Kinetic Monte Carlo simulations of the oscillatory CO oxidation at high pressures: The surface oxide model

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Chemical Physics 348 (2008) 11–20 www.elsevier.com/locate/chemphys

Kinetic Monte Carlo simulations of the oscillatory CO oxidation at high pressures: The surface oxide model V.K. Noussiou a,b, A. Provata a,* a

Institute of Physical Chemistry, National Center for Scientific Research ‘‘Demokritos’’, 15310 Athens, Greece b Department of Chemistry, University of Athens, 15701 Athens, Greece Received 21 December 2007; accepted 4 February 2008 Available online 16 February 2008

Abstract The oxidation of CO on metal surfaces is known to exhibit interesting oscillatory behaviour and spatiotemporal patterns. Oscillations arising at high pressures (mbar to atmospheric) are attributed to the ‘‘oxide model”, in which the slow oxidation and subsequent reduction of the surface is coupled to the steps of the CO oxidation mechanism. In the present work a mesoscopic skeleton model of this system is formulated in the form of a kinetic Monte Carlo (KMC) scheme which implements the Langmuir–Hinshelwood (LH) mechanism of CO oxidation with additional mechanistic steps taking into account the surface oxide formation. Oscillations in this KMC oxide model are obtained when a different reactivity is attributed to the two phases – metal surface and oxidised surface. The parameter space is explored and the ranges where oscillations are prominent are reported. As a general conclusion of this work, oscillations and clustering of the species are observed within the system’s ‘‘reactive” regions when either of the two phases has a considerably higher reactivity than the other. Larger amplitude oscillations are attained when the metal surface is assumed to be more reactive than the oxidised surface. Ó 2008 Elsevier B.V. All rights reserved. Keywords: Kinetic Monte Carlo simulations; CO oxidation; Ziff–Gulari–Barshad model; Oxide model

1. Introduction The oxidation of CO on Pt-group metal surfaces exhibits interesting nonequilibrium dynamic properties, such as rate oscillations and spatial or spatiotemporal patterns on the surface [1–5]. Oscillations that arise at low pressures (<1 mbar) are attributed to a well defined surface reconstruction mechanism of the catalyst. The so called ‘‘reconstruction model” has been extensively studied experimentally [1] (and references cited therein), [6–9] as well as through simulations [4] (and references cited therein), [10–12]. Oscillations at higher pressures (up to atmospheric) have been attributed to oxidation of the metal catalyst [1,13]. Models describing this mechanism, often called the ‘‘oxide model”, agree on the presumption that oscillations emerge due to a coupling of the reaction *

Corresponding author. Tel.: +30 210 6503964; fax: +30 210 6511766. E-mail address: [email protected] (A. Provata).

0301-0104/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2008.02.013

steps to a slower step of surface oxidation. There is however ongoing discussion about whether the emerging oxide phase is of lower or higher reactivity than the free metal surface. It was originally assumed that the oxide surface is inert or of low activity [13–15]. Sales et al. [13] pointed out in 1982 that the oscillations at atmospheric pressure are related to a slow oxidation/reduction of the catalytic surface. They found experimental evidence for the presence of two types of oxygen on Pt. One was chemisorbed oxygen, which was reported to react readily with chemisorbed CO. The other was the ‘‘oxide” type which forms at higher oxygen pressure and which according to Sales et al. is more strongly bound and non-stoichiometric. They thus reported a slower reaction rate for the oxide type than for the chemisorbed oxygen. Later studies showed that the reaction is actually faster in the oxide phase [16–21]. Experiments on Pt(1 1 0) and Pd(1 0 0) under O2 rich atmospheric pressure conditions,

