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2008, 112, 1308-1311 Published on Web 01/15/2008
Brønsted-Evans-Polanyi Relation of Multistep Reactions and Volcano Curve in Heterogeneous Catalysis Jun Cheng and P. Hu* School of Chemistry and Chemical Engineering, The Queen’s UniVersity of Belfast, Belfast BT9 5AG, U.K.
Peter Ellis,† Sam French,† Gordon Kelly,‡ and C. Martin Lok‡ Johnson Matthey Technology Centre, Reading RG4 9NH, U.K., and Billingham CleVeland, TS23 1LB, U.K. ReceiVed: NoVember 26, 2007; In Final Form: December 24, 2007
Multistep surface processes involving a number of association reactions and desorption processes may be considered as hypothetical one-step desorption processes. Thus, heterogeneous catalytic reactions can be treated kinetically as consisting of two steps: adsorption and desorption. It is also illustrated that the hypothetical one-step desorption process follows the BEP relation. A volcano curve can be obtained from kinetic analysis by including both adsorption and desorption processes.
Introduction Volcano curves are one of the most fundamental discoveries in heterogeneous catalysis.1 Traditionally, these phenomena have been understood in terms of the principle of Sabatier,2 which offers qualitative guidance in the search for new catalysts. Recently, a linear relationship between the activation energy and the enthalpy change of an elementary reaction, known as the Brønsted-Evans-Polanyi (BEP) relation,3 has been found by several groups from first-principles calculations,4-6 which makes it possible to quantitatively understand the volcano curve in heterogeneous catalytic systems. An important step toward this goal has been made by Nørskov and co-workers.7,8 They have applied the BEP relation to adsorption processes, that is, N2 dissociation in ammonia synthesis, with some kinetic consideration, to obtain some volcano curves, which is very useful for catalyst design.9 However, surface reactions and desorption processes have been inadequately addressed in the field. In order to fully understand the volcano curve, one must answer the following two questions: (i) Do surface reactions and desorption processes follow the BEP relation? (ii) How do they affect the overall reaction kinetics and volcano curves? In this work, we aim to answer these questions. The BEP relation offered an empirical way to estimate kinetic parameters from thermodynamic values. Thanks to the development of density functional theory (DFT), the activation energy and enthalpy change of a given elementary reaction can be readily obtained from first-principles calculations. The BEP relation has been found to hold well for many elementary reactions on different metal surfaces.4,5,6,10 Nørskov and coworkers combined the BEP relation of N2 dissociation and a simple kinetic model to obtain volcano curves for ammonia synthesis by plotting the reaction rate against N2 dissociative * Corresponding author. E-mail:
[email protected]. † Reading RG4 9NH, U.K. ‡ Billingham Cleveland, TS23 1LB, U.K.
10.1021/jp711191j CCC: $40.75
chemisorption energy. N2 dissociation is the rate-determining step in ammonia synthesis under typical reaction conditions;11 thus, the surface reactions and desorption processes can be neglected in the kinetic treatment. However, whether it is generally applicable is still an open question. For example, in CO hydrogenation CO dissociation is kinetically important, and the following hydrogenation of adsorbed C and O atoms is also closely related to the overall reaction rate.12 Surface reactions and desorption processes need to be appropriately taken into account in order to obtain a comprehensive understanding of chemical kinetics in heterogeneous catalysis. Alternatively, most adsorption processes are one-step dissociation reactions (i.e., CO and N2 dissociation), and the BEP relation can be directly applied to the kinetics of adsorption processes,6 whereas surface reactions and desorption processes are usually involved with multistep association reactions (e.g., C + 4H f CH + 3H f CH2 + 2H f CH3 + H f CH4). Although a linear relationship has been found to exist in elementary C-H bond breaking/forming4 processes, and the barrier of each elementary step can be estimated from the enthalpy change of the step, kinetic treatment of multistep association and desorption process is much more complicated because the relative stabilities of many different surface intermediates must be taken into account. Thus, it is much more difficult to apply the BEP relation directly to the multistep surface reactions and desorption processes than the one-step adsorption processes. Here we present a simple approach to overcome this obstacle, attempting to obtain a deeper understanding of volcano curves by including both adsorption and desorption processes. Method In this work, the SIESTA code13 is used with TroullierMartins norm-conserving scalar relativistic pseudopotentials.14 A double-ζ plus polarization (DZP) basis set is utilized. The localization radii of the basis functions are determined from an © 2008 American Chemical Society
Letters
J. Phys. Chem. C, Vol. 112, No. 5, 2008 1309
Figure 1. Illustrative energy profile of the catalytic reaction model. TS1 and TS2 are the transition state of the adsorption and the last elementary step of surface association reactions, respectively. ∆H is the enthalpy change of the overall reaction. The red curve represents the adsorption process. ∆HR is the enthalpy change of the adsorption, and ERdis and ERass are the barrier of the adsorption and its reverse reaction, respectively. The dashed blue curve illustrates the multistep surface reactions and desorption, and the solid blue curve stands for the hypothetical one-step desorption process. ∆HP is the enthalpy change of the desorption, and EPass and EPdis are the barrier of the hypothetical one-step desorption and its reverse reaction, respectively.
