ARTICLE pubs.acs.org/JPCC
Experiment-Based Kinetic Monte Carlo Simulations: CO Oxidation over RuO2(110) A. Farkas,† F. Hess,† and H. Over* Department of Physical Chemistry, Justus-Liebig-University, Heinrich-Buff-Ring 58, D-35392 Gießen, Germany
bS Supporting Information ABSTRACT: Kinetic Monte Carlo (kMC) simulations of the CO oxidation over RuO2(110) have been performed for a variety of different reaction conditions ranging from 107 to 10 mbar and temperatures from 300 to 600 K. The kMC simulations are based on reaction rates of elementary steps including diffusion, adsorption/ desorption, and recombination of surface CO and O. The activation barriers for these elementary processes are mostly taken from temperature programmed reaction and desorption experiments of well-defined coadsorbate layers on RuO2(110) under ultrahigh vacuum conditions. We show that the experimental kinetic reaction data under steady state reaction conditions both in the 107 mbar range and in a batch reactor up to 10 mbar are reconciled within this experiment-based kMC approach. Experimental in situ reflection absorption infrared (RAIR) spectra in the frequency range of the CO stretch vibration depend sensitively on both the adsorption site and the local environment of the CO molecules, encoding thus the surface distribution of CO and O during the reaction experiment. Simulated RAIR spectra of kMC-determined snapshots of the surface configuration of reactants under reaction conditions reproduce well the experimental ones. RAIR spectroscopy provides thus a clear-cut criterion for assessing the quality of kMC simulations in the CO oxidation on RuO2(110).
1. INTRODUCTION One of the main driving forces for studying elementary reaction steps in surface chemistry is the prospect to extrapolate these data via microkinetic modeling to industrially relevant temperatures and pressures, thereby bridging both the pressure and the materials gaps. Probably the most important reaction system which has ever been studied by this combined approach is the ammonia synthesis over Fe-based catalysts. Most of the elementary reaction steps have been determined by Ertl and coworkers under ultrahigh vacuum (UHV) conditions,1 whereas the extrapolation of the reaction kinetics to practical conditions (200300 bar, T = 600800 K) was successfully carried out by Stoltze and Norskov2 and by Bowker et al.3 Phenomenological microkinetic modeling relies on the assumption that only the averaged surface coverages of reaction intermediates enter the differential rate equations.4 This so-called mean field approximation is appropriate only if the reactants form an ideal mixture on the surface5 which, however, is often not met in real systems. For instance for the simple CO oxidation reaction over Pt(111), Gland and Kollin concluded from temperatureprogrammed desorption studies that the reacting O atoms and CO molecules adsorbed at the surface are not randomly distributed but rather are separated in CO and O domains where the surface reaction takes place at the perimeters of the oxygen islands.6 This view was later confirmed by in situ STM investigations7 and corroborated by careful kMC simulations.8 To overcome the shortcomings of phenomenological kinetic modeling, kinetic Monte Carlo (kMC) simulations can be utilized. r 2011 American Chemical Society
kMC simulations take into account the interaction between the molecules, their diffusion on the surface, adsorption/desorption of the reactants including different site demands, and the activation barriers for elementary reaction steps. In principle, kMC simulations provide the correct spatial distribution of the adsorbed intermediates on the surface since only reactants in the proper mutual positions participate in the surface reaction. In the seminal work of Ziff, Gulari, and Barshad9 (ZGB), the CO oxidation on a quadratic lattice was studied by kMC simulations, demonstrating that even a simple adsorption/reaction system leads to kinetic phase separation of the reactants on the surface depending on the stoichiometry of the reaction mixture. The kinetic phase separation is traced to different site demands of O2 and CO adsorption on the surface and to the formation of two neighboring vacant sites following the CO + O recombination step, whereas CO needs a single free surface site, dissociative adsorption of O2 requires two adjacent surface sites. The ZGB model neglects many details of a real system like mobility and interactions of surface species and the differences between adsorption sites. Despite these obvious shortcomings, qualitative insight may be gained in some instances like the CO oxidation over RuO2(110), where evidence from in situ RAIR spectroscopy points clearly toward kinetic phase separation.10 For quantitative comparison with experiment in more general cases, such as Received: May 20, 2011 Revised: October 27, 2011 Published: October 27, 2011 581
dx.doi.org/10.1021/jp204703p | J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
the CO oxidation over Pt(100), more sophisticated kinetic simulations methods have been developed.11,12 An evident step forward is to couple standard kMC simulations with ab initio calculations as suggested by Fichthorn and Weinberg13 and realized first by Hansen and Neurock.14 The socalled “ab-initio” kMC approach was recently also applied to study the kinetics of CO oxidation reaction over RuO2(110).15 Reuter et al. could qualitatively reproduce the experimental kinetic reaction data at T = 350K16 as a function of the CO/O2 feed ratio in the pressure range of 107 mbar. However, the maximum reaction rate was not found with a stoichiometric reaction mixture p(CO)/p(O2) = 2 (as in the experiment) but rather with p(CO)/p(O2) = 3.5 and the activity for other reaction mixtures was systematically underestimated. The most important elementary reaction step determining the overall-kinetics of the CO oxidation was argued to be the recombination between on-top CO and on-top O on RuO2(110) due to the relatively low energy barrier and the large abundance of both surface species. Reuter and Scheffler concluded that the population of bridging CO for typical gas feed compositions is negligibly small.17 However, these conclusions from ab initio kMC simulations are at variance with recent in situ RAIRS experiments (RAIRS: reflection absorption infra red spectroscopy) under identical reaction conditions.10 The RAIRS study has clearly indicated that bridging CO molecules are abundantly formed during the CO oxidation reaction at stoichiometric conditions over a wide pressure range (107 to 103 mbar) keeping the sample temperature at 350 K. The presence of bridging CO molecules is consistent with degenerate energy barriers for the recombination of on top CO with on-top O and bridging O.18 The presence of bridging CO is also reconciled with the high resolution electron energy loss spectroscopy (HREELS) experiment of Wang et al.16 whose kinetic experiments served as benchmark for the first principles kMC simulations of Reuter et al.15 After the CO oxidation reaction substantial amounts of bridging CO and the removal of most of the bridging O atoms have been identified with HREELS.16 It was this unsatisfying situation which motivated us to perform kMC simulation on the same reaction system, using, however, instead of ab initio calculated activation energies, as many experimentally determined energies as available from temperature programmed reaction experiments on well-defined and carefully prepared CO and O coadsorbate layers. We emphasize that the present kMC simulations are based purely on experimental data without any a posteriori adjustable parameters. We will show that this experimentally based kMC approach is able to reconcile both the kinetic reaction data and the in situ RAIRS data under a broad range of steady state reaction conditions. In principle one could have used simpler methods than kMC for micro modeling the CO oxidation over RuO2(110). However, from our RAIRS data10 it becomes clear that at least partial phase separation of the reactants occurs on the surface during the reaction so that the kMC method is required. Indeed, a direct comparison of kMC and kinetic modeling based on mean field approximations leads to significantly different results for the CO oxidation on RuO2(110).19
Figure 1. Ball and stick model of the (a) stoichiometric RuO2(110) surface and (b) mildly reduced RuO2 (110) surface, where all bridging O atoms are removed. The green balls are the oxygen atoms, the blue and red balls are the bulk and surface Ru atoms, respectively. At the stoichiometric surface there are two types of undercoordinated atoms, the bridging O atoms (Obr) and the 1f-cus Ru site; 1f-cus stands for onefold coordinatively unsaturated site. Removing the Obr atoms leave the 2f-cus Ru sites exposed (b). For the rest of the paper, we use simple representation of the mildly reduced surface by purple and red lines for the rows of 2f-cus and 1f-cus sites respectively, and adsorbed oxygen as green balls (a) and adsorbed CO as black balls (c).
