Langmuir 1997, 13, 4013-4017
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A Dimer-Monomer Catalyzed Reaction Process with Surface Reconstruction Coupled to Reactant Coverages Ezequiel V. Albano* Instituto de Investigaciones Fisicoquı´micas Teo´ ricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Sucursal 4, Casilla de Correo 16, (1900) La Plata, Argentina. Received December 19, 1996X A lattice gas model for the catalyzed reaction A + 1/2B2 f AB is studied. Motivated from experiments on the catalytic oxidation of CO on Pt surfaces, it is assumed that the catalyst surface undergoes reactantinduced reversible phase transitions between two different structures, i.e., a stable (reconstructed) phase in the low (high) A coverage limit. Also the sticking coefficient of B2 species depends on the surface structure, being negligible in the stable phase. For low pressures of A species the systems have a reactive regime, while increasing such pressure a first-order irreversible phase transition onto an A poisoned state is observed. The structural transitions of the surface coupled with reactant coverages causes an oscillatory behavior in the reactive regime of the reaction. Away from the critical point, oscillations are periodic; however, close to criticality the onset of no-periodic oscillations is observed. Also, on approaching criticality the average period of the A rich phase diverges algebraically with exponent η ) 1, in agreement with the fact that just at the critical edge and in the t f ∞ limit the surface will be fully covered with A species.
I. Introduction
A(a) + B(a) f AB(g) + 2S
The kinetics of heterogeneously catalyzed reactions often exhibits a rich and complex nonlinear dynamic behavior which may include multistability, oscillations, chemical waves, poisoning, bifurcations, chaos, phase transitions, etc. In standard or thermodynamic phase transitions the behavior of the system under consideration changes qualitatively when a certain control parameter (e.g., pressure or temperature) passes through a critical point. Analogously, surface-catalyzed reaction processes may change, between a stationary reactive state and an inactive state with the surface fully covered by the reactants, when the control parameter (e.g., the partial pressures of the reactants) is finely tuned through a critical value. The inactive state is also known as the poisoned state, i.e., the surface becomes poisoned by the reactants. These kinds of transitions are known as irreversible phase transitions (IPTs), in contrast to thermally driven transitions which are reversible. If the change in the reaction rate is stepwise at the critical point, the IPT is discontinuous and belongs to the first-order class. However, if the change is smooth, the IPT is continuous and belongs to the second-order class. The study of IPTs in reaction systems has experienced a dramatic growth since the publication of the pioneering work of Ziff, Gulari, and Barshad (ZGB);1 for recent reviews see, e.g., refs 2-4. The ZGB-model deals with the monomer-dimer reaction 2A + B2 f 2AB which mimics the oxidation of carbon monoxide, i.e., A is CO, B2 is O2 and AB is CO2. The ZGB is a lattice gas reaction model, where it is assumed that the reaction proceeds according to a Langmuir-Hinshelwood mechanism
A(g) + S f A(a)
(1)
B2(g) + 2S f 2B(a)
(2)
* FAX: 0054-21-254642. E-mail:
[email protected]. X Abstract published in Advance ACS Abstracts, June 15, 1997. (1) Ziff, R. M.; Gulari, E.; Barshad, Y. Phys. Rev. Lett. 1986, 56, 2553. (2) Evans, J. W. Langmuir 1991, 7, 2514. (3) Zhdanov, V. P. Z.; Kasemo, B. Surf. Sci. Rep. 1994, 20 (3), 111. (4) Albano, E. V. Heterog. Chem. Rev. 1996, 3, 389.
