An Energy Descriptor To Quantify Methane Selectivity in Fischer

8858

J. Phys. Chem. C 2009, 113, 8858–8863

An Energy Descriptor To Quantify Methane Selectivity in Fischer-Tropsch Synthesis: A Density Functional Theory Study Jun Cheng,† P. Hu,*,† Peter Ellis,‡ Sam French,‡ Gordon Kelly,§ and C. Martin Lok§ School of Chemistry and Chemical Engineering, The Queen’s UniVersity of Belfast, Belfast BT9 5AG, United Kingdom, Johnson Matthey Technology Centre, Reading RG4 9NH, United Kingdom, and Johnson Matthey Technology Centre, Billingham CleVeland, TS23 1LB, United Kingdom ReceiVed: February 5, 2009; ReVised Manuscript ReceiVed: April 8, 2009

Selectivity is a fundamental issue in heterogeneous catalysis. In this study, the CH4 selectivity in Fischer-Tropsch synthesis is chosen to be investigated: CH4 selectivity on Rh, Co, Ru, Fe, and Re surfaces is computed by first-principles methods. In conjunction with kinetic analyses, we are able to derive the effective barrier difference between methane formation and chain growth (∆Eeff) to quantify the CH4 selectivity. By using this energy descriptor, the ranking of methane selectivity predicted from density functional theory (DFT) calculations is consistent with experimental work. Moreover, a linear correlation between ∆Eeff and the chemisorption energy of C + 4H (∆H) is found. This fundamental finding possesses the following significance: (i) it shows that the selectivity, which appears to have kinetic characteristics, is largely determined by thermodynamic properties; and (ii) it suggests that an increase of the binding strength of C + 4H will suppress methane selectivity. 1. Introduction Selectivity is one of the most important issues in heterogeneous catalysis. Despite its significance, understanding of this issue still falls well short of chemists’ expectations: selectivity in many catalytic systems has not been well understood at a level that many chemists would like. In this work, we use methane selectivity as an example to tackle this fundamental issue. Methane selectivity in Fischer-Tropsch (FT) synthesis was chosen for the following reasons. First, it is one of the most complicated systems in heterogeneous catalysis, and any approaches developed from this one may be extended to other systems. Second, the production of hydrocarbons from synthesis gas (CO + H2) in FT synthesis1-10 over transition metals is one of the most promising sources of transportation fuels (gasoline and diesel) and chemicals (in particular, 1-alkenes) from non-petroleum-based feedstocks such as natural gas, biomass, and coal. In FT technology, synthesis gas production via steam re-forming typically accounts for 60∼70% of the capital and the running costs of the total plant. Hence, maximum utilization of synthesis gas in the downstream FT reactors is very important. The formation of CH4, however, is inevitable in FT synthesis. It is totally wasteful because it reverses the steam re-forming process. Therefore, suppressing CH4 formation is of paramount importance in FT synthesis. In this work, we investigate CH4 selectivity over several transition metals (Rh, Co, Fe, Ru, and Re) from density functional theory (DFT) calculations, and we provide insight into how to suppress CH4 selectivity. Ru, Fe, and Co are the most active catalyst metals for FT synthesis. Of the three metals, Ru has the best activity and selectivity. However, the low availability and high cost of Ru * Corresponding author. † The Queen’s University of Belfast. ‡ Johnson Matthey Technology Centre, Reading. § Johnson Matthey Technology Centre, Billingham Cleveland.

