Methane Oxidation by Lanthanum Oxide Doped with Cu, Zn, Mg, Fe, Nb, Ti, Zr, or Ta: The Connection Between the Activation Energy and the Energy of Oxygen-Vacancy Formation
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- Derk, A.R., Li, B., Sharma, S. et al. Catal Lett (2013) 143: 406. doi:10.1007/s10562-013-0985-7
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We measure the effective activation energy of methane oxidation catalyzed by La2O3 doped with Cu, Zn, Mg, Fe, Nb, Ti, Zr, or Ta. We find that the measured activation energy is a linear function of the calculated energy of oxygen-vacancy formation.
KeywordsHeterogeneous catalysisActivation energyOxidationLanthanaMethaneDoped oxide
Oxides catalyze many interesting alkane-activation reactions, but often their performance is poor. One of the strategies for improving an oxide’s catalytic activity is to replace a fraction of the cations in its surface layer with other cations. For example, to improve a La2O3 catalyst we might replace some of the La ions with Mg. In this case we call Mg a substitutional dopant (or dopant) and La2O3 the host oxide.
It has been frequently assumed that the energy of oxygen-vacancy formation, ΔEv, is an indicator of the reactivity of surface oxygen atoms: smaller ΔEv means a more reactive surface oxygen. This is relevant to oxidation reactions, catalyzed by oxides, which take place through a Mars–van Krevelen mechanism. In this mechanism the reductant (e.g., an alkane) reacts with one or more oxygen atoms in the surface layer, is converted to the oxidation product, and causes the formation of one or more oxygen vacancies in the surface. The reduced oxide made in this way is reoxidized by gas-phase O2. In most cases the reoxidation step is fast (at least at the oxygen concentrations used in most experiments) and therefore the overall oxidation rate is controlled by the reaction of the reductant with the oxygen atoms in the surface layer. In the case of alkane oxidation the rate-limiting reaction is the dissociative adsorption that converts the gas-phase R-H into an alkoxide (R–Os, where Os is an oxygen atom in the surface layer) and a hydroxyl (H–Os). If the surface oxygen atoms are made more reactive (by some chemical modification such as doping), the R–Os and the H–Os bonds are stronger, and the energy of the dissociative adsorption reaction, ΔEdis, is higher (more exothermic). According to the Brønsted-Evans-Polanyi rule there is a linear relationship between the activation energy Ea,dis for the dissociative adsorption and the reaction energy ΔEdis: the more exothermic the reaction, the lower the activation energy. This chain of assumptions leads us to state the following rule: the smaller the energy ΔEv of oxygen vacancy formation, the smaller the activation energy Ea,dis for the dissociative adsorption of an alkane. Since dissociation is the rate-limiting step in alkane activation, Ea,dis dominates the measured effective activation energy, Ea, of the alkane oxidation reaction. In summary, we expect that the effective activation energy Ea for methane oxidation by various doped-lanthana catalysts should be an increasing function of the energy of oxygen vacancy formation ΔEv in the surface of the doped oxide.
In this article we test this qualitative rule suggested by the calculations, by preparing La2O3 doped with Cu, Zn, Mg, Fe, Nb, Ti, Zr, or Ta. We use density functional theory (DFT) to calculate ΔEv for these systems and experiments to measure the effective activation energy Ea for catalytic oxidation of methane. Our results confirm the rule. Moreover, we find that the measured Ea is linearly related to the calculated ΔEv. The graph of Ea versus ΔEv consists of two straight lines: one valid for La2O3 doped with lower-valence dopants and the other for La2O3 doped with higher-valence dopants.
We emphasize that it is practically impossible to prepare a doped oxide surface that is guaranteed to have the same morphology and composition as the models used in calculations. Because of this, we expect the correlations suggested (and tested) here to be qualitative only. If deviations occur, we do not know whether they are due to errors in DFT or to our inability to prepare the intended material.
2 DFT Calculation Methodology
The details of the calculations were explained in previous work . Briefly, spin-polarized DFT calculations were performed using the VASP  program, with the rPBE functional  and PAW basis . We used a La2O3 (001) slab 15 atomic layers thick, with a 2 × 2 supercell. The size of the vacuum layer was 15 Å and we tested that the results did not change when the size was increased. All ionic positions were optimized until the forces acted on them were <0.02 eV/Å. Applying Hubbard’s correction does not qualitatively affect the results  and therefore we did not use DFT + U. One should keep in mind that DFT calculations are not accurate and that our goal is to verify a qualitative rule.
3 Experimental Methodology
It is difficult to determine for certain whether a catalyst is substitutionally doped. The possibility that the dopant forms very small oxide clusters on the surface of the host oxide is very difficult to rule out because such clusters will not be detectable by XRD and will have an XPS signature different from the bulk oxide of the dopant. Nevertheless, we considered our La2O3 catalyst to be doped when (1) lanthanum oxide (or oxy-carbonate) is the only phase present in XRD and (2) the dopant is detectable by XPS. The latter condition indicates that the dopant is present at or near the surface. For each synthesis of the doped oxides, the dopant concentration was varied so that the material met the conditions (1) and (2). These precautions do not guarantee that we have prepared a doped oxide since the dopants might make oxide clusters that are not crystalline or large enough to be detected by XRD.