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showed that the oxide film formed is superior in catalytic activity. Hendriksen et al. [20,21] suggested that the high reaction rate on the oxide results from the low stability of the oxide. They also suggested that whereas the reaction kinetics on the metallic surface follows the Langmuir–Hinshelwood scheme (adsorbed CO reacts with adsorbed O atoms), the reaction kinetics in the oxide phase follow a Mars–van Krevelen (MvK) mechanism [22]. According to the MvK mechanism, oxygen that is bound to the surface as oxide can directly react with gas phase CO molecules, instead of with adsorbed CO molecules in the LH mechanism. The interchange between the two mechanisms dominating the metallic and oxide phase is what drives the oscillations according to Hendriksen et al. Numerous theoretical works have been conducted based on one or the other perception of the oxide model. Simulations of the oscillations attributed to the ‘‘oxide” model according to Sales et al. have been going on for long [23– 27]. However, after the recent experimental findings on surface oxide properties, there have been theoretical works which treat the oxide as highly reactive [28,29]. The present work presents a skeleton kinetic Monte Carlo model of a system in which one of the species (oxygen) undergoes a transformation such that its dynamics of interaction with other species (CO) is modified. In the oxide model, oxygen bonds to the catalyst, oxidising it, while its dynamics of reaction with the adsorbed CO change. The transition of the adsorbed oxygen on metal phase to the oxide phase is synergetic – groups of O atoms cooperate in oxidising the surface – and occurs collectively – many groups do that at the same time – [21]. The oxide surface that has formed can then be removed through reaction with CO – at a slower or faster rate. These two actions can lead to a repeated oxidation/reduction of the catalytic surface, affecting the dynamics and resulting in oscillations of the species concentrations. The model proposed here studies the emergence of oscillations when the reactivity of the oxide is different than the reactivity on the metal, whether it is larger or smaller – both possibilities are explored. The proposed model initially follows the main traits of the Ziff–Gulari–Barshad (ZGB) model (1986) [30], making however substantial extensions to take into account the surface oxide formation. The standard ZGB model used the kinetic Monte Carlo method to implement on lattice a Langmuir–Hinshelwood (LH) scheme describing the CO oxidation mechanism. The ZGB model has a single independent variable, y CO , which is the mole fraction of CO in the gas phase and expresses the probability of CO adsorption. CO thus adsorbs on one lattice site with probability y CO . O2 adsorbs with probability y O2 ¼ 1  y CO (the two mole fractions constitute the whole of the gas phase: y CO þ y O2 ¼ 1) and it is assumed to dissociate to two oxygen atoms, needing two neighbouring lattice sites for adsorption. The reaction of the adsorbed CO and O (atom) and desorption of the CO2 product in the standard ZGB model take place instantaneously.

The ZGB model produced rich critical behaviour and important features of the real system, that is, ‘‘poisoned” and ‘‘reactive” steady states, which are seen also in experiments on the CO–O2 system. A ‘‘poisoned” steady state is a state where the surface is fully covered by one of the species, whereas a ‘‘reactive” steady state is when more than one species coexist and interact on the lattice. In the ZGB model, poisoning by O (lattice fully covered by adsorbed O) is possible (although it is absent in the real system) and is found to occur for 0 6 y CO < 0:389; the reactive area is positioned at 0:389 6 y CO 6 0:525 and the COðadsÞ poisoning state at 0:525 < y CO 6 1. The kinetic phase transitions between the O-poisoned steady state and the ‘‘reactive” steady state at y CO ¼ 0:389 is continuous and is classified as a second order kinetic transition. The second transition from the reactive steady state to poisoning by CO at y CO ¼ 0:525 is an abrupt, first order kinetic transition. The ZGB model was also proven to be robust and has constituted a reliable basis for subsequent more detailed models. Modifications on the ZGB model include diffusion [31,32], desorption [31], lateral adspecies interactions [31], surface roughness [32], surface reconstruction [4,33,34], different sticking coefficients for adsorbing species [35], formation of surface oxide [24,36], etc. In the present work the ZGB model is extended to account for the oxidation of the catalyst by the adsorbed oxygen atoms, which has been found to occur under high pressure conditions and which leads the system to oscillations. The extended model, which is formulated in the following section, will be referred to hence as the ‘‘KMC (kinetic Monte Carlo) oxide model”. The emergence of oscillations at variable parametric values and the surface distribution of the species are studied in Section 3. The results are briefly recapitulated in the concluding Section 4 and open problems are posed. 2. Model and simulation algorithm The KMC oxide model is a nontrivial extension with respect to the standard ZGB model, in order to take into account the formation of the catalytic surface oxide. It is a mesoscopic skeleton model that can be viewed as a basis for a mechanistic discussion on the emergence of oscillations in the catalytic CO oxidation at high pressures. A square lattice is used to represent the catalytic surface at all times. Every lattice site ði; jÞ has four nearest neighbours (NN), which are: ði  1; jÞ, ði þ 1; jÞ, ði; j  1Þ, ði; j þ 1Þ. The lattice sites can be found in one of four states – CO, O, ox (oxide) and  (vacant). Interactions are possible only between nearest neighbouring (NN) sites. Periodic boundary conditions are applied at the lattice borders. It is assumed that oxygen atoms form a chemical bond to the metal atoms of the surface when oxygen is abundant on the surface (surface + adsorbed oxygen ? surface oxide). Thus, when a coverage threshold is attained, a high percentage of the adsorbed oxygen atoms are converted to

