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J. Phys. Chem. C 2008, 112, 6082-6086
Chain Growth Mechanism in Fischer-Tropsch Synthesis: A DFT Study of C-C Coupling over Ru, Fe, Rh, and Re Surfaces Jun Cheng,† P. Hu,*,† Peter Ellis,‡ Sam French,‡ Gordon Kelly,§ and C. Martin Lok§ School of Chemistry, The Queen’s UniVersity of Belfast, Belfast BT9 5AG, U.K. and Johnson Matthey Technology Centre, Reading RG4 9NH, U.K. and Billingham CleVeland, TS23 1LB, U.K. ReceiVed: NoVember 20, 2007; In Final Form: January 27, 2008
A quantitative approach is used to understand the chain growth mechanism in FT synthesis on the Ru, Fe, Rh, and Re surfaces. The C-C coupling reactions are extensively calculated on the stepped metal surfaces. Combining the coupling barriers and reactant stabilities, we investigate the reaction rates of all possible C1 + C1 coupling pathways on the metal surfaces. It is found that (i) all the transition-state structures are similar on these surfaces, while some coupling barriers are very different; (ii) the dominant chain growth pathways on these surfaces are different: C + CH and CH + CH on Rh and Ru surfaces, C + CH3 on Fe surface, and C + CH on Re surface. The common features of the major coupling reactions together with those on the Co surface are also discussed.
1. Introduction Fischer-Tropsch (FT) synthesis1-7 transforms syngas (CO + H2) into a multitude of high-molecular-weight hydrocarbons which can be converted into high-quality transportation fuels and chemicals. Because of the increasing worldwide energy demand and the limited reservoir of crude oil, a great deal of attention has been paid to this process.8-19 The FT synthesis involves an intricate reaction network composed of many surface intermediates and elementary reaction pathways. Generally, the reaction complex includes CO activation, hydrogenation of carbon-containing species and oxygen, hydrocarbon chain growth, and termination processes. Over 80 years of persistent research efforts have helped to resolve many significant issues about the overall reaction chemistry. However, the heart of the mechanism, the chain growth pathway, is still under heavy debate.3 In the literature, three mechanisms have been proposed: the carbene mechanism,20 the hydoxy-carbene mechanism,21 and the CO-insertion mechanism.22 With the development of surface science techniques,23 many CxHy species were observed on metal surfaces.24-26 Furthermore, a large volume of experimental27-29 and theoretical work30-33 provided evidence to support the carbene mechanism, which is currently the most popular of the three. The carbene mechanism, in a board sense, includes all the possible pathways of a growing chain coupling with a monomer. The traditional one proposed by Fischer and Tropsch20 is the CH2 + CH3 coupling, which may not be responsible for chain growth due to the high barrier33 and low stability of CH234,35 from density function theory (DFT) calculations. Accordingly, van Santen and co-workers31 suggested two coupling cycles (CH + CH2 and CH + CH3) on Ru(0001). They argued that CH is the most likely monomer because CH is the most stable C1 species on flat Ru(0001). Liu and Hu33 proposed the CH + CH coupling on stepped Ru(0001) due to its low barrier. Recently, we studied C-C coupling reactions on both flat and stepped †
The Queen’s University of Belfast. Johnson Matthey Technology Centre, Reading. § Johnson Matthey Technology Centre, Billingham Cleveland. ‡
Co(0001) to provide a quantitative understanding of the chain growth mechanism.36,37 The reaction rates of all possible coupling pathways were compared with consideration of both the surface concentrations of the species involved and the coupling barrier. It was found that (i) coupling reactions are generally favored on stepped surfaces, (ii) the coupling of C + CH3 and CH2 + CH2 are the major chain growth pathways for C1, and (iii) after C1 the coupling of C + CH-like (C + CR, R ) alkyl group) and CH + CH-like (CH + CR) are also important for chain growth. In this work, we will apply our quantitative approach proposed in the previous work36 to other metals with the aim of obtaining a deeper understanding of the chain growth process in the FT synthesis. The other two commonly used FT catalyst metals, Fe and Ru, are studied. We also investigate C-C coupling reactions on Rh and Re surfaces for comparison. Since surface steps have been shown to be active for C-C coupling/ breaking,36,38 we only consider C-C coupling on stepped surfaces. The paper is arranged as follows. In the next section, some calculation details will be given. Then we will show the calculation results of C1 + C1 coupling on stepped surfaces. In the Discussion, we will quantitatively analyze all the coupling channels on different metal surfaces. Finally, some conclusions will be summarized. 