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Critical Point Properties of the Surface Structure During CO Oxidation
Guczi, L et d.(Editors),New Frontiers in Cufalysis Proceedings of the 10th International Congress on Catalysis, 19-24 July, 1992,Budapest, Hungary 0 1993 Elsevier Science Publishers B.V. All rights reserved
CRITICAL POINT PROPERTIES OF THE SURFACE STRUCTURE DURING CO OXIDATION
M.Kolb
Institut de Recherches sur la Catalyse, 2 ave A. Eisntein, 69626 Villeurbanne Cedex, France and Laboratoire Chimie Theorique, Ecole Normale Superieure, 46 Allee d'Italie, 69364 Lyon Cedex 07, France
Abstract A geometrical model which captures the basic features of CO oxidation on a planar surface has been investigated in the bistable regime between low and high CO surface coverage. For a specific value of pressure and temperature one observes properties that are similar to those found at second order phase transitions in equilibrium systems: long range spatial correlations, divergence of thermodynamic quantities and slow relaxation times.
1.Introduction Experimental observations and model calculations have demonstrated that for many catalytic reactions - and notably for the oxidation of CO on Pt - the reaction rates and the surface coverages there is a rich variety of phenomena such as bistability and oscillations, bifurcation schemes and chaos, solitary and spiraling wavesl-11. Modeling based on the elementary reaction steps has been successful, at least for some of the experiments. Here we investigate a modified version of an irreversible geometrical model which describes the surface structure of a catalyst for a Langmuir-Hinschelwood monomer-dimer process.
2. Model The irreversible model is defined as followss: 1) Each site of a flat surface is either empty, occupied by a CO or occupied by an 0, 2) Gaseous CO ( 0 2 )adsorbs (adsorbddissociates) randomly on a single (two nearest neighbor) surface site(s), 3) Any neighboring CO and 0 reactldesorb instantaneously. The sole parameter of the model is the partial pressure of the gaseous CO (pco) resp. 0, (po=I-pc,). For large pco, a transition towards a CO poisoned state is predicted. A low to high CO surface coverage transition is also seen experimentally.
2838 In order to remove the artifact of total CO poisoning, and to introduce a parameter that allows to search for a critical point, another step is included in the reaction: 4) CO desorbs randomly, with desorption rate dco.
3. Monte Carlo results Monte Carlo simulations were performed for pco close to the poisoning transition of the irreversible model and for small desorption rates dco. Figure 1 shows the CO, production, the oxygen coverage and the CO pressure pco vs. the CO coverage. Note that the CO2 production is largest for dco>O, for pco in the range where the surface would poison without desorption.
-
DCO
c OXY coz
-0
N
0 0
0
0.2
0.4
co
0.8
v.6
1
Fig. 1: Desorption rate (dco) (x), oxygen coverage (+) and C 0 2 production (A) at steady state for a CO partial pressure ~ ~ ~ ' 0 . 6 .
0 0
0.52
0.53
0.54
0.55
0.56
0.57
0.58
p,
Fig. 2: Phase diagram: CO coverage vs. CO partial pressure pco, with dco (.Ol
2839 In Fig. 2 the equilibrium CO-coverage is plotted vs. pco, with dco as a parameter. It has the typical appearance of a first order phase equilibrium diagram. The same data is plotted in Fig. 3, with pco and dco exchanged. It also looks like an equilibrium phase diagram. 1
0.8
0.6
r
1
0
0
0.4
0.2
0 0
0.02
0.04
0.06
0.00
0.1
0.1 2
dco
Fig. 3: Phase diagram: CO coverage vs. CO desorption rate dco, with pco (.53
Fig. 4: Typical surface state (0for oxygen; * for CO) close to the critical point.
2840 1 00
- .-
F
.
1 0-
--------
'
541/.041 .541/.04Z .542/.043 .542/.044 .543/.044 .543/.045
_I
10-2
1 0
.-
In-* 10"
10'
10"
x
Fig. 5: Log-log plot of CO-CO correlation function c(x) near the critical point for different pairs pco/dco. The large x correlations increases strongly near criticality. The susceptibility is expected to diverge at the critical point. Correspondingly, near criticality our finite size simulations show a maximum which increases with increasing system size. Discussion The singular behavior near the critical point of the present model is expected to he generic for the type of reaction considered. Therefore it ought to be observable in any of the experiments with the corresponding reaction mechanism. The critical temperature and pressure do vary from system to system, of course. If the analogy with equilibrium systems holds true, the singularities (correlations, susceptibility) would not depend on the details of the experiment. An additional feature expected near the second order transition is the slowing down of the relaxation towards the steady state. The simulations do show such a slowing down - it should also show up in the experiments.
References I F.O. and R.A.Schmitz, Catal.Rev.-Sci.Eng. 28, 89 ( 1986) 2 G.Ertl, Advances in Catalysis 37,213 (1990) 1.Kevrekidis.L.D.Schmidtand R.Aris, Surf.Sci. 137, IS1 (1984) 3 4 M.Eiswirth and G.Ertl, Surface Science 117.90 (1986) 5 R.Ziff, E.Gulari and Y.Barshad, Phys.Rev.Lett. 56,2553(1986) 6 R.Dickman, Phys.Rev. A34,4246 (1986) 7 P.Araya, W.Porod, R.Sant and E.E.Wolf, Surf.Sci. 208, LBO (1989) 8 M.Ehsasi,C.Seidel, O.Frank, H.Ruppender,W.Drachsel and J.H.Bloch, Surf.Sci. 210, L198 (1989) 9 H.H.Rotermund, S.Jakubith, A. von Oertzen and (;.Ed, J.Chem.Phys. 91,4942 (1989) K.Fichthorn, E.Gulari and R.Ziff, Phys.Rev.Lett. 14.1527 ( 1989) 10 J.W.Evans and M.S.Miesch. Surf.Sci. 245, 401 (1991) II
CRITICAL POINT PROPERTIES OF THE SURFACE STRUCTURE DURING CO OXIDATION
M.Kolb
Institut de Recherches sur la Catalyse, 2 ave A. Eisntein, 69626 Villeurbanne Cedex, France and Laboratoire Chimie Theorique, Ecole Normale Superieure, 46 Allee d'Italie, 69364 Lyon Cedex 07, France
Abstract A geometrical model which captures the basic features of CO oxidation on a planar surface has been investigated in the bistable regime between low and high CO surface coverage. For a specific value of pressure and temperature one observes properties that are similar to those found at second order phase transitions in equilibrium systems: long range spatial correlations, divergence of thermodynamic quantities and slow relaxation times.