V.K. Noussiou, A. Provata / Chemical Physics 348 (2008) 11–20

the oxide state. In the simulations appearing in this work, the linear size of the square lattice was L ¼ 256 (with the exception of the surface snapshots in Figs. 9 and 10). The interactions taking place on the lattice can be described by the following scheme: k1

COðgÞ þ  ! COðadsÞ 1k 1

O2ðgÞ þ 2  ! 2OðadsÞ k2

COðadsÞ þ OðadsÞ ! CO2ðgÞ þ 2 k3

OðadsÞ ! ox under the condition ½OðadsÞ  > CT k4

COðadsÞ þ ox ! CO2ðgÞ þ 2

ð1aÞ ð1bÞ ð1cÞ ð1dÞ ð1eÞ

where the (ads) and (g) indices denote the adsorbed and gaseous species, respectively, while  and ox denote the vacant lattice sites and the oxide species, respectively. The parameters k i , i ¼ 1; . . . ; 4 are the kinetic constants and their meaning as well as their relation to the y parameters of the ZGB model are explained in the next paragraph. CT is a critical threshold value of oxygen coverage above which the adsorbed oxygen atoms are involved in oxide formation with a probability determined by the kinetic parameter k 3 of the corresponding mechanistic step. More explicitly, the above mechanism means that: COðgÞ adsorbs on one vacant lattice site and O2ðgÞ adsorbs dissociatively in two neighbouring sites. Neighbouring COðadsÞ and OðadsÞ react, producing CO2 which desorbs instantaneously and the two sites that were previously occupied by COðadsÞ and OðadsÞ are left vacant. When the oxygen coverage is high enough (greater than CT), oxygen can form a chemical bond to the surface, which transforms it to an oxide (ox) particle. Now, oxygen that is bound as oxide (ox) is also available to react with COðadsÞ and produce CO2 . The rates of the above events depend on the kinetic parameters chosen. The kinetic parameters k 1 and 1  k 1 , corresponding to the adsorption of COðgÞ and O2ðgÞ respectively, are: k 1 ¼ y CO (step (1a)), 1  k 1 ¼ y O2 (step (1b)), where y CO and y O2 are the mole fractions (partial pressures) of CO and O in the gas phase, as in the original ZGB model. k 2 (step (1c)) reflects the probability for neighbouring COðadsÞ and OðadsÞ to combine towards CO2 . k 3 is the probability for oxygen OðadsÞ to be transformed to oxide (ox) when the oxygen coverage has reached a critical threshold (CT) value. This condition implies the requirement for synergetic oxidation of the surface – the formation of the oxide layer requires the simultaneous presence of groups of oxygen atoms interacting with metal atoms. Finally, k 4 represents the probability of reaction between the oxide (ox) particles and COðadsÞ . k 2 and k 4 are varied so that both k 2 > k 4 (higher reactivity of metal surface) and k 4 > k 2 (higher reactivity of oxide surface) cases are explored. These scenarios are both investigated here, since they have both been considered plausible in previous works. As in the original ZGB model, the values of k 1 and 1  k 1 correspond to the mole fractions of CO and O2 in