S0743-7463(96)02118-X CCC: $14.00
(3)
where S is an empty site on the surface, while (a) and (g) refer to the adsorbed and gas phase, respectively. The relative impingement rates of A and B2 species, which are proportional to their partial pressures, are normalized (YA + YB ) 1), so the model has a single parameter, i.e., YA. For more details on the ZGB model see, e.g., refs 1 and 4. Interest in the ZGB model arises due to their rich and complex irreversible critical behavior. In fact, in two dimensions and for the asymptotic regime (t f ∞), the system reaches a stationary state whose nature solely depends on the parameter YA. For YA e Y1A = 0.3907 (YA g Y2A = 0.5250 ) the surface becomes irreversibly poisoned by B (A) species, while for Y1A < YA < Y2A a steady state with sustained production of AB is observed.1,4 Figure 1 shows plots of the rate of AB production (RAB ) and the surface coverage with A (θA) and B (θB) species versus YA. So, just at Y1A and Y2A the MD model exhibits IPTs between the reactive regime and poisoned states, which are of second and first order, respectively. Experimental evidence of a first-order “transition-like” behavior has been reported for the catalytic oxidation of carbon monoxide on Pt(210) and Pt(111).5 Here, we used the term “transitionlike” because an abrupt decrease in RAB is in fact observed when the pressure is tuned around a critical value; however, the formation of a true poisoned state with CO is prevented by the (rather small) desorption rate of such species. For detailed studies on the first-order IPT within the ZGB framework, see, e.g., refs 6-8. The second-order IPT is rather well understood, and it has been established that it belongs to the universality class of directed percolation or equivalently Reggeon field theory.9-12 In spite of the fact that this second-order (5) Ehsasi, M.; et al. J. Chem. Phys. 1989, 91, 4949. (6) Evans, J. W.; Miesch, M. S. Surf. Sci. 1991, 245, 401. (7) Evans, J. W.; Miesch, M. S. Phys. Rev. Lett. 1991, 66, 833. (8) Ziff, R. M.; Brosilow, B. J. Phys. Rev. A 1992, 46, 4630. (9) Grinstein, G.; Lai, Z.-W.; Browne, D. A. Phys. Rev. A. 1989, 40, 4820. (10) Jensen, I.; Fogedby, H. C.; Dickman, R. Phys. Rev. A. 1990, 41, 3411. (11) Grassberger, P.; De La Torre, A. Ann. Phys. (N. Y.) 1979, 122, 373. Grassberger, P. J. Phys. A. (Math., Gen.) 1989, 22, 3673.
© 1997 American Chemical Society
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Figure 1. Plots of the rate of AB production (RAB) and the surface coverage with A (θA) and B (θB) species versus YA, for the ZGB model.
transition has not been observed experimentally, it has extensively been studied using a variety of theoretical approaches.9,10,12,13 Obviously, this failure of the ZGB model is due to the crude assumptions involved, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, etc. Efforts to overcome these shortcomings have been performed; see, e.g., refs 14-18 etc. It should be mentioned that assuming the operation of the Eley-Rideal mechanism, i.e., adding the following step to the ZGB model
A(g) + B(a) f AB(g) + S
(4)
poisoning of the surface by complete occupation by the B-species is no longer possible.19-21 However, it is expected that the Eley-Rideal mechanism may not play a crucial role within the range of temperatures and pressures where the first-order transition has been experimentally observed,5,22 so this simplistic assumption cannot account for the B-poisoning dilemma. For this purpose the ZGB model has to be drastically modified including more realistic mechanisms. In this work it is shown that surface reconstructions, coupled with the reactant’s coverages, as experimentally observed,22,23 can naturally explain the absence of the continuous transition while the discontinuous one remains. Surface reconstruction causes the oscillatory behavior of the reactant’s coverages, a topic which is also studied in detail. II. The Model and the Simulation Technique It is well-known that the the catalytic oxidation of CO on Pt surfaces exhibits oscillatory behavior, within a (12) Albano, E. V. Phys. Rev. E. 1994, 49, 1738. (13) Meakin, P.; Scalapino, D. J. J. Chem. Phys. 1987, 87, 731. (14) Kaukonen, H. P.; Nieminen, R. M. J. Chem. Phys. 1989, 91, 4380. (15) Brosilow, B. J.; Ziff, R. M. Phys. Rev. A 1992, 46, 4534. (16) Albano, E. V. Appl. Phys. A 1992, 55, 226. (17) Luque, J. J.; Jime´nez-Morales, F.; Lemos, M. C. J. Chem. Phys. 1992, 96, 8535. (18) Satulovsky, J.; Albano, E. V. J. Chem. Phys. 1992, 97, 9440. (19) Mai, J.; von Niessen, W. Chem. Phys. 1991, 156, 63. (20) Meakin, P. J. Chem. Phys. 1990, 93, 2903. (21) Zhang, B.; Pan, H-Y. J. Phys. A. (Math., & Gen.), in press. (22) Imbihl, R. Prog. Surf. Sci. 1993, 44, 185. (23) Imbihl, R.; Ertl, G. Chem. Rev. 1995, 95, 697.
