- Email: [email protected]
Monte Carlo simulation of temperature programmed reaction and surface explosion during CO oxidation on a Pt catalyst
Surface Science North-Holland
Letters
297 (1993) L127-L134
surface science letters
Surface Science Letters
Monte Carlo simulation of temperature programmed reaction and surface explosion during CO oxidation on a Pt catalyst Y. Boudeville a and E.E. Wolf b,* a Institut de Recherches sur la Catalyse, CNRS, Avenu A. Einstein, 69626 Villeurbanne, France b Chemical Engineering Department, University of Notre Dame, Notre Dame, IN 46556, USA Received
23 April
1993; accepted
for publication
14 August
1993
A Monte Carlo model of CO oxidation on a Pt(ll1) surface that includes finite rates of adsorption-desorption and reaction and the effect of the catalyst temperature is presented. The results show that, as expected from the reaction-adsorption probabilities, the surface coverage changes from being almost completely covered by CO at low temperature (6O”C), to being completely covered by oxygen at high temperature (160°C). Furthermore, it was found that an unstable state occurs when cooling down the oxygen covered surface from 160°C to 60°C. It is shown that if a site for CO adsorption is created under this metastable state, a surface explosion that propagates spatially occurs. Thus the MC simulations provide a method to describe a catalytic reaction on surfaces with strongly non-linear spatio-temporal dynamics.
1. Introduction Theoretical studies of catalytic reactions by Monte Carlo (MC) models give insight on the limitations of continuous uniform models such as the Langmuir-Hinshelwood (LH) model, and are a powerful tool to understand local non-linear properties in catalysis, like bifurcation points such as ignition and extinction and chaotic or oscillatory behaviors of surface reactions. There are various MC models of surface reactions [l-9]. The so-called Ziff-Gulari-Barshad model [l] (ZGB), is the simplest approach since all the probabilities of surface events are zero or one. This model considers adsorption-desorption with a probability of unity and an infinite surface reaction rate, and has attracted a great deal of interest because is only formal, however is highly unrealistic. Kolb and Boudeville [2] used the ZGB model using undeterministic cellular automaton rules, to analyze the size, shape and fractality of local clusters of chemisorbed species or empty
* To whom correspondence 0039-6028/93/$06.00
should
be addressed.
0 1993 - Elsevier
Science
Publishers
reactive platinum catalytic site. This model, although it also considers infinite rate constants for the reaction and contains only topological and fractal geometric concepts, it describes the simplest surface “ensembles” of co-adsorbed atoms and molecules for the CO + l/20, + CO, reaction. Wolf and coworkers 191 reported a MC simulation that is a further development of the ZGB approach, by assuming finite adsorption-desorption and surface reaction rates that place it a step closer to the chemisorption-reaction reality. Using this more realistic approach, it was possible to relate experimentally measured IR absorption shifts with theoretical MC predictions [lo]. In this communication the effect of varying temperatures on the predictions of the MC calculations is presented. We consider a catalytic uniform surface under the effect of a temperature programmed ramp. The surface is considered to be uniform with each Pt atom having the same adsorption, desorption and reaction probabilities that are determined by the macroscopic variables selected, such as the reactants partial pressure and the surface temperature. The results demonstrate the effect of temperature on coverage and
B.V. All rights reserved
Y: Boudeville, EL
Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
Probabilities of the various events Event
Probabili~ rate
Rate expression
Adsorption Yl = k,/N
k, = 0.54 x (0.53 x 10-2) (28TY-“Z
r, = k&is/N
k, = 0.38 x (0.47 x 1O-z) (32T)-“”
Desorption k-1 co~s-co,+s
Y-, = k-,/N
k_~=4~10z1exp[-(275~-5000~~/~~]
20~s-----+o*g+2s
Y-, = k._,/N
k _z = 2.4 x 1013exp[ - (52 000 - 12 000.9)/RTI
Y3cco)
k, = 1 x lOi exp[-(12000)/RT]
co,+
--!.J-+ c0.s
ozg + 2s -
k,
2o.s
k-2
Surface reaction co.s+o.s-
k,
co,,
f 2s
= k3-F,o,/2~J
&cti> = k,Xi,co/2N N= k, + k, + k,/2 + k_, + k_2r J&s = fraction of neighboring empty sites, Xi,,. CO and oxygen respectively, B = total surface coverage. the possibili~ of the fo~ati~n of unstable states, which when altered, can lead to dramatic transitions between steady states via surface explosions.