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the gaseous mixture respectively, and thus indirectly to their relative partial pressures. However, a precise representation of pressure is not possible in this minimalistic model, as will be discussed in the sequel. The rules comprising the algorithm of the KMC oxide model are the following. Initially the lattice of size L  L is assumed to be empty. At each elementary time step (ETS): 1. A random site ði; jÞ on the lattice is chosen. 2. If the lattice site ði; jÞ is empty ðÞ then with probability equal to k 1 COðgÞ adsorbs, or else, with probability 1  k 1 , if a randomly selected nearest neighbour ðir ; jr Þ is also empty, then O2 adsorbs dissociatively on ði; jÞ and ðir ; jr Þ. 3. If ði; jÞ contains a COðadsÞ particle and a randomly selected nearest neighbour ðir ; jr Þ contains an OðadsÞ particle, then with probability equal to k 2 the two particles interact, producing CO2ðgÞ – which leaves the lattice – and two vacant lattice sites. 4. If ði; jÞ contains OðadsÞ and a randomly selected nearest neighbour ðir ; jr Þ contains COðadsÞ , then with probability equal to k 2 the two particles interact and produce CO2ðgÞ – which leaves the lattice – and two vacant sites. 5. Also, if ði; jÞ contains OðadsÞ and cannot react as required above, then whenever the overall OðadsÞ coverage exceeds CT, OðadsÞ changes to oxide (ox) with probability k 3 . 6. If ði; jÞ contains an ox particle and a randomly selected neighbour ðir ; jr Þ contains COðadsÞ , then with probability equal to k 4 , the ox and COðadsÞ species react, producing CO2ðgÞ and two vacant sites. 7. If ði; jÞ contains COðadsÞ and a randomly selected neighbour ðir ; jr Þ contains ox, then with probability equal to k 4 , COðadsÞ and ox react, producing CO2ðgÞ and two vacant sites. 8. An ETS is completed and the algorithm returns to step 1. Note that L  L ETS add up to 1 Monte Carlo Step (MCS), which is the time unit of these simulations. At each ETS only one of the described events at most is realised, after which the ETS terminates. As was mentioned earlier, the measure of pressure in this KMC oxide model is incorporated indirectly, through the relative partial pressures of the CO and O2 gasses which determine the probabilities of adsorption for each gas molecule. Thus absolute pressure is not determined, but it is accepted that it is found in the mbar–bar range, where oscillations related to oxide formation occur. In a real system pressure is a determining factor for the dynamics; a high partial pressure of oxygen is required for oxide formation [18,20]. This experimental observation can guide our simulations to investigate for possible oscillatory phenomena in parameter ranges which correspond to high relative O2ðgÞ partial pressure. Since the absolute value of the O2ðgÞ partial pressure is not directly calculated in this model, one can look only at its relative value to the COðgÞ partial

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3. Results and discussion 3.1. Emergence of oscillations In the absence of surface oxide formation (steps (1a)– (1c)), the system’s steady states can be classified, as in the case of the standard ZGB model, as poisoning states, where the surface is fully covered (‘‘poisoned”) by one of the species, and reactive states, where species coexist and interact on the surface. In general when the gas phase is rich in oxygen – low k 1 – the system reaches a steady state where it is poisoned by oxygen, then for a range of k 1 values it reaches a reactive steady state, while a CO-rich gas phase at high k 1 leads to poisoning by COðadsÞ . The steady state is also determined by k 2 , the rate at which the reactants react and leave the surface, while k 3 and k 4 are irrelevant when the oxide formation is not taken into account. Fig. 1 shows the COðadsÞ steady state coverage versus k 1 at different k 2 values. As k 2 decreases, the COðadsÞ versus k 1 diagrams shifts to the left, i.e., one finds a reactive state at a lower k 1 region. Also, the width of the reactive area decreases. The oxide phase arises in the model as a perturbation to the system. Therefore, the system’s reactive and poisoned states are determined as shown in Fig. 1, even in the presence of oxide. That is, in the case of oxide, oscillations can

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pressure pO2 =pCO  ð1  k 1 Þ=k 1 . A high relative pressure of O2ðgÞ then corresponds to lower values of k 1 (higher values of 1  k 1 ). Similarly, there is no measure for temperature in the KMC oxide model, the kinetic parameters are fixed for every simulation run. It is known that CO oxidation at pressures relevant to the oxide model is non-isothermal. Since, however, the mechanism of the interplay between pressure, temperature and kinetic rates is not clear enough, locally and globally, temperature variations are not incorporated at this level, to keep the model as simple as possible and the number of parameters to the minimum. To formulate the simplest possible representation of the oscillatory system, these simulations take into account only those events that are considered to regulate the oscillatory behaviour. The transition from adsorbed oxygen on metal to oxide takes place depending on the global surface concentration of oxygen. Thus the well-established island growth mechanism, according to which a group of neighbouring oxygen atoms synergetically oxidise the surface, is indirectly implemented in the KMC oxide model. The simple assumption is made that when the global coverage of oxygen is sufficiently high (>CT), local OðadsÞ concentrations will also be high and many groups of sufficient size for oxide formation will be present. The existence of global oscillations in the real system, exhibiting oxide ‘‘bursts”, supports the scenario that a collective formation of oxide islands occurs at those bursts. Also, local oxide island formation though not imposed on the system in the simulations, takes place nonetheless, as oxide regions emerge implicitly.