2. Method In this work, the SIESTA code was used with TroullierMartins norm-conserving scalar relativistic pseudopotentials.39-41 A double-ζ plus polarization (DZP) basis set was utilized. The localization radii of the basis functions were determined from an energy shift of 0.01 eV. A standard DFT supercell approach with the Perdew-Burke-Ernzerhof form of the generalized gradient approximation (GGA) functional was implemented, and the Kohn-Sham orbitals were expanded in a localized basis (double-ζ) set with a mesh cutoff of 200 Ry. All the reactions were calculated at monatomic steps with the vacuum region between slabs around 10 Å. (211) and (210) planes were used for fcc metal (Rh) and bcc metal (Fe),
10.1021/jp711051e CCC: $40.75 © 2008 American Chemical Society Published on Web 03/20/2008
C-C Coupling over Ru, Fe, Rh, and Re Surfaces
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TABLE 1: Relative Stabilities of CHi (i ) 1-3) with Respect to C Atom and Chemisorption Energies of the C Atom with Respect to Gaseous CH4 on Stepped Metal Surfacesa E1 E2 E3 ∆H
Rh
Co
Ru
Fe
Re
0.12 0.56 0.61 -1.00
0.07 0.66 0.43 -0.80
0.05 0.54 0.57 -1.19
0.37 1.32 1.09 -1.40
0.17 0.83 1.28 -2.47
a See the main text for the definition of Ei (i ) 1-3) and ∆H. The units for Ei and ∆H are eV.
respectively. For Rh and Fe, 12-layer slabs were employed with the bottom 6 layers of metal atoms fixed, relaxing the top 6 layers of metal atoms and adsorbates. In most of the calculations, p(1 × 2) unit cells were utilized and the surface Monkhorst Pack meshes of 4 × 5 × 1 k-point sampling in the surface Brillouin zone were used for Rh(211), and p(2 × 1) unit cells were utilized and the surface Monkhorst Pack meshes of 4 × 4 × 1 k-point sampling were used for Fe(210). In a few cases (the coupling of CH2 + CH2 and CH3 + CH2), larger unit cells were employed to avoid the interaction between the adsorbates in neighboring unit cells: p(1 × 3) unit cells with the 4 × 3 × 1 k-point sampling for Rh and p(3 × 1) unit cells with the 3 × 4 × 1 k-point sampling for Fe. Since no low-index plane has a monatomic step structure for hcp metals (Ru and Re), surface defects were modeled by removing two neighboring rows of metal atoms in the top layer on close-packed (001) surfaces. For Ru and Re, four-layer slabs were used with the bottom two layers fixed and the top two layers and adsorbates relaxed. Usually, p(4 × 2) unit cells were utilized and the surface Monkhorst Pack meshes of 3 × 5 × 1 k-point sampling were used for these hcp metal surfaces. In calculating the coupling of CH2 + CH2 and CH3 + CH2, p(4 × 3) unit cells with 3 × 4 × 1 k-point sampling were utilized. Spin polarization was included in the calculations on the Fe surface. More calculation details can be found in our previous work, and the accuracy of the calculation method and model was also fully checked therein.36,42 The transition states (TSs) were searched using a constrained optimization scheme.43-45 The distance between the reactants is constrained at an estimated value, and the total energy of the system is minimized with respect to all the other degrees of freedom. The TSs can be located via changing the fixed distance and must be confirmed by the following two rules: (i) all forces on atoms vanish and (ii) the total energy is a maximum along the reaction coordinate but a minimum with respect to the rest of the degrees of freedom. 3. Results 3.1. Chemisorption at Step Sites. In the work of Gong, Raval, and Hu,34 the adsorption of CHi (i ) 0-3) and H was studied on stepped Co(0001). It was found that (i) the most stable site of C and CH is the corner site; (ii) for CH2 and CH3 it is the edge-bridge site; and (iii) H is favored on the nearedge-hcp site. We further studied the adsorption of C1 species and H at step sites on Ru, Rh, Fe, and Re surfaces. The calculated structures are very similar to those on stepped Co(0001). In Table 1, we list the relative stabilities of CHi (i ) 1-3, Ei) with respect to the C atom on the five stepped metal surfaces (Rh, Co, Ru, Fe, and Re). Ei (i ) 1-3) is defined as the total energy difference between CHi + (4 - i)H and C + 4H adsorbed on the metal surfaces. For example, the relative stability of CH, E1, is equal to the energy difference between CH + 3H and C + 4H on surfaces. The larger it is, the less
