A Monte Carlo simulation of the CO+NO surface reaction involving molecular NO adsorption and several reaction paths

Surface Science 401 (1998) 185–198

A Monte Carlo simulation of the CO+NO surface reaction involving molecular NO adsorption and several reaction paths O. Kortlu¨ke *, W. von Niessen Institut fu¨r Physikalische und Theoretische Chemie, Technische Universita¨t Braunschweig, D-38106 Braunschweig, Germany Received 20 August 1997; accepted for publication 25 November 1997

Abstract In this paper, a simple lattice gas model for the catalytic CO+NO reaction is studied that takes molecularly adsorbed NO into account. The approaches are Monte Carlo simulations and a model involving a stochastic cluster approximation. We take into consideration the diffusion and desorption of CO and NO and the possibility of three distinct reaction pathways leading to the reaction products CO , N , and N O. The square and triangular lattices are used to model the surface of an ideal catalyst. In this 2 2 2 model, the desorption of CO and NO is a necessary condition for the simulation to remain in a reactive state. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Catalysis; Computer simulations; Low index single crystal surfaces; Models of surface chemical reactions; Nitrogen oxides; Surface chemical reaction

1. Introduction The CO+NO reaction is a very important reaction in the catalytic control of vehicle emissions [1]. Because government regulation in the US and the EC will demand that 95% of the NO produced x by the engine has to be converted into N , we 2 have to gain a better understanding of why NO x is produced in the engine and how to reduce these emissions. There is a peculiar problem associated with this reaction; it is highly sensitive to the metal substrate used as a catalyst and to the type of surface. There are different ways to gain a better insight into this very interesting mechanism of the catalytic NO reduction by CO. One can employ

* Corresponding author. Fax: (+49) 531 391 4577; e-mail: [email protected] 0039-6028/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 97 ) 0 10 7 3 -X

experimental methods such as kinetic measurements over single crystal and dispersed catalysts. These experimental investigations, using new spectroscopical methods, are very demanding to carry out and frequently can resolve neither the individual steps nor the actual sites of the different species on the surface [2]. Another method consists of theoretical approaches using a stochastic ansatz involving master equations that describe the reaction steps and the spatial distribution of the particles on the surface, e.g. the cluster approximation [3–6 ] or the correlation analysis [7], but today, these approaches do not master the complexity of real reaction systems and can only be applied to simple idealized models. In this case, computer simulations as a third possibility are a good tool for studying details of such reactions. They are easy to employ but somewhat expensive because of the necessary computing time. However, they

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may turn out to be auxiliary tools supplementary to the experimental investigations. Although the NO+CO reaction is one of the best-explored catalytic surface reactions comparatively, little is known about the elementary reaction steps. A short summary of the most frequently proposed reaction steps is given below, where the labels (g) and (a) stand for gas phase and adsorbed particle, respectively. Adsorption and desorption steps: CO(g)=CO(a),

(A1)

NO(g)=NO(a).

(A2)

Dissociation step: NO(a)N(a)+O(a).

(D1)

Reaction and desorption steps: N(a)+N(a)N (g), (R1) 2 NO(a)+N(a)N (g)+O(a), (R2) 2 NO(a)+N(a)N O(g), (R3) 2 CO(a)+O(a)CO (g), (R4) 2 2NO(a)N (g)+2O(a), (R5) 2 2NO(a)N O(a)+O(a), (R6) 2 CO(a)+NO(a)CO (g)+N(a). (R7) 2 Intermediate N O steps: 2 N O(a)N O(g), (I1) 2 2 N O(a)N (g)+O(a). (I2) 2 2 In general, it is assumed that the reaction mechanism is of the Langmuir–Hinshelwood (LH ) type, but a few special results are in general explained by the Eley–Rideal ( ER) mechanism [8]. There are many contradicting results in the literature with regard to the most important reaction steps and the rate-limiting step. Furthermore, even the question of the adsorption sites is not fully answered yet. There has been a lively discussion of whether NO adsorbs on top or bridge sites. Recent results indicate that CO is adsorbed on top sites and NO unexpectedly at hollow sites at least on Ni(111) [9], Pt(111) [10], Pd(111) [11], and Rh(111) [2,12–14]. Most of these results are obtained using modern methods in spectroscopy