1.Introduction Experimental observations and model calculations have demonstrated that for many catalytic reactions - and notably for the oxidation of CO on Pt - the reaction rates and the surface coverages there is a rich variety of phenomena such as bistability and oscillations, bifurcation schemes and chaos, solitary and spiraling wavesl-11. Modeling based on the elementary reaction steps has been successful, at least for some of the experiments. Here we investigate a modified version of an irreversible geometrical model which describes the surface structure of a catalyst for a Langmuir-Hinschelwood monomer-dimer process.
2. Model The irreversible model is defined as followss: 1) Each site of a flat surface is either empty, occupied by a CO or occupied by an 0, 2) Gaseous CO ( 0 2 )adsorbs (adsorbddissociates) randomly on a single (two nearest neighbor) surface site(s), 3) Any neighboring CO and 0 reactldesorb instantaneously. The sole parameter of the model is the partial pressure of the gaseous CO (pco) resp. 0, (po=I-pc,). For large pco, a transition towards a CO poisoned state is predicted. A low to high CO surface coverage transition is also seen experimentally.
2838 In order to remove the artifact of total CO poisoning, and to introduce a parameter that allows to search for a critical point, another step is included in the reaction: 4) CO desorbs randomly, with desorption rate dco.
3. Monte Carlo results Monte Carlo simulations were performed for pco close to the poisoning transition of the irreversible model and for small desorption rates dco. Figure 1 shows the CO, production, the oxygen coverage and the CO pressure pco vs. the CO coverage. Note that the CO2 production is largest for dco>O, for pco in the range where the surface would poison without desorption.
-
DCO
c OXY coz
-0
N
0 0
0
0.2
0.4
co
0.8
v.6
1
Fig. 1: Desorption rate (dco) (x), oxygen coverage (+) and C 0 2 production (A) at steady state for a CO partial pressure ~ ~ ~ ' 0 . 6 .
0 0
0.52
0.53
0.54
0.55
0.56
0.57
0.58
p,
Fig. 2: Phase diagram: CO coverage vs. CO partial pressure pco, with dco (.Ol
2839 In Fig. 2 the equilibrium CO-coverage is plotted vs. pco, with dco as a parameter. It has the typical appearance of a first order phase equilibrium diagram. The same data is plotted in Fig. 3, with pco and dco exchanged. It also looks like an equilibrium phase diagram. 1
0.8
0.6
r
1
0
0
0.4
0.2
0 0
0.02
0.04
0.06
0.00
0.1
0.1 2
dco
Fig. 3: Phase diagram: CO coverage vs. CO desorption rate dco, with pco (.53
Fig. 4: Typical surface state (0for oxygen; * for CO) close to the critical point.
2840 1 00
- .-
F
.
1 0-
--------
'
541/.041 .541/.04Z .542/.043 .542/.044 .543/.044 .543/.045
_I
10-2
1 0
.-
In-* 10"
10'
10"
x
Fig. 5: Log-log plot of CO-CO correlation function c(x) near the critical point for different pairs pco/dco. The large x correlations increases strongly near criticality. The susceptibility is expected to diverge at the critical point. Correspondingly, near criticality our finite size simulations show a maximum which increases with increasing system size. Discussion The singular behavior near the critical point of the present model is expected to he generic for the type of reaction considered. Therefore it ought to be observable in any of the experiments with the corresponding reaction mechanism. The critical temperature and pressure do vary from system to system, of course. If the analogy with equilibrium systems holds true, the singularities (correlations, susceptibility) would not depend on the details of the experiment. An additional feature expected near the second order transition is the slowing down of the relaxation towards the steady state. The simulations do show such a slowing down - it should also show up in the experiments.
References I F.O. and R.A.Schmitz, Catal.Rev.-Sci.Eng. 28, 89 ( 1986) 2 G.Ertl, Advances in Catalysis 37,213 (1990) 1.Kevrekidis.L.D.Schmidtand R.Aris, Surf.Sci. 137, IS1 (1984) 3 4 M.Eiswirth and G.Ertl, Surface Science 117.90 (1986) 5 R.Ziff, E.Gulari and Y.Barshad, Phys.Rev.Lett. 56,2553(1986) 6 R.Dickman, Phys.Rev. A34,4246 (1986) 7 P.Araya, W.Porod, R.Sant and E.E.Wolf, Surf.Sci. 208, LBO (1989) 8 M.Ehsasi,C.Seidel, O.Frank, H.Ruppender,W.Drachsel and J.H.Bloch, Surf.Sci. 210, L198 (1989) 9 H.H.Rotermund, S.Jakubith, A. von Oertzen and (;.Ed, J.Chem.Phys. 91,4942 (1989) K.Fichthorn, E.Gulari and R.Ziff, Phys.Rev.Lett. 14.1527 ( 1989) 10 J.W.Evans and M.S.Miesch. Surf.Sci. 245, 401 (1991) II