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Dual reverse spill-over: Microkinetic simulations of the CO oxidation on Pd nanocatalysts
Chemical Physics Letters 461 (2008) 235–237
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Dual reverse spill-over: Microkinetic simulations of the CO oxidation on Pd nanocatalysts C.J. Harding *, S. Kunz, V. Habibpour, U. Heiz Lehrstuhl für Physikalische Chemie, Technische Universität München, Lichtenbergstr. 4, D-85748 Garching, Germany
a r t i c l e
i n f o
Article history: Received 21 April 2008 In final form 3 July 2008 Available online 9 July 2008
a b s t r a c t Simulations of cluster-based catalytic oxidation of CO were performed using a dual reverse spill-over microkinetic model (DRSO-MK simulations) in order to improve the description and understand the underlying physics of the experimental turn-over data. The description of mass-selected Pd13 TOF profiles as a function of mole fraction was reproduced to an excellent level at a range of temperatures. The DRSOMK model was extended to produce predictions of reactants which are both mobile on the support, illustrating the predictive power of the model and the importance of support interactions in the accurate modelling of cluster-based nanocatalysts. Ó 2008 Elsevier B.V. All rights reserved.
The field of model catalysis has diversified from the use of single crystals [1,2] as a catalytic medium to supported nanoparticles and clusters [3–6]. The potential to optimise the turn-over of reactants while reducing overheads in the production of bulk chemicals provides industrial applications in this area of research. The softlanding of metallic clusters on metal-oxide substrates has shown highly tuneable properties, turn-over frequencies and remarkably low temperature catalysis [3,6,7]. To understand the physics behind the processes experiments can be performed and augmented with kinetic simulations which include intrinsic support effects of two reactants. Non-intrinsic support effects such as the role of films in dimensionality cross-over [8,9] or charge transfer [10,11] are typically not measured by such methods. Recently intrinsic support effects have been added to a kinetic model, but the reverse spill-over of only one reactant was considered. The simultaneous dual reverse spill-over (of the two reactants) [12] in microkinetic simulations (herein referred to as DRSO-MK simulations) show interesting results and furthermore offers an added dimension to the predictive power of the model. Microkinetic simulations of oxidation reactions have already shown themselves to provide an excellent theoretical model of the CO oxidation reactions on nanoparticles and cluster-based nanocatalysts [13,14]. The catalytic material itself consists of support material namely a thin metal-oxide film such as MgO [15]. After growing a film to a thickness of 10 ML, clusters can be deposited onto the film to produce the model catalyst. Mass selection of the clusters allows the tuning of the catalytic material affecting the turn-over frequency [3,16,17]. Experimental measurements of such catalysts form the basis of a comparison between the simulations and the physical situation. They are realised through a high * Corresponding author. Fax: +49 89 289 13389. E-mail address: [email protected] (C.J. Harding). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.07.017
level of control over the reactants. The use of two pulsed molecular beams, each containing a reactant, allows the mole fraction of the reactants to be accurately manipulated [3,16]. Coupled with the ability to independently vary the reaction temperature, coverage and size of clusters, a detailed investigation into turn-over frequency profiles shows remarkable effects such as the near room temperature catalysis of reactions ordinarily not observed for other catalytic systems. For a given temperature and coverage, varying the mole fraction of the reactants allows a turn-over frequency reaction profile for the catalyst to be determined [3]. The variation of these profiles with temperature then provides the basis for kinetic information to be extracted. This was achieved by the comparison of microkinetic simulations to the experimentally measured data. Based on Langmuir laws, microkinetic simulations have shown to reproduce experimental data based on larger nanoparticles [14,18] as well as smaller clusters [13]. Although Langmuir laws have been shown for Pd single crystals [1,2] it has not been clearly shown if the same mechanism applies to small size-selected clusters. Theoretical calculations have indeed shown that the Mars-van Krevelen mechanism involving a Pd nano-oxide could also offer a route to the catalytic oxidation of CO [19]. However as the Langmuir laws have been shown to be suitable for nanoparticles this mechanism is consequently adopted for smaller Pd clusters. For the smaller clusterbased catalysts, important experimental observations were only reproduced when the kinetic formulations were augmented by an additional calculation; that of reverse spill-over using the capture-zone model [20–22]. It has been illustrated that for small clusters (Pd13), due to the ratio of active centres to support material, the theoretical description is greatly enhanced by the addition of the migration of reactant molecules from the support to the reactive centres (reverse spill-over) using the capture-zone model. An increase in support