such as angle-resolved photoelectron spectroscopy (ARPES ), scanning tunneling microscopy (STM ) or X-ray photoelectron diffraction ( XPD), and by kinetic measurements investigating the competitive adsorption of N, O, and NO. However, some results lead to the conclusion that NO adsorbs on top or bridge sites [15–19]. A very interesting discussion about the difficulty to correctly interpret data obtained from vibrational spectroscopy can be found in Ref. [2]. Even more difficult is the examination of the type and relative importance of the elementary reaction steps. The catalytic NO+CO reaction turns out to be highly substrateand structure-sensitive. On Rh(111), NO dissociation is very fast, and on Pt(111), it is very slow [2] or even absent [17]. Another point is that N O was not found as a product [20] over Rh(111) 2 until 1993 and now turns out to be the main N-containing product over this surface with a selectivity of about S =0.7 [21–23]. For N2O Pt(100), the situation is very similar. Generally, N O is not detected as a product [24,25], but 2 sometimes, it is found to appear among the major products [26 ] CO and N in the range of up to 2 2 10% of the corresponding yield of CO . Further 2 unclear aspects are the mobility of the surface species, the influence of the Eley–Rideal mechanism, the subsurface diffusion of N and O, the nature of the rate-limiting reaction step, the direct reaction between NO molecules or CO and NO molecules and so on. A number of important results are given in a paper by Belton et al. [18], who carried out very comprehensive isotope labeling experiments in the reaction on Rh(111). They were able to exclude the reaction steps (R2), ( I2), (R5), and (R6). Permana et al. [12,23] showed that the NO dissociation is the rate-limiting step and that the re-adsorption of N O (I1) does not 2 occur. On account of the structure sensitivity, these results may not be valid for another surface. Because of the vast number of (sometimes contradictory) experimental results, we try to obtain a deeper insight into the reaction mechanism using Monte Carlo (MC ) simulations, in which we follow an extension of the model introduced by Ziff et al. [27] ( ZGB model ). In addition, we use a stochastic cluster approximation, which is described in detail elsewhere [7]. Most previous

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work considers only the dissociative adsorption of NO [4,28–31], and this literature is discussed extensively in our previous article [32]. Yaldram and Khan [28] used a somewhat unrealistic model for the adsorption of NO in which the NO molecules can only dissociate in the adsorption process. After they have been molecularly adsorbed on to the lattice, dissociation is impossible, and the NO molecules can only be removed through a reaction with N. In a study of Meng et al. [33], molecular NO adsorption and desorption is considered. The dissociation of NO is applied with an infinite rate as soon as a nearest neighbor site of the NO molecule is vacant. However, in their model, O is the only product of NO dissociation because N atoms are neglected, thus mimicking the rapid recombinative desorption of N . In the model 2 presented here, we use the adsorption steps (A1) and (A2), the dissociation step (D1), and the reaction steps (R1) to (R4). The reaction is only possible between nearest neighbors on the lattice. Within this reaction model, we attempt a systematic investigation of all physical reasonable processes of diffusion and desorption. The square and triangular lattices are used to model single crystal surfaces with four and six nearest neighbors, respectively. The paper is organized as follows. In Section 2, we describe the details of the simulation. Section 3 contains the results, and conclusions are derived in Section 4.

2. The simulation In the simulation, we keep lists of all lattice particles so that we can directly pick out free sites for adsorption, CO and NO molecules for diffusion, desorption, or dissociation. Therefore, and because of the possibility of comparing the temporal behavior with other models, we choose the adsorption process to define the time unit in contrast to the usual Monte Carlo step (MCS ). Other processes such as diffusion, desorption, and dissociation are scaled to this time unit. This time unit can be rescaled to MCS by taking into account the probability that such a free site would be found, i.e. it has to be divided by the fractional coverage of free lattice sites. The diffusion is

187

implemented as a function of the coverage of the mobile species. We define a diffusion constant D i of species i scaled to the time unit defined by the adsorption process. The number of moving particles per adsorption step is now given by H i , (1) iH V which depends on the actual coverage situation on the lattice. By coverage, we always mean fractional coverages normalized to unity. H is the lattice i coverage of species i, and V stands for a vacant site. The desorption is modeled in the same way and gives the number of desorbing molecules as n

i,dif

=D

H (2) =K i , i,des iH V with the desorption constant K . Finally, the i number of dissociating NO molecules per adsorption step is given by n