RuO2(110) by accounting for fluctuations, correlations, and the spatial distribution of the reaction intermediates on the surface. The active sites of RuO2(110) surface (cf. Figure 1), i.e., the 1f-cus Ru sites, form one-dimensional chains which are separated by rows of one-dimensional bridging oxygen (Obr) rows.20 The origins of the kMC algorithm go back to the pioneering work of Bortz et al., while its first application to the coarse grained time evolution of chemical reactions is due to Gillespie.22 This form of the kMC algorithm will be described in detail in the next section. 2.1. kMC Algorithm. For performing kMC simulations on RuO2(110), the periodic lattice has to be defined first. In identifying the relevant surface sites, we recall briefly possible processes occurring in the CO oxidation at the RuO2(110) surface known from the literature. For instance on the stoichiometric RuO2(110) surface the 2f-cus Ru sites are occupied by bridging O (Obr), whereas the 1f-cus Ru sites are vacant (cf. Figure 1a). If oxygen or CO is exposed to the stoichiometric RuO2(110) surface at 200 K, on-top O (Oot) or on-top CO (COot) is formed above the 1f-cus Ru sites.23,24 CO on-top of 1f-cus Ru can react with both oxygen species Obr and Oot.25,26 If CO reacts with Obr, a bridging vacancy is formed in which CO can readily adsorb, forming a bridging CObr. Therefore, the periodic lattice for the kMC simulations of the oxidation of CO over RuO2(110) is chosen to consist of a two-dimensional array of on-top sites (ot) above 1f-cus-Ru and bridge sites (br) between neighboring 2f-cus Ru sites (cf. Figure 1b). The unit cell is 6.38 Å 3.11 Å = 19.84 Å2, containing one (ot) and one (br) site so that the area of an active site is about 10 Å2. The chosen lattice is finite with Nx and Ny repetition units in [001] and [110] direction, respectively and imposing periodic boundary conditions. The elementary steps considered in the kMC simulation of the catalytic CO oxidation on RuO2(110) encompass adsorption,
2. COMPUTATIONAL DETAILS kMC simulations are conducted to provide atomic-scale understanding of the steady-state CO oxidation reaction over 582
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
Table 1. List of Elementary Steps at the Surface Considered in the kMC Simulations of the CO Oxidation Reaction over RuO2(110)a elementary process
activation barrier (energy in kJ/mol)
frequency factor (1/s)
underlying data, ref
P1: adsorption: Oot
0
kinetic gas theory
TPD31
P2: adsorption: Obr P3: adsorption: COot
0 0
kinetic gas theory kinetic gas theory
TPD23 TPD24
P4: adsorption: CObr
0
kinetic gas theory
TPD32
P5: desorption: Oot + Oot f O2
2 84 = 168
microreversibility
TPD23
P6: desorption: Obr + Obr f O2
2 207 = 414
microreversibility
TPD23
P7: desorption: Oot + Obr f O2
84 + 207 = 291
microreversibility
P8: desorption: COot
129
microreversibility
TPD24
P9: desorption: CObr
193
microreversibility
TPD32
P10: diffusion Oot fOot: P11: diffusion Oot fObr
106 68
kBT/h kBT/h
theory23 STM33 theory27
P12: diffusion Obr fOot
68 + 123=191
microreversibility
P13: diffusion Obr fObr
87
kBT/h
theory23
P14: diffusion COot fCOot
106
kBT/h
theory29 STM33
P15: diffusion COot fCObr
58
kBT/h
theory23
P16: diffusion CObr fCOot
58 + 64=122
microreversibility
theory23
P17: diffusion CObr fCObr P18: recombination COot+Oot
87 89
kBT/h kBT/h
theory17 TPR34
P19: recombination CObr+Obr
133
kBT/h
TPR34
P20: recombination CObr+Oot
91
kBT/h
TPR34
P21: recombination COot+Obr
89
kBT/h
TPR34
a
Activation energies are given in kJ/mol and frequency factors are indicated. kBT/h (kB = Boltzmann constant, h = Planck constant, T = absolute temperature in K) is the universal frequency factor known from transition state theory.28 The frequency factors were set kBT/h assuming that the quotient of involved partition functions is of the order of unity.
partial pressure, area of the surface site (10 Å2), molecular mass, Boltzmann constant, absolute temperature, and sticking coefficient, respectively. The sticking coefficients S0 are assumed to be on the order of unity, which is close to the experimentally found values (1.0 for CO29 and 0.7 for O23). From the frequency factors for adsorption, those of the desorption processes are determined by imposing the constraint of micro reversibility (detailed balance).30 Assuming an initial distribution of CO and O on the lattice, the kMC iteration starts with the determination of the rate constants kn(α) of all possible elementary (local) processes α for a specific site n = (nx, ny) on the periodic lattice which are compatible with the local configuration of site n. For instance, if process α would be a diffusion process, then at least one neighboring site must be vacant. After identifying all possible reaction steps, their rates are summed up over all sites to obtain the rate Γ at which the next elementary step would occur. Rates of processes which need two sites, such as the dissociative adsorption of oxygen, are counted with a factor of 0.5. We use a single summation index i in the following which starts with the first site and the first process, running over all possible processes at this site, then the next site is considered and all possible processes at this site (cf. Table 1) and so on and so forth
desorption of the reactants CO and O2, diffusion of oxygen and CO on the surface along the [001] and the [110] directions, and four different elementary surface reactions of CO and O, namely the recombination of on-top CO with on-top O and bridging O as well as the recombination of bridging CO and on-top O and bridging O,27 leading altogether to a set of 21 elementary processes whose parameter values are summarized in Table 1. In addition to these 21 parameters the repulsion between on-top CO is explicitly included. Already from this compilation in Table 1, it is evident that there is not a single rate-determining step governing the reaction rate, but rather at least 8 elementary steps reveal similar activation energies of 6090 kJ/mol. The binding energies and the reaction barriers are determined from the kMC simulations of dedicated temperature programmed desorption (TPD) and temperature programmed reaction (TPR) experiments starting from well-defined coadsorbate structures on RuO2(110), while the diffusion barriers are taken from recent DFT calculations in combination with available STM experiments. The elementary processes are described within the transition state theory (TST),28 characterized by the activation energy and the frequency factor. According to TST the frequency factor is given by kBT/h times the quasi-partition function of the transition state divided by the partition function of the initial state. Similarly to the kMC-implementation of Reuter et al.,17 the ratio of partition functions for the surface processes (diffusion and recombination) is set of the order of unity, since these partition functions involve only vibrational degrees of freedom. For the adsorption processes kinetic gas theory is applied: kad = S0((Ap)/(2πmkBT)1/2) with p, A, m, kB, T, and S0 denoting the
Γ¼
sites el:steps
∑n ∑α
kn ðαÞ ¼
N
∑ ki i¼1
ð1Þ
Subsequently a random number F1 is chosen from the uniform distribution in the unit interval to select the process i0 by the 583
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
Figure 2. Left: Flowchart of the kMC algorithm. Right: Illustration of the criterion for choosing the next elementary process to be executed.