steady state CO coverage

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be anticipated within the ‘‘reactive” regions of Fig. 1. For example, at k 2 ¼ 0:85, oscillations may be found for k 1 between about 0.342 and 0.384. Oscillations are indeed possible within the reactive areas of Fig. 1, while outside these areas the system becomes poisoned eventually. Figs. 2 and 3 depict the oscillatory amplitudes (as measured from the COðadsÞ coverage oscillations) in the phase space of the k 2 =k 4 and k 1 =k 4 variables, respectively. Probability k 3 was kept at 0.7 in all simulations that will be presented in this work. The threshold value for the transformation of adsorbed oxygen to oxide was set to CT ¼ 0:5. In Fig. 2, each diagram shows oscillatory amplitudes for varying k 2 and k 4 , at k 1 constant. Oscillations then are found to be possible when k 4 is significantly different than k 2 , their amplitude rising away from the line where k 2 ¼ k 4 . The ratio k 2 =k 4 is representative of the relative reactivity of OðadsÞ to the reactivity of ox. It is notable that oscillations are more prominent below the k 2 ¼ k 4 line, where k 2 > k 4 . Fig. 3 displays the oscillatory amplitude for varying k 1 and k 4 , at k 2 ¼ 0:60 and k 2 ¼ 0:85. It is clear that oscillations are obtained only for those values of k 1 that belong in the reactive areas – for the respective k 2 values – indicated in Fig. 1, i.e., at k 2 ¼ 0:60: 0:33 < k 1 < 0:36 and at k 2 ¼ 0:85: 0:345 < k 1 < 0:38. At k 2 ¼ 0:85, when k 1 is set to 0.38 and k 4 is varied, oscillations of larger or smaller amplitude emerge (Fig. 4). The surface concentration of COðadsÞ moves towards the steady state predicted in Fig. 1 ( 0:2) at times where oxide particles are practically absent. At the same time, the coverage of OðadsÞ rises until its critical value ðCT ¼ 0:5Þ at which a high percentage of them – that is, k 3 (=70%) – turns to oxide. When a large part of the surface is covered by oxide particles, COðadsÞ finds few OðadsÞ atoms, with which it reacts with higher probability, and many oxide particles with which COðadsÞ reacts with lower probability. Overall, COðadsÞ reacts less frequently and thus the COðadsÞ surface concentration increases. Oxide particles decrease gradually due to their reaction with COðadsÞ and

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Fig. 2. Distribution of observable oscillations: The different shades of the squares in the above graphs indicate the amplitudes of the COðadsÞ coverage oscillations in the phase space of k 2 (x-axis) and k 4 (y-axis). The graphs correspond to different k 1 values. k 2 and k 4 axes have been rescaled to values between 0 and 100 instead of 0–1.

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Fig. 3. The colours of the squares indicate the amplitudes of the COðadsÞ coverage oscillations in the phase space of k 1 (x-axis) and k 4 (y-axis). The graph on the left was obtained for k 2 ¼ 0:60 and the one on the right for k 2 ¼ 0:85 (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

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of COðadsÞ towards the ‘‘steady state”. In this case, where k 2 is large, oscillations are obtained practically only for k 2 > k 4 . As expected, when k 4 is close to k 2 , the oscillations fade. This is because when k 2 ¼ k 4 , both O(ads) and ox interact with COðadsÞ at the same rate. Thus for k 4 over 0:85, no observable oscillations arise; even at k4 ¼ 1 (k 4  k 2 ¼ 0:15), oscillations are obscured by fluctuations. In the opposite case, when k 4 > k 2 (as in the right-hand graph of Fig. 5), the COðadsÞ coverage rises in the absence of oxide particles and falls when the oxide transformation – oxide concentration ‘‘burst” – takes place. Oxide particles now have a high reaction probability with COðadsÞ , thus their presence has a negative effect on the COðadsÞ coverage, but their fast consumption leads to an increase of COðadsÞ again – meanwhile the OðadsÞ atoms have little readiness to react. The oscillations in the left-hand graph of Fig. 5 are obtained with k 2 > k 4 , so the interpretation of the oscillations in the case of Fig. 4 stands also here. The oscillations of the COðadsÞ coverage attain greater amplitudes while k 2 > k 4 . The oscillations at k 4 > k 2 never reach an amplitude of the order of, e.g., 0.2, which is obtained at k 2 ¼ 0:85 and k 4 ¼ 0:05. The COðadsÞ coverage at k 4 ¼ 1 and k 2 ¼ 0:20 is driven towards 0.1 when the system is poor in oxide particles; moreover the oxide bursts, due to the high value of k 4 , drive the COðadsÞ coverage to even lower values. The amplitudes for both k 2 > k 4 and k 4 > k 2 , however, become comparable if the oscillating concentrations are normalised by their mean values. For the oscillations reported above, periodicity has been certified through Fourier Transform of the time series. Indicatively, the FT for the low amplitude oscillations at k 1 ¼ 0:292, k 2 ¼ 0:20 and k 4 ¼ 1 is shown in Fig. 6. The FT was performed over a run of 5  105 MCS, for a clearer distinction of the peak.