H

NO . (3) NO H V The simulation is carried out as follows. In an adsorption step (CO or NO), a vacant site is chosen at random. The probability for CO and NO adsorption is determined by the gas phase concentrations y and 1−y , respectively. For CO CO each adsorption step, we choose the number of diffusing and desorbing particles calculated using Eqs. (1) and (2) and randomly pick these particles from the lists. In the case of desorption, the particle is removed from the lattice. In the case of diffusion, we choose one nearest neighbor site (NN ) at random. If this NN is vacant, the diffusing particle hops to it, otherwise it remains on its original site. The NO dissociation needs a vacant NN, too, and is performed in a similar way. Here, we distinguish three different dissociation possibilities stimulated by the work of Brandt et al. [8,34] and Mu¨ller et al. [35] who carried out experiments with gasphase oriented NO resulting in N-end and O-ends sticking to the catalyst surface. Although the N-end adsorption is energetically favored, there may be some O-end adsorption (at least temporarily) via a direct chemisorption channel [35]. n

NO,dis

=S

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However, note that we do not concentrate on the question of precursor adsorption and detailed kinetics of NO dissociation but only take the O-end sticking as a model for oriented adsorption or dissociation in order to keep the model as simple as possible. . (a) (b) . (c) Both dissociation paths with probabilities p and p such that p +p =1. a b a b In our model, we use an infinite reaction rate. Every time that a particle occupies a new site, the neighborhood is checked for possible reactions, e.g. after adsorption of a CO molecule, all NN are checked for the presence of an O atom in random order. If O is present, CO forms and desorbs 2 spontaneously leaving two vacant sites on the lattice. For the reaction of N and NO, we consider three distinct reaction paths as discussed in the literature: (I ) Reaction (R1) only: NO and N do not react. This may be the case over Pt(100) where N O 2 is not found as a product. (II ) Reactions ( R1)+(R2): NO and N react giving N as the only product and one O atom 2 remaining on the lattice. These reactions do not lead to N O either. However, note that the 2 reaction step (R2) can be ruled out on Rh(111) [18]. (III ) Reactions (R1)+(R3): NO and N react and form N O, which immediately desorbs from 2 the lattice, leaving two new vacant sites. Combined with the three different possibilities of dissociation, this leads to a very complex and demanding model, but, we believe, also to very interesting results. The investigation of the correlation functions between the species on the lattice leads to a deeper insight into the structure of the adsorbate layer. The correlation function g between two particles ij i and j is given by

N (r) N (r)/N i, g (r)= ij = ij ij N* (r) z(r)H ij j i, jµ{V, CO, O, N, NO}.

(4)

This is a measure of the spatial correlation between the (not necessarily different) particles i and j as a function of their distance r on the lattice. i and j denote free sites as well as CO, O, N, and NO particles. N (r) is the number of connections ij between i and j particles at the distance r.

N (r) is the average value over all particles of ij type i, whereas N* (r) is the corresponding number ij at a random particle distribution without correlations [g* (r)=1], which is given by the product of ij the number z(r) of sites at the distance r around the central site i and the coverage H of the j j particles. We use the regular square lattice and the triangular lattice (which can be easily mapped on to the square lattice) to model single crystal surfaces. Generally, we use L×L lattices with L=256 and cyclic boundary conditions. For every independent simulation run, the simulation time is greater or equal to 25 000 of the present units, thus exceeding at least 50 000 conventional MCS. For each set of parameters, five independent runs are performed. The critical points of the phase transitions are those values for y , where all independent runs CO remain in the reactive state for the first time ( y ) 1 or for the last time ( y ). All critical points shown 2 in the tables are determined with an error of 1×10−2 or better, except where specified otherwise. The numerical data are only given with an accuracy of 10−2 because we want to focus on the general properties of this model and not on the exact position of any phase transition. In all simulations, NO is able to dissociate, of course, otherwise no reaction would be possible because of the absence of O and N. Therefore, we do not explicitly mention the dissociation of NO if it is not necessary. In several cases, the simulations are supported, or even substituted, by the stochastic cluster approximation because of the much lower computational costs. First of all, short simulation runs are performed on small lattices (L=64) to determine the coverages and the correlation lengths. If short-range correlations are found to dominate in the reaction system, the cluster approximation is used. If longer-ranged correlations have been found, only MC simulations have been performed. The stochastic ansatz is described in detail in

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Ref. [5]. Its qualitative agreement with MC simulations has been shown [5], and it has proved to be a useful tool to verify simulation results [6 ].