eliminate its use for large-scale applications. Thus, only Fe and Co have been used in industry. Although Co-based catalysts are more expensive than Fe ones, they are more resistant to deactivation. Hence, Co-based catalysts appear to be the optimal choice for synthesis of long-chain hydrocarbons due to its high stability, activity, and selectivity, and huge efforts have been dedicated to Co-based catalysts in the past decade.11-24 The major disadvantage of Co-based catalysts is that they are too hydrogenating and produce more CH4 than Fe-based catalysts. Therefore, modification of Co-based catalysts to decrease CH4 selectivity will lead to huge commercial profits. Vannice25 observed that the average hydrocarbon molecular weight produced in FT synthesis decreases in the order Ru > Fe > Co > Rh > Ni > Ir > Pt > Pd. This result can also be interpreted as the CH4 selectivity increases in the order Ru < Fe < Co < Rh < Ni < Ir < Pt < Pd. However, the following questions need to be answered in the field: (i) What is the key factor that leads to this ranking of CH4 selectivity? (ii) Is there an intrinsic property of metal surfaces controlling the ranking? (iii) If the answer to the second question is yes, how can it be used as a guide to suppress CH4 selectivity? Aiming to answer these questions, we choose metallic Re, Ru, Fe, Co, and Rh to study CH4 selectivity in this work. It should be mentioned that it was found experimentally that iron carbide is the active phase for FT reactions in Fe-based catalysts.26 In the present study, we use only metallic Fe as a model system to understand the intrinsic trend of CH4 formation and chain growth processes on transition metals. Re is also investigated for the same purpose. The paper is arranged as follows: In the next section, calculation details will be described. Following this, the calculation results of CH4 formation on the stepped metal surfaces will be presented, and the reaction rate of CH4 formation and chain growth will be evaluated and thus CH4 selectivity will be discussed. In the last section, some conclusions will be summarized.

10.1021/jp901075e CCC: $40.75  2009 American Chemical Society Published on Web 04/29/2009

Energy Descriptor To Quantify Methane Selectivity 2. Methods In this work, the SIESTA code was used with Troullier-Martins norm-conserving scalar relativistic pseudopotentials.27-29 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. The accuracy of the setting was tested in our previous work.30 All the reactions were calculated at defects, that is, B5 sites. (211) and (210) planes were used for face-centered cubic (fcc) metal (Rh) and body-centered cubic (bcc) metal (Fe), respectively. In these cases, 12 layer slabs were employed with the bottom six layers of metal atoms fixed, while the top six layers of metal atoms and adsorbates were relaxed. For hexagonal close-packed (hcp) metals (Ru, Co, 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, Co, and Re, four-layer slabs were used with the bottom two layers fixed and the top two layers and adsorbates relaxed. Unit cell sizes were chosen to ensure that the surface species and their neighbors do not share bonding with the same metal atoms. Namely, half the surface step sites were occupied for all the surfaces in our calculations. Spin polarized calculations were applied on Fe and Co surfaces. Sufficient k-point samplings were carefully chosen for different sizes of unit cells to ensure good accuracy. Transition states (TSs) were searched by use of a constrained optimization scheme.31-33 The distance between the reactants is constrained at an estimated value, and the total energy of the system is minimized with respect to all 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 remaining degrees of freedom. 3. Results and Discussion 3.1. CH4 Formation. Aiming to investigate CH4 selectivity, we first study CH4 formation, that is, C + 4H f CH + 3H f CH2 + 2H f CH3 + H f CH4, on Rh, Ru, Fe, and Re surfaces. The chemisorption of C1 species and the transition states (TSs) of hydrogenation reactions are computed. It is found that the optimized structures are generally in line with the work of Gong et al.34 on stepped Co surface except that the preferred adsorption site of CH2 on stepped Fe surface is the corner site at steps, different from the edge-bridge site on the other surfaces. The energy profiles of C hydrogenation to CH4 from our DFT results are plotted and shown in Figure 1a. It is interesting to see from Figure 1a that the total energy of the TS increases in a stepwise manner along the hydrogenation coordinate. This means that the last step has the highest TS energy, indicating that CH3 hydrogenation is the rate-determining step of C hydrogenation to CH4.30,35,36 It should be pointed out that this finding is consistent with the experimental result.37 Interestingly, similar stepwise-increasing energy profiles were also found in the sequential hydrogenation reactions of CO to methanol.38 Hence, the preceding hydrogenation steps may reach quasi-equilibrium, and the coverages of the C1 species (θCHi) can be expressed with respect to the C coverage (θC) on these stepped surfaces (see ref 16 for derivation detail):