stable the C1 species. From Table 1, we can see that on the five stepped metal surfaces the C atom is the most stable C1 species, CH is slightly less stable than the C atom, and CH2 and CH3 are much more unstable compared with C and CH. It should be mentioned that this trend of the stability is slightly different from flat metal surfaces. For example, CH was found to be the most stable C1 species on flat Co(0001) and Ru(0001).34,35 To measure the chemical activity of these metals toward CH4 dissociative chemisorption, chemisorption energies of C + 4H (∆H) with reference to gaseous CH4 are also listed in Table 1. Note that ∆H is negative when a chemisorption process is exothermic: The more negative the value, the stronger the bonding and thus the more active the metal surface. Two features can be found in Table 1: (i) the stability of CH (E1) with respect to adsorbed C atom changes only slightly on different metal surfaces and (ii) in contrast, the relative stability of CH2 (E2) and CH3 (E3) vary considerably, generally increasing with the metal activity. These findings can be rationalized by the valency number of CHi (i ) 0-3). Since the bonding between CHi and the metal surface is mostly covalent in nature, the higher the valency is, the more sensitive the bonding strength is to the metal activity. Thus, the bonding strength of C and CH are affected greatly by the metal activity, while for CH2 and CH3 the changes are small. Hence, the energy difference between C and CH is almost constant, leading to the small change in the relative stability of CH, while the relative stability of CH2 (E2) and CH3 (E3) change considerably. 3.2. C1 + C1 Coupling at Step Sites. C-C coupling reactions on both flat and stepped Co(0001) were extensively studied in our previous work.36,37 Generally, C-C coupling reactions are favored at step sites. Therefore, we further calculated C1 + C1 coupling reactions on stepped Rh, Ru, Fe, and Re surfaces. From our calculations, it is found that the transition-state (TS) structures of C1 + C1 coupling reactions on stepped Rh, Ru, Fe, and Re surfaces are very similar to those on the stepped Co surface reported previously.36 In Figure 1a-i we show the calculated TS structures on Rh(211). As we can see, C and CH are usually on the high coordination sites: 4-fold corner site and 3-fold hcp hollow site on the lower terrace, respectively. For example, at the TSs of the coupling of C + C, C + CH, and C + CH2, C is always on the hcp hollow site with the other reactants on the edge-bridge site; when C reacts with CH3, it even stays on the corner site. At the TSs of the coupling of CH + CH and CH + CH2, CH is on the hcp hollow site, and for the CH + CH3 coupling, CH is on the corner site, being similar to C + CH3. When CH couples with C, it is activated to the edge-bridge site. Except CH3 is on the off-top site at the TS of the CH2 + CH3 coupling, CH2 and CH3 are always on the edgebridge site. It is worth noting that the calculated TS structures completely agree with the rule proposed by Michaelides and Hu:46 The higher the valency of the adsorbate, the greater its tendency to access a TS close to a high coordination site. The calculated coupling barriers and C-C distances (dC-C) at TSs are listed in Table 2. The previous results on stepped Co(0001)36 are also given for comparison. Since the TS structures of C1 + C1 coupling reactions are very similar, the change of C-C distances at TSs with different metal surfaces is very small. For example, for the CH + CH3 coupling, the biggest difference of dC-C is only 0.06 Å. In contrast, the barriers of some C1 + C1 coupling reactions vary greatly with different metal surfaces. For example, the barriers of the CH2 + CH2 coupling change from 0.27 to 1.42 eV. For the coupling of C + CH2 and CH + CH2, the variation is less than 0.5 eV. With consideration of the similar initial state (IS) and TS structures,
6084 J. Phys. Chem. C, Vol. 112, No. 15, 2008
Cheng et al.
