J. Phys. Chem. 1996, 100, 14417-14423
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Theoretical Inquiry into the Microscopic Origins of the Oscillatory CO Oxidation Reaction on Pt{100} M. Gruyters, T. Ali, and D. A. King* Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K. ReceiVed: January 30, 1996; In Final Form: June 3, 1996X
An improved model is presented which simulates temporal behavior in the CO + O2 reaction on the Pt{100} surface. The model is based on an experimentally determined strongly nonlinear power law for (1 × 1)-CO island growth rate from the hexagonal (hex) phase with an apparent reaction order of about 4 in the local CO coverage on the hex phase. The power law describes the phase transition from the hexagonal phase of the reconstructed Pt surface to the (1 × 1) phase. Rate parameters from recent adsorption and desorption experiments are used in the modeling. The variations of all adsorbate coverages, the reaction rates, and the surface phase are monitored to provide extensive information about the reaction. New insight into the mechanisms driving the experimentally observed oscillations is gained, and an interpretation of the actual dynamics of the underlying surface processes is also given.
1. Introduction Temporal oscillations in the rate of chemical reactions have been extensively studied in numerous systems under substantially different physical conditions such as the gas-phase, the solution-phase, the liquid-solid interface, and the gas-solid interface. Although strikingly different fields in physical chemistry are involved, many common features can be concluded. In recent years, a strong tendency has emerged to generalize the experimentally observed behavior and to produce simplified underlying mechanistic schemes in order to obtain more general models which can be expressed in mathematical terms. Because of the great variety of spontaneous periodic phenomena in natural science, this approach is highly desirable, but it can only be useful if the simplifications used entirely contain and properly represent the crucial aspects of individual systems. Only by thoroughly understanding the detailed behavior of particular systems can unifying features be derived before being implemented in more general theories. The first step in the evaluation of a theoretical model for a specific chemical reaction occurring at a solid surface is finding the appropriate rate equations. For systems which show temporal oscillatory behavior, these frequently turn out to be of great complexity. However, the precise determination of the corresponding rate constants from adsorption and desorption experiments is of no less importance for a realistic description of the reaction. Numerous detailed investigations into the kinetics and dynamics of the reactions of CO and of O2 with Pt{100} have been performed in our laboratory over recent years1-7 in order to improve and complete the already available experimental data on this specific system. Clean Pt{100} reconstructs to form a close-packed quasihexagonal surface layer on top of bulk planes with square periodicity.8 The stable structure of Pt is referred to as hexR0.7° or simply hex-R. In addition to the stable hex-R phase, a metastable hexagonal (hex) phase, slightly rotated by 0.7° with respect to the hex-R phase, and a metastable (1 × 1) phase can also be prepared. The (1 × 1) phase irreversibly reconstructs above 400 K into the hex phase,9,10 which in turn reconstructs into the hex-R phase at about 1100 K. The clean surface reconstruction reverts to the (1 × 1) phase on adsorption of a X
Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00287-0 CCC: $12.00
variety of gases such as CO, NO, H2, C2H4, etc. Critical adsorbate coverages are necessary to stabilize this phase. If the coverage falls below these values, the (1 × 1) f hex transition is initiated. The adsorbate-induced reversible hex T (1 × 1) phase transition is of crucial importance for the temporal and spatial oscillatory behavior of chemical reactions on Pt{100}. In all theoretical treatments of the (CO + O2)/Pt{100} reaction system a first-order process was assumed for the hex f (1 × 1) phase transition or, more precisely, for the (1 × 1)-CO island growth rate with respect to the local CO coverage on the hex phase. Contrary to this assumption, molecular beam studies have recently shown that the (1 × 1)-CO island growth rate follows a strongly nonlinear power law1,2
dθ1×1 hex n ) ) kCO(θCO dt
(I)
where θ1×1 is the fraction of the surface in the (1 × 1) phase hex is the local CO coverage on the hex phase. The and θCO power law plays a dominant role whenever the local CO coverage on the hex phase is small and the lifetime of CO on the hex phase is short. The latter is particularly true during the oscillatory CO + O2 reaction which takes place at temperatures between 460 and 540 K,11,12 within the temperature range of CO desorption from the Pt{100} surface.2 Nonlinear behavior is well-known to lie behind many of the observed oscillatory systems.13 The discovery of the nonlinear power law for the hex f (1 × 1) phase transition may therefore not only provide essential input for a theoretical understanding of the oscillatory mechanism in the CO + O2 reaction on Pt{100} but also for a theoretical understanding of many other similar processes at surfaces. Experimentally, temporal oscillations in this system have been found in the reaction rate, the reactant and product gas pressures, the work function, and the surface structural phase. The CO + O2 reaction on Pt singlecrystal surfaces is one of the less elaborate examples of heterogeneous catalysis and has taken precedence in elucidating the origins of temporal and spatial phenomena of self-organization at the gas-solid interface.11,14 Although many common features have been revealed by experimental and theoretical work on this system,11 the new input that has been brought about in recent years1-7 makes it necessary to revise the earlier © 1996 American Chemical Society
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Gruyters et al.