236
C.J. Harding et al. / Chemical Physics Letters 461 (2008) 235–237
αg
60
CO,O2
=1
product molecule, CO2, can be determined (r CO2 ). The important feature in the formulation between previous microkinetic simulations made on larger particles is the inclusion of the capture-zone via the 2 aCO;O value. The capture-zone model allows the reverse spill-over of g the reactants to be approximated by modelling a slow reservoir of the reactants which migrate from the support to the reactive centres (metal clusters). In these simulations the capture-zone is calculated by functionalising the saddle energy with the coverage 2 calculated from the kinetics equations. With aCO;O ¼ 1 the reverse g spill-over of one or both of the reactants can be removed from the calculation; this is illustrated in Fig. 1. Previous models have shown excellent agreement with aOg 2 ¼ 1 and aCO g 6¼ 1 whereas no such attempts have been undertaken with aOg 2 6¼ 1 because it is commonly considered that oxygen reverse spill-over can be safely ignored due to the magnitude of the interaction energies with MgO: a fair assumption. This has been found to produce high reproducibility of the experimentally measured mole fraction profiles (comparing Fig. 1b to Fig 2a). The inclusion of the coverage in the formulation of the saddle energy allows the phenomenon of the low temperature catalysis to be rationalised. The reverse spill-over effects of CO alone can be seen in Fig. 2a. The dramatic improvement in the low temperature catalysis regime is clearly illustrated. 2 In the solution of Eqs. (1)–(3) where aCO;O 6¼ 1, formulation of g the capture-zone model for both reactants is equivalent and the coverage dependency of the saddle energy is present in both cases. The effects of including the reverse spill-over of O2 can be seen in Fig. 2b. From a cursory glance, the incorporation of the dual spill-
a
40
-1
TOF (CO2 s )
20
0
b
Experiment
40
30
20
10
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction (xCO) Fig. 1. Turn-over profiles for the oxidation of CO using Pd13 clusters (at a coverage of 0.47%ML) supported on a MgO film (10 ML) measured at four different temperatures: 358 K (solid), 417 K (dotted), 440 K (dot-dashed) and 478 K (dashed). (a) Simulated mole fraction profiles using no reverse spill-over in the simulation. (b) Experimental values determined by a dual pulsed-beam technique.
CO CO g
r CO ¼ g a
kd hCO kL hCO hO
a
αgO 2 = 1 30
20
10 -1
TOF (CO2 s )
to cluster ratio should lead to an increase in the importance of reverse spill-over effects. Although the microkinetic modelling accurately describes the mole fraction turn-over profiles, it is based only on the reverse spill-over of one reactant (the oxygen reverse spill-over being ignored). When considering the CO oxidation, accurate descriptions can be achieved by considering only slow reservoirs of CO. Without considering both reactants spill-over explicitly, the agreement achieved by the model could be attributed to a fortuitous cancellation of errors which arise as both the Langmuir laws and the capture-zone formulation rely (to different extents) on approximations. The reverse spill-over of the second reactant can, however, be added. The DRSO-MK formulation1 (including the capture-zones of both reactants) is based on three key equations:
αgCO ≠ 1
40
0
αgCO,O 2 ≠ 1
30
b
20
ð1Þ
r O ¼ 2gO2 aOg 2 kL hCO hO
ð2Þ
r CO2 ¼ kL hCO hO
ð3Þ
where hCO,O is the coverage of reactants, kd is the desorption rate constant, kL is a Langmuir-based rate constant for the reaction, gCO;O2 is proportional to the incoming flux of reactants, rCO,O is the 2 rate of change of the reactants and aCO;O is the reverse spill-over g sticking coefficient for the reactants (also referred to as the global sticking coefficient). Eqs. (1)–(3) can be solved numerically using the GNU Scientific Library [23] and the turn-over frequency of the 1 A more detailed formulation is given in the supplementary material along with which the source, details and magnitudes for the numerical values are given.