Figure 1. Top view and side view (inserted) of the TS structures of C1 + C1 coupling reactions on Rh(211): (a) C + C; (b) C + CH; (c) C + CH2; (d) C + CH3; (e) CH + CH; (f) CH + CH2; (g) CH + CH3; (h) CH2 + CH2; (i) CH2 + CH3. The big balls are Rh atoms, the small gray ones are C atoms, and the small white ones are H atoms.
TABLE 2: Barriers (Ea) and C-C Distances (dC-C) at the TSs of the C1 + C1 Coupling Reactions on Stepped Metal Surfacesa Rh
Co
Ru
Fe
Re
C-C Ea C-C Ea C-C Ea C-C Ea C-C Ea C+C C + CH C + CH2 C + CH3 CH + CH CH + CH2 CH + CH3 CH2 + CH2 CH2 + CH3
2.26 2.43 2.25 1.99 2.12 2.16 1.92 1.99 2.03
2.26 1.66 1.58 1.50 1.44 1.56 1.60 0.86 0.87
2.31 2.63 2.52 1.97 2.27 2.26 1.91 2.16 2.01
2.46 1.96 1.36 1.12 1.74 1.34 1.57 0.27 0.76
2.30 2.38 2.23 2.02 2.19 2.17 1.91 1.99 1.95
1.80 1.29 1.13 1.28 1.26 1.25 1.62 0.92 1.17
2.35 2.41 2.26 2.01 2.28 2.24 1.97 2.16 2.13
2.93 2.15 1.12 1.10 2.04 1.25 1.41 0.27 0.78
2.29 2.29 2.22 1.92 2.13 2.15 1.93 1.92 1.98
2.23 1.64 1.53 1.93 1.68 1.69 2.60 1.42 1.66
a The units for the barrier are eV, and the units for the distance are Å.
the large variations of barriers are surprising. This may be because the potential-energy surfaces of CHi (i ) 0-3) are quite different from one metal surface to the other. 4. Discussion Recently, our DFT calculations showed that CH3 hydrogenation is the slowest step in the sequence of C hydrogenation on Co surface,36 which is consistent with experimental work.26 The preceding hydrogenation steps may reach quasi-equilibrium. Thus, the coverages of surface species CHi (i ) 1-3) can be referenced to the C coverage as follows
θCHi ) e-(Ei/RT)θC
θiH θi*
) e-(Ei/RT)θCti, i ) 1-3
(1)
where θCHi, θH, and θ* are the coverage of CHi, H, and free surface site, respectively, t is equal to θH/θ*, and Ei is the relative stability of CHi with reference to the C atom (see section 3.1). It should be mentioned that the ratio of H to free surface site
coverage, t, is related to the H2 partial pressure and H chemsorption energy. Our previous work36 showed that it is about 1 on the Co surface under typical reaction conditions. Since H chemisorption energy hardly changes on different metal surfaces, we expect that t may be constant. According to transition-state theory (TST), the C1 + C1 coupling reaction rate can be expressed as
rCHi+CHj ) Ae-(Ei/RT)θCHiθCHj, i, j ) 0-3
(2)
where Ei,j is the barrier of the CHi + CHj coupling reaction and A is the pre-exponential factor. Substituting eq 1 into eq 2, we can obtain the following equation
rCHi+CHj ) Ae-[(Ei,j+Ei+Ej)/RT]ti+jθC2, i, j ) 0-3
(3)
For surface chemical reactions,47 the pre-exponential factor A is usually about 1013. Parameter t is about 1 and can be ignored. On the same metal surface, C coverage is the same. Therefore, it can be found from eq 3 that the reaction rate of each C1 + C1 coupling pathway is mainly determined by Ei,j + Ei + Ej, the barrier of the coupling reaction, and the stabilities of the reactants. It should be mentioned that under typical FT reaction conditions the C + C coupling reactions are usually considered to be irreversible.48,49 Thus, the reverse reactions of C + C coupling are omitted in our discussion. From the results listed in Tables 1 and 2, we calculate the values of Ei,j + Ei + Ej of C1 + C1 coupling reactions on the five metal surfaces, which are listed in Table 3. The previous results on stepped Co(0001)36 are also included. According to Table 3, on the Rh and Ru surfaces, the coupling of C + CH and CH + CH are the most important; on the Co surface, C + CH3 and CH2 + CH2 are the fastest; on the Fe and Re surfaces, there is only one major coupling pathway, C + CH3 and C + CH, respectively. The values of Ei,j + Ei + Ej of the fastest coupling pathways are displayed in bold in Table 3. These values