following condition: i0 1
∑
i¼1
ki < F1 Γ e
i0
∑ ki
i¼1
ð2Þ
The selected process i0 is executed and the clock time is advanced from t to: t lnðF2 Þ=Γ
ð3Þ
by randomly choosing a second number F2 ∈ (0,1]. This closes the kMC iteration. The total number of kMC iterations executed until steady state conditions are established is typically 106 for a 30 30 lattice and 107 for a 50 50 lattice. A flowchart of the present kMC implementation is shown in Figure 2. The computational framework used in this study is similar to that of Reuter et al.15 and Hong et al.35 A detailed description of the consistency tests carried out with the present kMC implementation is given in Appendix 1 in the Supporting Information. The starting configurations of the kMC were chosen with the aim to speed up the kMC simulation. If the CO oxidation reaction is studied under oxidizing conditions (i.e., excess of oxygen), then the stoichiometric RuO2(110) is taken as starting configuration, while the mildly reduced surface is used for kMC simulations of reducing reaction conditions. We carefully checked that the outcome of the kMC simulations did not depend on the choice of starting configuration. Steady state conditions of the kMC simulations were checked by monitoring the turn over frequency (TOF) and even more reliably, the actual surface coverage by O and CO. What kind of atomic scale information can be extracted from kMC simulations? Obviously, the most detailed information delivered by the kMC method concerns the distribution of the adsorbed species at the catalyst surface. Of special interest here is that such detailed theoretical information on the steady state surface configuration is amenable to confirmation by experimental methods. An experimental method of a comparable degree of accuracy as kMC is reflectionabsorption IR spectroscopy (RAIRS). By comparing simulated IR spectra for the kMC-computed stationary states with experimentally measured IR spectra, a very sensitive connection between theory and experiment can
Figure 3. Temperature programmed oxygen desorption spectrum (mass 32) from an oxygen precovered RuO2(110) surface. Blue line: kMC simulated TPD spectrum of oxygen obtained by adjusting the adsorption energies of bridging O and on-top O to align the peak temperatures; green line: experiment.23
be established. In addition to actual surface configurations, the number of produced CO2 molecules per active site and second, i.e., the turn over frequency (TOF), and the decomposition of this overall rate into elementary reactions steps can be determined. After reaching steady state, the time interval necessary to produce 1000 CO2 molecules is determined. The required time interval is evaluated several times (typically 5 times) and then averaged to provide the TOF via the differential quotient. 2.2. Evaluation of TPD and TPR Experiments. In TPR and TPD experiments, the sample temperature is increased linearly with time, for instance with 4.5 K/s as used in the present experiments. With kMC the desorption of reactants (TPD) or product (TPR) can be simulated with time dependent reaction rates using the First Reaction Method described by Gillespie36 and Jansen;37 details of its present implementation being given in Appendix 2 in the Supporting Information. We start with the experimental TPD spectra of oxygen on the RuO2(110) surface, which was saturated by exposing 10 L of O2 at room temperature whereby all bridge and 86% of the on-top sites were initially occupied by O.23 The TPD spectrum and the corresponding initial configuration are shown in Figure 3. The desorption of the surface-O species occurs associatively, the peaks at 400 and 1000 K corresponding to the Oot + Oot and 584
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
First we consider a stoichiometric RuO2(110) surface, which is exposed to 3 L CO at 200 K. This preparation leads to a surface where practically all 1f-cus Ru sites are occupied by COot and all 2f-cus Ru sites are occupied by Obr. While increasing the sample temperature, both the CO and CO2 signals are simultaneously monitored by a mass spectrometer. From the simulation of the CO2 trace (cf. Figure 4), we evaluate the activation energy for the recombination of on-top CO and bridging O to be 89 kJ/mol, whereas from the CO TD spectrum, the adsorption energy of on-top CO is found to be 129 kJ/mol. Splitting of the CO desorption peak around 300K is traced to an effective COotCOot pair interaction which is repulsive by 10.6 kJ/mol, which also causes a splitted CO2 formation peak, assuming a factor of 0.45 in the Bronsted EvansPolanyi relation. In a further experiment,26 the RuO2 (110) surface was exposed to 10 L of CO at room temperature, briefly annealed to 400 K and then exposed to molecular oxygen at 250 K. This preparation leads to a surface, where all bridging O atoms are replaced by bridging CO and the 1f-cus Ru sites are occupied to about 86% by on-top O. Since the sample temperature is 250 K, no reaction takes place between on-top O and bridging CO. Upon heating the sample, CO2 forms by recombination of on-top O and bridging CO at around 320 K and via oxygen diffusion into the bridge vacancies, bridging CO recombines with bridging O at 480 K (Figure 5, lower panel). A direct exchange process (scrambling) between CObr and Oot is not considered in this kMC simulation so that the experimentally observed desorption of on-top CO at 320 K (Figure 5, upper panel) cannot be reproduced. The simulation of the CO2 TPR data yield an activation energy of 91 and 133 kJ/mol for the recombination of bridging CO with ontop O and bridging O, respectively. The simulation of the CO desorption around 480 K from the reduced RuO2(110) surface provides an adsorption energy of bridging CO of 193 kJ/mol, neglecting CObrCObr repulsion. The activation energy of the remaining elementary reaction step, namely the recombination of on-top CO with on-top O, can be estimated from recent isotope labeling experiments.40 A mixed on-top CO and on-top O phase was prepared on RuO2(110) by exposing first 1 L 18O2 at room temperature and subsequently codosing 5 L CO at 200 K to saturate the surface. This leads to a mixed COot + 18Oot layer on the RuO2(110) surface containing only 16Obr lattice oxygen. Upon increasing the sample temperature, CO2 with mass 46 is formed at the same temperature as in the case of the on-top CO and bridging O recombination on stoichiometric RuO2(110) in Figure 4. From this experiment we conclude that the activation barrier for the recombination of on-top CO and on-top O is also 89 kJ/mol. At first glance, identical activation barriers for the recombination of on-top CO with on-top and with bridging O are surprising since the adsorption energy of O in on-top and in bridge sites differs by more than 120 kJ/mol. However, a recent DFTbased decomposition41 of the activation barriers indicates that not the activation of O, but rather the activation of CO determines the actual activation barrier for the COot + Oot and COot + Obr recombination reactions. Since the adsorption energy of CO is in both cases identical, the activation energies should also be identical.
