Monte Carlo simulation of oscillations in the NO–H2 reaction on Pt(1 0 0)

Applied Catalysis A: General 187 (1999) 61–71

Monte Carlo simulation of oscillations in the NO–H2 reaction on Pt(1 0 0) 夽

V.P. Zhdanov a,b,∗ , B. Kasemo a a

Department of Applied Physics, Chalmers University of Technology, S-412 96, Goteborg, Sweden b Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia

Abstract We present Monte Carlo simulations of phase separation during kinetic oscillations in catalytic reactions accompanied by adsorbate-induced surface restructuring. As an example, we analyze the NO–H2 reaction on Pt(1 0 0). The lattice-gas model employed to describe surface restructuring and the reaction steps takes into account substrate–substrate, substrate–adsorbate and adsorbate–adsorbate lateral interactions. Using a reduced generic mechanism of the reaction, we show the type of spatio-temporal patterns which might be observed on the nm scale. ©1999 Elsevier Science B.V. All rights reserved. Keywords: Computer simulations; Models of surface chemical reactions; Kinetic oscillations; Surface reconstruction

1. Introduction This issue of Applied Catalysis is focused on general aspects of fast catalytic reactions. Such words as ‘fast’ and ‘slow’ are always relative. In particular, the meaning of these words in combination with ‘reaction’ (i.e., ‘fast reaction’ and ‘slow reaction’) is slightly different in UHV surface-science studies, aimed at understanding of fundamental principles of heterogeneous chemistry, and in atmospheric-pressure studies more oriented to practical catalysis. In the former case, catalytic reactions are often considered to be fast if the rate constants of the Langmuir–Hinshelwood steps are so large that the reaction rate is limited by adsorption (with no gradients in the gas phase due to molecular flow conditions). In the latter case, especially in 夽 Contribution to a special issue of Applied Catalysis A: General on fast and ultrafast reactions. ∗ Corresponding author. Fax: +46-31-7723134, +7-3832-344687 E-mail address: [email protected] (V.P. Zhdanov)

chemical engineering, catalytic reactions are usually assumed to be fast if the reaction rate is limited by gas-phase diffusion (e.g., by diffusion in pores for reactions occuring in porous pellets). The common denominator between these two cases is that ‘fast’ means so fast on the surface that reactant supply from the gas phase is the limiting factor. Both these definitions are of course conventional, and in specific subfields of heterogeneous catalysis one can find other meanings of the words ‘fast reaction’ and ‘slow reaction’. Below, we consider the former case when the rate is limited by adsorption. The most important feature of such reactions is that they often occur far from the adsorption–desorption equilibrium and are accompanied by kinetic phase transitions [1,2], oscillations and chaos [3–6]. Conversely, slow reactions are usually characterized as being close to the adsorption–desorption equilibrium. Often, kinetic oscillations arise when a rapid bistable catalytic cycle is combined with a slow side process. Examples of physically sound side processes

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include adsorbate-induced surface restructuring [3,4], formation of surface oxide [7] or carbon deposits [8], and diffusion limitations in the gas phase [9]. Despite long standing interest, the understanding of oscillatory kinetics is far from complete, because experimental in situ data clarifying details of adsorbate behaviour during oscillations are still limited (for a recent review, see [4,10]). Simulations of oscillations are numerous [6,11–15], but the assumptions employed in calculations are often very simplified and not always realistic. At UHV conditions, kinetic oscillations are often connected with adsorbate-induced surface restructuring [3,4]. A classical example is CO oxidation on Pt(1 0 0) [16]. In this case, the (1 × 1) arrangement of metal atoms on the clean surface is metastable compared to a close packed quasi-hexagonal (‘hex’) arrangement. CO adsorption may, however, stabilize the (1 × 1) phase. The latter provides a feedback between CO and oxygen adsorption because the rate of oxygen adsorption on the (1 × 1) patches is much higher than on the ‘hex’ patches. This mechanism of oscillations proposed by Ertl and co-workers on the basis of their pioneering experiments [16] is now generally accepted. Ertl and co-workers were also the first to demonstrate [17] that oscillations in the rate of CO2 production on Pt(1 0 0) are often accompanied on the 0.1-mm scale by beautiful spatio-temporal patterns (for a review, see [10]). Later on, surface restructuring was found to play a key role in oscillatory and chaotic kinetics of other catalytic reactions as well. Examples include such reactions as CO + NO, NO + H2 , and NO + NH3 on Pt(1 0 0) [3,4]. The theoretical studies of kinetic oscillations accompanied by surface restructuring have primarily been aimed at CO oxidation on Pt. The treatments employing the mean-field (MF) kinetic equations [3,4,11,12] and Monte Carlo (MC) technique [13–15] were quite successful in reproducing the evolution of reactant coverages and reaction rate observed during oscillations. The MF models (see e.g., [11,12]) takes into account phase separation but, nevertheless, cannot be used to analyze spatio-temporal distribution of adsorbed reactants on the nm scale because they operate only with average coverages for each of the phases. In MC simulations, the distribution of adsorbed species can be calculated, but there is another shortcoming connected with describing the

