figure 4. Equilibrium concentration of defect HPW Keggin units as a function of temperature and water partial pressure.

barrier of 146.2 kJ mol-1. Although adsorbed water may aid in distributing protons around the Keggin unit, it does not formally increase the rate of defect formation. Equilibrium Concentration of Defects. The defect formation process at an Ob atom is considered in two steps: (1) proton hopping: H3PW12O40 f (H2Ob)HPW12O39 ∆Ecombine ) 67.6 kJmol-1 (2) constitutional water desorption: (H2Ob)HPW12O39 f HPW12O39 + H2O ∆Edesorption ) 78.6 kJmol-1 Step 1 constitutes all the movement of protons from their optimal, distributed locations to combine two protons on a single oxygen atom. The equilibrium coefficient for the first step is

K1 )

qcombined -∆Ecombine/RT e qinitial

(3)

where qinitial is the vibrational partition function for the structure with the protons in their optimal locations, qcombined is the vibrational partition function for the structure with two protons on the Ob atom, and R is the universal gas constant. To approximate changes in the vibrational partition functions during defect formation, only the 9 vibrations associated with two protons and the Ob atom are included. Step 2 is the final water desorption step. The equilibrium constant for the second step in defect formation is

K2 )

qH2O Naqcombined

e-∆Edesorption/RT

(4)

where qH2O is the total partition function of gas-phase water and Na is Avogadro’s number. The partition function of the defect Keggin unit does not appear in the numerator of eq 4 because only vibrational modes involving the atoms of the desorbed water were considered. Figure 4 illustrates the equilibrium concentration of defect Keggin units, expressed as the percent of Keggin units with a defect, as a function of temperature and water partial pressure, with a total pressure of 1 atm. This applies only to the formation of a single defect in each HPW Keggin unit. The equilibrium percentage of Keggin units with two protons combined on a single oxygen atom never reaches 0.1%. This indicates that at the temperatures necessary to mobilize the protons to combine on a single oxygen atom, the entropic driving force for water desorption is sufficient to favor desorption. The temperature range of defect formation is

4176 J. Phys. Chem. B, Vol. 110, No. 9, 2006 dramatically influenced by the gas phase concentration of water. At extremely low water partial pressures (1 × 10-12 atmospheres), a significant number of defects may be present at 373 K. Extremely dry systems may allow for defect formation at these low temperatures, and defect formation is a viable deactivation mode at temperatures of interest for acid-catalyzed reactions. A small amount of water (1 ppm) shifts the temperature at which there is substantial equilibrium defect formation by over 100°, indicating that the inclusion of water in the reaction environment may suppress defect formation at temperatures of interest for acid-catalyzed reactions. A water partial pressure of 1 × 10-3 atmospheres shifts the temperature at which defect formation is thermodynamically favored to greater than 573 K, with all Keggin units having defects at 850 K. The temperature behavior during experimental studies (TGA, DTA, in situ XRD) of HPA thermal decomposition may be significantly affected by small amounts of water in the system. Differences in the amount of water in the experimental atmosphere may explain the variations observed in HPA decomposition temperatures. As indicated in Table 5, HPW ranks as one of the most stable compositions of Keggin unit HPAs. For a given temperature and water partial pressure, compositions with lower ∆Edef values are expected to have a higher equilibrium defect composition. Merging of Keggin Units and Further Decomposition. The loss of a constitutional water molecule leaves a single proton on the HPW Keggin unit. Further loss of constitutional water requires two protons on different Keggin units to combine with a structural oxygen atom. This likely occurs through the merging of Keggin units, or the transformation of multiple Keggin units into a larger mixed oxide species. The merging of Keggin units, leading to further decomposition through the loss of a second constitutional water molecule, eventually leads to the final decomposition product, a tungsten-phosphorus mixed-oxide. The energetics for merging two Keggin units and the loss of a second constitutional water molecule have been examined. The presence of an adjacent Keggin unit can stabilize a defect structure by sharing a structural oxygen atom with the defect site. The stabilization energy, ∆Estabilization, is defined as the reaction energy of