Table 1 Values of the phase transition points y on the square lattice p and y and y on the triangular lattice and the width D of the 1 2 reactive interval for the simulations with NO dissociation and NO desorption

3. Results and discussion

S NO

K

1 10 100 1 10 100 1 10 100

1 1 1 10 10 10 100 100 100

The main result is that desorption of at least CO or NO is a necessary condition for this reaction model to show steady-state reaction kinetics, independent of the type of dissociation and reaction mechanism used. These reactive intervals are very narrow and are found at low CO gas phase concentrations y in the case of NO desorption or at CO large values of y in the case of CO desorption. CO Simultaneous desorption of CO and NO results in a broad reactive interval y µ[ y , 1]. The behaCO 1 vior of this model is very similar on both the square and the triangular lattice in many cases. Therefore, we only explicitly distinguish between these lattices when the results are qualitatively different. These results are in marked contrast to the reaction model without molecular NO adsorption as discussed in Ref. [32]. In that case, a steady-state reaction exists only on the triangular lattice. 3.1. Reaction R1 only In the simulations without desorption, the reaction model always reaches an absorbing (poisoned) state in which both the square and the triangular lattices (surfaces) are mainly covered by NO and CO with a phase transition at y =0.5. CO For y <0.5, NO, and for y >0.5, CO is the CO CO predominating species on the lattice. At small dissociation and diffusion rates, this transition is of second order, whereas at higher dissociation rates, it changes to a first-order transition. If one combines the mobility of all lattice species with fast NO dissociation, a reactive point results at y =0.5 with a rather small value of the summed CO fractional coverages of about H =0.2. tot If only NO is allowed to desorb from the lattice, no reactive interval appears on the square lattice. Below a certain phase transition point, y , the p lattice is mainly covered with O and, above this phase transition, with CO. y depends on the NO p

NO

y p

y 1

y 2

D

0.12 0.37 0.45 0.03 0.17 0.39 <0.01 0.03 0.19

0.10 0.36 0.47 0.03 0.15 0.40 <0.01 0.02 0.17

0.19 0.44 0.49 0.04 0.25 0.45 <0.01 0.05 0.26

0.09 0.08 0.02 0.02 0.10 0.05 <0.01 0.03 0.09

dissociation constant S and the NO desorption NO constant K as shown in Table 1. The phase NO transition is moved to larger values of y with CO increasing S and decreasing K . If the NO NO NO dissociation is fast compared to the desorption, most of the NO is removed by dissociation into N and O. The rapid production of O atoms effectively removes CO from the surface, leading to a much larger value of y for the phase transition. p However, a rapid NO desorption leads to a low coverage of NO and therefore to a low production of O atoms. CO adsorption is favoured relative to NO adsorption, resulting in CO poisoning for almost every value of y if NO desorption is about CO 10 times faster than NO dissociation. On the triangular lattice, very narrow intervals y µ[ y , y ] with a steady-state reaction exist (see CO 1 2 Table 1). The reason for this behavior is that on the square lattice, checkerboard-like structures of N atoms are built, reducing the number of vacant pairs of nearest neighbor sites that are necessary for NO dissociation. This is supported by the result that the reactive intervals on the triangular lattice start at values of y approximately equal 1 to y , where the phase transition occurs on the p square lattice. For CO gas phase concentrations slightly higher than y , the system can remain in a 1 reactive state because of the more effective NO dissociation and CO removal until CO adsorption overwhelms the creation of O atoms via NO dissociation. This is similar to the basic model with dissociative NO adsorption [32].

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If we let CO desorb from the triangular lattice, a steady-state reaction occurs at high CO gas phase concentrations y
chiometric point. If only NO desorption is considered, all phase transitions occur in the range 00.5 above the stoichiometric point. Because CO NO desorption rules the behavior for y <0.5 CO and CO desorption rules the behavior for y >0.5, it is very interesting to study the CO behavior of this reaction model with simultaneous desorption of both CO and NO. In this case, one can expect a wide reactive interval from very low values of y to y =1 because the poisoning with CO CO CO at relatively low values of y such as in the CO simulations with only NO desorption is impossible on account of the additional CO desorption. The model with simultaneous CO and NO desorption may be interpreted as an extension of the basic model with dissociative NO adsorption [6,32]. If CO and NO are allowed to desorb from the lattice, CO and NO molecules only temporarily disturb the formation of the N structures. The only difference, therefore, is that NO is adsorbed molecularly. However, sooner or later, a NO molecule will be removed through dissociation or desorption. Desorption is trivial, but molecularly adsorbed NO combined with dissociation leads to some interesting features of the model on the square lattice. NO molecules can be adsorbed into an existing checkerboard-like structure of N atoms because they need only one vacant site. If one of the four nearest neighbor N atoms is removed

