Methane is the main constituent in natural gas and it is abundant in nature. The conversion of methane to the more useful methanol or other liquid fuels has attracted extensive interest in energy production and transportation fuels for several decades [1]. Transition metal and metal oxide catalysts have been widely studied in the past decades because of their catalytic properties in alkane transformations [2]. The C–H bond activation is generally the rate determining step (RDS). However, new strategies have still to be developed for the efficient, economical, and direct conversion of methane to more valuable products. The main difficulty is to achieve a highly selective activation of the enormously strong C–H bond, which has a bond dissociation energy of 4.5 eV [3]. Therefore, the design and synthesis of new catalysts for C–H bond splitting is an important topic in modern chemistry. These catalysts can lead to the economical conversion of methane and other low-carbon alkanes into industrially useful products.
Recently, advances in the research of nanomaterials have given new opportunities for designing and screening well- defined catalysts for catalytic oxidation reactions [4, 5, 6, 7, 8]. Reducible metal oxides, due to their distinct redox properties, have been extensively studied for various catalytic reactions such as CO oxidation and alkane oxidation [9, 10, 11]. Among these oxides, spinel cobalt oxide (Co3O4) has been reported to be a promising transition metal oxide catalyst for methane catalytic oxidation [12, 13, 14]. Recently, we reported the controllable synthesis of different shapes of Co3O4 nanocrystals by a hydrothermal process with a cobalt hydroxide precursor [15, 16]. The conversion and temperature-programmed reduction (TPR) results for methane combustion showed that the nanocrystal (112) and (011) planes were much more reactive for methane conversion than the (001) plane. Many previous literature reports have speculated that the high oxidation capacity of the Co3O4 surfaces can be attributed to the presence of octahedrally coordinated Co species, which can easily convert between trivalent Co3+ and divalent Co2+ by the redox process [8, 17, 18, 19, 20, 21, 22]. However, knowledge about the active sites for methane conversion on Co3O4 nanocrystals is still lacking due to its complex surface structure. Therefore the mechanism of C–H bond activation is still not known. Few studies have looked at the crystal plane effect in surface oxidation reactions. Here the crystal plane effect refers to the observation that the different surfaces exposed by Co3O4 nanocrystals exhibit different reactivities in CH4 activation.
In this paper, a comparative density functional theory (DFT) investigation was performed on C–H bond activation at various possible active sites on the Co3O4(001) and (011) surfaces. By comparing the energetics of the different reaction pathways for C–H bond activation, we demonstrated that the activity of C–H bond cleavage exhibited distinct dependence on the exposed crystal plane and active sites. The nature of the high activity of CH4 conversion on Co3O4 nanocrystals is discussed. A microkinetic model was used to analyze the activity at the different sites and to estimate the reaction temperature of C–H bond activation. Our results are consistent with previous experimental observations.
The theoretical calculations were carried out by using DFT and the DMol3 program (version 4.0) developed by Accelrys, Inc. [23, 24, 25]. The generalized gradient approximation (GGA) with the PBE functional was chosen to describe the exchange-correlation effects [26]. The localized double-numerical basis sets with polarization functions (DNP) were used to describe the valence orbitals of the atoms. Relativistic effective core potentials (ECP) were used to replace the core electrons of Co [22, 24]. In the geometry optimization, the convergence criterion was set as 1×10–4 eV, 1×10–3 eV/Å, 5×10–3 Å for energy, energy gradient, and geometry, respectively. A Fermi surface smearing of 0.2 eV and a real-space cutoff of 4.5 Å were used. In the geometry relaxation calculations, the spin-polarization Kohn-Sham formalism was used for the self-consistent field (SCF) iterations and molecular symmetry was not enforced. In all the calculations, stoichiometric supercell models were used. All the slabs were periodically repeated with a vacuum spacing of 15 Å between the images in the direction perpendicular to the surface. Two-dimensional Brillouin integration was performed with an 8 × 8 × 8 k-point mesh for the bulk crystal and a 4 × 4 × 1 k-point mesh for the slabs. Larger k-point meshes were also tested, and the total energy showed nearly converged behavior. The transition states were obtained using the complete LST/QST method, which used a linear synchronous transit (LST) calculation followed by repeated conjugate gradient (CG) minimization and quadratic synchronous transit (QST) maximization until a transition state was located [27]. The convergence criterion for each transition state was set at 0.05 eV/Å. Furthermore, a harmonic vibrational analysis was performed to make sure that the transition state has only one imaginary frequency. The zero point energy (ZPE) was included in all energetics. The structural parameters, magnetic mo ments, and band gap of bulk Co3O4 were first calculated to evaluate the computational methods used in this work. The calculated results of bulk Co3O4 listed in Table 1 were close to the experimental data and were also in good agreement with previous computational studies, indicating that the selected exchange-correlation functional and computational approach were appropriate.