HPW12O39 + H3PW12O40 f H4P2W24O79 ∆Estabilization (5) The two Keggin unit defect structures are shown in Figure 5. In each structure, an Od atom from one Keggin unit sits in the defect site of a second Keggin unit. In Figure 5, the Keggin unit on the left has a defect and only a single proton remaining, while the Keggin unit on the right has three protons remaining. The stabilization energy is -168.3 kJ mol-1 for a defect at the terminal Od position, -26.4 kJ mol-1 for a bridging Oc position, and 41.0 kJ mol-1 for a bridging Ob position (Table 6). The Ob defect does not appear to be stabilized by the presence of a second Keggin unit. Merging with a second Keggin unit reverses the order of lowest energy defect site from that for a single Keggin unit, with the Od defect of lowest energy. The sharing of an Od atom between two Keggin units is lower in energy as it allows for a greater P-P distance, minimizing the proximity of oxygen atoms between the two Keggin units. As seen in Figure 5, the two Keggin unit Ob and Oc defects lead to a single oxygen atom bridging between three tungsten atoms. The optimal configuration for this structure places the oxygen atom in the plane of the three tungsten atoms. Though the WdOd bond is lengthened from 1.73 to 1.89 Å, the Od atom remains sp2 hybridized. The optimal W-Oc-W angle of 118° within

Janik et al.

Figure 5. Linking of two Keggin units by sharing an Od atom in a defect site. The two Keggin unit structure can be considered as a defect Keggin unit on the left, with an Od atom of the intact Keggin unit on the right filling the defect site. One proton remains on the left Keggin unit, three on the right. (a) left Keggin unit has an Ob defect, P-P distance 9.02 Å. (b) left Keggin unit has an Oc defect, P-P distance 9.25 Å. (c) left Keggin unit has an Od defect, P-P distance 10.67 Å. Distance labels in Å.

TABLE 6: Energy of Stabilization of Defect Structures by a Second Keggin Unit in KJ Mol-1 position

∆Edef

∆Estabilization

total

Ob Oc Od

161.1 185.9 306.8

+41.0 -26.4 -168.3

202.1 159.5 138.6

the Keggin unit allows the tungsten d-orbitals to efficiently overlap with the lone pair electrons of the Od atom, while the optimal W-Ob-W angle of 133° does not match with the Od lone pair configuration. An oxygen atom on an adjacent Keggin unit cannot stabilize the defect site during formation. The interaction between oxygen atoms on adjacent Keggin units is repulsive, and steric constraints do not allow an oxygen atom on an adjacent Keggin unit to approach the defect site until the constitutional water molecule is removed. Therefore, it is proposed that defect formation first occurs on a single Keggin unit, which is subsequently stabilized by interaction with a second Keggin structure. The Ob defect will be kinetically preferred, as the initial formation of an Od defect is substantially higher in energy. It would then be thermodynamically preferred to rearrange, with an adjacent stabilizing Keggin unit, to allow for an Od defect

Decomposition of Keggin-Structured Heteropolyacids

J. Phys. Chem. B, Vol. 110, No. 9, 2006 4177

TABLE 7: The Energetics of Decomposition of HPW from the Anhydrous Form into Mixed Oxides. Values Are in KJ Mol-1 step

∆E

Eactivation

(1) form Ob defect (2) isomerize to Od defect, merge Keggin units (3) transfer H+ between KUs (4) form a second (Ob) defect (5) merge Keggin units, decompose into mixed oxides PW12O38.5f 1/2 P2O5 + 12 WO3

161.1 -22.5 -83.9 161.7 -98.9

161.1 ? ∼100 161.7 ?