J. Phys. Chem. C, Vol. 113, No. 20, 2009 8859

θCHi ) e-Ei ⁄ RTθC(θH ⁄ θ*)i ) e-Ei ⁄ RTθCti

i ) 0, 1, 2, 3

(1) where t is the ratio of H coverage to free surface site coverage (θH/θ*), and Ei is the energy difference between adsorbed CHi and C + iH, as illustrated in Figure 1b. Parameter t is determined by the standard free energy change of H2 adsorption and the H2 partial pressure, provided that the process is equilibrated under reaction conditions. This is because H2 dissociative adsorption is spontaneous on most transition metals (on late transition metals, such as Cu, it possesses a small barrier). We calculated the free energy change on the Co surface in our recent work30 and found that parameter t is around 1 under typical reaction conditions. When the temperature was 500 K, t was estimated to be 1-5 when H2 partial pressure was 1-25 atm. It is well-known that H adsorption energy varies in a very narrow range on transition metals,39 and hence it is expected that the values of t on the other four metal surfaces are similar to that on the Co surface. Therefore, the effect of t will be ignored in our following discussions. The CH4 formation rate (rCH4) can be expressed as

rCH4 ) Ae-Ea

θCH3θH ) Ae-(Ea

hy⁄RT

hy+E

3)

t θCθH )

⁄ RT 3

Ae-Eeff,CH4 ⁄ RTt3θCθH (2) where θCH3 is evaluated by use of eq 1, A is the pre-exponential factor, and Eahy is the reaction barrier to CH3 hydrogenation. The pre-exponential factor A is usually around 1013 for surface reactions (adsorption and desorption excluded), which appears a reasonable approximation.40 Eeff,CH4, being equal to Eahy + E3,

Figure 1. (a) Energy profiles of C hydrogenation to CH4 on stepped Re, Fe, Ru, Co, and Rh surfaces. The total energy of CH4 in the gas phase is chosen as the zero point. (b) Schematic illustration of the effective barrier to CH4 formation (Eeff, CH4). The red drawing shows how the binding strength of C + 4H on surfaces influences Eeff, CH4. Note that adsorbed H is not shown in the reaction coordinate.

8860

J. Phys. Chem. C, Vol. 113, No. 20, 2009

Cheng et al.

TABLE 1: Effective Barriers and Chemisorption Energies on Stepped Metal Surfacesa Eeff,CH4 Eeff,C-C ∆Eeff ∆H

Rh

Co

Ru

Fe

Re

1.23 1.68 -0.45 -1.00

1.31 1.55 -0.24 -0.80

1.44 1.34 0.10 -1.19

2.13 2.19 -0.06 -1.40

2.50 1.81 0.69 -2.47

a Eeff,CH4, Eeff,C-C, and ∆Eeff are the effective barriers to CH4 formation and chain growth and their difference, respectively. ∆H is the chemisorption energy of C + 4H with respect to gaseous CH4. Note that the more negative ∆H is, the stronger the binding is. The unit is electronvolts.

is defined as the effective barrier to CH4 formation, as illustrated in Figure 1b (in black). The values of Eeff,CH4 on the five metal surfaces are computed and given in Table 1. 3.2. C1 + C1 Coupling. Because CH4 formation competes with C-C coupling reactions, the rate of each coupling pathway must be evaluated in order to determine CH4 selectivity. Recently, using DFT calculations we studied chain growth processes in FT synthesis, that is, C + C coupling reactions, on stepped Rh, Co, Fe, Ru, and Re surfaces and quantitatively determined the major coupling pathways on each metal surface.30,35,36 It was found that the major chain growth pathway can vary from one surface to the other, but the fastest pathways are always among the four coupling reactions of C + CH, CH + CH, CH2 + CH2, and CH3 + C. For a general coupling reaction, one can write30,35,36

rCHi+CHj ) Ae-Ei,j ⁄ RTθCHiθCHj ) Ae-(Ei,j+Ei+Ej) ⁄ RTti+jθC2 i, j ) 0 ∼ 3

(3)

where θCHi and θCHj are evaluated by use of eq 1 and Ei,j is the barrier to CHi + CHj coupling reaction. As we can see, the rate of each coupling pathway is mainly determined by Ei,j + Ei + Ej. By comparison of the values of Ei,j + Ei + Ej for each pathway, the major chain growth pathways were identified on the five metal surfaces. In principle, the total chain growth rate should be equal to the sum of all these coupling channels. Since the reaction rates of other coupling channels are smaller than the major one, we can consider only the fastest channel to describe the total chain growth rate (rC-C). Thus

rC-C )