adsorbate-induced changes in the surface. In all the available MC models [13–15], the purely mathematical rules employed to realize the steps related to surface restructuring are far from those prescribed by statistical mechanics. For example, surface diffusion of CO molecules is neglected or considered to be independent of the state of metal atoms. Surface restructuring is assumed to occur in the regions where local CO or oxygen coverages are high. With such prescriptions, well-developed phases with atomically sharp phase boundaries, that are possible, are lacking, e.g., CO molecules are not able to induce the formation of (1 × 1) islands at relatively low coverages, because there is no driving force for phase separation. In contrast, experiments indicate that such islands are formed on Pt(1 0 0) already at θCO ' 0.08 ± 0.05 ML for T ' 500 K [18] or even at θCO ' 0.01 ML for T ' 400 K [19]. There are also direct observations of phase separation on the nm scale during kinetic oscillations in such reactions, e.g., as H2 and CO oxidation occuring on a Pt(1 0 0) tip of a field ion microscope [20,21]. All these findings mean that the adsorbate-induced restructuring of the (1 0 0) face of Pt in a more complete treatment than hitherto, should be described in terms of the theory of first-order phase transitions. This is the problem we address here. It should be noted that the mathematical rules used in MC simulations so far have nothing in common with the theory of first-order phase transitions. An accurate description of adsorbate-induced surface restructuring on the basis of statistical theory of phase transitions is rather difficult because the understanding of microscopic details of this phenomenon is far from complete. As a starting point, it therefore seems reasonable to formulate a simple well-defined lattice-gas model treating surface restructuring as a first-order phase transition and to employ this model for analyzing oscillatory kinetics. This approach was partly realized in our recent paper [22] where we proposed such a model and used it to analyze the influence of adsorbate-induced surface changes on thermal desorption spectra and propagation of chemical waves in bistable reactions. In the present work, the same model is employed to treat kinetic oscillations in the NO–H2 reaction on Pt(1 0 0). Our main goals are (i) to demonstrate how the principles of statistical physics can be incorporated into the kinetic model and (ii) show the type of spatio-temporal patterns which might

V.P. Zhdanov, B. Kasemo / Applied Catalysis A: General 187 (1999) 61–71

be observed on the nm scale. Focusing our presentation on these aspects, we deliberately simplify the reaction scheme and omit many details which may be important in a full treatment (and may be incorporated into the model) but are not necessary to illustrate the main points. The generic reaction scheme used in our study is therefore simpler compared to that employed to describe the CO–O2 /Pt(1 0 0) system.

2. Specifics of the NO–H2 reaction on Pt(1 0 0) Kinetic oscillations in the NO–H2 reaction on Pt(1 0 0) were first observed by Nieuwenhuys et al. [23,24] at PNO = 3 × 10−9 bar, PH2 = 3–10 × 10−9 bar, and T = 420–520 K. Later on, this phenomena was studied by Ertl et al. [25,26] at PNO = 1.1 × 10−9 bar, PH2 = 3–10 × 10−9 bar, and T = 430–455 K. The latter group combined kinetic data with work-function and LEED measurements. The temperature region in which oscillations were observed was found to coincide with the lifting of the ‘hex’ reconstruction. The latter seems to indicate that the (1 × 1)-‘hex’ phase transition plays a role in the mechanism of oscillations. To determine if this was the case, in situ LEED experiments were conducted. In none of these experiments were the oscillations accompanied by periodic variation of the (1 × 1)-‘hex’ intensities. However, a number of observations have demonstrated that the reaction system is sensitive to the electron beam and it is still an open question if this affected the observations. Moreover, the LEED measurements might miss the structural oscillations due to too small domains. MF simulations of kinetic oscillations in the NO–H2 reaction on Pt(1 0 0) were performed by Lombardo et al. [27], Gruyters et al. [28], and more recently by Makeev and Nieuwenhuys [29,30]. In the two former studies, surface restructuring was assumed to play a key role in oscillations. In contrast, Makeev and Nieuwenhuys [29,30] are of the opinion that the oscillations result from the steps which are not directly connected with surface restructuring. First [29], they simply ignored the adsorbate-induced phase transition. Later on [30], surface reconstruction has been taken into account, and for the chosen set of model parameters it was found that the time dependence of the fraction of the surface in the (1 × 1) state is nearly negli-