Figure 4. Temperature programmed desorption (CO trace, upper panel) and temperature programmed reaction (CO2 trace, lower panel) spectra from a CO precovered stoichiometric RuO2(110) surface. Blue line: kMC simulation, green line: experiment.26
Figure 5. Temperature programmed desorption (CO trace, upper panel) and temperature programmed reaction (CO2 trace, lower panel) experiments from a mildly reduced RuO2(110) surface, where all bridging O are replaced by CO and the 1f-cus Ru sites are occupied by on-top O. Blue line: kMC simulation, green line: experiment.26
Obr + Obr recombinations, respectively. The experimentally measured peak at 1000 K is much larger than the kMC simulated one due to the contribution of O2 molecules resulting from the decomposition of the RuO2(110) layer, a process which was not considered in the kMC simulations. From these experimental spectra the activation energies for O2 desorption were determined by comparison with kMC-simulated TPD spectra obtained on a 100 100 lattice. Assuming nonactivated adsorption, the kMC simulated spectra depend only on two adjustable parameters, namely the adsorption energies of Oot and Obr, which are determined iteratively by aligning the positions of the two O2 desorption peaks in the kMC simulated and the experimental TPD spectrum. The adsorption energies of Oot and Obr turned out to be 84 and 207 kJ/mol, respectively, against 1/2 O2 molecule in the gas phase. Both derived values agree well with values from recent ab initio calculations.18,35,38,39 Next we simulated temperature programmed reaction (TPR) experiments to determine the activation energies of the recombination of CO and O on the surface as well as temperature programmed desorption data to determine the adsorption energies of CO.26
3. RESULTS AND DISCUSSION In the following we discuss the kMC simulations for various CO oxidation reaction scenarios under steady state conditions, 585
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
Figure 6. TOF as a function of the reactant feed ratio p(CO)/p(O2) during CO oxidation over RuO2(110) at 350 K. The partial pressure of oxygen was set to 107mbar. Circles: kMC simulation based on the parameter set of Table 1, squares: experimental values.16 kMC calculated spatial distributions of reactants at the surface during the CO oxidation reaction over RuO2(110) at 350 K are indicated for three different reaction feeds p(CO)/p(O2) = 1/2, 2, 10 while keeping the partial pressure of oxygen fixed at 107 mbar. Color code: green: oxygen, black: CO, purple stripes with gray background: free 2f-cus Ru sites, red stripes: free 1f-cus Ru sites.
Figure 7. Arrhenius plot of kMC-calculated TOF for the CO oxidation reaction over RuO2(110) in the 320390 K temperature range. The partial pressures p(CO) = 3 107 mbar and p(O2) = 1 107 mbar are kept constant. Snapshots of the surface configurations are indicated for selected temperatures. Color code: green: oxygen, black: CO, purple stripes with gray background: free 2f-cus Ru sites, red stripes: free 1f-cus Ru sites.
TOF (p(CO)/p(O2) ≈ 2), most of the bridging O atoms are replaced by CO and the rest of the 2f-cus Ru sites are vacant or occupied by bridging O. The 1f-cus Ru sites are mostly vacant and only a few on-top CO are visible, indicating that most of the on-top CO molecules react easily with oxygen to form CO2. This distribution of CO and O on the RuO2(110) surface is fully reconciled with the RAIR spectrum (cf. Figure 11), where mostly bridging CO is seen as a vibrational CO stretch band at 1866 cm1. For oxidizing reaction conditions (Figure 6, p(CO)/p(O2) = 1/2), the surface is mainly covered by bridging O and on-top O. The few CO molecules found on the surface reside mostly in bridge position. CO molecules which adsorb in the vacant on-top positions readily recombine with neighboring O, thus explaining the residual activity of this surface and the absence of on-top CO in the kMC snapshot. The great advantage of kMC simulations is that the overall reaction rate can be decomposed into the contributions of the relevant elementary reaction steps; this kind of information is not readily available by experiments. As seen in Figure 14 (right panel), the most frequently occurring reaction steps are the recombination of on-top CO with both bridging O and on-top O. Under strongly reducing reaction conditions (p(CO)/p(O2) = 10), the 2f-cus Ru sites are almost exclusively occupied by bridging CO. About half of the 1f-cus-Ru sites is populated by CO while the other half remains vacant, COot forming thus an approximately ordered (1 2) adsorbate layer. The incomplete coverage of on-top CO, despite the strongly reducing gas mixture, is due to the maximum in COot desorption at 320 K and the small CO partial pressure of 107 mbar. This surface is not poisoned by CO but rather should be quite active, as also experimentally observed. Between neighboring on-top CO there are several vacant 1f-cus sites on which molecular oxygen adsorbs dissociatively. Subsequently, on-top O and on-top CO recombine rapidly to form CO2, so that in the kMC snapshot no on-top O is visible. As seen in Figure 14 (right panel), the most frequently occurring reaction steps are the recombination of on-top O with both on-top CO and bridging CO. For the optimum reaction conditions p(CO)/p(O2) ≈ 2, all three recombination steps are equally important for CO oxidation reaction (cf. Figure 14).