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leave space for O2 to adsorb. The reaction of COðadsÞ and OðadsÞ then becomes more frequent, leading to a decrease

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V.K. Noussiou, A. Provata / Chemical Physics 348 (2008) 11–20

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3.2. Oscillations of the CO2 production rate

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The oxidation of CO advances at a rate which is a function of k 2 and k 4 . In addition, the concentrations of the species as well as their local distribution on the surface, are also very important. When k 2 is large, the reaction is conducted preferably by way of the CO(ads) + O(ads) step, while when k 4 is large, CO(ads) + ox takes place more easily. In the diagrams of Fig. 7 the overall rate of the CO oxidation (production of CO2ðgÞ ), as well as the partial rates of steps (1c) and (1e) (production of CO2ðgÞ via the COðadsÞ þ OðadsÞ and COðadsÞ þ ox steps, respectively) are shown versus time at variable k 4 values. Here, k 1 was set to 0.292 and k 2 to 0.20. When k 4 ¼ k 2 , the rates of the two different paths of CO oxidation completely counterbalance one another and the overall CO2ðgÞ production remains constant within the limits of fluctuations. For k 4 > k 2 , the oxide particles react with COðadsÞ faster, thus with every oxide burst, the overall CO2ðgÞ production rises. However, it is notable that the mean value of the overall CO2 production falls as k 4 increases. This is due to the lower production of CO2ðgÞ through COðadsÞ þ OðadsÞ reaction. Although k 2 remains at 0.20, the COðadsÞ concentration on the surface is lower and subsequently the reaction with OðadsÞ less frequent. Also, the excessive vacant sites produced while COðadsÞ and ox react and leave the surface due to reaction, appear to favour O2 adsorption more than CO adsorption. In steady state conditions the ratio of the actual or ‘‘effective” adsorption rate of CO on the lattice to the actual adsorption rate of O2 is found to be equal to 2. Here, a lower ratio was found, resulting in a higher OðadsÞ coverage (than the one reached if the quantity of the vacant sites was the same as in the steady state) and

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Fig. 7. The CO2ðgÞ production rate and the partial rates of CO2ðgÞ production through COðadsÞ þ OðadsÞ and COðadsÞ þ ox are displayed over time. k 1 ¼ 0:292, k 2 ¼ 0:20 and k 4 is varied.

a lower COðadsÞ coverage. The reactive interfaces between COðadsÞ and OðadsÞ are reduced, leading to a low CO2ðgÞ production. 3.3. Surface distribution of the species and clustering Monitoring the evolution of the species distribution on the surface during the oscillations contributes to a more complete overview of the system, since locality is important in surface reactions. Representations of the surface at different times are shown below for parameter sets that were used in Sections 3.1 and 3.2. In Fig. 8 oscillations of the COðadsÞ coverage are reported for k 1 ¼ 0:38, with k 2 > k 4 (k 2 ¼ 0:85 and k 4 ¼ 0:05). The boxes drawn on the oscillatory time series of Fig. 8 correspond to the instants at which the snapshots of Fig. 9 were taken. Variations of the populations of the three species with time in the surface snapshots are obvious. At times: t ¼ 1510 MCS and t ¼ 2410 MCS, in Fig. 9, the COðadsÞ population (black squares) is at a peak, with a lag behind the oxide (green) coverage maximum. Oxide (green) and OðadsÞ (red) populations oscillate in opposite phase. Oxide particles disappear completely for periods of times. The species tend to group with their kin, forming clusters. COðadsÞ and ox clusters are robust, while OðadsÞ forms relatively open clusters, allowing the presence of vacant sites among