2. Theory The basic Monte Carlo model used in this work is the one proposed for CO oxidation on Pt by Araya et al. [91. Details of the formalism have been presented elsewhere [9,10], consequently only a brief description is given here. It considers finite rates for the adsorption, desorption and reaction processes that translate in finite probabilities for these events. The surface is represented by a 100 X 1!30 atomic grid with nearest neighbor interactions limited to the four nearest sites (for a square lattice). In this model no lateral interactions between adsorbed molecules are considered. The simulation starts with the random choice of a site on the surface. If the site is empty, the adsorption of CO or oxygen is selected by comparing their adsorption probabilities with a random number, R (0G R SG1). If the site is occupied, reaction or desorption of the adsorbed species is selected according to the
Xi,ox: nearest neighbor surface coverage of
probabili~ of each one of these processes in proportion to R. Once an event is selected, a new site is chosen until all the sites on the surface have been visited, completing one MC iteration. The probabilities of the various events are defined and have the values listed in table 1. These were selected on the basis of our earlier MC work, as well as rate constants from continuous simulations of experimental results obtained in onr laboratory [ill. The factor N is introduced to normalize the relative probabilities of the various processes such that: .Zyi 6 1, (i = - 1,1,2,3,4), which allows comparison with the random number R between 0 and 1. The MC calculations based on the above algorithm leads to the simulation of the surface coverage for a given set of physical conditions (i.e., pressure, temperature, type of surface). In this model the simulations are conducted at a given temperature for various MC times, and then the temperature is stepped up by 10°C until a maximum is reached. Then the temperature is decreased by the same procedure until the initial temperature is reached again. This procedure
Fig. 1. (left) Surface coverage at three different temperatures, (a) CO covered at 6O”C, (b) mixed coverage at lOO”C, (c) nearly oxygen poisoned at 160°C. “Red” CO adsorbate; “deep blue” oxygen adsorbate; “green blue” empty platinum site. Fig. 4. fright) Effect of removing one adsorbed oxygen atom to create an empty platinum atom onto a complete oxygen adlayer coofed down from 160°C to 60°C. Blue represents 0 coverage and red CO coverage.
A
B
C
Y. Boudeville, E.E. Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
simulates temperature programmed experiments previously conducted in our group [ 111.
3. Results and discussion Simulations of the surface coverage at three different temperatures after 100 MC iterations are presented in fig. 1 (1 MC iteration corresponds to visiting the 10000 sites of the lattice and to a real time of about lo-’ s). The three colors representing the coverage of CO (red), empty Pt sites (light blue) and oxygen atoms (blue). At 60°C the surface is predominantly covered by CO as the CO adsorption probability is large compared with the reaction and desorption probability (fig. la). At 100°C the coverages of CO and oxygen are similar and equal to about l/3 (fig. lb) and at 160°C the surface is mainly covered by large clusters of oxygen (fig. lc). The main effect of increasing the temperature is an increase in the rate of CO desorption and surface
reaction, which results in the decrease of CO coverage and in the increase in the oxygen coverage. This obviously is expected from the temperature dependence of the various rate processes involved, which affects the corresponding probabilities The complete temperature behavior of the reaction can be described in terms of the coverage versus temperature, as it increases from 50°C to 160°C and decreases likewise as shown in fig. 2. In this case, at each temperature, 200 MC iterations were performed. The coverages are relative coverages because they have been normalized from zero to one by dividing the number of atoms covered by one species by its maximum value. The solid line represents relative CO coverage that decreases as temperature increases, it reaches a negligible value, and then it increases again as the temperature decreases. The broken line represents relative oxygen coverage that, as expected, shows the opposite trend than adsorbed CO but with a small asymmetry due to the
Temperature
Fig. 2. Double
temperature
ramp
at 200 Monte
Carlo
“C
seconds, solid line: CO coverage, oxygen coverage.