Table 2 Values of the phase transition points y on the square lattice (sq) with dissociation path (a) and on the triangular lattice (tr), the 1 values of y with the highest reaction rate R , y (R ), for the MC simulations with NO dissociation and CO desorptiona CO max CO max S NO

K CO

y

1 10 100 1 10 100 1 10 100

1 1 1 10 10 10 100 100 100

0.69 0.56 0.55 0.69 0.57 0.56 0.69 0.57 0.56

aR

max

1,sq

is given in arbitrary units.

y (R ) CO max,sq

R

0.77 0.62 0.62 0.80 0.67 0.66 0.80 0.67 0.66

0.065 0.175 0.190 0.090 0.180 0.195 0.090 0.180 0.195

max,sq

y 1,tr

y (R ) CO max,tr

R max,tr

0.59 0.51 0.51 0.62 0.52 0.52 0.61 0.52 0.52

0.70 0.56 0.56 0.73 0.61 0.60 0.73 0.61 0.60

0.105 0.275 0.295 0.130 0.260 0.275 0.135 0.255 0.270

O. Kortlu¨ke, W. von Niessen / Surface Science 401 (1998) 185–198

through the reaction, however, the system behavior depends on the dissociation mechanism. With dissociation mechanism (a), the N structure is removed more rapidly as compared to the basic model. This can be seen in Fig. 1a. If the NO molecule dissociates, it leaves the N atom on its former site surrounded by three nearest neighbor N atoms, which spontaneously leads to a reaction removing two N atoms and creating two new vacant nearest neighbor sites. If the NO molecule dissociates via path (b), the situation is completely different. The original N structure is restored with a non-removable O atom in the central site (see Fig. 1b). Therefore, it could be expected that dissociation path (a) accelerates the removal and path (b) the growth of the N structures. Path (c) with p =p =0.5 (see above) should be comparable to a b the basic model [32]. These tendencies can directly be seen in the temporal behavior of the correlation functions. If we exclusively use dissociation path (a), the N structures grow up to an upper average size of about r=10. The same holds for the correlation functions (see Fig. 2). The correlation length grows in time until at t=103, a steady state is reached, and the correlation functions remain almost unchanged in time. If the square lattice is divided into two virtual sublattices in a checkerboard-like manner, a further indication for a real reactive steady state emerges. The temporal evolution of the N coverages, H , on the black and white sites N shows very small fluctuations, and the coverages are almost equal. A completely different behavior

191

is found in the simulation using dissociation path (b). In this case, the correlation lengths grow very rapidly until the whole lattice is covered by one large checkerboard structure of N atoms (if the lattice has an even side length). The N coverages on the virtual sublattices grow independently at the very beginning of the simulation. If the N coverage on the first virtual sublattice becomes larger than on the second one because of fluctuations, it grows until the first sublattice is fully covered by N atoms, resulting in N coverages of H =0.5 on the first and H =0 on the second N N sublattice (see Fig. 3). If we combine the dissociation mechanisms (a) and (b) with equal probability p =p =0.5 to obtain dissociation a b mechanism (c), the correlation lengths grow slower compared to (b). Additionally, large fluctuations appear, and the whole simulation results seem to be very similar to the basic model with dissociative adsorption (see Fig. 4 and compare with Ref. [32]). Brosilow and Ziff gave a proof that the simulation of the basic model must end in an absorbing state on a finite square lattice with an even side length [6,29]. This proof only deals with the N atoms produced by dissociative adsorption so that all other processes such as CO and O diffusion or CO desorption play no role and cannot prevent the system from running into an absorbing state. The N coverages on the virtual sublattices perform a random walk that depends on the position of the new NO adsorption site relative to the neighborhood of the N clusters. Therefore, if the square lattice is finite and of an even side length, one

Fig. 1. The two different dissociation mechanisms of NO. NO can be adsorbed via (a) the N atom side and (b) via the O atom side. This leads to different structures on the surface.

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Fig. 2. Temporal evolution of the correlation function g and of the N coverage H on the checkerboard like sublattices in model NN N I with dissociation path (a).