C-C Coupling over Ru, Fe, Rh, and Re Surfaces
J. Phys. Chem. C, Vol. 112, No. 15, 2008 6085
TABLE 3: Values of Ei,j + Ei + Ej of the C1 + C1 Coupling Reactions on Stepped Metal Surfacesa C+C C + CH C + CH2 C + CH3 CH + CH CH + CH2 CH + CH3 CH2 + CH2 CH2 + CH3
Rh
Co
Ru
Fe
Re
2.26 1.78 2.14 2.11 1.68 2.24 2.34 1.97 2.04
2.46 2.04 2.02 1.55 1.89 2.07 2.08 1.59 1.86
1.80 1.34 1.67 1.84 1.36 1.84 2.23 2.00 2.28
2.93 2.52 2.45 2.19 2.79 2.94 2.87 2.91 3.20
2.23 1.81 2.35 3.21 2.02 2.69 4.06 3.08 3.77
a The values in bold highlight the important coupling pathways on each metal surface. The units for Ei,j + Ei + Ej are eV.
are usually several tenths of electronvolts smaller than the others. Note that a difference of Ei,j + Ei + Ej as small as 0.1 eV will change the reaction rate 10 times at 500 K. Thus, the reaction rates of these coupling pathways are several orders of magnitude faster than the others. Namely, these coupling pathways dominate the chain growth rate, and the other pathways may be neglected. Two very interesting findings can be obtained from Table 3. First, the major C1 + C1 coupling pathways are different on different metal surfaces except for Rh and Ru (C + CH and CH + CH). This can be attributed to two facts: (i) the relative stability of the C1 species varies considerably on the different metal surfaces (see Table 1) and (ii) the coupling barriers are also quite different on different metal surfaces (see Table 2). Second, all the major coupling pathways are the following four coupling reactions: C + CH, CH + CH, C + CH3, and CH2 + CH2. Considering the complicated nature of Ei,j + Ei + Ej, this observation is surprising. More interestingly, these four coupling types are exactly the same as the major coupling pathways after C1 on stepped Co(0001).35,37 It was reported in a previous paper37 that on stepped Co(0001) the coupling of C + CH-like (C + CR, R ) alkyl group) and CH + CH-like have smaller barriers than the coupling of C + CH and CH + CH, leading to these two coupling reactions being as important as the coupling of C + CH3-like and CH2 + CH2-like after C1. This may also be true on the Fe surface. We calculated the C + CH3C coupling and found that its barrier is 1.58 eV, 0.57 eV smaller than that of C + CH (2.15 eV). It means that the C + CH-like coupling may become even faster than the C + CH3-like coupling after C1 on the Fe surface. From Table 3, one can see that on the Rh, Ru, and Re surfaces the couplings of C + CH and CH + CH are the fastest channels. After C1 smaller barriers of these two coupling types will lead to them being even faster. Thus, we can see that all the major chain growth pathways on the five metal surfaces involve the coupling types of C + CH and/or CH + CH. One reason for these two coupling types being major pathways is that the reactants (C, CH, and CH-like species) are very stable on these metal surfaces. For example, on all five metal surfaces C is the most stable C1 species and CH is only slightly less stable than C (see Table 1). In contrast, both CH2 and CH3 are much more unstable. Unless the coupling reactions involving CH2 or CH3 have very small barriers, these pathways will be less important. For instance, one can see from Table 3 that the coupling of CH2 + CH2 and CH2 + CH3 on the Fe and Re surfaces may be about 10 orders of magnitude slower than the corresponding major coupling pathway. The coupling of CH2 + CH2 on the stepped Co surface is an exception: It is one of the major chain growth pathways due to its very low barrier (0.27 eV). The other reason, as we can see from Table 2, is that the coupling of C + CH and CH + CH possesses moderate barriers. In the C + C