restricted range of pressures and temperatures. Such oscillations are coupled with adsorbate-induced surface phase transitions.22,23 In fact, in their clean states the reconstructed surfaces of some crystallographic planes, e.g., Pt(100) and Pt(110), are thermodynamically stable. However, the reconstruction can be lifted by adsorbed species such as CO, NO, O2, etc. So, the atoms of the topmost layer move back into their 1x1 positions. The adsorbate-induced transition (AIT) between the reconstructed and the 1x1 phases is reversible and therefore can be driven by critical adsorbate coverages. For a detailed discussion on the nature of the transition see refs 22 and 23. The observed variations in the catalytic activity occur due to the change in the surface geometry which takes place as a consequence of the AIT and also the adsorption properties of the surface change. On Pt surfaces the O2 sticking coefficient (SO2) is highly structure dependent, and since the oscillations occur when oxygen adsorption is rate-limiting, the catalytic activity is thus periodically modulated by the AIT. Oxygen adsorption experiments on Pt(100) show that SO2 ) 0.1 on the 1x1 phase while a drastic decrease of about 2-3 orders of magnitude is observed for the reconstructed phase. On Pt(110) the variation is also observed but it is smaller. A single oscillatory cycle can be described asfollows22 CO coverage surface structure O2 adsorption catalytic activity
high 1x1 SO2 large high
low reconstructed SO2 small low
Starting with a CO-covered 1x1 surface, one has a high SO2 value. This leads to a high reaction rate causing the CO coverage (θCO) to decrease. Below a certain critical value, θ1CO, the surface relaxes into the reconstructed phase. Now SO2 is small and the reaction rate also decreases causing the growth of θCO. Above another critical value, θ2CO, an AIT of the surface takes place and the catalyst recovers the initial 1x1 structure again. In order to simulate the ZGB model with adsorbateinduced surface phase transitions, we have used a square lattice of side L, with periodic boundary contitions, in order to represent the catalytic surface. Let θ1A and θ2A be the critical coverages at which the reversible phase transitions of the surface take place and S1B2 and S2B2 be the corresponding sticking probabilities. The Monte Carlo algorithm for the simulation is as follows: (i) A or B2 molecules are selected randomly with relative probabilities YA and YB, respectively. These probabilities are the relative impingement rates of both species, which are proportional to their partial pressures. Due to the normalization, YA + YB ) 1, we used YA as a parameter. If the selected species is A, one surface site is selected at random, and if that site is vacant, A is adsorbed on it (eq 1). Otherwise, if that site is occupied, the trial ends and a new molecule is selected. If the selected species is (B2) a pair of nearest neighbor sites is selected at random. Only if they are both vacant does adsorption proceed according to (eq 2), but with probabilities S1B2 or S2B2 depending on the structure of the surface. Such structure is updated after each event comparing θA with the critical coverages θ1A and θ2A. It is worth mentioning additional details on this procedure. The cycle of AIT starts when θA decreases below θ1A and surface reconstruction takes place. Then, the surface remains reconstructed until θA exceeds θ2A where the 1x1 phase develops. The subsequent decrease of θA below θ1A causes reconstruction again and the cycle is restablished. In all cases AIT is global, i.e., affecting the whole sample, and reconstruction or unreconstruction is triggered by the total coverage of A species at certain critical values. (ii) After each adsorption
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Figure 2. Plots of the rate of AB production (RAB) and the surface coverage with A (θA) and B (θB) species versus YA, for the ZGB model with adsorbate induced surface phase transitions. Most data is taken using L ) 256 but close to criticality L ) 512 is used.