SCHEME 1: Kinetic Model of a Heterogeneous Catalytic Reaction: (a) Reactant Adsorption Followed by Multistep Surface Reactions and Desorption; (b) Multistep Surface Reactions and Desorption Are Treated as One-Step Desorption Processesa
a The symbol in the second and third equations of part a means reaching quasi-equilibrium, and * stands for free surface site.
energy shift of 0.01 eV. A standard DFT supercell approach with the Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation (GGA) functional15 is implemented with a mesh cutoff of 200 Ry. The accuracy of the code and these settings have been checked.16 The transition states (TSs) are searched using a constrained optimization scheme.17 Results and Discussion It is well known that a heterogeneous catalytic reaction starts with reactant adsorption, followed by surface reactions and product desorption. We use the following kinetic model to describe the process (Scheme 1a): The reactant R adsorbs on a surface to produce the key intermediate I, which is subsequently converted to a second surface species, I2, which in turn desorbs to give the product, P. It should be mentioned that for clarity there is only one reactant and one product in each elementary reaction in this model. However, we believe that this model captures the key features of catalytic reactions. The energy profile of this catalytic reaction model is illustrated in Figure 1. Dissociation of a diatomic molecule is a typical example of an adsorption process, and BEP relations for the activation of diatomic molecules, such as CO and N2, is well-established.7 We also calculated the relationship between activation energies (ERdis) and enthalpy changes (∆HR) for CO, NO, and N2 dissociation at step sites (i.e., surface defects) on many transition-metal surfaces18 in order to obtain quantitative results for the analysis discussed below. Our extensive DFT calculations show that a linear relationship holds very well across the
Figure 2. BEP plot of CO, NO, and N2 dissociation on stepped surfaces.22
periodic table, as shown in Figure 2. The obtained linear equation, Eadis ) 0.93∆HR + 1.14, is consistent with the work of Nørskov and co-workers.7,19 Because catalytic processes typically involve a series of bondforming reactions after initial dissociation, kinetic analysis is an intricate procedure. However, it was found recently that the multistep hydrogenation of a C atom on a Co surface can be considered in quasi-equilibrium except for the last step (CH3 hydrogenation) in Fischer-Tropsch (FT) synthesis.20 Namely, the multistep hydrogenation reactions can be regarded as a onestep reaction with a C atom and four H atoms on the surface as the initial state (IS) and the transition state (TS) of the last hydrogenation step as the “overall” TS. Similarly, this treatment can be applied to our proposed catalytic model and may be further extended to the other multistep association reactions in general. Thus, our model can be simplified as shown in Scheme 1b (also illustrated in Figure 1): The surface intermediate I directly forms the product P via TS2 (the TS of the slowest elementary step) in the hypothetical one-step desorption process; the energy difference between intermediate I and TS2 is the effective desorption barrier (EPass), and the energy difference between product P and intermediate I is the enthalpy change of the desorption (∆HP). It should be noted that the enthalpy change is negative when a process is exothermic. We calculated the formation of CH4, NH3, and H2O on a number of metal surfaces aiming to obtain the relationship between the effective desorption barriers (EPass) and the enthalpy
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Figure 3. BEP plots of CH4, NH3, and H2O dissociation on stepped (a) and flat (b) surfaces.