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4. Conclusions : surface snapshots taken

CO coverage

0.5

0.4

0.3

0.2 1500

2000

2500

3000

t (MCS) Fig. 8. Oscillations at k 1 ¼ 0:38, k 2 ¼ 0:85, k 3 ¼ 0:70 and k 4 ¼ 0:05. The boxes denote the instants at which the snapshots of Fig. 9 were taken.

the oxygen atoms. Interfaces between clusters of the three species are complex and may follow a fractal scaling. At k 1 ¼ 0:292, k 2 ¼ 0:20 and k 4 ¼ 1, where k4 > k2, the low amplitude oscillations of the COðadsÞ population are less notable in the surface snapshots of Fig. 10, due to their low average coverage. The bursts of the oxide population (green) and their subsequent decrease are very prominent, on the other hand. Complex interfaces between the same species clusters are found here as well.

This work proposes a mesoscopic skeleton model of the CO oxidation on Pt at high pressures. The Langmuir–Hinshelwood scheme of CO oxidation was implemented on lattice, coupled with steps describing the formation of an oxide species at high surface concentration of O. This ‘‘KMC oxide model” can constitute a starting point for discussing the mechanisms which are responsible for the concentration oscillations in the CO oxidation at high pressures. Up to the late 1990s oxygen participating in a surface oxide compound was mainly considered to be inert and the reaction of CO oxidation was believed to be possible only by oxygen adsorbed on the clean metal. Recent experimental findings however reverse this picture. The surface oxide is reported as more reactive towards CO oxidation than the adsorbed oxygen. These simulations demonstrate that whenever the emerging oxide is assumed to be of significantly different reactivity than O, oscillations are possible. The population of the oxide species in the present model rises abruptly as a perturbation to the system; these oxide ‘‘bursts” temporarily drive the system away from the original steady states (in the absence of oxide) depending on the value of k 4 , which determines the probability of reaction between COðadsÞ and ox. When k 4 is low, the coverage of COðadsÞ increases and the production of CO2 decreases with the ‘‘bursts”, while when k 4 is high, the oxide bursts lead to a decrease of COðadsÞ coverage and an increase in CO2 production. The repeated ‘‘bursts” and subsequent relaxation

Fig. 9. The distribution of the species on the surface is displayed at consecutive times, shown below the images. The parameter values used were: k 1 ¼ 0:38, k 2 ¼ 0:85, k 3 ¼ 0:70 and k 4 ¼ 0:05. Sites filled with COðadsÞ are represented by black points, OðadsÞ by red, ox by green, vacant by white. COðadsÞ oscillations taking place are notable, while the predominance of ox alternates with the predominance of OðadsÞ (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

V.K. Noussiou, A. Provata / Chemical Physics 348 (2008) 11–20

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Fig. 10. The distribution of the species on the surface is displayed at consecutive times, shown below the images. The parameter values used were: k 1 ¼ 0:292, k 2 ¼ 0:20, k 3 ¼ 0:70 and k 4 ¼ 1. Sites filled with COðadsÞ are represented by black points, OðadsÞ by red, ox by green, vacant by white. Alternating high OðadsÞ and ox coverages are clearly observed. The coverage of COðadsÞ oscillates less notably than in Fig. 9 due to their overall small number (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

periods compose the system’s oscillatory behaviour. The oscillations are generally larger when the probability k 2 of the COðadsÞ þ OðadsÞ reaction is higher than k 4 (CO(ads) + OX reaction) than in the opposite case. Visualisation of the surface distribution of the species during the oscillatory evolution of the system shows the formation of clusters with complex interfaces between them. With respect to locality, an important step towards a more realistic approach to the system under study could be the inclusion of local oxide formation and of species diffusion. It is an open problem whether interfaces between species clusters, as well as interfaces between oxide and metal phases, have fractal properties. The temporal evolution of the interfaces, their shape and size, and their influence on the CO2 production rate also remain to be investigated. In addition, a direct way of taking pressure and temperature into account would help to clarify the mechanisms producing oscillations under high pressures in more detail. Acknowledgments V.K.N. acknowledges financial support through the National Centre for Scientific Research ‘‘Demokritos” PhD

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