Fig. 3. Temporal evolution of the correlation function g and of the N coverage H on the checkerboard like sublattices in model NN N I with dissociation path (b).

sublattice must become fully covered by N atoms in a finite time. The process of dissociative adsorption onto a pair of vacant nearest neighbor sites with random orientation of the adsorbing NO can

be compared to the dissociation of a NO molecule into a vacant nearest neighbor site with dissociation mechanism (c) and p =p . For p >p , the a b a b removal of the N structures is preferred as

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193

Fig. 4. Temporal evolution of the correlation function g and of the N coverage H on the checkerboard like sublattices in model NN N I with dissociation path (c).

described above (see Fig. 1a). This makes a steadystate reaction possible, which was verified with simulations with p ≥0.6 in our work. a The contradiction for the NO+CO reaction between experimental work [steady-state reaction on Pt(100)], and previous MC simulations (no reaction on the square lattice) can be resolved by taking into account molecular NO adsorption with partly oriented adsorption or dissociation. Brandt et al. [8,34] and Mu¨ller et al. [35] found that N-end adsorption of NO molecules is preferred over O-end adsorption in a ratio of approximately 70:30. In our simulation, this gives a steady-state reaction with p =0.7 and p =0.3 determining the a b probabilities for dissociation mechanism (a) and (b), respectively. However, in this model, the desorption of NO and CO is a new necessary condition for the simulation to stay in a reactive state. On the triangular lattice, the dissociation mechanism as discussed above plays no role. It does not matter whether, in the dissociation process, the N or the O atom remains on the initial adsorption site. Both sites have in common two other nearest neighbor sites. This always allows a reaction to take place if these sites are properly occupied,

which is not the case for the square lattice. Thus, no special structures are built. This is simply a property of the triangular lattice, which is not bipartite. Again, desorption is necessary for a steady-state reaction, although with fast dissociation, there seems to be a reactive point at y =0.5 even without any desorption. With CO desorption of both CO and NO, the system shows large reactive intervals with y and R dependent 1 max on S , K , and K . This is very similar to the NO CO NO model with dissociation mechanism (a) on the square lattice. Because short range correlations appear, we used the cluster approximation to investigate the system behavior. As shown in Table 3, the reaction rate is mainly determined by the NO dissociation rate. y is shifted to larger 1 values of y with increasing NO dissociation and CO decreasing CO and NO desorption. If the desorption processes are too fast, the reaction rate drops because the coverage by vacant sites becomes very large (e.g. H =0.8 in the case of K =10). The V NO overall reaction rate is larger than on the square lattice. In this reaction model, CO diffusion has only a minor influence on the system behavior. With increasing CO diffusion, O removal from the sur-

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Table 3 Values of the phase transition points y and values of 1 y (R ) with the highest reaction rate R for the cluster CO max max approximation on the triangular lattice with NO dissociation and CO and NO desorptiona S NO

K NK CO NO

y 1

y (R ) CO max

R max

0.1 1.0 10.0 0.1 1.0 10.0 0.1 1.0 10.0

0.1 0.1 0.1 1.0 1.0 1.0 10.0 10.0 10.0

0.02 0.14 0.46 0.01 0.08 0.34 0.01 0.02 0.13

0.17 0.44 0.51 0.14 0.35 0.51 0.06 0.18 0.41

0.01 0.18 0.50 0.03 0.21 0.52 0.01 0.08 0.34

aR

max

is given in arbitrary units.

face is accelerated, leading to more vacant pairs of nearest neighbor sites, thus increasing the reaction rate. However, even with very rapid CO diffusion, the reaction rate is only shifted by about 20%. NO diffusion does not change the system behavior in this case because NO does not react directly. It can only be removed by dissociation or desorption from the surface.

3.2. Reactions R1 and R2 If NO can react directly with N atoms, no checkerboard-like structure of N atoms can be built. This is the most important difference between this model and model I. Because the reaction step (R2) can be ruled out at least on Rh(111) [18], we concentrate on the basic aspects of this reaction model. As in model I, CO and NO desorption is necessary to lead to a steady-state reaction. NO dissociation is the rate-limiting step. CO and NO diffusion have only a small influence on the reaction rate. The NO dissociation rate determines the value of y of the phase transition into the reactive 1 interval in combination with the CO and NO desorption rate in a very similar way to model I (see above). N is the only N-containing product 2 with production rates significantly higher than in model I with comparable parameters.