change (∆HP). It was found that the dissociation barrier (EPdis) of these molecules is a linear function of ∆HP , as shown in Figure 3. Namely, EPdis ∝ ∆HP . Because EPass ) EPdis -∆HP , EPass should also be linear to ∆HP; that is, the hypothetical onestep desorption processes also follow the BEP relation well. Figure 3a and b shows the BEP plots of CH4, NH3, and H2O dissociation on the stepped and flat surfaces, respectively. The fitted linear equations on the stepped and flat surfaces are very similar: The slopes are almost the same, ∼0.27, and the difference in the intercept is ∼0.15 eV. In contrast to CO, NO, and N2 dissociation, there are two obvious differences in the BEP relation: (i) The slope of CO, NO, and N2 dissociation is around 0.9, much larger than that of CH4, NH3, and H2O dissociation. The large slope indicates that the TSs of CO, NO, and N2 dissociation are final state (FS, i.e., the dissociative adsorption state) like. An increase of the adsorption strength will reduce the dissociation barrier significantly. In contrast, the TSs of CH4, NH3, and H2O dissociation are more IS (the molecule in the gas phase) like with respect to the FS with C or N or O and H on the surface. An increase of the adsorption strength hardly decreases the dissociation barrier, but greatly enhances its reverse reaction barrier, that is, the effective desorption barrier (EPass). Thus, in ammonia synthesis and CO hydrogenation improving the adsorption energy can facilitate the dissociative adsorption and yet hinders the desorption process. (ii) Logadottir et al.6 showed that the difference in the intercept of the BEP relation between the flat and stepped surfaces is ∼0.7 eV for CO, NO, and N2 dissociation, which is much larger than that in CH4, NH3, and H2O dissociation (0.15 eV). This big difference reflects the advantageous geometrical effect of the step sites for CO, NO, and N2 dissociation compared to the flat surfaces. Our result suggests that in the dissociation of CH4, NH3, and H2O the geometrical effect of the step sites is not significant. This is in agreement with the work of Liu and Hu,21 who showed that the geometrical effect is small in CH4 dissociation, leading to this reaction being structure-insensitive or not very structure-sensitive. The BEP relation is generally applicable to desorption processes, regardless of how many elementary steps they contain. In other words, the reactions in a catalytic system can be divided into two simple steps: adsorption and desorption. Furthermore, each step follows the BEP relation, and the activation energies (ERdis, ERass, EPdis, and EPass) can be described by the bonding strength of the key intermediate (∆HR). Thus, it is possible to determine the reaction rate from ∆HR. In order to investigate the influence of desorption process on the overall reaction rate, we studied the kinetic model in Scheme 1b and derived the kinetic equations of the reaction rate as a function of ∆HR. (See the Supporting Information for
Figure 4. Plot of TOF against ∆HR. Red curve: both adsorption and desorption are considered. Green curve: adsorption is considered to be the rate-determining step. Blue curve: desorption is considered to be the rate-determining step.
derivation details.) The plot of the reaction rate in terms of turnover frequency (TOF) against ∆HR is shown in Figure 4. The red curve is obtained by taking both the adsorption and desorption processes into account kinetically. The green curve is plotted assuming that adsorption is the rate-determining step with the desorption in quasi-equilibrium. Likewise, the blue curve is obtained when the desorption step is rate-determining. It can be seen from Figure 4 that all three curves show a volcano-shaped relationship between TOF and ∆HR but the peaks of the volcano curves are different. This indicates that if either adsorption or desorption is treated as the rate-determining step then a volcano curve can be still obtained. However, this treatment may not be complete. Interestingly, although the kinetic model we used is very simple the optimal ∆HR is in the range from -1 to -2 eV, consistent with the work of Nørskov and co-workers.8 Conclusions In summary, many multistep processes involving a number of bond-forming reactions and molecular desorption can be considered as hypothetical one-step desorption processes. This finding greatly simplifies the kinetic analysis of catalytic systems, allowing them to be treated approximately as twostep processes involving only an adsorption and desorption step. We also show that the hypothetical one-step desorption process follows the BEP relation, similar to the adsorption process. A volcano curve of the reaction rate against the bonding energy of the key intermediate can be obtained from kinetic consideration by including both adsorption and desorption. Acknowledgment. We gratefully thank The Queen’s University of Belfast for computing time. J.C. acknowledges Johnson Matthey for financial support.