dotted
line: empty
Pt sites, broken
line:
Y Boudeville, E.E. Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
existence of empty Pt islands as shown by the dotted line. CO, production reaches a maximum at the intersection of CO and oxygen coverage. While the results look a bit ragged due to the 10°C temperature step used, it was adopted to save computational time. The results would look smoother with a smaller AT, but they are essentially the same. The double ramp shows hysteresis of islands of adsorbates during the heating and cooling periods of the ramp. To investigate the dynamics of the hysteresis behavior, fig. 3 was constructed as a folded diagram of the curves shown in fig. 2, with the temperature varying between 60°C and 160°C on the abscissa and arrows indicating increasing and decreasing temperatures. The number of MC iterations used during each temperature step are 50, 200 and 1000 for figs. 3a-3c, respectively. Fig. 3a shows quite clearly that at 50 MC iterations per temperature step, a significant hysteresis of empty platinum sites occurs (dotted curves), whereas the hysteresis curve for adsorbed oxygen (broken curves> is less pronounced. The wellshaped CO adsorbate “ensembles” (solid curves) show a hysteresis-free sigmoid curve with increasing and decreasing temperatures. The hysteresis effect occurs because when the number of MC iterations is too small, the surface does not reach equilibrium and the number of sites covered in the heating period of the ramp is higher than during the cooling period of the ramp. This a result of the differences in the temperature dependence of the adsorption and desorption rate constants. As the number of iterations changes from 50 to 1000, the surface reaches a point in which there are no empty sites available and it is fully covered by oxygen atoms. Full coverage occurs because of the almost negligible rate of oxygen desorption that prevails at the conditions used in the calculations. At 160°C this surface is inactive since there are no empty sites for CO adsorption, dissociation, and reaction. There are three significant results on the calculations displayed in figs. 3a-3c. First the effect of MC iterations on the apparent hysteresis, then the continuous decrease of the platinum empty sites at the upper temperature of T = 160°C. Furthermore, by increasing the threshold of the MC
time from 50 MCs to 1000 MCs iterations, at 160°C the surface changes from being covered mainly by some CO (fig. la> to being covered by a complete monolayer of oxygen adsorbed without free platinum atoms and adsorbed CO (fig. 1~). Under this condition, the oxygen covered surface is dynamically poisoned at 160°C. However if the structure shown in fig. 3c, is cooled down, from for instance, 160°C to 60°C the surface remains unchanged and completely covered by oxygen causing the system to be metastable. The instability of this complete oxygen covered surface is very strong at 60°C because the macroscopic conditions favor largely a CO covered surface. CO is excluded from being adsorbed due to the total coverage of oxygen and the almost null probability for oxygen desorption at 160°C due to the high activation energy for oxygen desorption. At much higher temperatures (= 8Oo”C), the oxygen desorption rates are finite leaving empty Pt sites. This metastability is the basis for a bifurcation that occurs between this metastable oxygen covered state and the thermodynamically stable, fully CO covered surface. It should be emphasized that if the simulation is performed at 160°C but at completely isothermal conditions, i.e., without the stepping temperature increase, the surface does not reach the point of complete poisoning by oxygen even if performed for as long as 100 000 MC iterations. Thus, clearly the temperature history affects the final state of the surface since island formation is different if one proceed via a temperature ramp or at a constant temperature. Upon reaching the metastable state, an empty Pt atom was randomly imposed in the calculation to simulate the effect of a point laser hole. That is to say one platinum atom free of adsorbate on the 10000 sites was created on the fully oxygen covered catalyst at 60°C. Thus, artificially by removing an adsorbed 0 atom (on a randomly selected site) and leaving an empty Pt atom (one green square) from the 10 000 (deep blue squares) oxygen covered platinum atoms of the surface. This gives rise (vertical green arrow at 60°C on fig. 3~) to a complete ignition (2D explosion) on the surface. Figs. 4a-4c are selected snapshots of the propagation of the CO island adsorption dur-
I’. Boudeville, E.E. Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
ing the reversal between an oxygen covered surface and a CO covered surface, in order of increasing MC time (500, 700 and 1400 MC iterations, respectively). At the end of the explosion
process (more than 160 snapshots), the surface is identical to fig. la, i.e., it is nearly poisoned by CO. The catalyst, then, can go on for further cycles if the temperature ramp is repeated. This
1.0
0.9
0.6
0.7 zk E
0.6
9 t
0.5
.z m z
0.4
0.3
0.2
0.1
0.0 60
70
60
90
100
110
60
70
80
90
100
110
of MC threshold
140
150
160
150
“C
130
120
Temperature
Fig. 3. Effect
130
120
Temperature
140
150
160
150
“C
time on Pt hysteresis: (a) 50 MCs, (b) 200 MCs, (c) and 1000 MCs, solid line: CO coverage, line: empty Pt sites, broken line: oxygen coverage.