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gible. From our point of view, the question about significance of adsorbate-induced changes in the surface for oscillations in the reaction under consideration is still open for discussions. In this field, one first needs to understand in more detail the physics behind the oscillations and analyze the mechanism of the oscillations from this perspective. It is not enough to find the mathematical scheme that reproduces the oscillations and chaos observed experimentally (because the scenario of the transition from oscillations to chaos is often universal [31], and quite different kinetic schemes can easily result in apparently similar kinetics). Specifically, we need to scrutinize the possible implication of the fact that adsorbate-induced surface restructuring results in phase separation, since the kinetic equations describing explicitly chemical reactions on islands in the two-phase system are quite different compared to those used in the MF approximation. The conventional mechanism of the NO–H2 reaction on Pt(1 0 0) is as follows (H2 )gas 2Hads ,

(1)

NOgas NOads ,

(2)

NOads → Nads + Oads ,

(3)

2Nads → (N2 )gas ,

(4)

2Hads + Oads → (H2 O)gas ,

(5)

3Hads + Nads → (NH3 )gas ,

(6)

NOads + Nads → (N2 O)gas .

(7)

Here, steps (5) and (6) are not elementary (e.g., the NH3 formation (6) is usually assumed to occur via sequential addition of Hads to Nads ). In general, one needs to take into account all the steps above. Practically, however, the reaction scheme can be reduced for the following reasons. (i) Our attention will be focused on the reaction behaviour at relatively high temperatures (T ' 460 K) where one can observe the transition from oscillations to chaos [24]. In this case, the rate of N2 O formation is relatively low [24] and accordingly step (7) can as a first approximation be omitted. (ii) Step (6) can be omitted as well because the rate of NH3 formation is lower than that of N2 desorption [24] provided that the H2 pressure is not too high (in principle, the NH or NH2 coverages might be appreciable, but such a scenario

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is not supported by the earlier simulations [27–30]). (iii) The steps resulting in H2 O formation are known to be very fast [32]. N2 desorption is rather fast as well (the activation energy for this process is about 20 kcal/mol [27]). This means that the products of the NO decomposition (step (3)) can in simulations be simply removed from the surface just after successful decomposition trials. (iv) The main role of H2 adsorption is to provide H atoms for step (5) (the effect of adsorbed hydrogen on surface restructuring is minor because the H coverage is low). But, removing Oad just after NO decomposition, we do not need to analyze in detail step (5). In other words, we do not need to include H2 adsorption explicitly. In summary, our reduced scheme of the NO–H2 reaction on Pt(1 0 0) contains only two steps, namely, reversible NO adsorption (2) and decomposition (3). The decomposition products are removed from the surface immediately. Thus, we have only one adsorbed species, NO. If one ignores NO-induced surface restructuring and assumes that all the adsorption sites are active in NO decomposition, the reduced scheme of course does not yield oscillations. But in combination with surface restructuring, it predicts fairly interesting kinetics. One could argue that this is a too simplified scheme. However, in our view, it rather focuses on a central point, namely that NO-induced surface restructuring alone, in a treatment including phase separation on the surface, is enough to produce oscillatory kinetics.

3. Model Adsorbate-induced surface restructuring results from lateral interactions between adsorbed particles, A (A ≡ NO), and metal atoms, M. On Pt(1 0 0), the surface densities of M atoms in the stable and metastable structures are slightly different and the adsorbate-induced phase transition is then accompanied by ‘forcing up’ some of the M atoms (the terms ‘stable’ and ‘metastable’ will hereafter always refer to the states which are stable and metastable on the clean surface). Full-scale simulations of the latter phenomenon are hardly possible at present. In our analysis, this complicating factor is ignored, i.e., the densities of M atoms in the stable and metastable structures are considered to be equal. In this case, the

Fig. 1. Schematic arrangement of particles on the surface. Filled circles and pluses exhibit adsorbed particles and substrate atoms in the metastable state, respectively. Metal atoms in the stable state are not shown.