Letters Supporting Information Available: Kinetic derivation to obtain the volcano curve plots in Figure 4. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Boudart, M. in Ertl, G., Kno¨zinger, H., Weitkamp, J. Handbook of Heterogeneous Catalysis; Wiley-VCH: Weinheim, 1997. (2) Sabatier, P. Ber. Dtsch. Chem. Ges. 1911, 44, 1984. (3) (a) Brønsted, N. Chem. ReV. 1928, 5, 231. (b) Evans, M. G.; Polanyi, N. P. Trans. Faraday Soc. 1938, 34, 11. (4) Pallassana, V.; Neurock, M. J. Catal. 2000, 191, 301. (5) Liu, Z. -P.; Hu, P. J. Chem. Phys. 2001, 114, 8244. (6) Logadottir, A.; Rod, T. H.; Nørskov, J. K.; Hammer, B.; Dahl, S.; Jacobsen, C. J. H. J. Catal. 2001, 197, 229. (7) Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Bahn, S.; Hansen, L. B.; Bollinger, M.; Bengaard, H.; Hammer, B.; Sljivancanin, Z.; Mavrikakis, M.; Xu, Y.; Dahl, S.; Jacobsen, C. J. H. J. Catal. 2002, 209, 275. (8) Bligaard, T.; Nørskov, J. K.; Dahl, S.; Matthiesen, J.; Christensen, C. H.; Sehested, J. J. Catal. 2004, 224, 206. (9) (a) Jacobsen, C. J. H.; Dahl, S.; Clausen, B. S.; Bahn, S.; Logadottir, A.; Nørskov, J. K. J. Am. Chem. Soc. 2001, 123, 8404. (b) Toulhoat, H.; Raybaud, P. J. Catal. 2003, 216, 63. (10) (a) Michaelides, A.; Liu, Z. -P.; Zhang, C. J.; Alavi, A.; King, D. A.; Hu, P. J. Am. Chem. Soc. 2003, 125, 3704. (b) Gong, X.-Q.; Liu, Z.-P.; Raval, R.; Hu, P. J. Am. Chem. Soc. 2004, 126, 8. (11) (a) Honkala, K.; Hellman, A.; Remediakis, I. N.; Logadottir, A.; Carlsson, A.; Dahl, S.; Christensen, C. H.; Nørskov, J. K. Science 2005, 307, 555. (b) Logadottir, A.; Nørskov, J. K. J. Catal. 2003, 220, 273. (12) Geerlings, J. J. C.; Zonnevylle, M. C.; de Groot, C. P. M. Surf. Sci. 1991, 241, 302. (13) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejo´n, P.; Sa´nchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (14) Troullier, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993.
J. Phys. Chem. C, Vol. 112, No. 5, 2008 1311 (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (16) Liu, Z.-P.; Gong, X.-Q.; Kohanoff, J.; Sanchez, C.; Hu, P. Phys. ReV. Lett. 2003, 91, 266102. (17) Alavi, A.; Hu, P.; Deutsch, T.; Silvestrelli, P. L.; Hutter, J. Phys. ReV. Lett. 1998, 80, 3650. (18) Eleven transition metals (Fe, Ru, Co, Rh, Ir, Ni, Pd, Pt, Cu, Ag, and Au) were extensively computed to study the BEP relation. In calculating flat metal surfaces, closed-packed planes were used: (001) plane for hcp metals, (111) plane for fcc metals. Monatomic step was employed to model surface defect. (211) and (210) planes were used for fcc metals (e.g., Rh and Pt) and bcc metal (Fe), respectively. Because no low index plane appears monatomic step structure for hcp metals (Ru and Co), surface defect was modeled by removing two neighboring rows of metal atoms in the top layer on close-packed (001) surfaces. (19) There are slight differences that may come from different XC functionals. Nørskov’s results were obtained from RPBE functional, and ours were calculated from PBE functional. (20) Cheng, J.; Gong, X. -Q.; Hu, P.; Lok, C. M.; Ellis, P.; French, S. J. Catal., in press. (21) Liu, Z. -P., Hu, P. J. Am. Chem. Soc. 2003, 125, 1958. (22) It should be noted that there are some negative barriers because the molecule in the gas phase was selected as an IS. There are good reasons for choosing this reference state: (i) In a typical molecular dissociation reaction, there are two elementary steps; molecular adsorption and the dissociation of the adsorbed molecule. The molecular adsorption step and its reverse step (the molecular desorption) can usually reach quasiequilibrium. Then the state of the molecule in the gas phase is kinetically equivalent to the state of the adsorbed molecule on the surface. (ii) The advantage of taking the molecule in the gas phase as a reference state is that this state is the same for the molecule to dissociate on different metal surfaces. Thus, one can readily obtain trends of molecular dissociation on different surfaces.