dotted
Y Boudeville,
E.E. Wolf / MC simulation
of TPR and surface explosion during CO oxidation on a Pt catalyst
0.9
0.6
0.2
0.1
60
70
60
90
100
110
130
120
Temperature
140
150
160
150
“C
Fig. 3. Continued.
demonstrates that spatial propagation occurs in surfaces as a phenomenon that originates in one surface atom and, in the absence of a gas synchronization and heat effects, it can only be communicated to other atoms on the surface via a spatially propagating front. It should be emphasized that in this model, for a given temperature, the sites comprising the 100 X 100 surface are at the same temperature since in the case of a single crystal the high conductivity of a metal will assure isothermality throughout the crystal. The boundary conditions have no effect on the quasi-metastability of the oxygen coverage. The only important parameter is the characteristic time of desorption for 1 oxygen, which is independent of other adsorbed oxygen atoms or boundaries. Once one oxygen has desorbed or an empty Pt atom is introduced, the probability for CO to adsorb and to react is almost unity, and the 2D CO explosion sweeps out all the surface changing the coverage from 0 to CO. It can be speculated that the explosion phenomenon emerging from the simulation might be at the root of oscillatory behavior observed in supported catalysts involving significant temperature effects which propagate spatially [11,12]. On
polycrystalline Pt supported on silica powders, the surface is far from regular and if its adsorption-reaction properties are not synchronized, one has to deal with truly spatially distributed properties. Results from Kellow and Wolf [12], show for instance that during CO and C,H, ignition and oscillations on Rh/ SiO,, the surface temperature is locally non-homogeneous. Thus, it is possible to envision that crystallites in an area of lower temperature can be poisoned by one of the reactants, but they can be ignited in a high temperature area, or may be halfway increasing in temperature in another part. According to the MC results presented here, this temperature inhomogeneity could be a crucial ingredient in the description of non-isothermal oscillatory states. A more complex model is necessary, however, to link sites at different temperatures dispersed on a non conductive support.
4. Conclusions A global temperature effect, simulated by a double temperature ramp via a Monte Carlo method, gives, by a fine tuning of the time thresh-
Y. Boudeville, E.E. Wolf / MC simulation
of TPR
oId length, an unstable state by coohng down an oxygen covered surface from 160°C to 60°C. It is shown that if a Pt site for CO adsorption is created under this metastable state, a surface explosion that propagates spatially occurs. Thus the MC simulations provides a method to describe a surface reaction with strongly non-linear effects, dynamically moving in time, and highly spatially dependent.
and surface explosion during CO oxidation on a Pt catalyst
121 M. Kolb and Y. Boudeville, J. Chem. Phys. 92 (1990) 393.5. 131 M. Ehsasi, M. Matloch, 0. Frank, J.H. B&h,
[4] [5] [6] [7] [8]
Acknowledgement
E.E.W. gratefully acknowledges the support provided by CNRS during his sabbatical leave at the IRC.
[9] [lo] [II] [12]
References [l] R.M. Ziff, E. Gulari and Y. Barshad, Phys. Rev. Lett. 56 (1986) 2553.
K. Christmann, F.S. Rys and W. Hirswald, J. Chem. Phys. 91 (1989) 4949. E.V. Albano, J. Chem. Phys, 94 (1991) 1499. J.W. Evans and MS. Miesch, Phys. Rev. Lett. 66 (1991) 833. J. Mai and W. von Niessen, Phys. Rev. A 43 (19911 1770. D. ben-Avraham, S. Redner, D.B. Considine and P. Meakin, J. Phys. A 23 (1990) L613. P. Meakin and D.J. Scalapino, J. Chem. Phys. 87 (1987) 731. P. Araya, W. Porod, R. Sant and E.E. Wolf, Surf. Sci. 208 (1989) LSO. P. Araya, W. Porod and E.E. Wolf, Surf. Sci. 230 (1990) 245. D. Kaul, R. Sant and E.E. Wolf, Chem. Eng. Sci. 42 (1987) 1399. J.C. Kellow and E.E. Wolf, AICHE J. 37 (1991) 1844.