10
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction (xCO) Fig. 2. Simulated turn-over profiles for the oxidation of CO using Pd13 clusters (at a coverage of 0.47%ML) supported on a MgO film (10 ML) measured at four different temperatures: 358 K (solid), 417 K (dotted), 440 K (dot-dashed) and 478 K (dashed). (a) The model including only the reverse spill-over of the CO reactant. (b) The model including only the reverse spill-over of both the CO and O2 reactants.
C.J. Harding et al. / Chemical Physics Letters 461 (2008) 235–237
40
478 K
-1
TOF (CO2 s )
30
20
10
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction (xCO) Fig. 3. DRSO-MK simulations of mole fraction dependent turn-over profiles illustrating the oxidation of CO using Pd13 cluster-based catalysts at 478 K. The model includes the reverse spill-over of both reactants. The sticking coefficient of O2 on the MgO film is arbitrarily chosen to be 0.25 (dashed), 0.5 (dot-dashed), 0.75 (dotted) and 1 (solid) to illustrate the effects of increasing mobility of a the a second reactant.
over has no dramatic effect on the simulated values. By considering the magnitude of the parameters (interaction of O2 and MgO) involved, this result is not surprising. However, a closer inspection shows that although the low temperature regime is predominantly unaffected by the O2 reverse spill-over, at higher temperatures small deviations occur. The position of the maximum of the TOF profile (most notably at 478 K) shifts marginally to lower mole fraction values but more noticeably is the effect of the TOF profile onset. The experiment (Fig. 1b) shows a displacement of the onset to higher mole fraction, deviating from the nested structure observed for lower temperature measurements. This increase in the deviation occurs as reverse spill-over of the CO is included and becomes more pronounced as the reverse spill-over of oxygen is incorporated into the model. Overall, dual reverse spill-over appears to improve the agreement between experiment and theory. Although the DRSO-MK model supports previously made assumptions, it should be noted that better agreement is achieved by including dual reverse spill-over. Given the nature of the reaction and the sticking propensity of O2 the changes are small. This model, however, offers the possibility for substantial improvements in the agreement between experimental measurements and theoretical simulations based on molecules with a more efficient reverse spill-over. The benefits of the dual reverse spill-over may be highlighted by simply reducing the O2 sticking probability on MgO and hence increasing the reverse spill-over of the second reactant. Although this cannot physically be achieved the importance of the dual reverse spill-over is illustrated and shows how the DRSO-MK model may be used to describe future experiments. In Fig. 3 the variation of the TOF profile at 478 K can be seen as the sticking coefficient is changed from 0.25 to unity. The effects illustrate the usefulness of the dual reverse spill-over. As the sticking coefficient of O2 on MgO is reduced from unity, the overall TOF begins to decrease. Within this range a decrease in the TOF more than twofold is observed. The actual values of the TOF, although reproduced very well by the DRSO-MK model, should be considered to be fortuitous, due to the fact that the model is based on Langmuir laws. However, the relative trends can be relied upon. As for the shape of the profile, the onset maintains a constant gradient but the decay of the CO2 production as the mole fraction is increased
237