∑ rCH +CH ) ∑ Ae-(E

i, j+Ei+Ej)

i, j

i

j

t θC2 ≈

⁄ RT i+j

i, j

-(Ei, j+Ei+Ej) ⁄ RT i+j

max[Ae

t θC2] ) Ae-[min(Ei,j+Ei+Ej)] ⁄ RTti+jθC2 ) Ae-Eeff,C-C ⁄ RTti+jθC2

(4)

Eeff,C-C stands for the effective barrier to the chain growth process, which is identical to the minimum of Ei,j + Ei + Ej on each metal surface. It should be noted that the effective barrier, Eeff,C-C, contains not only the barrier (Ei,j) but also information on relative concentrations of coupling species, CHi and CHj, which is reflected in Ei and Ej. The effective barriers on the five metal surfaces are listed in Table 1: Ei,j + Ei + Ej of CH + CH on Rh surface, C + CH3 on Co and Fe surfaces, and C + CH on Ru and Re surfaces. It should be mentioned that contributions to the chain growth corresponding to other mechanisms involving oxygenate intermediates, that is, the hydroxycarbene and CO-insertion mechanisms, are neglected because their contributions may be small compared with the carbide mechanism (C-C coupling). In our recent work, we showed that the key intermediate (CHOH) in the hydroxycarbene mechanism is very unstable, and CH3 +

CO reaction in the CO-insertion mechanism possesses a high barrier on Co surface. By comparing them to the C-C coupling, we found that these two mechanisms cannot compete with the carbide mechanism. Interestingly, recent work of Inderwildi and co-workers41,42 found an alternative route of C-O bond cleavage followed by hydrogenation of adsorbed CO, rather than direct CO dissociation, on the flat Co surface. In this route, oxygenate intermediates CHO and CH2O play an important role in breaking the C-O bond. Thus, the first step (C-O bond cleavage) in the traditional carbide mechanism may need to be modified. 3.3. CH4 Selectivity. To quantify the CH4 selectivity on each metal surface, we employ the ratio of CH4 formation rate to chain growth rate. By combination of eqs 2 and 4, the ratio can be written as

rCH4 ⁄ rC-C )

Ae-Eeff,CH4 ⁄ RTt3θCθH Ae-Eeff,C-C ⁄ RTti+jθC2

)

t3-i-j(θH ⁄ θC)e-(Eeff,CH4-Eeff,C-C) ⁄ RT ) t3-i-j(θH ⁄ θC)e-∆Eeff ⁄ RT

(5) where ∆Eeff is the difference between effective barriers to CH4 formation and chain growth. Since it was found that parameter t is around 1 under typical FT reaction conditions,30 it can be approximately omitted. The ratio of H to C coverages, θH/θC, is quite complicated; it is determined by the balance between CO activation, chain growth, and termination processes. It is strongly related to catalyst surface and reaction conditions (such as H2/CO ratio, pressure, and temperature). Estimation of θH/ θC is beyond the scope of this paper. Nevertheless, it is still worth pointing out how θH/θC varies. On earlier transition metals, CO easily dissociates, thus forming more C atoms and leading to lower θH/θC and lower methane selectivity. Most importantly, rCH4/rC-C, as shown in eq 5, depends on ∆Eeff exponentially. If ∆Eeff changes by 0.1 eV, rCH4/rC-C will change 10-fold at 500 K. Therefore, it is expected that ∆Eeff is more important than θH/θC and t and may be a good descriptor to qualitatively measure the CH4 selectivity on different metal surfaces. A metal surface with a small ∆Eeff may have a high CH4 selectivity, and the surface with a large ∆Eeff should be good for production of long-chain hydrocarbons. From the effective barriers to CH4 formation and chain growth, the values of ∆Eeff are calculated and listed in Table 1. As we can see, ∆Eeff increases in the order Rh < Co < Fe < Ru < Re, which indicates that the CH4 selectivity decreases in the order Rh > Co > Fe > Ru > Re. It is worth mentioning that the comparison is conducted at the same temperature. Interestingly, the order of the selectivity on Rh, Co, Fe, and Ru agrees well with experimental work of Vannice.25 For Rh, Co, and Ru, their effective barriers to CH4 formation and chain growth appear to be quite close, but some differences can still be clearly seen in our quantitative comparison: (i) Eeff,CH4 of Ru is the largest, followed by Co and then Rh. It means that CH4 formation is the easiest on Rh and the most difficult on Ru, and Co is in the middle. (ii) Eeff,C-C follows the order opposite to Eeff,CH4. This implies that Ru is the best for C-C coupling reactions and Rh is the worst. Both aspects strongly suggest that Ru is the best catalyst for hydrocarbon formation, Co is a moderate one and Rh has the highest CH4 selectivity. For Fe, both Eeff,CH4 and Eeff,C-C are much higher than those on Rh, Co, and Ru. In other words, methanation is difficult on Fe because of its high Eeff,CH4. But a high Eeff,C-C counteracts this positive effect. As a result, the CH4 selectivity on Fe is