adsorbate-induced surface restructuring can be described by employing the lattice-gas model as shown in Fig. 1. The main ingredients of this model are as follows [22]: 1. M atoms form a square lattice. Every M atom may be in the stable or metastable states. The energy difference of these states is 1E. The nearest-neighbour (nn) M–M interaction is considered to be attractive, −MM (MM > 0), if the atoms are in the same states, and repulsive, MM , if the states are different (really, the total nn M–M interactions are of course attractive; the interactions −MM and +MM introduced describe the deviation from the average value). The next-nearest-neighbour (nnn) interactions are ignored. With this choice of the M–M interactions, the model describes the tendency of substrate atoms to be either all in the stable or all in the metastable state. 2. Adsorbed particles occupy hollow sites (this assumption is not essential, because in the case of adsorption on top sites the structure of the formal equations will be the same). The adsorption energy of a given particle is considered to increase linearly with the number of nn substrate atoms in the metastable state (this is a driving force for the phase transition). In particular, the increase of the adsorption energy of an A particle after the tran-

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Fig. 2. (a) NO decomposition rate (per site per MCS) and (b) NO coverage and fraction, κ, of Pt atoms in the metastable state as a function of time for pNO = 0.03.

sition of one nn substrate atom from the stable to the metastable state is AM (AM > 0). 3. The nn adsorbate–adsorbate interaction is considered to be negligible or repulsive, AA ≥ 0. The Hamiltonian corresponding to the assumptions above contains the substrate, adsorbate–substrate, and adsorbate–adsorbate interactions, H = Hs + Has + Ha , Hs = 1E

(8)

X nM i i

−4MM

X i,j

nM i

1 − 2



nM j

 1 − , 2

(9)

X M Has = − AM nA j ni ,

(10)

i,j

Ha =

X A AA nA i nj ,

(11)

i,j

where nM i is the variable characterizing the state of atom i (nM i = 1 or 0 is assigned to the metastable and the occupation number stable states, respectively), nA iP of the adsorption sites, and ij means summation over nn pairs. An elementary analysis [22] shows that the model outlined predicts an adsorbate-induced first-order phase transition provided that the adsorbate–substrate interaction is sufficiently strong. Thus, what we need in our simulations is to introduce the rate constants

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for all the relevant elementary rate processes in accordance with the model. General prescriptions of how to realize this procedure are described in [33]. The simplest reasonable set of rules for simulating elementary reaction steps is as follows. Adsorption of A particles occurs on vacant adsorption sites with unit probability. Desorption of A particles is affected by A–A and A–M lateral interactions. The normalized dimensionless probability of desorption of a given particle is defined as (we use kB = 1)   Ei , (12) Wdes = exp T P A M where Ei = j (AA nj − AM nj ) is a sum of nn interactions. Diffusion of A particles occurs via jumps to nn vacant sites. The probabilities of these jumps usually depend [33] on lateral interactions in the ground and activated states (the terms ‘activated’ and ‘ground’ correspond here to the transition state theory). Taking into account that the details of diffusion complicated by adsorbate–substrate lateral interactions are not well established, we use for the jump probabilities the Metropolis (MP) rule, Wdif = 1

for

1E ≤ 0

and

  1E Wdif = exp − T

for

1E > 0,

where 1E is the energy difference between the final and initial states. This rule, compatible with the detailed balance principle, seems to be reasonable in our case (at least as a first approximation) because it predicts rather rapid diffusion on perfect stable or metastable patches, rapid jumps at the phase boundaries from the perfect to the metastable phase, but slow jumps in the opposite direction (because the adsorption energy on metastable patches is higher). Decomposition of A (i.e., of NO) occurs provided that (i) at least one nn site is vacant and (ii) all the M atoms adjacent to A and to a vacant site are in the metastable state (the latter condition takes into account that NO decomposition occurs primarily on the (1×1) phase [27]). The effect of lateral interactions on the A-decomposition rate is for simplicity neglected (if