coupling reactions, the reactant, C atom, is the most stable yet the barriers are too high, resulting in them being insignificant. Two points should be noted: First, in eq 3 ti+j can change the reaction rate of each coupling pathway (i + j is the sum of H numbers in the reactants). An increase of parameter t (via, for example, increasing H2 partial pressure) can improve the contributions of coupling pathways involving high H numbers (e.g., CH2 + CH2 and CH2 + CH3) to the whole chain growth rate. Nevertheless, unless the change of parameter t is dramatic, its effect may be still trivial compared with Ei,j + Ei + Ej. Second, the coverage effect is not included in calculating the relative stabilities and coupling barriers. However, the coadsorption of C1 species was calculated on stepped Co surface in our previous work.34 It was found that the energy loss due to coadsorption is small (less than 0.3 eV). Regarding surface reaction barriers, the surface coverage may affect ISs and TSs in a similar manner, and hence, the effects may be cancelled to a large extent. As a result, the reaction barriers may not change considerably. After examining the chain growth pathways in such a quantitative manner, it can be seen that the traditional mechanism,20 the CH2 + CH3 coupling, is not the preferred pathway on the five metal surfaces. The main problem is the low stability of the reacting species (see Table 1). The two coupling cycles on Ru(0001), CH + CH2 and CH + CH3, proposed by van Santen and co-workers31 are also not among the major chain growth pathways. Although they noticed that CH is the most stable intermediate on flat Ru(0001) and likely to be the monomer, the other intermediates are not found to be stable. Therefore, they are not considered to be major pathways. Interestingly, the mechanism C + CH on stepped Ru(0001), proposed by Liu and Hu,31 is one of the major pathways demonstrated in this work. 5. Conclusions In this work we carried out extensive DFT calculations to investigate C-C coupling reactions on four metal surfaces (Rh, Ru, Fe, and Re). On the basis of quantitative analyses, we now have a better understanding on chain growth mechanisms in FT synthesis. Some of the main findings are summarized as follows. (i) On the five stepped surfaces, the C atom is the most stable C1 species, CH is slightly less stable than the C atom, and CH2 and CH3 are quite unstable. The relative stability of CH with reference to the C atom changes very little on different metal surfaces, while the stability of CH2 and CH3 with respect to C varies greatly. (ii) The calculated TS structures of coupling reactions are very similar on different stepped metal surfaces. In contrast, the barriers differ considerably from one surface to the other. (iii) For C1 + C1 coupling, the major chain growth pathways are different on different metal surfaces: C + CH and CH + CH on Rh and Ru surfaces, CH2 + CH2 and C + CH3 on the Co surface (ref 36), C + CH3 on the Fe surface, and C + CH on the Re surface. (iv) Although the determining factors of the coupling reaction rate (see eq 3) are intricate, the major chain growth channels are always among the coupling of C + CH, CH + CH, CH2 + CH2, and C + CH3 on these metal surfaces. In particular, the coupling of C + CH-like and CH + CH-like should play an important role in chain growth on the five metal surfaces. Acknowledgment. We gratefully thank The Queen’s University of Belfast for computing time. J.C. acknowledges Johnson Matthey for financial support.
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