Energy Descriptor To Quantify Methane Selectivity

Figure 2. Plots of the effective barriers to CH4 formation (Eeff,CH4, blue) and chain growth (Eeff,C-C, green) and their difference (∆Eeff, red) as a function of the binding strength of C + 4H (∆H) on stepped Re, Fe, Ru, Co, and Rh surfaces. The calculated values are given in Table 1.

higher than that on Ru. Re could have the lowest CH4 selectivity of the five metals because it has a very high Eeff,CH4 and moderate Eeff,C-C. Regarding eq 5, there are two points worth noting: (i) The entropy effect that is in the pre-exponential factor A is small for surface reactions if no gaseous species is involved in the initial state and transition state. Both CH4 formation and chain growth belong to this case. Thus, the pre-exponential factors for these two processes may be canceled. (ii) Although the reaction barriers and energetics of surface carbon species were calculated at low surface coverages, the coverage effect (lateral interaction) may have a limited impact on our results: For surface reaction barriers, the lateral interactions between initial state/transition state and the surrounding species are similar and the lateral interaction effect will be considerably reduced due to the cancellation. For the same reason, the lateral interaction effect on the relative energetics of surface species, such as the energy difference between adsorbed C and C + H, should be small. Moreover, we studied the coadsorption of C1 species at steps on a Co surface in our recent work,24 which showed that coadsorption has small effects on the adsorption energies of C1 species. 3.4. Insight into the Energy Descriptor and Suppressing CH4 Selectivity. If the reaction coordinate from C + 4H (IS) to CH4 (FS) is considered, according to our recent work,43 the TS of CH3 hydrogenation (the last hydrogenation step) is much more like the final state (FS) than the initial state (IS). In other words, changing the binding strength of C + 4H on the surface will not much affect the energy of the TS of CH3 hydrogenation. This is depicted in Figure 1b (in red). As we can see, lowering the total energy of C + 4H on surfaces (increasing the binding strength) does not decrease the total energy of the TS of CH3 hydrogenation very much. Consequently, the effective barrier to methanation (Eeff,CH4) will increase. Hence, enhancing the binding strength can increase the barrier to CH4 formation, thereby hindering the production of CH4. The calculated chemisorption energies of C + 4H with respect to gaseous CH4 (∆H) on these surfaces are listed in Table 1. From Table 1, we can see that Eeff,CH4 increases as ∆H decreases. In fact, there is a linear relationship between Eeff,CH4 and ∆H, as shown in Figure 2 (in blue). However, we have not found a similar correlation between the effective barrier to chain growth (Eeff,C-C) and ∆H. For example, on the Re surface the chemisorption of C + 4H is the

J. Phys. Chem. C, Vol. 113, No. 20, 2009 8861

Figure 3. Schematic illustration on how binding strength on surfaces affects activity and CH4 selectivity.