becomes less severe. The most noticeable effect is, nevertheless, the migration of the maximum turn-over to lower mole fraction values. Additionally, although not presented here, the DRSO-MK model can also make predictions of the sticking coefficients and illustrate the coverage variation at different mole fraction values and temperatures. This offers a way to model the underlying physics of the system when such measurements are experimentally viable. In conclusion, for a catalyst which contains a large support to cluster ratio the role of the film in the reaction profile is extremely important and appears to be the main origin of the low temperature catalytic properties. For the reaction of CO and O2 on Pd-cluster-based catalysts the reverse spill-over of the O2 reactant is shown to play a small role in the improved description of the experimental data, whereas the CO makes a much larger improvement. As the main origin of the observed variations is the interaction of the reactants with the support, theoretical modifications to the reactant properties illustrate the importance of incorporating double reverse spill-over into microkinetic simulations for more mobile reactants. These are summarised by a decrease in the TOF values and a shift in the maximum of the TOF profile to lower mole fraction values. Consequently, the DRSO-MK formulation offers great potential for future simulations of more complicated reaction mechanisms such as the reaction of NO and CO on model catalysts. Acknowledgements We acknowledge financial support of the Deutsche Forschungsgemeinschaft (DFG) and of the European Union within the COST D41 program. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2008.07.017. References [1] T. Engel, G. Ertl, J. Chem. Phys. 69 (1978) 1267. [2] T. Engel, G. Ertl, Chem. Phys. Lett. 54 (1978) 95. [3] C.J. Harding, S. Kunz, V. Habibpour, V. Teslenko, M. Arenz, U. Heiz, J. Catal. 255 (2008) 234. [4] C.R. Henry, C. Chapon, B. Mutaftschiev, Surf. Sci. 163 (1985) 409. [5] J. Libuda, H.J. Freund, Surf. Sci. Rep. 57 (2005) 157. [6] M.A. Röttgen et al., J. Am. Chem. Soc. 129 (2007) 9635. [7] K. Judai, S. Abbet, A.S. Wörz, U. Heiz, C.R. Henry, J. Am. Chem. Soc. 126 (2004) 2732. [8] D. Ricci, A. Bongiorno, G. Pacchioni, U. Landman, Phys. Rev. Lett. 97 (2006). [9] M. Sterrer et al., Phys. Rev. Lett. 98 (2007). [10] M. Sterrer, T. Risse, M. Heyde, H.P. Rust, H.J. Freund, Phys. Rev. Lett. 98 (2007). [11] B. Yoon et al., Science 307 (2005) 403. [12] G. Prevot, C.R. Henry, J. Phys. Chem. B 106 (2002) 12191. [13] C.J. Harding, S. Kunz, V. Habibpour, U. Heiz, Phys. Chem. Chem. Phys. (2008), doi: 10.1039/B805688A. [14] J. Hoffmann, I. Meusel, J. Hartmann, J. Libuda, H.J. Freund, J. Catal. 204 (2001) 378. [15] U. Heiz, F. Vanolli, L. Trento, W.-D. Schneider, Rev. Sci. Instrum. 68 (1997) 1986. [16] M.A. Röttgen, K. Judai, J.-M. Antonietti, U. Heiz, S. Rauschenbach, K. Kern, Rev. Sci. Instrum. 77 (2006) 013302. [17] A.S. Wörz, K. Judai, S. Abbet, U. Heiz, J. Am. Chem. Soc. 125 (2003) 7964. [18] J. Libuda, T. Schalow, B. Brandt, M. Laurin, S. Schauermann, Microchim. Acta 156 (2006) 9. [19] B. Huber, P. Koskinen, H. Häkkinen, M. Moseler, Nat. Mater. 5 (2006) 44. [20] C.R. Henry, C. Chapon, C. Duriez, J. Chem. Phys. 95 (1991) 700. [21] M. Boudart, M.A. Vannice, J.E. Benson, Z. Phys. Chem.—Frankfurt 64 (1969) 171. [22] V. Matolin, E. Gillet, Surf. Sci. 166 (1986) L115. [23] M. Galassi, GNU Scientific Library Reference Manual, Network Theory Ltd., 2003.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Dual reverse spill-over: Microkinetic simulations of the CO oxidation on Pd nanocatalysts C.J. Harding *, S. Kunz, V. Habibpour, U. Heiz Lehrstuhl für Physikalische Chemie, Technische Universität München, Lichtenbergstr. 4, D-85748 Garching, Germany
a r t i c l e
i n f o
Article history: Received 21 April 2008 In final form 3 July 2008 Available online 9 July 2008
a b s t r a c t Simulations of cluster-based catalytic oxidation of CO were performed using a dual reverse spill-over microkinetic model (DRSO-MK simulations) in order to improve the description and understand the underlying physics of the experimental turn-over data. The description of mass-selected Pd13 TOF profiles as a function of mole fraction was reproduced to an excellent level at a range of temperatures. The DRSOMK model was extended to produce predictions of reactants which are both mobile on the support, illustrating the predictive power of the model and the importance of support interactions in the accurate modelling of cluster-based nanocatalysts. Ó 2008 Elsevier B.V. All rights reserved.