3.3. Reactions R1 and R3 Again, no N structures can grow because of the direct reaction of NO with N. Therefore, the system properties on the square and triangular lattice are very similar. In the case of N O as a 2 reaction product, we again have to distinguish the different dissociation mechanisms (see below). In general, we observe a narrow reactive interval below the stoichiometric gas phase concentration y if NO is allowed to desorb from the surface. s With CO desorption, a steady-state reaction occurs for values of y >y . In addition, a very narrow CO s reactive interval seems to exist on the triangular lattice at or around y for fast NO dissociation s and CO and NO diffusion rates even without desorption. In general, the system behavior is very similar to the results discussed above. Therefore, we do not want to give details regarding the phase transition points, and only concentrate on the important results. The reaction rate increases with the NO dissociation rate. S as well as K and NO CO K determine the value of y . NO 1 If we consider the two reaction pathways (R1) and (R3), there are two different products N and 2 N O. The ratio of the reaction rates R to R 2 N2 N2O for a given y is determined by the NO dissociCO ation constant S , by the type of dissociation NO path (a) or (b), and by p and p , respectively, in a b the case of path (c). Let us consider the different possibilities. In the case of dissociation path (a), N O is the only 2 reaction product. If a NO molecule is adsorbed into a nearest neighbor site to a N atom, N O is 2 produced and removed immediately. If it adsorbs into a next nearest neighbor site to a N atom, the NO molecule can dissociate, but neither N O nor 2 N can be formed if one neglects surface diffusion 2 of NO and N (see Fig. 5a) because we do not obtain two N atoms on nearest neighbor sites. For N production in this case, one has to add the 2 process of N diffusion. If NO dissociates via path (b), N can be 2 formed. Consider a NO molecule on a next nearest neighbor site to a N atom. Now, NO can dissociate giving a N atom on a nearest neighbor site that results in N production (see Fig. 5b). In this case, 2 the selectivity for the N-containing products is

O. Kortlu¨ke, W. von Niessen / Surface Science 401 (1998) 185–198

195

Fig. 5. Oriented NO dissociation determines the selectivity for N O and N . 2 2

determined by S at a given y . The dependence NO CO on y is weak in slow NO dissociation and almost CO absent in rapid NO dissociation. In Table 4, the N O selectivity is shown for different values of 2 S . For dissociation path (c), the N O selectivity NO 2 additionally depends on the value of p =1−p . b a With increasing p , the production of N O b 2 decreases and production of N increases. A 2 second point is that on account of the oriented dissociation of NO and the N production, the 2 overall reaction rate increases, too. This can be seen in the CO production rate R in Fig. 6. 2 CO2 CO diffusion has very little influence on the overall reaction rate and NO diffusion almost none, but if NO is mobile on the lattice, then an increasing NO diffusion rate increases the selectivity for N O against N as the major N-containing 2 2 product.

Table 4 Values of the N O selectivity for different values of the NO 2 dissociation constant S at y =0.4 (upper part) and y = NO CO CO 0.5 ( lower part) on the square lattice with K =K =1.0 CO NO S NO

R

0.1 1.0 10.0 100.0 0.1 1.0 10.0 100.0

1.16×10−4 6.61×10−3 4.06×10−2 2.24×10−2 1.24×10−4 6.49×10−3 4.28×10−2 5.78×10−2

N2

R N2O

R N2O R +R N2O N2

1.12×10−2 7.11×10−2 1.04×10−1 4.26×10−2 9.89×10−3 5.90×10−2 1.04×10−1 1.10×10−1

0.99 0.92 0.72 0.66 0.99 0.90 0.71 0.66

4. Conclusions In this paper, we have investigated a model for the catalyzed NO+CO surface reaction with molecular NO adsorption. A general result is that desorption of CO and NO is a condition for this model to show a steady-state reaction. To obtain broad reactive intervals, both species must be able to desorb. This condition holds independently of the reaction and dissociation models considered here. In our model, the NO dissociation is the rate-limiting reaction step. CO and NO diffusion have only a small quantitative influence on the reaction kinetics. Without the direct reaction between NO and N, the model is very dependent on the lattice structure. In this case, the reaction is possible on the triangular lattice as soon as CO and NO are able to desorb. On the square lattice oriented NO adsorption or dissociation is a second necessary point for a steady-state reaction. This hinders the N structures from growing over the whole lattice. If NO can react directly with N, the influence of the lattice structure moves into the background, and the results for the square and the triangular lattice are very similar. The reaction rate is again determined by the NO dissociation as the ratelimiting step. The orientation and the rate of NO dissociation rule the N O selectivity in the reaction 2 products of model III. In the case of the reaction between NO and N giving N O, the overall reac2 tion rate is increased slightly by NO diffusion. More importantly, NO diffusion increases the N O selectivity in this model. 2