The Co3O4(001)-p(1×1) (a = 5.79 Å, b = 5.79 Å) and Co3O4(011)-p(1×1) (a = 8.19 Å, b = 5.79 Å) surface slab models cleaved from an ideal bulk spinel structure were used to model the Co3O4 planes. Due to the special structure of the spinel lattice, there are two types of surface structure for each plane for different cleaved depths. In the present study, we chose the most stable slab model with the lower surface energy for the (001) and (011) faces, which is shown in Fig. 1. Investigations on the stability of the different surface models can be found in previous theoretical studies [28, 29]. There are two types of oxygen ions on each surface, denoted respectively as Oo and Ot in Fig. 1, which differ in the way they are bonded in the lattice structure. Ot is bonded to one Co2+ ion and 1–3 Co3+ ions, while all atoms near Oo are Co3+ ions. Both the Ot and Oo ions on the (001) surface are threefold coordinated, while on the (011) surface the Ot ions are twofold coordinated and Oo ions are threefold coordinated.
As the Co2+ sites are located in the subsurface layer, only the Co3+ sites on the surface layer were considered for CH4 adsorption. The adsorption configurations are shown in Fig. 2. On the (001) and (011) surfaces, the C atom was located at 2.76 Å and 2.57 Å above the surface, respectively. The C–H bond lengths in the adsorption configuration on both surfaces were unchanged with respect to the calculated value for free CH4 molecule, which was 1.10 Å (close to the experimental value of 1.09 Å), indicating that little interaction existed between CH4 and the Co3O4 surfaces. The CH4 adsorption energy was calculated using the formula
Eadsorption = (Eslab+adsorbate – Eslab –Eadsorbate), where Eslab is the energy per surface unit cell of the slab model containing n bulk unit cells, Eslab+adsorbate is the energy of the adsorption complex including those of the relaxed surface and adsorbed CH4, and Eadsorbate is the energy of the isolated CH4 molecule. The calculated CH4 adsorption energies were –0.11 and –0.08 eV for the (001) and (011) planes, respectively, implying that the CH4 molecule was only weakly physisorbed on the Co3O4 surfaces.
Many previous studies on the CH4 oxidation mechanism proposed that the first C–H bond activation is the key step for CH4 conversion [2, 38]. Generally, the first C–H bond cleavage can be divided into *CH3 species binding to one surface site and H* species binding to an adjacent site. As an example, Psofogiannakis et al. [38] reported C–H scission accompanied by *CH3 and *H binding to two adjacent Pt sites. In the present study, the Co3O4 surfaces contained both Co ions and O ions. Although CH4 cannot chemisorb at the surface Co site, we found that CH4 can be activated at Co–O ion pairs by charge polarization of the C–H bond, leading to the formation of Co–CH3 and O–H species. To understand the activation nature of the C–H bond on Co3O4 nanocrystals, the transition states of the elementary steps were searched using DFT calculations on the Co3O4(001) and (011) model surfaces. On each surface, two reaction pathways for C–H bond activation were investigated, for where the proton ended up either on the Ot site or Oo site.