starting with the kinetic reaction experiments of Wang et al.16 for various CO/O2 feed ratios in the 107 mbar range while keeping the sample temperature at 350 K. For simulating the Arrhenius type experiments, we varied the temperature from 320 to 390 K keeping the pressure at 107 mbar. Subsequently we analyzed the reaction data available for the CO oxidation reaction at the same temperature of 350 K but increasing the pressure from 107 mbar up to 103 mbar.10 Here, in situ infrared (RAIRS) data on stretch vibrations of adsorbed CO are available, which supply detailed information on the distribution of CO and O at the surface. Finally we analyze the kinetic CO oxidation data at higher pressures in mbar range and temperatures from 500 to 650 K.42 We would like to emphasize that these kMC simulations are based exclusively on the activation energies listed in Table 1 with no other adjustable parameters. 3.1. CO Oxidation at Low Temperatures and an Oxygen Partial Pressure of 107 mbar. We start the discussion of our kMC results with a comparison of the turnover frequency (TOF: number of produced CO2 molecules per surface area and second) as a function of the reactant feed ratio p(CO)/p(O2), while keeping the partial pressure of oxygen constant at 107 mbar and the sample temperature at 350 K (cf. Figure 6). Our simulated TOF values, based on the semiempirical parameter set of Table 1, are greater by a factor of 2.5 than the experimentally determined ones (near the optimum reaction conditions). On the other hand, the dependence of the TOF as a function of the reactant feed ratio is well reproduced. In particular for oxidizing reaction conditions, where the kMC simulations of Reuter and Scheffler17 indicate full deactivation, virtually the same activity as in the experiment is obtained with the present kMC approach. The same holds true for the reducing reaction conditions. For three typical reaction conditions p(CO)/p(O2) = 1/2, 2, 10 the surface configurations are shown as snapshots of the kMC simulations after steady state conditions have been reached (cf. Figure 6 insets). At optimum reaction conditions with highest 586
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
Figure 8. Decomposition of the kMC-determined overall reaction rate (320390 K) into the contributions of the three relevant recombination reaction steps on the surface, i.e., COot + Oot, CObr + Oot, and COot + Obr. The sum of the rates of these elementary reaction steps gives the overall reaction rate since the CObr + Obr recombination can be neglected. The partial pressures p(CO) = 3 107mbar and p(O2) = 1 107mbar are kept constant.
Figure 9. Arrhenius plot of the TOF data for the CO oxidation over RuO2(110) at sample temperatures in the range 470625 K and partial pressures p(CO) = 14 mbar and p(O2) = 5.50 mbar. The experimentally determined activation barrier of 77 ( 10 kJ/mol42 (solid green squares) is well reproduced by the present kMC results (solid blue discs) for temperatures up to 550 K, where saturation of the TOF values (not observed in the experiment) sets in. Snapshots of the kMC simulated surface configurations are indicated for selected temperatures. Color code: green: oxygen, black: CO, purple with gray background: free 2f-cus Ru sites, red: free 1f-cus Ru sites.
The temperature dependence of the activity can be simulated in kMC by setting different temperature values while keeping p(CO) = 3 107 mbar and p(O2) = 107 mbar fixed. The kMC simulated activity data are summarized in the form of an Arrhenius plot in Figure 7. Between 320 and 360 K the ln(TOF) increases linearly with 1/T. The corresponding apparent activation energy is 79 kJ/mol close to the value of 82 kJ/mol found in experiments.41 For higher temperatures the ln(TOF) trace bends over and reaches a nearly constant value. This behavior indicates that the TOF is determined by at least two elementary reaction processes, one of them achieving equilibrium at higher temperatures. From snapshots of the spatial distribution of reactants on the surface (cf. insets of Figure 7) the surface configuration related to the kinetic branch of the Arrhenius plot is dominated by CO adsorption. At 345 K the bridge positions are occupied by bridging CO, while about half of the 1f-cus sites are vacant and the rest is mostly occupied by on-top CO; only little on-top O is visible in this snapshot. At 380 K, i.e., in thermodynamic part of the Arrhenius plot, the bridge sites of RuO2(110) are occupied by both CO and oxygen, while the 1f-cus sites are mostly vacant. For low temperatures around 320 K, all bridge sites are occupied by CO and about 60% of the 1f-cus sites are occupied by CO; only rarely on-top O is seen. As indicated in Figure 8, the overall reaction rate is the sum of three elementary reaction steps, i.e., the recombination reactions: COot + Oot, CObr + Oot, and COot + Obr. The recombination rate of CObr + Obr is so small that this elementary step is omitted in Figure 8. Below 335 K, the CO oxidation reaction is dominated by the recombination of on-top CO with on-top O, although the recombination of CObr+Oot is still quite high (only by a factor of 23 smaller than that of COot + Oot). Increasing the temperature reduces the steady state coverage of on-top CO and therefore the recombination of COot + Oot decreases steeply. The recombination CObr + Oot dominates now the reaction behavior, since the bridge sites are mostly occupied by CO and the 1f-cus sites are mostly unoccupied, readily allowing for the adsorption of oxygen. This behavior is quite in contrast to the conclusions drawn from first principles kMC simulations by Reuter et al..15,17 At temperatures above 360 K, the bridge sites become gradually
populated by Obr, thus increasing the probability that a gas phase CO adsorbing on-top would recombine with a neighboring bridging O. Therefore at high temperatures, both types of recombinations CObr + Oot and COot + Obr are quite efficient. 3.2. CO Oxidation at Temperatures above 500 K and an Oxygen Partial Pressure in the mbar Range. We have shown that the experimentally determined activation barriers of elementary steps used in the present kMC simulations are able to describe the kinetic reaction data at 107 mbar at varying feed ratios and a reaction temperature of 350 K. In the following we will demonstrate that kMC with the very same activation barriers as used in section 3.1 is able to reproduce the experimental temperature dependence of the reaction kinetics at pressures of the order of 10 mbar as well. In Figure 9 we present an experimentally determined Arrhenius plot for the CO oxidation over RuO2(110) for partial pressures of p(CO) = 14 mbar and p(O2) = 5.50 mbar and temperatures ranging from 490 to 626 K. The experimentally determined apparent activation energy is 77 kJ/mol.42 With kMC simulations the TOF were determined in the temperature range from 470 to 625 K, using the same partial pressures as in the experiment. All kMC-simulated TOF values are by a constant factor of 65 higher than the experimental TOF values at low temperature. The kMC derived Arrhenius plot leads to an apparent activation energy of 80 kJ/mol in excellent agreement with the experiment. We should note that none of the 21 elementary processes in Table 1 has an activation energy of 80 kJ/mol but many of the activation energies are close to this value, such as the diffusion of CO and O and three of the four recombination reactions (CO + O). The good agreement with the experimental apparent activation energy evidence that the intricate interplay of these elementary processes is well accounted for in the present experiment-based kMC simulations. The main difference between kMC simulations and experiment is a saturation of the TOF above 550 K, which is not observed experimentally. This deviation indicates that values 587
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
Figure 10. Decomposition of the kMC-determined overall reaction rate (470625 K) into the contributions of the three relevant recombination reaction steps on the surface, i.e., COot + Oot, CObr + Oot, and COot + Obr. The sum of the rates of these elementary reaction steps gives the overall reaction rate since the CObr + Obr recombination can be neglected. The partial pressures p(CO) = 14 mbar and p(O2) = 5.50 mbar are kept constant.