Letters
297 (1993) L127-L134
surface science letters
Surface Science Letters
Monte Carlo simulation of temperature programmed reaction and surface explosion during CO oxidation on a Pt catalyst Y. Boudeville a and E.E. Wolf b,* a Institut de Recherches sur la Catalyse, CNRS, Avenu A. Einstein, 69626 Villeurbanne, France b Chemical Engineering Department, University of Notre Dame, Notre Dame, IN 46556, USA Received
23 April
1993; accepted
for publication
14 August
1993
A Monte Carlo model of CO oxidation on a Pt(ll1) surface that includes finite rates of adsorption-desorption and reaction and the effect of the catalyst temperature is presented. The results show that, as expected from the reaction-adsorption probabilities, the surface coverage changes from being almost completely covered by CO at low temperature (6O”C), to being completely covered by oxygen at high temperature (160°C). Furthermore, it was found that an unstable state occurs when cooling down the oxygen covered surface from 160°C to 60°C. It is shown that if a site for CO adsorption is created under this metastable state, a surface explosion that propagates spatially occurs. Thus the MC simulations provide a method to describe a catalytic reaction on surfaces with strongly non-linear spatio-temporal dynamics.
1. Introduction Theoretical studies of catalytic reactions by Monte Carlo (MC) models give insight on the limitations of continuous uniform models such as the Langmuir-Hinshelwood (LH) model, and are a powerful tool to understand local non-linear properties in catalysis, like bifurcation points such as ignition and extinction and chaotic or oscillatory behaviors of surface reactions. There are various MC models of surface reactions [l-9]. The so-called Ziff-Gulari-Barshad model [l] (ZGB), is the simplest approach since all the probabilities of surface events are zero or one. This model considers adsorption-desorption with a probability of unity and an infinite surface reaction rate, and has attracted a great deal of interest because is only formal, however is highly unrealistic. Kolb and Boudeville [2] used the ZGB model using undeterministic cellular automaton rules, to analyze the size, shape and fractality of local clusters of chemisorbed species or empty
* To whom correspondence 0039-6028/93/$06.00
should
be addressed.
0 1993 - Elsevier
Science
Publishers
reactive platinum catalytic site. This model, although it also considers infinite rate constants for the reaction and contains only topological and fractal geometric concepts, it describes the simplest surface “ensembles” of co-adsorbed atoms and molecules for the CO + l/20, + CO, reaction. Wolf and coworkers 191 reported a MC simulation that is a further development of the ZGB approach, by assuming finite adsorption-desorption and surface reaction rates that place it a step closer to the chemisorption-reaction reality. Using this more realistic approach, it was possible to relate experimentally measured IR absorption shifts with theoretical MC predictions [lo]. In this communication the effect of varying temperatures on the predictions of the MC calculations is presented. We consider a catalytic uniform surface under the effect of a temperature programmed ramp. The surface is considered to be uniform with each Pt atom having the same adsorption, desorption and reaction probabilities that are determined by the macroscopic variables selected, such as the reactants partial pressure and the surface temperature. The results demonstrate the effect of temperature on coverage and
B.V. All rights reserved
Y: Boudeville, EL
Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
Probabilities of the various events Event
Probabili~ rate
Rate expression
Adsorption Yl = k,/N
k, = 0.54 x (0.53 x 10-2) (28TY-“Z
r, = k&is/N
k, = 0.38 x (0.47 x 1O-z) (32T)-“”
Desorption k-1 co~s-co,+s
Y-, = k-,/N
k_~=4~10z1exp[-(275~-5000~~/~~]
20~s-----+o*g+2s
Y-, = k._,/N
k _z = 2.4 x 1013exp[ - (52 000 - 12 000.9)/RTI
Y3cco)
k, = 1 x lOi exp[-(12000)/RT]
co,+
--!.J-+ c0.s
ozg + 2s -
k,
2o.s
k-2
Surface reaction co.s+o.s-
k,
co,,
f 2s
= k3-F,o,/2~J
&cti> = k,Xi,co/2N N= k, + k, + k,/2 + k_, + k_2r J&s = fraction of neighboring empty sites, Xi,,. CO and oxygen respectively, B = total surface coverage. the possibili~ of the fo~ati~n of unstable states, which when altered, can lead to dramatic transitions between steady states via surface explosions.