event, the nearest neighbors of the added molecule are examined in order to account for the reaction given by eq 3. If more than one [B(a),A(a)] pair is identified, a single one is selected at random and removed from the surface. The Monte Carlo time step (t) involves L2 trials, so each site of the lattice will be visited once, on average, during each time unit. Simulations are started with empty lattices. The first 104 time steps are disregarded in order to allow the establishment of a stationary state, then subsequent 8 x 104 time steps are used to compute the averaged quantities of interest, i.e., the coverages with A and B species given by θA and θB, and the rate of AB production RAB, respectively. Otherwise stated, simulations are performed assuming S1B2 ) 1.0, S2B2 ) 0.0, θ1A ) 0.10, and θ2A ) 0.485. It is found that variations of these parameters cause only qualitative changes in the results. A similar model has early been proposed and studied by Moller et al.24 Celular automata simulations were performed mostly aimed to describe the propagation of two-dimensional patterns. In contrast, in the present work our interest is focused on studying the irreversible critical behavior of the reaction process in a model which incorporates adsorbate-induced reversible structural transitions of the catalyst surface to ZGBs framework. The oscillatory behavior of the catalytic process close to the critical edge is also studied. III. Results and Discussion III.a. The Phase Diagram. Figure 2 shows plots of the averaged surface coverages with the reactants and the rate of AB-production versus YA. On comparison with results of the ZGB model (see, e.g., Figure 1), it becomes evident that the introduced mechanism causes the inhibition of the B-poisoned state, and consequently the secondorder irreversible phase transition (IPT) between such state and the reactive regime is no longer observed, in qualitative agreement with the experimental results of Ehsasi et al.5 Furthermore, the phase diagram retains a dicontinuous IPT of first order at the critical point YAc = 0.5235 ( 0.0005, i.e., a value very close to the standard (24) Moller, P.; Wetzl, K.; Eiswirth, M.; Ertl, G. J. Chem. Phys. 1986, 85, 5328.
Figure 3. (a) Plots of θA and θB versus time, measured at YA ) 0.50, i.e. rather away from criticality. Note that θB -values were shifted up by adding 0.5 for the sake of clarity. (b) Plots of θA versus θB showing closed loops which evolve anti-clockwise in time.
ZGB model. These results are also in qualitative agreement with experimental results.5 A minor difference is that in actual experiments a truly CO-poisoned state is not achieved due to CO desorption. This fact can be easily taken into account in the simulations and the result is that for rather small desorption probabilities of A species one also observes first-order-like transitions.15,16 It should be noted that most simulations were performed using lattices of side L ) 256. However, close to criticality L ) 512 was also used in order to check any possible shift of the critical point due to finite size effects. The error bars reported for YAc account for diffrences obtained using different lattice sides. So, as expected, finite size effects have little influence on the location of the first-order critical point, provided that metastabilities are not relevant, in contrast to second-order transition where the study of finite size effects deserves careful consideration.4 III.b. The Oscillatory Behavior. Figure 3a shows the temporal dependence of the reactant’s coverages measured at YA ) 0.50, i.e., rather away from criticality.
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Figure 4. (a) Plots of θA and θB versus time, measured at YA ) 0.5230, i.e. rather close to criticality. Notice the no-periodic behavior and also that θB -values were shifted up by adding 0.5 for the sake of clarity. (b) Plots of θA versus θB showing closed loops which evolve anti-clockwise in time. Notice the existence of two kind of loops, denotes as L1 and L2, which roughly correspond to the two periods observed in Figure 4(a).