To provide the mechanistic details of the first C–H bond activation, we considered the thermodynamic reaction energies Er of the C–H splitting and the kinetic barrier energies Ea. The calculated results are shown in Table 2. The positive reaction energy indicated that the oxidation process is endothermic, where a negative value corresponds to an exothermic process following the thermodynamic convention. Despite the high CH3–H(g) bond dissociation energy (~4.5 eV), the Co3O4 nanocrystal surfaces exhibit remarkable reactivity for the first C–H cleavage with rather low barriers (less than 1.1 eV). The geometries of the reactants, transition states (TS), and products at each Co–O pair site are given in Figs. 3 and 4. The bond distances are given in Tables 3 and 4. Compared to the configurations of the reactants, the transition states on both surfaces have a similar configuration transition that accompanies the elongation of the C–H and Co–O bonds and the approaching of the C and Co atoms. Finally, these transition processes led to the production of Co–CH3 and O–H species. Therefore, it can be inferred that the formation of surface Co–C and O–H bonds decreases the barriers of C–H bond scission and also weakens the surface Co–O bonds.
Table 2 shows that the energy barriers for the first C–H bond activation at the Co–Ot pair are, respectively, 0.11 and 0.29 eV lower than at the Co–Oo pair on the (001) and (011) surfaces, suggesting that the Co–Ot pairs on both the (001) and (011) surfaces are more reactive than the Co–Oo pairs. Therefore, the Co–Ot pairs are the active sites for C–H bond activation on the Co3O4 surfaces. In particular, the Co–Ot pairs are expected to be highly active for the C–H bond activation on the (011) surface due to the smaller barrier 0.81 eV and the highly exothermic energy –0.62 eV. For the Co–Ot site, the C–H bond activation is exothermic on the (011) surface and endothermic on the (001) surface, indicating that the C–H scission process on the (011) surface is thermodynamically more favorable (by ~0.78 eV) than on the (001) surface. Concerning the kinetic aspect, however, the barriers on both surfaces are very close, and the entropy contribution may also affect the reactivity.
To understand the interaction of a CH4 molecule with the active sties on the Co3O4 surfaces, Mulliken population analysis was performed on the reactants and products during C–H dissociation. As shown in Table 5, upon CH3 and H species adsorption, the Co3+ ions became less positively charged on both surfaces, indicating that they were reduced to low valent Co ions in the C–H bond activation. Our results also imply that the C−H bond breaking is a heterolytic process (i.e., CH4 ® CH3δ–(*) + Hδ+(*)). This conclusion is in accord with previous speculation that the high oxidation ability of Co3O4 originates from the presence of octahedrally coordinated Co3+ ions, which become even more oxidizing on the surface due to dangling bonds [8, 17, 18, 19, 20, 21, 22].
By comparing the C–H bond activation at different Co–O pairs, we found that the different coordination environment for the oxygen ions in the lattice structure is also an essential factor that affects the activity. For example, the Ot ions on both the Co3O4 surfaces are more active than the Oo ions. In other words, the low coordination surface ions contribute to the high activity for methane conversion. Especially, the four-coordinated Co3+ ions and two-coordinated Ot ions on the (011) surface are more active than the five-coordinated Co3+ ions and three- coordinated Ot ions on the (001) surface. The critical role of the low-coordination oxygen ion on Co3O4(011) in catalytic CO oxidation was reported recently by Jiang et al [31].
Previously, we reported the experimental results of the catalytic properties of Co3O4 nanocrystals with different shape for methane combustion by thermal decomposition [15, 16]. CH4 conversion catalyzed by the Co3O4 nanocrystals can occur at a temperature of ~225 oC, and the activity exhibited a significant crystal plane effect: the reaction temperature for CH4 combustion on the (011) surface was ~25 oC lower than on the (001) surface. To compare the experimental observations with our calculated energetics of the C–H bond activation, we obtained the reaction rate under specific reaction conditions from a microkinetic analysis to see if there is a one-to-one correspondence between C–H bond activation and the CH4 combustion process on Co3O4 nanocrystals.