strongest among the five metals, leading to the highest Eeff,CH4, and yet Eeff,C-C is even smaller than that on the Fe surface (see Table 1). Nevertheless, it is noticed that while ∆H changes considerably from one surface to the other, Eeff,C-C varies in a narrow range, except that it is slightly higher on the Fe surface. The relationship between Eeff,C-C and ∆H is displayed in Figure 2 (in green). Thus, it is not surprising that the difference between Eeff,CH4 and Eeff,C-C (∆Eeff) correlates well with ∆H, as shown in Figure 2 (in red). This is a fundamental finding for the following reasons: First, ∆Eeff containing barriers is a kinetic term in nature and ∆H is a thermodynamic property, and the linear relationship between them suggests that the selectivity appearing to be a result of reaction kinetics is mainly determined by the thermodynamic property. Second, this linear relationship tells us how to suppress CH4 selectivity: A decrease of ∆H, that is, increasing the binding strength of C + 4H on surfaces, can enhance ∆Eeff and reduce CH4 selectivity. 3.5. General Discussion. It should be emphasized that the rate of each pathway must be considered rather than only barriers to elementary steps being compared. It is also worth noting that selectivity should be considered in conjunction with activity for any catalytic system. It is well-established from previous work43-46 that a volcano curve can be obtained by plotting the activity of catalysts for a certain catalytic reaction against the chemisorption energy of the key intermediate, as illustrated in Figure 3. A good catalyst should have a moderate binding strength: neither too strong nor too weak. Thus, the chemisorption energy is a very useful parameter to measure the activity of catalysts. In this work, we further demonstrate that selectivity is also related to the chemisorption energy. Strong chemisorption of C + 4H on the surface can suppress CH4 selectivity. Considering both activity and selectivity in FT synthesis (Figure 3), we can obtain the following understanding: First, the optimal choice of binding strength should be on the left side of the volcano curve and close to its top (red area in Figure 3). On such catalysts, good activity can be achieved while relatively low CH4 selectivity can be obtained. In contrast, on the right side of the volcano curve the CH4 selectivity is always higher than on the left. Second, if very low CH4 selectivity is essential, it is clear from the figure that one has to sacrifice the activity. A good catalyst is the best compromise between activity and selectivity. From our results, Re may have the lowest CH4 selectivity. However, we have to consider the activity/stability of Re for FT synthesis. Surface species (i.e., adsorbed C and O from CO dissociation) adsorb on Re too strongly to be removed from surfaces, which is reflected by the high Eeff,CH4 in Table 1. This

8862

J. Phys. Chem. C, Vol. 113, No. 20, 2009

will lead to low activity or an even worse situation, deactivation by coking or oxide formation. Finally, it is worth discussing two metals, Fe and Co, currently used in industry. The main reason why Co produces more CH4 than Fe is that Co is a better hydrogenation catalyst than Fe: Eeff,CH4 of Co is 1.31 eV, while it is as high as 2.13 eV on Fe (Table 1). Fortunately, Co is also a better catalyst for C-C coupling reactions. Thus, improving Eeff,CH4 on Co catalysts is essential to restrain CH4 production. According to our calculations, increasing the binding strength of C + 4H on surfaces, for example, by doping some transition metals that lie to the left of Co in the periodic table, may enhance Eeff,CH4 without affecting Eeff,C-C much, and hence suppress the CH4 selectivity. As mentioned before, experimental work showed that Fe will transform to carbide (e.g., Ha¨gg carbide χ-Fe5C2) under FT reaction conditions, which was suggested to be the true active phase. Consequently, the foregoing results on metallic Fe surface may not be representative of real Fe-based catalysts. However, our recent study (to be published) showed that ∆Eeff of iron carbide is close to that of Fe, suggesting a similar methane selectivity, while the activity of iron carbide is higher. The difference of Fe and carbide can be understood as follows: The adsorption of carbon-related species is too strong on Fe to desorb from the surface, leading to the accumulation of surface carbon species and thereby driving the phase transition from Fe to carbide; once the carbide forms, the adsorption of carbon species becomes weaker and hence facilitates the desorption of hydrocarbon, giving rise to a higher activity. Finally, it should be noted that FT synthesis is far more complicated than just methane formation and C-C coupling as we are concerned with here; many other processes exist, such as coking, oxygenate formation, and water gas shift reaction (pronounced on Fe-based catalysts). Our attempt in this study is to point out that even for a catalytic reaction complex like FT synthesis it is still possible to identify an energy descriptor (adsorption energies of C + 4H) to measure selectivity. Guided by this descriptor, one may be able to search for new catalysts to improve catalytic performance. It is worth noting that this descriptor may be also related to coking: too-strong bonding of carbon species will give rise to superfluous carbon species on surfaces, which can aggregate to coke. 4. Conclusions In this paper, we present a systematic investigation of CH4 selectivity in Fischer-Tropsch synthesis: CH4 formation on Rh, Co, Ru, Fe, and Re surfaces has been studied by use of DFT calculations. Combining CH4 formation with C-C coupling reactions and, more importantly, DFT results with reaction kinetics, we are able to take a step toward an understanding of selectivity: Not only have we determined an energy descriptor to quantify CH4 selectivity, using which the ranking of CH4 selectivity predicted from DFT calculations is in agreement with experimental work, but also our results provide insight into suppressing CH4 selectivity. The following conclusions are reached: (i) On the surfaces of Rh, Co, Fe, Ru, and Re, the total energies along the coordinate of C hydrogenation to CH4 increase in a stepwise manner. This indicates that the last step, CH3 hydrogenation, is rate-determining in sequential hydrogenation reactions. (ii) The effective barrier to CH4 formation (Eeff,CH4, see eq 2) is a good measurement of the CH4 production rate. The chain growth rate can be measured by the effective barrier to chain growth (Eeff,C-C, see eq 4). Their difference (∆Eeff, see eq 5),