The field of model catalysis has diversified from the use of single crystals [1,2] as a catalytic medium to supported nanoparticles and clusters [3–6]. The potential to optimise the turn-over of reactants while reducing overheads in the production of bulk chemicals provides industrial applications in this area of research. The softlanding of metallic clusters on metal-oxide substrates has shown highly tuneable properties, turn-over frequencies and remarkably low temperature catalysis [3,6,7]. To understand the physics behind the processes experiments can be performed and augmented with kinetic simulations which include intrinsic support effects of two reactants. Non-intrinsic support effects such as the role of films in dimensionality cross-over [8,9] or charge transfer [10,11] are typically not measured by such methods. Recently intrinsic support effects have been added to a kinetic model, but the reverse spill-over of only one reactant was considered. The simultaneous dual reverse spill-over (of the two reactants) [12] in microkinetic simulations (herein referred to as DRSO-MK simulations) show interesting results and furthermore offers an added dimension to the predictive power of the model. Microkinetic simulations of oxidation reactions have already shown themselves to provide an excellent theoretical model of the CO oxidation reactions on nanoparticles and cluster-based nanocatalysts [13,14]. The catalytic material itself consists of support material namely a thin metal-oxide film such as MgO [15]. After growing a film to a thickness of 10 ML, clusters can be deposited onto the film to produce the model catalyst. Mass selection of the clusters allows the tuning of the catalytic material affecting the turn-over frequency [3,16,17]. Experimental measurements of such catalysts form the basis of a comparison between the simulations and the physical situation. They are realised through a high * Corresponding author. Fax: +49 89 289 13389. E-mail address: [email protected] (C.J. Harding). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.07.017
level of control over the reactants. The use of two pulsed molecular beams, each containing a reactant, allows the mole fraction of the reactants to be accurately manipulated [3,16]. Coupled with the ability to independently vary the reaction temperature, coverage and size of clusters, a detailed investigation into turn-over frequency profiles shows remarkable effects such as the near room temperature catalysis of reactions ordinarily not observed for other catalytic systems. For a given temperature and coverage, varying the mole fraction of the reactants allows a turn-over frequency reaction profile for the catalyst to be determined [3]. The variation of these profiles with temperature then provides the basis for kinetic information to be extracted. This was achieved by the comparison of microkinetic simulations to the experimentally measured data. Based on Langmuir laws, microkinetic simulations have shown to reproduce experimental data based on larger nanoparticles [14,18] as well as smaller clusters [13]. Although Langmuir laws have been shown for Pd single crystals [1,2] it has not been clearly shown if the same mechanism applies to small size-selected clusters. Theoretical calculations have indeed shown that the Mars-van Krevelen mechanism involving a Pd nano-oxide could also offer a route to the catalytic oxidation of CO [19]. However as the Langmuir laws have been shown to be suitable for nanoparticles this mechanism is consequently adopted for smaller Pd clusters. For the smaller clusterbased catalysts, important experimental observations were only reproduced when the kinetic formulations were augmented by an additional calculation; that of reverse spill-over using the capture-zone model [20–22]. It has been illustrated that for small clusters (Pd13), due to the ratio of active centres to support material, the theoretical description is greatly enhanced by the addition of the migration of reactant molecules from the support to the reactive centres (reverse spill-over) using the capture-zone model. An increase in support