In the transition state theory, the rate constant is defined as a preexponential (frequency) factor multiplied by a Boltzmann factor [38]:
k = Aexp(‒Ea/kBT) = kBT/h exp(‒ΔS≠/kB)*exp(‒Ea/kBT)
In this definition, the preexponential factor A is approximately proportional to the temperature, i.e., an elevated temperature will increase the collision frequency between the reactant molecules. This treatment is reasonable for a gas phase reaction because the motion of all the reactants are enhanced with increasing temperature. However, in the present study, the CH4 molecule reacts with the Co3O4 surface via a gas-solid reaction. From a kinetic perspective, the elevated temperature will enhance the desorption of CH4 and to some extent decrease the probability of its collision with the active site. Therefore, we have modified the rate constant formula by changing the frequency term according to collision theory:
where P is the partial pressure of CH4 in the gas phase, m is the mass of CH4 molecule, and C is the concentration of the active sites per unit area on the surface. Here P was set to equal 2×103 Pa to be consistent with our previous study, and C equals 5.9×1018 m–2 on the (001) surface and 4.2×1018 m–2 on the (011) surface. In this definition, the collision frequency of CH4 with the surface active sites is described more accurately in the relatively high temperature range, where the elevated temperature has a negative effect on the frequency of CH4 collision with the surface active sites. A similar treatment for adsorption can be found in a recent study on the microkinetic simulation of temperature-programmed desorption (TPR) on the RuO2(110) surface [39].
The estimated rate constants on the different sites on both the Co3O4 surfaces are shown in Fig. 5. The order of the rate constants for C–H bond activation, Co–Ot-(011) > Co–Ot-(001) > Co–Oo-(001) > Co–Oo-(011), was consistent with the order of the calculated energy barriers in Section 3.2. These results implied that the barriers on the Co3O4 nanocrystals dominated the activity of C–H bond activation, while the entropy contribution had little effect on the reaction rate of C–H bond activation.
Generally, a range of rate constant of 1-100 s–1 site–1 indicates that the reaction processes can be observed in experimental measurements [40]. Therefore, the C–H bond activation on the (011) surface was estimated for 150-200 °C, which was not far from the experimental observation that CH4 combustion occurs at the temperature of ~225 °C. On the (001) surfaces the reaction temperature at the Co–Ot site was calculated to be ~30 °C higher than on the (011) surface, which was consistent with experimental results of CH4 oxidation reactivity on the different Co3O4 nanocrystals [15]. Our results reveal the existence of the crystal plane effect in CH4 combustion that was observed in our previous experimental study. While we only focused on the first C–H bond activation process, this C–H splitting step is the key step in CH4 oxidation processes on Co3O4 surfaces, as supported by the fact that the reaction temperature of CH4 combustion in the experiments correlated with the estimated theoretical temperature for C–H bond activation.
We presented a theoretical study of C–H bond activation on the Co3O4(001) and Co3O4(011) surfaces. Two pathways for the first C–H bond cleavage at Co–O pair sites on the two surfaces were studied using DFT calculations with a slab surface model. The surface Co–O pairs are the active sites, where the two ions provide a synergistic effect for the first C–H bond activation to yield surface Co–CH3 and O–H species. The Co–Ot pairs with Ot bonded to one Co2+ ion on the (011) surface are more active for C–H bond activation, with a small barrier of 0.81 eV and an exothermic reaction energy of –0.62 eV. A microkinetic analysis revealed that CH4 combustion on the Co3O4 surface can proceed at ~150–200 °C and exhibited significant dependence on the crystal plane and active sites, consistent with our experimental findings. The low-coordination surface ions are also shown to have high activity for methane conversion. Overall, our microkinetic analysis approach can provide a guide for designing and screening nanocrystal catalysts with high activity and selectivity.
The calculations were performed by using supercomputers at the Computer Network Information Center, Chinese Academy of Sciences, Tsinghua National Laboratory for Information Science and Technology, and the Shanghai Supercomputing Center.
2014, Vol. 35 Issue (4): 462-467
PDF (582KB)
2014, Vol. 35 Issue (4): 462-467
PDF (582KB)