Cheng et al. the energy descriptor, can quantify the CH4 selectivity on each metal surface. (iii) The metal surface with a smaller ∆Eeff will produce more CH4, and the surface with a larger ∆Eeff should be superior for the formation of long-chain hydrocarbons. Calculated values of ∆Eeff show that CH4 selectivity decreases in the order Re > Ru > Fe > Co > Rh. Although our results show Re may have excellent selectivity, it is not a good FT catalyst due to its low activity/stability. (iv) Eeff,CH4 has a linear relationship with the chemisorption energy of C + 4H (∆H), while a similar relationship is not seen between Eeff,C-C and ∆H. Thus, ∆Eeff correlates well with ∆H. This correlation suggests that an increase in the binding strength of C + 4H on surfaces may suppress CH4 selectivity. This result may be of great interest in FT industries. References and Notes (1) Dry, M. E. Appl. Catal., A 1996, 138, 319. (2) Dry, M. E. Catal. Today 2002, 71, 227. (3) Schulz, H. Appl. Catal., A 1999, 186, 3. (4) Geerlings, J. J. C.; Wilson, J. H.; Kramer, G. J.; Kuipers, H. P. C. E.; Hoek, A.; Huisman, H. M. Appl. Catal., A 1999, 186, 27. (5) Biloen, P.; Sachtler, W. M. H. AdV. Catal. 1981, 30, 165. (6) Rofer-Depoorter, C. K. Chem. ReV. 1981, 81, 447. (7) Iglesia, E. Appl. Catal., A 1997, 161, 59. (8) Jager, B.; Espinoza, R. Catal. Today 1995, 23, 17. (9) Adesina, A. A. Appl. Catal. A: Gen. 1996, 138, 345. (10) Khodakov, A. Y.; Chu, W.; Fongarland, P. Chem. ReV. 2007, 107, 1692. (11) Lok, C. M. Stud. Surf. Sci. Catal. 2004, 147, 283. (12) Bertole, C. J.; Mims, C. A.; Kiss, G. J. Catal. 2004, 221, 191. (13) Panpranot, J.; Goodwin, J. G., Jr.; Sayari, A. J. Catal. 2003, 213, 78. (14) Ciobıˆcaˇ, I. M.; Kramer, G. J.; Ge, Q.; Neurock, M.; van Santen, R. A. J. Catal. 2002, 212, 136. (15) Jacobs, G.; Das, T. K.; Zhang, Y.; Li, J.; Racoillet, G.; Davis, B. H. Appl. Catal., A 2002, 233, 263. (16) Storæter, S.; Chen, D.; Holmen, A. Surf. Sci. 2006, 600, 2051. (17) Borg., Ø.; Eri, S.; Blekkan, E. A.; Storæter, S.; Wigum, H.; Rytter, E.; Holmen, A. J. Catal. 2007, 248, 89. (18) Morales, F.; de Smit, E.; de Groot, F. M. F.; Visser, T.; Weckhuysen, B. M. J. Catal. 2007, 246, 91. (19) Beitel, G. A.; de Groot, C. P. M.; Oosterbeek, H.; Wilson, J. H. J. Phys. Chem. B 1997, 101, 4035. (20) Bezemer, G. L.; Radstake, P. B.; Falke, U.; Oosterbeek, H.; Kuipers, H. P. C. E.; van Dillen, A. J.; de Jong, K. P. J. Catal. 