236
C.J. Harding et al. / Chemical Physics Letters 461 (2008) 235–237
αg
60
CO,O2
=1
product molecule, CO2, can be determined (r CO2 ). The important feature in the formulation between previous microkinetic simulations made on larger particles is the inclusion of the capture-zone via the 2 aCO;O value. The capture-zone model allows the reverse spill-over of g the reactants to be approximated by modelling a slow reservoir of the reactants which migrate from the support to the reactive centres (metal clusters). In these simulations the capture-zone is calculated by functionalising the saddle energy with the coverage 2 calculated from the kinetics equations. With aCO;O ¼ 1 the reverse g spill-over of one or both of the reactants can be removed from the calculation; this is illustrated in Fig. 1. Previous models have shown excellent agreement with aOg 2 ¼ 1 and aCO g 6¼ 1 whereas no such attempts have been undertaken with aOg 2 6¼ 1 because it is commonly considered that oxygen reverse spill-over can be safely ignored due to the magnitude of the interaction energies with MgO: a fair assumption. This has been found to produce high reproducibility of the experimentally measured mole fraction profiles (comparing Fig. 1b to Fig 2a). The inclusion of the coverage in the formulation of the saddle energy allows the phenomenon of the low temperature catalysis to be rationalised. The reverse spill-over effects of CO alone can be seen in Fig. 2a. The dramatic improvement in the low temperature catalysis regime is clearly illustrated. 2 In the solution of Eqs. (1)–(3) where aCO;O 6¼ 1, formulation of g the capture-zone model for both reactants is equivalent and the coverage dependency of the saddle energy is present in both cases. The effects of including the reverse spill-over of O2 can be seen in Fig. 2b. From a cursory glance, the incorporation of the dual spill-
a
40
-1
TOF (CO2 s )
20
0
b
Experiment
40
30
20
10
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction (xCO) Fig. 1. Turn-over profiles for the oxidation of CO using Pd13 clusters (at a coverage of 0.47%ML) supported on a MgO film (10 ML) measured at four different temperatures: 358 K (solid), 417 K (dotted), 440 K (dot-dashed) and 478 K (dashed). (a) Simulated mole fraction profiles using no reverse spill-over in the simulation. (b) Experimental values determined by a dual pulsed-beam technique.
CO CO g
r CO ¼ g a
kd hCO kL hCO hO
a
αgO 2 = 1 30
20
10 -1
TOF (CO2 s )
to cluster ratio should lead to an increase in the importance of reverse spill-over effects. Although the microkinetic modelling accurately describes the mole fraction turn-over profiles, it is based only on the reverse spill-over of one reactant (the oxygen reverse spill-over being ignored). When considering the CO oxidation, accurate descriptions can be achieved by considering only slow reservoirs of CO. Without considering both reactants spill-over explicitly, the agreement achieved by the model could be attributed to a fortuitous cancellation of errors which arise as both the Langmuir laws and the capture-zone formulation rely (to different extents) on approximations. The reverse spill-over of the second reactant can, however, be added. The DRSO-MK formulation1 (including the capture-zones of both reactants) is based on three key equations:
αgCO ≠ 1
40
0
αgCO,O 2 ≠ 1
30
b
20
ð1Þ
r O ¼ 2gO2 aOg 2 kL hCO hO
ð2Þ
r CO2 ¼ kL hCO hO
ð3Þ
where hCO,O is the coverage of reactants, kd is the desorption rate constant, kL is a Langmuir-based rate constant for the reaction, gCO;O2 is proportional to the incoming flux of reactants, rCO,O is the 2 rate of change of the reactants and aCO;O is the reverse spill-over g sticking coefficient for the reactants (also referred to as the global sticking coefficient). Eqs. (1)–(3) can be solved numerically using the GNU Scientific Library [23] and the turn-over frequency of the 1 A more detailed formulation is given in the supplementary material along with which the source, details and magnitudes for the numerical values are given.