theoretical studies. A brief report has been published16 that outlines the model which is developed in detail here. Similarities and differences to former theoretical approaches by other groups and the new insight gained into the origins of the reaction behavior are discussed. 2. The Mathematical Model The present model of the catalytic CO oxidation on Pt{100} is based on the following rate equations which are now wellestablished11,17,18
COg + *hex a COhex
(1)
COg + *1×1 f CO1×1
(2)
CO1×1 f COg + *1×1,f
(3)
COhex + *1×1 a CO1×1 + *hex
(4)
/2O2,g + *1×1 f O1×1
(5)
1
/2O2,g + *1×1,f f O1×1
(6)
CO1×1 + O1×1 f CO2,g + 2*1×1,f
(7)
nCOhex + m*hex f nCO1×1 + m*1×1
(8)
*1×1 f *hex
(9)
1
where * symbolizes a vacant adsorption site and the indices hex and 1×1 refer to the hex and the (1 × 1) phases, respectively. In addition to the steps considered in earlier modeling,17,18 adsorption sites that are made available by CO desorption or CO2 formation (CO reaction with 1/2O2) are distinguished from other (1 × 1) sites and are called “freed” sites. Such sites are indexed with 1×1,f and are always vacant (unoccupied by adsorbates), and their number increases with increasing fraction of the surface in the (1 × 1) phase. CO adsorption onto and desorption from areas of hex phase are represented by the first step (eq 1). Adsorption of O2 on the hex phase can be neglected because the sticking probability SOhex2 is only ∼10-4,5,19 about 4 orders of magnitude lower than that for CO. The next two steps (eqs 2 and 3) describe adsorption onto and desorption from the (1 × 1) phase, paying particular attention to the creation of freed sites in the third step (eq 3). The role of freed sites will be explained in context with the differential equations. Migration of CO from the hex phase onto the (1 × 1) phase (trapping) and the reverse process (untrapping) are included in the fourth step (eq 4). The fifth and sixth (eqs 5 and 6) refer to oxygen adsorption with adsorption on freed sites differentiated from adsorption on other (1 × 1) sites. Freed sites are also created by CO reaction with oxygen, which is described by the seventh step (eq 7). The formation of CO2 takes place exclusively on the (1 × 1) phase. From the fifth and sixth steps, respectively, to the seventh step, the number of vacant sites is increased which leads to an autocatalytic reaction if the local CO coverage on the (1 × 1) phase is high. The hex T (1 × 1) surface phase transition is represented by the eighth and ninth steps (eqs 8 and 9), paying particular attention to the revised mechanism for the hex f (1 × 1) transformation according to eq I. The process of untrapping described in eq 4 leads to the formation of “nonfreed” (1 × 1) sites, which are also created during the hex f (1 × 1) phase transition represented by eq 9. Islands of (1 × 1) grow with a local coverage of about 0.4 which means that simultaneous with the phase transition a considerable
amount of nonfreed (1 × 1) sites is created. In addition, it should be stressed that after the (1 × 1) f hex phase transition (i.e., after the autocatalytic reaction to clean off the oxygen) most of the surface returns to the hex phase and the “freed sites” are no longer vacant. Then a new cycle with the creation of nonfreed sites mainly due to the hex f (1 × 1) phase transition starts again. In the present model, three reaction steps had to be added to the originally used six steps17,18 in order to take into account the formation of and the reaction with freed sites and the nonlinear (1 × 1)-CO island growth rate. The variations in the adsorbate coverages on the hex and the hex 1×1 , θCO , θO1×1), the fraction of the surface in (1 × 1) phases (θCO the (1 × 1) phase (θ1×1), and the fraction of the (1 × 1) surface that is temporarily freed by desorption or reaction (θf1×1) are described by a set of five coupled differential equations (eqs 10-14). hex dθCO ) dt hex hex pCO - k2θCO k1SCO
hex 1×1 hex k4θCO B k5θCO B dθ1×1 θCO + + (10) θhex θhex dt θhex
hex 1×1 1×1 k4θCO B k5θCO B dθCO 1×1 1×1 pCO - k3θCO + ) k1SCO dt θ1×1 θ1×1 1×1 1×1 θO k7θCO
1×1 dθ1×1 θCO (11) dt θ1×1
dθO1×1 (1 - θf1×1) + SO1×1,f θf1×1)pO2 ) k6(SO1×1 2 2 dt dθ1×1 θO1×1 1×1 1×1 k7θCO θO (12) dt θ1×1