necessary, it can be taken into account as described in [34]). Surface restructuring occurs via changes of the state of M atoms. The probabilities of the transitions from the metastable to the stable state and back are given by the MP rule (as in the case of A diffusion). 4. Model parameters To simulate the reaction kinetics, we use the following set of parameters: 1E/T = 2, MM /T = 0.5, AM /T = 2 (such values are typical for surface restructuring). The A–A lateral interactions are for simplicity neglected, AA = 0. For this set of the model parameters corresponding to fixed temperature, we have T ' 0.40Tc , where Tc is the critical temperature for the first-order adsorbate-induced phase transition on the surface (Tc was calculated by analyzing the A adsorption isotherms at different temperatures). In addition, we need to introduce the dimensionless parameters, pres and prea (pres + prea ≤ 1), characterizing the relative rates of surface restructuring, adsorption–reaction steps, and diffusion of A particles. The rates of these processes are considered to be proportional to pres , prea , and 1 − pres − prea , respectively. In reality, the rate of surface restructuring is lower than that of the adsorption–reaction steps (i.e. pres < prea ) which are in turn much slower compared to A diffusion (i.e. pres +prea  1). In our simulations, we employ pres /(pres + prea ) = 0.3. In addition, we use the number Ndif ≡ (1 − pres − prea )/(pres + prea ) characterizing the ratio of the rates of A diffusion and the other processes. The results below are presented for Ndif = 1000. In our model, the catalytic cycle includes A (NO) adsorption, desorption, and decomposition. To simulate these steps, we introduce the dimensionless parameters pNO for A adsorption and pdes for A desorption. The rates of these processes are assumed to be proportional to pNO and pdes , respectively. The A decomposition rate is considered to be proportional to 1−pdes . The simulations were executed for pdes = 0.3 5. Algorithm of simulations The MC algorithm for simulating the reaction kinetics consists of sequential trials of reaction, surface

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Fig. 3. (a) and (b) Snapshots of a (200 × 200) lattice for the run, shown in Fig. 2, at stages (see arrows in Fig. 2(b)) when the fraction of Pt atoms in the metastable state is minimum and maximum, respectively. Panels (c) and (d) exhibit a (50 × 50) fragment of the lattices (a) and (b), respectively.

restructuring, and A diffusion. A random number ρ (ρ ≤ 1) is generated. If ρ < prea , an adsorption– reaction trial is realized (item 1). For prea < ρ < prea + pres , an attempt of surface restructuring is exe-

cuted (item 2). If ρ > prea + pres , an A-diffusion trial is performed (item 3). 1. An adsorption–reaction trial contains several steps. (i) An adsorption site is chosen at random.

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Fig. 4. (a) NO decomposition rate (per site per MCS) and (b) NO coverage and fraction of Pt atoms in the metastable state as a function of time for pNO = 0.07.

(ii) A new random number ρ 0 is generated. (iii) If the site selected is vacant, A adsorption is realized provided that ρ 0 < pNO . (iv) If the site selected is occupied by A, A desorption or decomposition is realized for ρ 0 < pdes and ρ 0 > pdes , respectively. For A desorption, a new random number ρ 00 is generated and the attempt is accepted if ρ 00 < Wdes , where Wdes ≤ 1 is the normalized desorption probability given by Eq. (12). For A decomposition, one of the nn sites is chosen at random and the trial is accepted if this site is vacant. 2. For surface restructuring, a M atom selected at random tries to change its state according to the MP rule. 3. For A diffusion, an adsorption site is chosen at random. If the site is vacant, the trial ends. Otherwise, an A particle located in this site tries to

diffuse. In particular, an adjacent site is randomly selected, and if the latter site is vacant, the A particle jumps to it with the probability prescribed by the MP rule. Simulating the reaction kinetics, we consider that initially (at t = 0) the surface is clean and all the M atoms are in the stable state. The results have been obtained for the (L × L)M lattices with L = 200 and periodic boundary conditions. For oscillatory kinetics accompanied by phase separations, these boundary conditions make sense provided that the typical size of islands is much lower than the lattice size. The latter requirement is fulfilled in our study. To measure time, we use the so-called MC step (MCS) defined as (L × L) attempts of the adsorption–reaction-surface-restructuring events. In principle, one might define one MCS as (L × L) tri-

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Fig. 5. (a) and (b) Snapshots of a (200 × 200) lattice for the run shown in Fig. 4 at stages (see arrows in Fig. 4(b)) when the fraction of Pt atoms in the metastable state is minimum and maximum, respectively. Panels (c) and (d) exhibit a (50 × 50) fragment of the lattices (a) and (b), respectively.

als of adsorption, reaction, A diffusion, and surface restructuring. In the latter case, the time scale would primarily be connected with A diffusion, because in our simulations this process is rapid compared to other steps. Our experience indicates, however, that

the effect of diffusion on the period of oscillations is fairly weak (provided that the time scale is not directly related to the diffusion rate). Under such circumstances, it does not make sense to choose the diffusion-based time scale.