Figure 11. Experimental RAIR spectra in the CO bond stretching range, recorded during the oxidation of CO over RuO2(110) at 350 K with p(O2) = 107 103 mbar and p(CO) = 2 p(O2).10
obtained under UHV for the desorption energies of CO (cf. Table 1) tend to be somewhat underestimated, leading to a shift of the adsorption/desorption equilibrium toward desorption at too low temperatures. In other words, kMC simulations at higher partial pressures but identical stoichiometry should result in a straight Arrhenius line over the whole experimental temperature range. Indeed this behavior has been observed in the kMC simulations for a reaction mixture of p(CO)= 1500 mbar, p(O2)= 500mbar (data not shown). As shown in Figure 10, below 530 K the CO oxidation reaction is dominated by the recombination of on-top CO with on-top O, although the recombination of on-top O with bridging CO is only by a factor of 2 less effective. In the range 530560 K the recombination of on-top CO with on-top O and the recombination of on-top O with bridging CO are equally efficient. Above 560 K, the activity of the COot + Oot recombination is only slightly higher than that of the other two elementary recombination steps, CObr + Oot and COot + Obr. Since all bridging positions are occupied by O, the contribution of COot + Obr is as high as that of COot + Oot for temperatures above 600 K. 3.3. CO Oxidation at 350 K and an Oxygen Partial Pressure from 107 to 103 mbar. In a recent RAIRS experiment10 the CO oxidation reaction on RuO2(110) was studied in situ at a constant temperature of 350K under the stoichiometric reactant mixture p(CO)/p(O2) = 2 and varying oxygen partial pressure form 107 to 103 mbar. Since the observed CO stretching frequency depends sensitively on the local environment, the RAIR spectra (Figure 11) have been shown to provide unique information about the distribution of the reactants on the surface. At p(O2) = 107 mbar, the IR spectrum reveals only one vibrational band at 1866 cm1 which is unambiguously assigned to bridging CO sparsely populating the 2f-cus-Ru sites with no 1fcus species in the direct neighborhood. By increasing the partial pressure of oxygen to 106 mbar while keeping the stoichiometry of the reactant feed, an on-top CO species is identified in addition to the bridging CO, both residing in domains with a high local CO coverage. These domains, characterized by the two vibrational bands at 2062 and 2083 cm1, are stable under reaction conditions because the high local CO coverage precludes the
Figure 12. Oxidation of CO over RuO2(110) at 350 K with stoichiometric reactant feed p(CO) = 2 p(O2). Left: adsorbate configurations from kMC simulations for p(O2) = 107103 mbar. Right: computed RAIR spectra for each respective configuration (red curve) and experimental RAIR spectra (black curve, from Figure 11). Color code: green: oxygen, black: CO, purple stripes with gray background: free 2f-cus Ru sites, red stripes: free 1f-cus Ru sites. IR spectra: red (calculated) and black (experimental) vertical bands highlight the characteristic IR absorptions of different structures of adsorbed CO (details are given in the text).
emergence of pairs of neighboring vacant sites, which are necessary for the adsorption of O2. Consequently, O2 cannot adsorb and react with CO in these domains, which would eventually grow to cover a larger fraction of the surface. This behavior is nicely seen in Figure 11, where with increasing reactant pressure the corresponding bands at 2062 and 2083 cm1 only grow in intensity without changing their shape. At the same time the emergence of similar domains containing only O, in both on-top and bridging positions can be observed. 588
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
The CO molecules which adsorb into vacancies within these O-covered domains lead to the vibrational band at 2146 cm1, as observed in Figure 11. The RAIR spectra remain qualitatively unchanged while further increasing the partial pressure of the reactants from 106 mbar to 103 mbar, indicating that adsorbed O and CO remain separated in distinct domains. In Figure 12 we present the kMC-simulated adsorbate configurations under the same conditions as in the RAIRS experiment of Figure 11 together with the respective RAIR spectra, experimental and computed. The dynamical parameters used in the computation of the IR spectra (cf. Appendix 3 in the Supporting Information) have been determined from an extended collection of experimental IR bands (fingerprints) measured on well-defined CO and O coadsorbate configurations prepared on RuO2(110).43 While the IR spectra of all ordered configurations used in the fingerprinting process are well reproduced by this choice of parameters, we anticipate that IR spectra of disordered configurations, such as those resulting from kMC simulations, can also be reliably computed using the same set of dynamical parameters. In Figure 12 we show a (26 26) section from the original kMC-generated configurations (50 50) used in the calculation of the IR spectra. Similarly to the experimental RAIR spectra (the black curves in Figure 12) a wide band peaking in the range 20602080 cm1 is the principal feature in the computed IR spectra (106103 mbar), correlating with the large CO coverages observed in the kMC-generated configurations. The CO species responsible for the principal band at 20602080 cm1 nicely substantiate the notion of oxygen-free, compact CO-covered domains (“islands”) proposed as a heuristic model in a recent work.10 The present kMC simulations
reveal that the high coverage CO domains actually consist of an extended network of bridging and on-top CO (Figure 12, insets). At p(O2) = 106105 mbar this network may be envisaged as a phase of on-top vacancies with approximately (1 2) symmetry, with characteristic IR absorption at 2062 cm1. Upon increasing the pressure to p(O2) = 104 mbar, the on-top vacancies are gradually filled by CO, inducing a stepwise transition from the (1 2) vacancy phase to a fully CO-covered surface, with characteristic IR absorption at 2083 cm1. In the calculated IR spectra (104103 mbar, Figure 12) this transition is reflected in the 2083 cm1 band becoming dominant over the 2062 cm1 band. We mention that in the RAIRS experiment such a transition does occur only for p(O2) g 102 mbar (cf. Figure 7.4 in ref 43). Throughout the entire pressure range (106103 mbar), the surface keeps its combined structure of a (1 2) vacancy phase (2062 cm1) with some fully CO-covered areas (2083 cm1). 3.4. Comparison of Experiment Based kMC with “FirstPrinciples” kMC. In Figure 13 we compare the kMC-simulated TOF values using the experiment based and the first principles parameter sets, plotted as a function of the reaction feed ratio p(CO)/p(O2) for T = 350 K and p(O2) = 107mbar, with the experimental values measured under the same conditions. The “first principles” parameter set of Reuter results in maximal TOF values which are almost in quantitative agreement with the experiment, but the optimum reaction feed is determined to be p(CO)/p(O2) = 3.5, while that of the experiment is p(CO)/ p(O2) = 2.5. For slightly more oxidizing reaction conditions than the optimum feed ratio of 3.5, the TOF drops dramatically by 2 orders of magnitude within a small variation of p(CO)/p(O2) which is not reconciled with the experiment. The experiment-based parameter set results in kMC-determined TOF values which are higher by a factor of 2.5; however, the overall dependence on the p(CO)/p(O2) feed ratio is in good agreement with the experiment. To assess the quality of agreement between the experiment-based kMC and the kinetic data of Wang et al.16 in Figure 13, one has to bear in mind that experimental TOF values are subject to large systematic uncertainties, due to changes in the sensitivity of the mass spectrometer toward CO2 in different reaction mixtures, in identifying steady state conditions when the mass spectrometer signal is drifting, and in estimating the number of active sites on the surface. On the other hand, the variation of TOF values with the feed ratio is a more robust indicator since most of the above uncertainties in the experimental TOF do not depend on the reaction mixture, to a first approximation. Not only the TOF values are differently reproduced by experiment and “first principles” based kMC simulation, but also