(
)
hex k4θCO dθf1×1 B 1×1 1×1 pCO + k6SO1×1,f p + θf + ) - k1SCO O2 2 dt θ1×1 1×1 k3θCO
{
dθ1×1 k [θhex]nθ ) 8 CO hex dt -k9(1 - c)θ1×1
1×1 1×1 + 2k7θCO θO (13)
if c g 1, if c < 1,
(14)
where
c)
1×1 θCO crit θCO
+
θO1×1 θOcrit
Since the total surface is either (1 × 1) or hex, θ1×1 + θhex ) 1. The adsorbate coverages refer to local coverages on the hex and the (1 × 1) phases. The latter are given in monolayers (ML) relative to the Pt atom density in the ideal (1 × 1) surface. The sum θ1×1 + θf1×1 is the whole ensemble of vacant sites on that fraction of the surface in the (1 × 1) phase θ1×1. This yields the further expression for the fraction of the surface in 1×1 . The the (1 × 1) phase, θ1×1 ) θ1×1 + θf1×1 + θO1×1 + θCO fraction of the surface in the hex phase is similarly given by hex , where θhex is the fraction of vacant sites on θhex ) θhex + θCO the hex phase. Coverage dependent sticking probabilities for phase . The each gas and for each surface phase are denoted Sgas final terms with dθ1×1/dt in eqs 10-12 maintain mass balance of adsorbates as θ1×1 changes. Equations 10 and 11 are identical to the differential equations for the same kind of modeling recently carried out for the CO + NO reaction on Pt{100}.20
Microscopic Origins of Oscillatory CO Oxidation
J. Phys. Chem., Vol. 100, No. 34, 1996 14419
TABLE 1: Temperature Dependent Parameters Used in the Mathematical Model description
parameter
Ea (kJ mol-1)
ν (s-1)
ref
CO desorption hex CO desorption (1 × 1) CO trapping CO untrapping hex f (1 × 1) (1 × 1) f hex
k2 k3 k4 k5 k8 k9
E2 ) 105 E3 ) 154 (Θ ) 0) 0 E3 - E2 ) 49 0 106
ν2 ) 3.7 × 1012 ν3 ) 1.0 × 1015 1×1 hex /ν3SCO ν5ν2SCO 4 1.0 × 10 4.9 × 104 2.5 × 1011
2 20 20 20 20 10
TABLE 2: Temperature Independent Parameters Used in the Mathematical Model description
parameter
CO impingement rate O2 impingement rate sticking probabilities: CO on hex CO on (1 × 1) O2 on (1 × 1) (1 × 1) boundary length critical coverages: for (1 × 1) f hex hex f (1 × 1) reaction order
1×1 ν2SCO hex ν3SCO
ref
k1 k6
2.22 × 10 ML mbar s 2.08 × 105 ML mbar-1 s-1
calcd calcd
hex SCO 1×1 SCO 1×1 SO2 SO1×1,f 2 B
0.78 0.91 (Θ ) 0) 0.28 (Θ ) 0) 0.31 (Θ ) 0) 1
2 2 5 7 20
CO θcrit O θcrit n
0.25 ML 0.4 ML 4.1
7,21 22 1,2
The latter two contain most of the new temperature or coverage dependent parameters used in the model (k2, k3, k4, k5, and 1×1 ) as described elsewhere.20,2 All parameters used are SCO listed in Tables 1 and 2. hex . It contains Equation 10 describes the variations in θCO parameters for adsorption (k1), desorption (k2), trapping (k4), and untrapping (k5). The CO sticking probability on the hex hex , and k2 are assumed to be coverage independent phase, SCO because the CO coverage on the hex phase is always low. The migration of CO from the hex phase onto the (1 × 1) phase (trapping) is taken to be nonactivated, while the reverse process (untrapping) is assumed to be activated with an energy barrier equal to the difference in the desorption energies from the hex and the (1 × 1) phases. This energy difference is in turn taken to be equal to the difference in the desorption activation energies from the hex and (1 × 1) surfaces. Since the adsorption on both surfaces is nonactivated, this is a reasonable assumption. The untrapping rate constant k5 is taken to be coverage independent, while the trapping rate k4 decreases with increasing coverage on the (1 × 1) phase. By considering a three-phase equilibrium between the adsorbates on the (1 × 1) and hex phases and the gas phase, it can be shown that
k4 ) ν5
value 5
(15)
where ν2 and ν3 are the pre-exponential factors for the desorption from the hex and the (1 × 1) phases, respectively, and ν5 is the pre-exponential factor for the rate constant for untrapping. The parameter B is the relative length of boundary between the hex and (1 × 1) areas. The appearance of θhex in the denominators of the third and fourth terms of eq 10, corresponding to the rates of CO trapping (hex f (1 × 1)) and untrapping ((1 × 1) f hex), respectively, and also θ1×1 in the third and fourth terms of eq 11 arises from the normalization of the partial rates hex 1×1 /∂t for these steps to the total fractional /∂t and ∂θCO ∂θCO amount of the surface in the respective phases. Since the local coverage on both phases remains virtually constant throughout island growth, B must be constant. A detailed discussion on the determination of the parameter B has been given.20 The variation in CO coverage on the (1 × 1) phase due to adsorption (k1), desorption (k3), trapping (k4), untrapping (k5),