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Finally, it seems to be reasonable to discuss the relationship between the dimensionless MC probabilities and time and real rate constants and time. Describing the catalytic cycle, we have considered that the sum of the maximum probabilities of desorption and decomposition is equal to unity. Physically, this means that pdes = kdes /(kdes + kdec ) and pdec ≡ 1 − pdes = kdec /(kdes + kdec ), where kdes and kdec are the maximum values of the desorption and decomposition rate constants. For A adsorption, we accordingly have pNO = kad PNO /(kdes +kdec ), where kad PNO is the rate (per site) of adsorption on a clean surface (kad is the adsorption rate constant, and PNO is the NO pressure). The MC time is defined in our simulations via the adsorption–reaction-surface-restructuring events. This means that the MC and real times are interconnected as tMC = (kdes + kdec + kres )t (kres is the maximum value of the rate constant of surface restructuring).

6. Results of simulations With the specification above (Section 4), we have only one governing parameter, pNO (this parameter is proportional to NO pressure). Well-developed oscillatory kinetics are found for 0.01 ≤ pNO ≤ 0.5. Physically, it is clear that oscillations can really be observed in such a broad interval only provided that the H2 pressure is changed together with the NO pressure in order to guarantee applicability of the reduced model (the experiment [24] does show oscillations in a wide NO-pressure range provided that the ratio of NO and H2 pressures is kept approximately constant). Typical oscillatory kinetics calculated for pNO = 0.03 are shown in Fig. 2. The NO coverage and amplitude of oscillations are in this case relatively small, and NO molecules are located in non-overlapping islands (Fig. 3). To rationalize the mechanism of oscillations, let us start from one of the points (see, e.g., Fig. 3(b)) when the fraction of Pt atoms in the metastable state is maximum. In this case, the restructured islands are relatively large, the local NO coverage inside islands is rather high, and an additional supply of NO molecules to the islands from the unrestructured patches is almost perfectly balanced by NO decomposition inside islands. The balance is however not completely perfect because NO decomposition is an autocatalytic process. Thus, the NO coverage inside is-

lands starts to decrease. The latter is accompanied by a slow decrease of the restructured islands and also by formation of defects on the island structure. With increasing time, the restructured islands become rather small. Supply of NO molecules to such islands from the unrestructured patches results in the increase of NO coverage inside islands. The latter stabilizes the island structure and the islands start to grow. Eventually, the islands again become relatively large. With increasing pNO , the NO coverage and amplitude of oscillations become larger (see e.g., Fig. 4 for pNO = 0.07), and the NO islands merge as shown in Fig. 5. Our preliminary simulations indicate [36] that with further increase in pNO the model predicts period doubling and chaos. The results presented were obtained for L = 200 and Ndif = 1000 for times up to 500 MCS. At much longer times (e.g., t = 3000 MCS), the period and amplitude of oscillations and shape of islands were proved to be the same as at t ' 500 MCS. In addition, we have proven that the kinetics calculated are stable with respect to variation of Ndif and L. The effect of increasing Ndif from 1000 to 10,000 on oscillations was found to be nearly negligible. For varying L from 100 to 400, the amplitude of oscillations decreases but only slightly. Thus, adsorbate diffusion is able in our case to maintain synchronization of oscillations. For very large lattices (L  500), this mechanism synchronization may in principle be weak at very long times (for a discussion, see [14]). Nevertheless, the oscillations can really be observed provided that the desynchronization time is longer compared to the time of measurements. Alternatively, synchronization of oscillations might occur via the gas phase (detailed discussion of the latter phenomenon is beyond our goals).

7. Conclusion We have shown that using the lattice-gas model one can explicitly simulate phase separation on the nm scale during kinetic oscillations in catalytic reactions accompanied by adsorbate-induced surface restructuring. As an example, we analyzed a generic reduced reaction scheme mimicking the NO–H2 reaction on Pt(1 0 0). In the present simulations, we employed the simplest set of lateral interactions and simplest dynam-

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ics of NO diffusion and decomposition and surface restructuring. Changing values of lateral interaction and rules for elementary processes, one can obtain new phenomena and kinetics. The model can also be employed to simulate oscillations in other reactions (e.g., CO oxidation or NO reduction on Pt(1 0 0) [35,37]). Acknowledgements We thank Prof. B.E. Nieuwenhuys for presenting us the results of simulations [30] before publication. Financial support for this work has been obtained from TFR (Contract No. 281-95-782) and from the NUTEK Competence Center for Catalysis at Chalmers. One of us (V.P. Zh.) is grateful for the Waernska Guest Professorship at Göteborg University. References [1] [2] [3] [4] [5] [6]

[7] [8] [9] [10] [11]

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