10
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction (xCO) Fig. 2. Simulated turn-over profiles for the oxidation of CO using Pd13 clusters (at a coverage of 0.47%ML) supported on a MgO film (10 ML) measured at four different temperatures: 358 K (solid), 417 K (dotted), 440 K (dot-dashed) and 478 K (dashed). (a) The model including only the reverse spill-over of the CO reactant. (b) The model including only the reverse spill-over of both the CO and O2 reactants.
C.J. Harding et al. / Chemical Physics Letters 461 (2008) 235–237
40
478 K
-1
TOF (CO2 s )
30
20
10
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction (xCO) Fig. 3. DRSO-MK simulations of mole fraction dependent turn-over profiles illustrating the oxidation of CO using Pd13 cluster-based catalysts at 478 K. The model includes the reverse spill-over of both reactants. The sticking coefficient of O2 on the MgO film is arbitrarily chosen to be 0.25 (dashed), 0.5 (dot-dashed), 0.75 (dotted) and 1 (solid) to illustrate the effects of increasing mobility of a the a second reactant.
over has no dramatic effect on the simulated values. By considering the magnitude of the parameters (interaction of O2 and MgO) involved, this result is not surprising. However, a closer inspection shows that although the low temperature regime is predominantly unaffected by the O2 reverse spill-over, at higher temperatures small deviations occur. The position of the maximum of the TOF profile (most notably at 478 K) shifts marginally to lower mole fraction values but more noticeably is the effect of the TOF profile onset. The experiment (Fig. 1b) shows a displacement of the onset to higher mole fraction, deviating from the nested structure observed for lower temperature measurements. This increase in the deviation occurs as reverse spill-over of the CO is included and becomes more pronounced as the reverse spill-over of oxygen is incorporated into the model. Overall, dual reverse spill-over appears to improve the agreement between experiment and theory. Although the DRSO-MK model supports previously made assumptions, it should be noted that better agreement is achieved by including dual reverse spill-over. Given the nature of the reaction and the sticking propensity of O2 the changes are small. This model, however, offers the possibility for substantial improvements in the agreement between experimental measurements and theoretical simulations based on molecules with a more efficient reverse spill-over. The benefits of the dual reverse spill-over may be highlighted by simply reducing the O2 sticking probability on MgO and hence increasing the reverse spill-over of the second reactant. Although this cannot physically be achieved the importance of the dual reverse spill-over is illustrated and shows how the DRSO-MK model may be used to describe future experiments. In Fig. 3 the variation of the TOF profile at 478 K can be seen as the sticking coefficient is changed from 0.25 to unity. The effects illustrate the usefulness of the dual reverse spill-over. As the sticking coefficient of O2 on MgO is reduced from unity, the overall TOF begins to decrease. Within this range a decrease in the TOF more than twofold is observed. The actual values of the TOF, although reproduced very well by the DRSO-MK model, should be considered to be fortuitous, due to the fact that the model is based on Langmuir laws. However, the relative trends can be relied upon. As for the shape of the profile, the onset maintains a constant gradient but the decay of the CO2 production as the mole fraction is increased