A self-sustained oscillatory behavior is clearly observed. Increments in the coverage of A species are in phase with drops in B coverage, and vice versa. Oscillations exhibit a well-defined periodicity, and for the example shown in Figure 3 the average periods for the phases of low and high B2 sticking coefficients are τ1 = 3.11 ( 0.02 and τ2 = 54.8 ( 0.2, respectively. Figure 3b shows that, within the reactive oscillatory regime, a plot of θB versus θA describes closed loops without any evidence of the presence of an attractor. The observed kinetic oscillations are a direct consequense of the coupling between the reconstructions of the surface and the sticking coefficient of B2 species. In fact, the absence of B2 adsorption when the coverage of the monomer drops below θ1A allows θA to increase until it reaches the critical value θ2A when B2 adsorption triggers a new cycle. When the critical threshold is approached, e.g., for YA ) 0.5230 as shown in Figure 4a, oscillations become nonperiodical, that is, oscillations of short period are followed
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Figure 5. (a) Plots of θA and θB versus time, measured at criticality. (b) Plots of θA versus θB showing closed loops which evolve anti-clockwise in time during a transient period but then the system is trapped by the attractor.
by long-lived oscillations. It seems that the occurrence of oscillations of different period does not follow any regular behavior, e.g., in the case of Figure 4a the short oscillation arround t = 23 500 is followed by three long oscillations and then three short oscillations are observed. This observation may suggest stochastic or chaotic behavior; however a more precise characterization of the process deserves careful studies. In plots of θB versus θA (Figure 4b) also closed loops without any evidence of the presence of an attractor are observed. However, in contrast to the results shown in Figure 3b, two different sets of loops are found: loops due to short (long) lived oscillations denoted by L1 (L2), respectively. Just at the critical point (see Figure 5), during a transient period of reactivity oscillations are nonperiodical and then the system evolves toward the poisoned state. A plot of θB versus θA describes closed loops during the transient period and then evolves toward the attractor (θB ) 0.0, θA ) 1.00). It is found that the period of the oscillations depends on YA as, e.g., it follows from Figures 3a and 4a. So, Figure 6 shows plots of τ1 and τ2 versus ∆YA ) YAc - YA.
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Figure 6. Plots of τ1 and τ2 versus ∆YA. The full straight line has slope η ) 1.0 and the doted line shows the asymptotic behavior of τ1.
Approaching the critical edge the τ2 diverges according to
τ2 ∝ ∆YAη
(5)
with η = 0.999 ( 0.004, strongly suggesting an exact linear divergency. In contrast, τ1 approaches a stationary value close to τ1 = 2.71 ( 0.03 as YA f YAc.
IV. Conclusions A dimer-monomer lattice gas reaction model of the type A + 1/2B2 f AB, which generalize the well-known ZGB model, in order to account for adsorbate-induced reversible transitions in the structure of the catalyst is introduced and studied. The proposed model exhibits a first-order irreversible phase transition between a reactive state and a poisoned phase where reaction stops. However, in contrast to the ZGB model, the B poisoned phase is not longer observed and consequently the second-order irreversible transition between such a phase and the reactive state does not exist. Due to the coupling between the surface structure and the sticking coefficient of the B2 species, the model exhibits a rich and complex oscillatory behavior. Periodic oscillations are observed away from the first-order irreversible transition. However, approaching criticality the oscillations become nonperiodic. These findings are in remarkable qualitative agreement with experimental results for the catalytic oxidation of carbon monoxide on Pt surfaces, pointing out that the mechanism introduced in the present work is essential for a more realistic study of the reaction. Therefore, the proposed model is, so far, an improved version of the the original ZGB model. Acknowledgment. This work was financially supported by the Consejo Nacional de Investigaciones Cientı´ficas y Te´cnicas (CONICET) and the Universidad Nacional de La Plata, Argentina. The computer facilities used to perform this work were granted by the Volkswagen Foundation (Germany) and the Commission of European Communities under Contract ITDC-122. LA962118S