Figure 13. kMC simulated TOF values as a function of the reaction feed ratio p(CO)/p(O2) with p(O2) = 1 107 mbar at T = 350 K, obtained using two different sets of energy barriers, one based on first principle calculations,15 the other on experiments (cf. Table 1). For comparison the experimental TOF are shown.16
Figure 14. Contributions of each elementary O + CO recombination step (Oot + COot, Oot + CObr, and Obr + COot) to the total TOF, simulated with the parameters sets of Reuter et al. (left) and the experimentally determined parameter set (cf. Table 1) (right). Due to the high activation barriers for Obr + CObr, this elementary process does not contribute significantly to the overall rate at 350 K and is therefore not shown here. 589
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
the most frequently occurring recombination step is different as shown in Figure 14. “First principles” kMC indicates that practically only one elementary reaction step, namely the recombination of on-top CO and on-top O (COot + Oot) occurs in the whole range of feed ratio p(CO)/p(O2) from 0.5 to 10. This can be easily understood since, by the first principles calculation, the activation barrier for the recombination of on-top CO with bridging O (COot + Obr) is by 40 kJ/mol higher than that of the COot + Oot recombination, the bridge positions remaining therefore almost exclusively occupied by oxygen. Quite in contrast, the present experiment-based kMC study indicates that all elementary recombination steps, except the recombination of bridging O with bridging CO, contribute significantly to the overall TOF value (cf. Figure 14). For all reaction feed ratios p(CO)/p(O2) studied, the recombination Oot + CObr occurs most frequently. Under optimum reaction conditions, the recombination of on-top CO with bridging O contributes as much as the dominant Oot + CObr recombination. Altogether, the preferred reaction mechanism determined by the kMC simulations, i.e., the most frequently occurring elementary reaction step, changes drastically when the “first principles” or the experiment-based activation energy set is used. Unlike the present results obtained with the experiment-based parameter set, “first principle” kMC simulations15,17 are not consistent with vibrational spectroscopy results, neither in the UHV (HREELS, RAIRS) nor in the mbar range (RAIRS). Passing review on the agreement of the present experimentbased kMC results with the available experimental data, it is fully justified to consider the experiment-based set of activation energies, rather than the first-principles derived one, as the more reliable one.
4. CONCLUSIONS kMC simulations of the CO oxidation over RuO2(110) have been devised for a variety of different reaction conditions for pressures in the 107 mbar range and temperatures from 320 to 390 K and for pressures up to 10 mbar and temperatures from 470 to 620 K. The kMC simulations are based on reaction rates of elementary steps including diffusion, adsorption/desorption and recombination of surface CO and O, which are treated within the transition state theory. The guiding principle in obtaining a consistent parameter set for the kMC simulations was to use experimentally derived values as extensively as possible; a similar approach was used previously for the CO oxidation on rhodium.44 The diffusion barriers, being experimentally not easily accessible, have been adopted from DFT calculations corroborated with STM derived values. The activation barriers for all other elementary processes (adsorption/desorption and recombination steps) have been obtained from temperature programmed reaction experiments of well-defined CO and O containing coadsorbate configurations, such that no adjustable parameter is left for the kMC simulations of the CO oxidation on RuO2(110). With this experiment-based kMC approach we are able to reconcile both the kinetic reaction data and the infrared spectroscopy data under steady state flow conditions in the 107 mbar range. The kMC simulations retrieved an apparent activation energy of 79 kJ/mol for a reaction mixture consisting of p(CO) = 3 107 mbar and p(O2) = 1 107 mbar. Kinetic MC simulations based on this very same parameter set of activation energies reproduce equally well the experimental Arrhenius plot for p(CO) = 14 mbar and p(O2) = 5.5 mbar for temperatures
up to 550 K, disclosing an apparent activation energy of 80 kJ/mol. The quantitative agreement of experimental and kMC simulated apparent activation energies42 shows that the intricate interplay of elementary reaction steps with similar activation energies in the range of 80120 kJ/mol is properly accounted for. Studies of the reaction kinetics at 350 K are particularly demanding, since various processes such as diffusion, different CO+O recombination steps and adsorption/desorption of CO have similar activation energies of 80120 kJ/mol. At 350 K all of these processes become therefore comparably important and must be considered simultaneously. Temperature dependent TOF measurements, represented in the form of Arrhenius plots, are particularly useful in judging the correct balance of activation energies in a kMC simulation. Besides being a versatile tool for the analysis of kinetic reaction data, kMC provides the proper scientific language to discuss reaction kinetics on the molecular level. A benchmark experiment in surface reaction kinetics should provide detailed information on the spatial distribution of reactants at the catalyst surface under reaction conditions. Among the surface sensitive techniques scanning tunnelling microscopy would provide the most direct access to the actual surface configurations under reaction conditions, serving as an experimental benchmark for kMC simulated snapshots.7,8 Similar information can also be retrieved by RAIRS since the stretching frequency of absorbed CO depends not only on the adsorption site but also on the local adsorption environment of the vibrating CO molecule. If systematic RAIRS experiments of the CO adsorption in a variety of well-defined local environments have been performed, such as is the case with the CO oxidation over RuO2(110),43 then the kMC simulated snapshots of the spatial distribution of reactants can directly be converted to a simulated RAIR spectrum which upon comparison with the experimental RAIR spectra, would give an important feedback on the accuracy of the simulated configurations and indirectly, on the reliability of the parameter set used. Examples in this direction, combining equilibrium MC simulations and simulated IR spectroscopy results are already available, illustrating the usefulness of this combined approach for simpler systems, like the adsorption/ desorption equilibrium of CO on Pt(111).45 For the more complex system of the CO oxidation reaction over a transition metal oxide surface, this valuable experiment-theory feedback connection has been successfully demonstrated here. This direct feedback loop between theory and experiment is able to provide a much needed validation procedure for the k-MC generated microscopic structures on the catalyst surface. We are convinced that a more extensive application of such atomically sensitive validation procedures will help to use more fully the potential of kMC in the interpretation of experimental data from reaction studies.