2006, 237, 152. (21) Bezemer, G. L.; Bitter, J. H.; Kuipers, H. P. C. E.; Oosterbeek, H.; Holewijn, J. E.; Xu, X.; Kapteijn, F.; van Dillen, A. J.; de Jong, K. P. J. Am. Chem. Soc. 2006, 128, 3956. (22) Tuner, M. L.; Marsih, N.; Man, B. E.; Quyoum, R.; Long, H. C.; Maitlis, P. M. J. Am. Chem. Soc. 2002, 124, 10456. (23) Ge, Q. F.; Neurock, M. J. Phys. Chem. B 2006, 110, 15368. (24) Cheng, J.; Song, T.; Hu, P.; Lok, C. M.; Ellis, P.; French, S. J. Catal. 2008, 255, 20. (25) Vannice, M. A. J. Catal. 1975, 37, 449. (26) Herranz, T.; Rojas, S.; Pe´rez-Alonso, F. J.; Ojeda, M.; Terreros, P.; Fierro, J. L. G. J. Catal. 2006, 243, 199. (27) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcı´a, A.; Junquera, J.; Ordejo´n, P.; Sa´nchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (28) Troullier, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (30) Cheng, J.; Gong, X.-Q.; Hu, P.; Lok, C. M.; Ellis, P.; French, S. J. Catal. 2008, 254, 285. (31) Alavi, A.; Hu, P.; Deutsch, T.; Silvestrelli, P. L.; Hutter, J. Phys. ReV. Lett. 1998, 80, 3650. (32) Zhang, C.-J.; Hu, P. J. Am. Chem. Soc. 2000, 122, 2134. (33) Zhang, C.-J.; Hu, P.; Alavi, A. J. Am. Chem. Soc. 1999, 121, 7931. (34) Gong, X.-Q.; Raval, R.; Hu, P. J. Chem. Phys. 2005, 122, 024711. (35) Cheng, J.; Hu, P.; Ellis, P.; French, S.; Kelly, G.; Lok, C. M. J. Phys. Chem. C 2008, 112, 6082. (36) Cheng, J.; Hu, P.; Ellis, P.; French, S.; Kelly, G.; Lok, C. M. J. Catal. 2008, 257, 221. (37) Geerlings, J. J. C.; Zonnevylle, M. C.; de Groot, C. P. M. Surf. Sci. 1991, 241, 302. (38) Cheng, J.; Hu, P.; Ellis, P.; French, S.; Kelly, G.; Lok, C. M. J. Phys. Chem. C 2008, 112, 9464. (39) Song, T.; Hu, P. J. Chem. Phys. 2007, 127, 234706.

Energy Descriptor To Quantify Methane Selectivity (40) (a) Boudart, M.; Dje´ga-Mariadassou, G. Kinetics of Heterogeneous Catalytic Reactions; Princeton University Press: Princeton, NJ, 1984. (b) Zhdanov, V. P.; Pavlicek, J.; Knor, Z. Catal. ReV. Sci. Eng. 1988, 30, 501. (41) Inderwildi, O. R.; Jenkins, S. J.; King, D. A. J. Phys. Chem. C 2008, 112, 1305. (42) Inderwildi, O. R.; Jenkins, S. J. Chem. Soc. ReV. 2008, 37, 2274. (43) Cheng, J.; Hu, P.; Ellis, P.; French, S.; Kelly, G.; Lok, C. M. J. Phys. Chem. C 2008, 112, 1308.

J. Phys. Chem. C, Vol. 113, No. 20, 2009 8863 (44) Cheng, J.; Hu, P. J. Am. Chem. Soc. 2008, 130, 10868. (45) Vannice, M. A. J. Catal. 1977, 50, 228. (46) Bligaard, T.; Nørskov, J. K.; Dahl, S.; Matthiesen, J.; Christensen, C. H.; Sehested, J. J. Catal. 2004, 224, 206.

JP901075E