237
becomes less severe. The most noticeable effect is, nevertheless, the migration of the maximum turn-over to lower mole fraction values. Additionally, although not presented here, the DRSO-MK model can also make predictions of the sticking coefficients and illustrate the coverage variation at different mole fraction values and temperatures. This offers a way to model the underlying physics of the system when such measurements are experimentally viable. In conclusion, for a catalyst which contains a large support to cluster ratio the role of the film in the reaction profile is extremely important and appears to be the main origin of the low temperature catalytic properties. For the reaction of CO and O2 on Pd-cluster-based catalysts the reverse spill-over of the O2 reactant is shown to play a small role in the improved description of the experimental data, whereas the CO makes a much larger improvement. As the main origin of the observed variations is the interaction of the reactants with the support, theoretical modifications to the reactant properties illustrate the importance of incorporating double reverse spill-over into microkinetic simulations for more mobile reactants. These are summarised by a decrease in the TOF values and a shift in the maximum of the TOF profile to lower mole fraction values. Consequently, the DRSO-MK formulation offers great potential for future simulations of more complicated reaction mechanisms such as the reaction of NO and CO on model catalysts. Acknowledgements We acknowledge financial support of the Deutsche Forschungsgemeinschaft (DFG) and of the European Union within the COST D41 program. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2008.07.017. References [1] T. Engel, G. Ertl, J. Chem. Phys. 69 (1978) 1267. [2] T. Engel, G. Ertl, Chem. Phys. Lett. 54 (1978) 95. [3] C.J. Harding, S. Kunz, V. Habibpour, V. Teslenko, M. Arenz, U. Heiz, J. Catal. 255 (2008) 234. [4] C.R. Henry, C. Chapon, B. Mutaftschiev, Surf. Sci. 163 (1985) 409. [5] J. Libuda, H.J. Freund, Surf. Sci. Rep. 57 (2005) 157. [6] M.A. Röttgen et al., J. Am. Chem. Soc. 129 (2007) 9635. [7] K. Judai, S. Abbet, A.S. Wörz, U. Heiz, C.R. Henry, J. Am. Chem. Soc. 126 (2004) 2732. [8] D. Ricci, A. Bongiorno, G. Pacchioni, U. Landman, Phys. Rev. Lett. 97 (2006). [9] M. Sterrer et al., Phys. Rev. Lett. 98 (2007). [10] M. Sterrer, T. Risse, M. Heyde, H.P. Rust, H.J. Freund, Phys. Rev. Lett. 98 (2007). [11] B. Yoon et al., Science 307 (2005) 403. [12] G. Prevot, C.R. Henry, J. Phys. Chem. B 106 (2002) 12191. [13] C.J. Harding, S. Kunz, V. Habibpour, U. Heiz, Phys. Chem. Chem. Phys. (2008), doi: 10.1039/B805688A. [14] J. Hoffmann, I. Meusel, J. Hartmann, J. Libuda, H.J. Freund, J. Catal. 204 (2001) 378. [15] U. Heiz, F. Vanolli, L. Trento, W.-D. Schneider, Rev. Sci. Instrum. 68 (1997) 1986. [16] M.A. Röttgen, K. Judai, J.-M. Antonietti, U. Heiz, S. Rauschenbach, K. Kern, Rev. Sci. Instrum. 77 (2006) 013302. [17] A.S. Wörz, K. Judai, S. Abbet, U. Heiz, J. Am. Chem. Soc. 125 (2003) 7964. [18] J. Libuda, T. Schalow, B. Brandt, M. Laurin, S. Schauermann, Microchim. Acta 156 (2006) 9. [19] B. Huber, P. Koskinen, H. Häkkinen, M. Moseler, Nat. Mater. 5 (2006) 44. [20] C.R. Henry, C. Chapon, C. Duriez, J. Chem. Phys. 95 (1991) 700. [21] M. Boudart, M.A. Vannice, J.E. Benson, Z. Phys. Chem.—Frankfurt 64 (1969) 171. [22] V. Matolin, E. Gillet, Surf. Sci. 166 (1986) L115. [23] M. Galassi, GNU Scientific Library Reference Manual, Network Theory Ltd., 2003.