’ ASSOCIATED CONTENT
bS
Supporting Information. Details about the consistency tests on the kMC code (Appendix 1), the implementation of temperature programmed reaction and desorption simulations (Appendix 2), as well as the calculation of IR spectra from surface configurations determined by kMC simulations (Appendix 3) are provided. This material is available free of charge via the Internet at http://pubs.acs.org.
590
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
The Journal of Physical Chemistry C
ARTICLE
’ AUTHOR INFORMATION
(34) Wendt, S.; Seitsonen, A. P.; Over, H. Catal. Today 2003, 85, 167–175. (35) Hong, S.; Karim, A.; Rahman, T. S.; Jacobi, K.; Ertl, G. J. Catal. 2010, 276, 371–381. (36) Gillespie, D. T. Markov processes: an introduction for physical scientists; Academic Press: New York, 1992; Chapter 5. (37) Jansen, A. P. J. Comput. Phys. Commun. 1995, 86, 1–12. (38) Kiejna, A.; Kresse, G.; Rogal, J.; De Sarkar, A.; Reuter, K.; Scheffler, M. Phys. Rev. B 2006, 73, 035404. (39) Wang, H.; Schneider, W. F. J. Chem. Phys. 2007, 127, 064706. (40) Wendt, S.; Knapp, M.; Over, H. J. Am. Chem. Soc. 2004, 126, 1537–1541. (41) Assmann, J, Narkhede, V., Breuer, N. A., Muhler, M., Seitsonen, A. P., Knapp, M., Crihan, D., Farkas, A., Mellau, G., Over, H. J. Phys.: Condens. Matter 2008, 20, 184017. (42) Over, H.; Balmes, O.; Lundgren, E. Catal. Today 2009, 145, 236–242. (43) Farkas A., 2008, PhD Thesis “In situ IR spectroscopic studies of the CO oxidation reaction over a ruthenium model catalyst ”; JLU Giessen; http://geb.uni-giessen.de/geb/volltexte/2008/5988/. (44) Hopstaken, M. J. P.; Niemantsverdriet, J. W. J. Chem. Phys. 2000, 113, 5457–5465. (45) Fichthorn, K. A.; Gulari, E.; Ziff, R. M. Surf. Sci. 1991, 243, 273–294.
Corresponding Author
*E-mail:
[email protected]. Fax: ++49-641-9934559. Author Contributions †
These authors contributed equally to the present paper.
’ ACKNOWLEDGMENT We thank Dr. Georg Mellau for stimulating discussions during the incipient phase of the present work. ’ REFERENCES (1) Ertl, G. Crit. Rev. Solid State Mater. Sci. 1982, 10, 349 and references therein. (2) Stoltze, P.; Norskov, J. K. Phys. Rev. Lett. 1985, 25, 2502–2505. (3) Bowker, M.; Parker, I.; Waugh, K. C. Surf. Sci. 1988, 197, L223–L229. (4) Laidler, K. J. Chemical Kinetics; Harper & Row: New York, 1987. (5) Stoltze, P. Prog. Surf. Sci. 2000, 65, 65–150. (6) Gland, J. L.; Kollin, E. B. J. Chem. Phys. 1983, 78, 963–974. (7) Wintterlin, J.; V€olkening, S.; Janssens, T. V. W.; Zambelli, T.; Ertl, G. Science 1997, 278, 1931–1934. (8) V€olkening, S.; Wintterlin, J. J. Chem. Phys. 2001, 114, 6382–6395. (9) Ziff, R. M.; Gulari, E.; Barshad, Y. Phys. Rev. Lett. 1986, 56, 2553–2556. (10) Farkas, A.; Mellau, G.; Over, H. J. Phys. Chem. 2009, 113, 14341–14355. (11) Liu, D. J.; Evans, J. W. Chem. Phys. Chem. 2010, 11, 2174–2181. (12) Liu, D. J.; Evans, J. W. Surf. Sci. 2009, 603, 1706–1716. (13) Fichthorn, K. A.; Weinberg, W. H. J. Chem. Phys. 1991, 95, 1090–1096. (14) Hansen, E. W.; Neurock, M. J. Catal. 2000, 196, 241–252. (15) Reuter, K.; Frenkel, D.; Scheffler, M. Phys. Rev. Lett. 2004, 93, 116105. (16) Wang, J.; Fan, C. Y.; Jacobi, K.; Ertl, G. J. Phys. Chem. B 2002, 106, 3422–3427. (17) Reuter, K.; Scheffler, M. Phys. Rev. B 2006, 73, 045433. (18) Seitsonen, A. P.; Over, H. Surf. Sci. 2009, 603, 1717–1723. (19) Temel, B.; Meskine, H.; Reuter, K.; Scheffler, M.; Metiu, H. J. Chem. Phys. 2007, 126, 204711. (20) Over, H.; Kim, Y. D.; Seitsonen, A. P.; Wendt, S.; Lundgren, E.; Schmid, M.; Varga, P.; Morgante, A.; Ertl, G. Science 2000, 287, 1474–1476. (21) Bortz, A. B.; Kalos, M. H.; Lebowitz, J. L. J. Comput. Phys. 1975, 17, 10–18. (22) Gillespie, D. T. J. Comput. Phys. 1976, 22, 403–434. (23) Kim, Y. D.; Seitsonen, A. P.; Wendt, S.; Wang, J.; Fan, C.; Jacobi, K.; Over, H.; Ertl, G. J. Phys. Chem. B 2001, 105, 3752–3758. (24) Kim, Y. D.; Seitsonen, A. P.; Over, H. Phys. Rev. B 2001, 63, 115419. (25) Fan, C. Y.; Wang, J.; Jacobi, K.; Ertl, G. J. Chem. Phys. 2001, 114, 10058–10062. (26) Wendt, S.; Seitsonen, A. P.; Kim, Y. D.; Knapp, M.; Idriss, H.; Over, H. Surf. Sci. 2002, 505, 137–152. (27) Over, H.; Muhler, M. Prog. Surf. Sci. 2003, 72, 3–17. (28) Chorkendorff, I., Niemantsverdriet, Concepts of Modern Catalysis and Kinetics; Wiley-VCH: Weinheim, Germany, 2003. (29) Kim, Y. D.; Seitsonen, A. P.; Over, H. Phys. Rev. B 2001, 63, 115419. (30) Kang, H. C.; Weinberg, W. H. Acc. Chem. Rec. 1992, 25, 253–259. (31) B€ottcher, A.; Niehus, H. Phys. Rev. B 1999, 60, 1439614404. (32) Seitsonen, A. P.; Kim, Y. D.; Knapp, M.; Wendt, S.; Over, H. Phys. Rev. B 2002, 65, 035413. (33) Kim, S. H.; Wintterlin, J. J. Phys. Chem B 2004, 108, 14565–14569. 591
dx.doi.org/10.1021/jp204703p |J. Phys. Chem. C 2012, 116, 581–591