2. Theory The basic Monte Carlo model used in this work is the one proposed for CO oxidation on Pt by Araya et al. [91. Details of the formalism have been presented elsewhere [9,10], consequently only a brief description is given here. It considers finite rates for the adsorption, desorption and reaction processes that translate in finite probabilities for these events. The surface is represented by a 100 X 1!30 atomic grid with nearest neighbor interactions limited to the four nearest sites (for a square lattice). In this model no lateral interactions between adsorbed molecules are considered. The simulation starts with the random choice of a site on the surface. If the site is empty, the adsorption of CO or oxygen is selected by comparing their adsorption probabilities with a random number, R (0G R SG1). If the site is occupied, reaction or desorption of the adsorbed species is selected according to the
Xi,ox: nearest neighbor surface coverage of
probabili~ of each one of these processes in proportion to R. Once an event is selected, a new site is chosen until all the sites on the surface have been visited, completing one MC iteration. The probabilities
Fig. 1. (left) Surface coverage at three different temperatures, (a) CO covered at 6O”C, (b) mixed coverage at lOO”C, (c) nearly oxygen poisoned at 160°C. “Red” CO adsorbate; “deep blue” oxygen adsorbate; “green blue” empty platinum site. Fig. 4. fright) Effect of removing one adsorbed oxygen atom to create an empty platinum atom onto a complete oxygen adlayer coofed down from 160°C to 60°C. Blue represents 0 coverage and red CO coverage.
A
B
C
Y. Boudeville, E.E. Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
simulates temperature programmed experiments previously conducted in our group [ 111.
3. Results and discussion Simulations of the surface coverage at three different temperatures after 100 MC iterations are presented in fig. 1 (1 MC iteration corresponds to visiting the 10000 sites of the lattice and to a real time of about lo-’ s). The three colors representing the coverage of CO (red), empty Pt sites (light blue) and oxygen atoms (blue). At 60°C the surface is predominantly covered by CO as the CO adsorption probability is large compared with the reaction and desorption probability (fig. la). At 100°C the coverages of CO and oxygen are similar and equal to about l/3 (fig. lb) and at 160°C the surface is mainly covered by large clusters of oxygen (fig. lc). The main effect of increasing the temperature is an increase in the rate of CO desorption and surface
reaction, which results in the decrease of CO coverage and in the increase in the oxygen coverage. This obviously is expected from the temperature dependence of the various rate processes involved, which affects the corresponding probabilities The complete temperature behavior of the reaction can be described in terms of the coverage versus temperature, as it increases from 50°C to 160°C and decreases likewise as shown in fig. 2. In this case, at each temperature, 200 MC iterations were performed. The coverages are relative coverages because they have been normalized from zero to one by dividing the number of atoms covered by one species by its maximum value. The solid line represents relative CO coverage that decreases as temperature increases, it reaches a negligible value, and then it increases again as the temperature decreases. The broken line represents relative oxygen coverage that, as expected, shows the opposite trend than adsorbed CO but with a small asymmetry due to the
Temperature
Fig. 2. Double
temperature
ramp
at 200 Monte
Carlo
“C
seconds, solid line: CO coverage, oxygen coverage.