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Fig. 6. The reaction rate R as a function of p for model IIIc at y =0.5 with K =K =1.0 and S =1.0. b CO CO NO NO

In comparison with the experimental work, we are able to qualitatively describe some of the reaction aspects. $ The NO dissociation is the rate-limiting step in our catalyzed NO+CO surface reaction model in agreement with most of the recent experimental kinetic measurements. Because the NO dissociation is very fast on Rh(111), this surface is highly suitable for this reaction. Of course, we cannot explain why Rh(111) is very active and Pt(111) is not, although these two surfaces have very similar geometries. Another point is that we suppose very fast molecular reaction steps. This holds for the CO+O and the N+N reaction steps [36 ] and should be valid for the N+NO step, too. $ As stated above, NO and CO desorption are necessary for a steady-state reaction. This appears to be a realistic aspect of this model because as far as we know, no experimental work exists in the literature where a steadystate reaction is observed below the NO desorption temperature. Another hint towards the necessity of desorption is that this reaction

$

$

$

shows surface explosion kinetics [37] and gas phase coupled oscillations [38]. Another point regarding reactant desorption is that the desorption rate should be slightly lower or comparable to the NO dissociation rate to obtain the highest possible overall reaction rates. NO desorption and NO dissociation are competitive reaction steps that should occur with comparable rates. If NO desorption is too fast, most of the adsorbed NO will desorb without any reaction. If NO desorption is too slow, only very few vacant sites are available for NO dissociation. Only at similar desorption and dissociation rates do sufficient vacant sites exist and NO dissociation is efficient for NO conversion. The N O selectivity over Rh surfaces can be 2 explained with oriented adsorption or dissociation, respectively. By simulating oriented dissociation, we can qualitatively describe the results of the adsorption experiments with oriented NO molecules carried out by Brandt et al. [8,34] and Mu¨ller et al. [35]. In our simulations, there are three ways to

O. Kortlu¨ke, W. von Niessen / Surface Science 401 (1998) 185–198

disturb the growth of the checkerboard-like N structures [or c(2×2) N structures]. The most effective one is of course the direct reaction of N and NO independent of the reaction products (N O or N and an adsorbed O atom). On all 2 2 surfaces that give N O as a reaction product, 2 this should be the main reaction step for removing small c(2×2) islands of N atoms. The second possibility is N atom diffusion. Almost nothing is known about the mobility of N atoms on catalyst surfaces. Little is known even about the kinetics and mobility of CO and NO molecules, although CO and NO diffusion are in general regarded as very fast surface processes. Therefore, we think that N atom diffusion can be neglected at least at low reaction temperatures. This agrees with thermal desorption spectra, which show N atom recombination starting at higher temperatures of about 700 K on many single crystal surfaces. The third way (in our simulation) is the oriented NO dissociation with dissociation path (a) as the principal route. This oriented dissociation corresponds to the possibilities of N-end and O-end sticking of NO. In this connection, it would be very interesting if reaction step R2 could be ruled out on Pt(100) as it was done on Rh(111) by Belton et al. [18]. In this case, and if N O is not found 2 as a reaction product in further studies, no direct reaction between N and NO occurs, and either N diffusion or oriented NO adsorption may be the reason for the absence of c(2×2) N structures, at least in the small low-temperature regime where the surface reconstruction 1×1hex does not occur. However, on account of the strong surface and substrate dependence of the NO+CO surface reaction, new aspects and energetic influences may occur on Pt(100) as well. Other experimental results cannot be explained by the present simulation model. The catalyzed NO+CO surface reaction is apparently of zero order in wide ranges of both the CO and NO gas phase concentration [12,36 ]. In our simulation, we find differences of almost an order of magnitude in the overall reaction rate between stoichiometric gas phase concentrations and excess concentrations of CO or NO. Another aspect is the

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competition for the adsorption sites found between NO, N and O but not CO. For example, CO is able to adsorb into a dense adsorbate layer of O, but NO is not. This is not included in our model because we use regular lattices to model the catalysts surface. These aspects will be the aim of our future work.

Acknowledgements The authors acknowledge financial support from the Deutsche Forschungsgemeinschaft via a fellowship for O.K. Part of this work was supported by the Fonds der Chemischen Industrie. The authors thank Professor V.N. Kuzovkov ( Riga, Latvia) for very helpful discussions.

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