All catalysts were prepared by combustion synthesis, a method employed extensively by Hegde . The precursors were lanthanum(III) nitrate, titanium(IV) oxyacetylacetonate, niobium(V) ammonium oxalate, tantalum(V) chloride, zirconyl nitrate, zinc(II) nitrate, magnesium nitrate, copper(II) nitrate, iron(III) nitrate. Oxalic dihydrazide (ODH) was used as fuel. Typically, 2.50 g of lanthanum(III) nitrate hexahydrate, and the appropriate amount of dopant precursor (e.g., 80 mg of titanium oxyacetylacetate to make 5 % titanium-doped La2O3) and of ODH (0.85 g for previous example) are dissolved in a minimal amount of water (Millipore). This mixture is put in a Pyrex™ dish and placed into a furnace, which is heated to 450 °C to induce spontaneous combustion. The combustion takes place very rapidly and produces an oxide powder. The combustion method for doped-oxide synthesis starts with a solution in which the cations of the dopant and those of the host oxide are uniformly mixed and the formation of the oxide is very rapid, which minimizes the opportunity for phase separation into segregated oxides.
X-ray Diffraction (XRD, Philips X’PERT diffractometer) and X-ray photoelectron spectroscopy (XPS, Kratos Axis Ultra X-ray Photoelectron Spectrometer) measurements were performed on all catalysts to confirm that the material has the structure of lanthanum oxide and that the dopant is present near the surface.
Catalytic characterization was performed with a packed bed reactor with a very short residence time (differential reactor). 25 mg of catalyst was mixed with 50 mg of 200 mesh GC-grade alumina and supported in the center of a quartz tube (4 mm inner diameter) with quartz wool. Gases were delivered using mass-flow controllers (MFCs, supplied by MKS). The mole ratio of methane:oxygen:argon was maintained at 1:1:3. Catalyst void fraction was measured volumetrically with methanol and the gas flowrate was set such that the space time was 0.18 s calculated at 20 °C, unless otherwise noted. The reactor effluent was measured by differentially pumped mass spectrometry (SRS). All gases had a purity of at least 99.99 %. The temperature was controlled and varied using a programmable controller (OMEGA CSC32). Software for the control and logging of the reactor studies was written using LabView™. Effective activation energies were calculated by performing linear regressions on Arrhenius plots. The data chosen to be regressed had small, but non-zero, methane conversion in order to determine an accurate conversion rate.
4 Results and Discussion
To avoid the formation of separate dopant oxide-phases, we kept the molar concentration of tantalum and niobium at 1 %. Titanium, magnesium, and zinc allowed a doping level of 2.5 % without showing separate dopant-oxide phases in XRD. Finally, the concentration of zirconium, copper, and iron dopants had to be 5 % to be observable in XPS. Even at this high concentration no phase separation was observed in XRD.
The measured effective activation energy and the calculated energy of oxygen-vacancy formation
We suggest that the reason for the existence of two curves can be understood based on the difference between the valence of the dopant and that of La. The valence of a dopant is, by definition, the valence the dopant has in its own oxide. For example, a Mg dopant is divalent because its only oxide is MgO. This definition cannot be used a priori for atoms that form multiple stable oxides. For example, NbO, NbO2, and Nb2O5 are all stable so it is difficult to decide a priori what valence Nb has when it is a substitutional dopant in La2O3. We use the term ‘lower-valence’ (or ‘higher-valence’) dopant when the valence of the dopant is lower (respectively, higher) than the valence of the cation of the host oxide. For example, Mg is a lower-valence dopant in La2O3, and Zr is a higher-valence dopant in La2O3.
The DFT calculations have shown that the presence of a lower-valence dopant (e.g., Fe, Cu, Mg, Zn) in the surface of La2O3 lowers the energy of oxygen-vacancy formation (Table 1) very substantially. Previous calculations  have shown that lower-valence dopants, such as Cu, Mg, Zn, lower the activation energy for methane dissociation.
The higher-valence dopants have a very small effect on ΔEv. In previous work , we suggested that a higher-valence dopant in the surface layer of an oxide adsorbs O2 from gas-phase and activates it. This adsorbed O2 can react with methane and oxidize it. In this mechanism the oxygen in the oxidation product originates from the gas, not from the oxide surface. Another possibility  is that, because the gas-phase O2 adsorbs on the higher-valence dopant, one should consider that the dopant is the MeO2 group, where Me is the doping cation. Since the O2 ties down (by making bonds) some of the electrons of M, the MO2 dopant is a lower-valence dopant that activates the surface oxygen atoms near it. Thus a higher-valence dopant has a double role: it activates the oxygen adsorbed from the gas and also the oxygen next to it (when it adsorbs O2 to form MeO2).
This possible difference in oxidation mechanism may explain why we obtain two straight lines for the dependence of Ea on ΔEv: one for lanthana doped with LVDs and another for lanthana doped with HVDs.
We conclude by summarizing for the reader some of the uncertainties in this work. First, one is never sure that a doped oxide has been prepared with the dopant atoms isolated and contained in the surface layer. Second, the calculations of ΔEv contain errors inherent to DFT and the flat-slab model we use is not a faithful model of the surface of a laboratory catalyst. Finally, the effect of the lower-valence dopants in the experiments may be chemically compensated  by coadsorption of Lewis bases such as H or CH3. One hopes that in spite of these uncertainties the trend (obtained by performing the same reaction, catalyzed by the same host oxide, doped with a variety of dopants) is robust and can serve as a guide for designing new doped oxide catalysts.
Funding was provided by the Air Force Office of Scientific Research (FA9550-09-1-0333 and FA9550-12-1-0147) and the U.S. Department of Energy (DE-FG02-89ER140048). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 0707430. Use of the Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. We made use of the California NanoSystems Institute Computer Facility, funded in part by the National Science Foundation (CHE 0321368). Financial support of GMM and the MRL Central Facilities are supported by the MRSEC Program of the NSF under Award No. DMR 1121053; a member of the NSF-funded Materials Research Facilities Network (www.mrfn.org).