dotted
line: empty
Pt sites, broken
line:
Y Boudeville, E.E. Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
existence of empty Pt islands as shown by the dotted line. CO, production reaches a maximum at the intersection of CO and oxygen coverage. While the results look a bit ragged due to the 10°C temperature step used, it was adopted to save computational time. The results would look smoother with a smaller AT, but they are essentially the same. The double ramp shows hysteresis of islands of adsorbates during the heating and cooling periods of the ramp. To investigate the dynamics of the hysteresis behavior, fig. 3 was constructed as a folded diagram of the curves shown in fig. 2, with the temperature varying between 60°C and 160°C on the abscissa and arrows indicating increasing and decreasing temperatures. The number of MC iterations used during each temperature step are 50, 200 and 1000 for figs. 3a-3c, respectively. Fig. 3a shows quite clearly that at 50 MC iterations per temperature step, a significant hysteresis of empty platinum sites occurs (dotted curves), whereas the hysteresis curve for adsorbed oxygen (broken curves> is less pronounced. The wellshaped CO adsorbate “ensembles” (solid curves) show a hysteresis-free sigmoid curve with increasing and decreasing temperatures. The hysteresis effect occurs because when the number of MC iterations is too small, the surface does not reach equilibrium and the number of sites covered in the heating period of the ramp is higher than during the cooling period of the ramp. This a result of the differences in the temperature dependence of the adsorption and desorption rate constants. As the number of iterations changes from 50 to 1000, the surface reaches a point in which there are no empty sites available and it is fully covered by oxygen atoms. Full coverage occurs because of the almost negligible rate of oxygen desorption that prevails at the conditions used in the calculations. At 160°C this surface is inactive since there are no empty sites for CO adsorption, dissociation, and reaction. There are three significant results on the calculations displayed in figs. 3a-3c. First the effect of MC iterations on the apparent hysteresis, then the continuous decrease of the platinum empty sites at the upper temperature of T = 160°C. Furthermore, by increasing the threshold of the MC
time from 50 MCs to 1000 MCs iterations, at 160°C the surface changes from being covered mainly by some CO (fig. la> to being covered by a complete monolayer of oxygen adsorbed without free platinum atoms and adsorbed CO (fig. 1~). Under this condition, the oxygen covered surface is dynamically poisoned at 160°C. However if the structure shown in fig. 3c, is cooled down, from for instance, 160°C to 60°C the surface remains unchanged and completely covered by oxygen causing the system to be metastable. The instability of this complete oxygen covered surface is very strong at 60°C because the macroscopic conditions favor largely a CO covered surface. CO is excluded from being adsorbed due to the total coverage of oxygen and the almost null probability for oxygen desorption at 160°C due to the high activation energy for oxygen desorption. At much higher temperatures (= 8Oo”C), the oxygen desorption rates are finite leaving empty Pt sites. This metastability is the basis for a bifurcation that occurs between this metastable oxygen covered state and the thermodynamically stable, fully CO covered surface. It should be emphasized that if the simulation is performed at 160°C but at completely isothermal conditions, i.e., without the stepping temperature increase, the surface does not reach the point of complete poisoning by oxygen even if performed for as long as 100 000 MC iterations. Thus, clearly the temperature history affects the final state of the surface since island formation is different if one proceed via a temperature ramp or at a constant temperature. Upon reaching the metastable state, an empty Pt atom was randomly imposed in the calculation to simulate the effect of a point laser hole. That is to say one platinum atom free of adsorbate on the 10000 sites was created on the fully oxygen covered catalyst at 60°C. Thus, artificially by removing an adsorbed 0 atom (on a randomly selected site) and leaving an empty Pt atom (one green square) from the 10 000 (deep blue squares) oxygen covered platinum atoms of the surface. This gives rise (vertical green arrow at 60°C on fig. 3~) to a complete ignition (2D explosion) on the surface. Figs. 4a-4c are selected snapshots of the propagation of the CO island adsorption dur-
I’. Boudeville, E.E. Wolf / MC simulation of TPR and surface explosion during CO oxidation on a Pt catalyst
ing the reversal between an oxygen covered surface and a CO covered surface, in order of increasing MC time (500, 700 and 1400 MC iterations, respectively). At the end of the explosion
process (more than 160 snapshots), the surface is identical to fig. la, i.e., it is nearly poisoned by CO. The catalyst, then, can go on for further cycles if the temperature ramp is repeated. This
1.0
0.9
0.6
0.7 zk E
0.6
9 t
0.5
.z m z
0.4
0.3
0.2
0.1
0.0 60
70
60
90
100
110
60
70
80
90
100
110
of MC threshold
140
150
160
150
“C
130
120
Temperature
Fig. 3. Effect
130
120
Temperature
140
150
160
150
“C
time on Pt hysteresis: (a) 50 MCs, (b) 200 MCs, (c) and 1000 MCs, solid line: CO coverage, line: empty Pt sites, broken line: oxygen coverage.