structure. The barriers to this rearrangement were not explored. The merging of two Keggin units through this stabilization facilitates further defect formation through the loss of constitutional water, suggesting this defect stabilization is a step toward the complete decomposition of the Keggin unit into a mixed bulk oxide. This indicates that defect sites on a single Keggin unit are only metastable intermediates in the decomposition process. The oligomerization of Keggin units through defect stabilization forms a second metastable structure, as further decomposition is exothermic as well. For a second constitutional water molecule to desorb, a proton from the stabilizing Keggin unit must move to the other defect Keggin unit. This movement is exothermic by -83.9 kJ mol-1 in the case of the stabilized Od defect structure, and the Od atom linking the two units then bridges more evenly. The two W-Od bonds which link the Keggin units are each 1.88 Å long with two protons on each Keggin unit, altered from 1.99 and 1.80 Å when there is one proton on a Keggin unit and three on the other. Proton hopping to combine two protons on a single oxygen atom then leads to a second defect. The total energy of formation of the second defect, referenced to the structure with two protons on each of two merged Keggin units and before any stabilization by a third Keggin unit, is almost identical to the first defect; 161.7 kJ mol-1 for an Ob atom, 187.0 kJ mol-1 for an Oc atom, and 306.8 kJ mol-1 for an Od atom. The overall process to form a second defect entails transferring a proton from the second Keggin unit (-83.9 kJ mol-1) then forming a defect (161.7 kJ mol-1 for Ob), and, therefore, has a total change in energy of 77.8 kJ mol-1. DTA experiments indicate that the final crystallization of the bulk oxide is exothermic.12-17 The total energy of bulk tungsten oxide (WO3) and phosphorus oxide (P2O5) were calculated to determine the total reaction energy of the subsequent stages of decomposition of the hexahydrate of phosphotungstic acid. A summary of the energetics of the individual steps in the decomposition of anhydrous HPW is given in Table 7. The crystallization of bulk oxides is exothermic, as found from DTA, thus providing a final verification of the energetics determined computationally. Acid Deactivation Through Defect Formation: Summary. The loss of constitutional water is a plausible deactivation path for heteropolyacid catalysts. The calculated equilibrium concentration of defects indicates that an appreciable number of defects may be formed at temperatures as low as 373 K in extremely dry systems. The inclusion of water vapor in the system shifts the defect formation equilibrium, suppressing or reversing defect formation. In situ infrared (IR) spectroscopy shows that 18O exchange between water vapor and the exterior structural-oxygen atoms of HPMo occurs rapidly at 423 K,57 further indicating that the consideration of an equilibrium system is appropriate. Previous experimental results have indicated that decomposition becomes irreversible following treatment at higher temperatures. For example, changes in the IR spectrum of HPW upon heating at 373 and 473 K are reversible whereas

IR features observed after heating to 573 K are irreversible.47 Regeneration of HPW following pentane skeletal isomerization at 473 K returned only a fraction of the original activity, indicating some degree of irreversible deactivation had occurred.28 This is not surprising, as regeneration of the complete decomposition products, a mixed oxide, is not expected and some carbonaceous species may remain on the surface. As shown earlier, following initial defect formation, the merging of Keggin units and movement of protons between Keggin units are exothermic steps. These steps in the decomposition process are likely difficult to reverse by treatment with water vapor. The inclusion of water in the reaction environment will decrease the equilibrium concentration of defects present. In other words, the main role of water is to favor the reverse reaction of step 1 in Table 7. This decreases the “reactant” concentration for the subsequent exothermic steps in the decomposition process, limiting the rate of step 2 in Table 7. Small amounts of water included in the reaction environment may help maintain catalyst activity, making heteropolyacids a viable solid acid catalyst for industrial hydrocarbon conversion processes. However, the role of water in the reaction environment is substantially more complex than simply shifting the equilibrium of the defect formation step. Adsorption of water on acidic protons is generally considered to poison an acid catalyst by reducing the acid strength. If water is to be included in the reaction environment, the optimal concentration must be determined based on these competing factors. Proton mobility is essential to defect formation, and in mobilizing protons, water may facilitate defect formation. Furthermore, Mestl et al. found that slow dehydration helped maintain intermediate decomposition structures, thereby indicating that small amounts of water may accelerate the final steps of decomposition.11 The dynamics of water adsorption, proton mobility, and defect formation must all be considered to generate a complete picture of the role of water in the deactivation and regeneration of heteropolyacids. As mentioned above, the build-up of carbonaceous species on the surface of heteropolyacid catalysts may also cause a substantial portion of the deactivation. Regeneration of catalysts by steam treatment is well-known, and could also account for the reactivation of HPAs by water. The build-up of heavy hydrocarbons during the alkylation of isobutane with butene will be a subject of future work. However, as HPA activity is also known to decrease with increasing pretreatment temperature, the deactivation due to thermal decomposition must represent some fraction of the catalyst deactivation. Conclusions The results presented herein detailed the kinetics and thermodynamics of heteropolyacid decomposition and the metastable structures formed along the path from the well-defined molecular Keggin structure and a bulk mixed-oxide. The loss of constitutional water is predicted to occur at temperatures of interest for acid- catalyzed reactions, indicating that defect formation is a plausible deactivation pathway for heteropolyacid catalysts. The presence of water vapor may suppress or reverse the initial defect formation step, maintaining or regenerating catalyst activity. The defect formation energy is less endothermic for the loss of a bridging oxygen atom than a terminal oxygen atom. The energy of defect formation may be used to rank the thermal stability of heteropolyacids of different composition, indicating a stability order of HPW > HSiW > HPMo > HSiMo, in agreement with experimental studies. This method was extended to systematically rank the stability of a wide range of compositions. The merging of Keggin units following defect

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