dotted
Y Boudeville,
E.E. Wolf / MC simulation
of TPR and surface explosion during CO oxidation on a Pt catalyst
0.9
0.6
0.2
0.1
60
70
60
90
100
110
130
120
Temperature
140
150
160
150
“C
Fig. 3. Continued.
demonstrates that spatial propagation occurs in surfaces as a phenomenon that originates in one surface atom and, in the absence of a gas synchronization and heat effects, it can only be communicated to other atoms on the surface via a spatially propagating front. It should be emphasized that in this model, for a given temperature, the sites comprising the 100 X 100 surface are at the same temperature since in the case of a single crystal the high conductivity of a metal will assure isothermality throughout the crystal. The boundary conditions have no effect on the quasi-metastability of the oxygen coverage. The only important parameter is the characteristic time of desorption for 1 oxygen, which is independent of other adsorbed oxygen atoms or boundaries. Once one oxygen has desorbed or an empty Pt atom is introduced, the probability for CO to adsorb and to react is almost unity, and the 2D CO explosion sweeps out all the surface changing the coverage from 0 to CO. It can be speculated that the explosion phenomenon emerging from the simulation might be at the root of oscillatory behavior observed in supported catalysts involving significant temperature effects which propagate spatially [11,12]. On
polycrystalline Pt supported on silica powders, the surface is far from regular and if its adsorption-reaction properties are not synchronized, one has to deal with truly spatially distributed properties. Results from Kellow and Wolf [12], show for instance that during CO and C,H, ignition and oscillations on Rh/ SiO,, the surface temperature is locally non-homogeneous. Thus, it is possible to envision that crystallites in an area of lower temperature can be poisoned by one of the reactants, but they can be ignited in a high temperature area, or may be halfway increasing in temperature in another part. According to the MC results presented here, this temperature inhomogeneity could be a crucial ingredient in the description of non-isothermal oscillatory states. A more complex model is necessary, however, to link sites at different temperatures dispersed on a non conductive support.
4. Conclusions A global temperature effect, simulated by a double temperature ramp via a Monte Carlo method, gives, by a fine tuning of the time thresh-
Y. Boudeville, E.E. Wolf / MC simulation
of TPR
oId length, an unstable state by coohng down an oxygen covered surface from 160°C to 60°C. It is shown that if a Pt site for CO adsorption is created under this metastable state, a surface explosion that propagates spatially occurs. Thus the MC simulations provides a method to describe a surface reaction with strongly non-linear effects, dynamically moving in time, and highly spatially dependent.
and surface explosion during CO oxidation on a Pt catalyst
121 M. Kolb and Y. Boudeville, J. Chem. Phys. 92 (1990) 393.5. 131 M. Ehsasi, M. Matloch, 0. Frank, J.H. B&h,
[4] [5] [6] [7] [8]
Acknowledgement
E.E.W. gratefully acknowledges the support provided by CNRS during his sabbatical leave at the IRC.
[9] [lo] [II] [12]
References [l] R.M. Ziff, E. Gulari and Y. Barshad, Phys. Rev. Lett. 56 (1986) 2553.
K. Christmann, F.S. Rys and W. Hirswald, J. Chem. Phys. 91 (1989) 4949. E.V. Albano, J. Chem. Phys, 94 (1991) 1499. J.W. Evans and MS. Miesch, Phys. Rev. Lett. 66 (1991) 833. J. Mai and W. von Niessen, Phys. Rev. A 43 (19911 1770. D. ben-Avraham, S. Redner, D.B. Considine and P. Meakin, J. Phys. A 23 (1990) L613. P. Meakin and D.J. Scalapino, J. Chem. Phys. 87 (1987) 731. P. Araya, W. Porod, R. Sant and E.E. Wolf, Surf. Sci. 208 (1989) LSO. P. Araya, W. Porod and E.E. Wolf, Surf. Sci. 230 (1990) 245. D. Kaul, R. Sant and E.E. Wolf, Chem. Eng. Sci. 42 (1987) 1399. J.C. Kellow and E.E. Wolf, AICHE J. 37 (1991) 1844.