-1 -1
and CO2 formation (k7) is described in eq 11. The coverage dependence of CO sticking probability on the (1 × 1) surface 1×1 is shown in Figure 1a, described as a series of linear SCO regions. It is based on the experimental curve reported in ref 2. In the calculations, the sticking probabilities are a function 1×1 + θO1×1). The coverage dependence of the total coverage (θCO of the desorption activation energy (E3), shown in Figure 1b, was determined from the temperature-programmed desorption (TPD) at an initial CO coverage of 0.57 ML,2 assuming a preexponential factor of 1 × 1015. Variations in θO1×1 are represented in eq 12. Adsorption (k6) and on the on freed sites θf1×1 with sticking probability SO1×1,f 2 is distinother (1 × 1) sites with sticking probability SO1×1 2 guished. Both sticking probabilities on the (1 × 1) phase are based on recent experimental investigations. Titration experiments of oxygen- and CO-precovered surfaces showed that the sticking probabilities on the CO-freed and oxygen-freed (1 × , are almost identical.7 But it turned out 1) phases, called SO1×1,f 2 is slightly higher than SO1×1 , the sticking probability that SO1×1,f 2 2 on a successively oxygen precovered (1 × 1) surface.5 This and SO1×1,f are shown as a can be seen in Figure 1a where SO1×1 2 2 series of linear regions. Furthermore, only the reaction (k7) with CO to form CO2 is considered in eq 12. Equation 13 describes the variation in the amount of temporarily existing freed sites on the area of (1 × 1) phase. These are created by CO desorption (k3) or CO2 formation (k7), but they are, in turn, partly reduced by CO or O2 adsorption (k1 or k6) and CO trapping (k4). The hex f (1 × 1) phase transition is described in eq 14. As mentioned above, the hex f (1 × 1) transformation follows the strongly nonlinear power law with a precisely determined value of n ) 4.11,2 (compare eq I). If the adsorbate coverage CO ) on the (1 × 1) phase falls below a critical coverage (θcrit O 0.25 ML, θcrit ) 0.4 ML), the reverse transition (1 × 1) f hex is initiated.7,21,22 The differential equations were integrated numerically, with time steps of between 10-4 and 10-5 s. 3. Results and Discussion The reaction steps (eqs 1-9) of the present CO + O2 model are similar to previous modeling on this system,11,18,19 differing mainly in the special treatment of the oxygen adsorption on
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1×1 Figure 1. Coverage dependencies (a, left) of CO and O2 sticking probabilities on Pt{100} - (1 × 1) (SCO , SO1×1 , and SO1×1,f ) and coverage 2 2 dependence (b, right) for CO desorption from Pt{100} - (1 × 1), used in the model.
Figure 2. Modeled temporal oscillations in the CO + O2 reaction on Pt{100} at T ) 500 K, pCO ) 1 × 10-5 mbar, and pO2 ) 1.6 × 10-4 mbar hex,1×1 (a, left). The fraction of the surface in the (1 × 1) phase θ1×1, local adsorbate coverages θAd , net sticking probabilities SCO (net) and SO2 (net), and the reaction rate to form CO2 rCO2 are shown. Steady states as a function of the fraction of the surface in the (1 × 1) phase for the same parameters as in (a) (b, right).
the (1 × 1) phase and the hex f (1 × 1) phase transition. Fundamental changes have been made in the differential equations 10-14 and their experimental input. The phase transition is based on the experimentally determined, strongly nonlinear power law (eq I), and migration of CO from areas of (1 × 1) to areas of hex phase (untrapping) is explicitly included. Both trapping and untrapping are treated independently of the phase transition. These changes and the coVerage dependencies 1×1 1×1,des and the activation energy for desorption ECO have for SCO been adopted from the recent CO + NO model on the same Pt surface.20 Furthermore, the experimentally determined O2 coVerage dependence of sticking probability on the (1 × 1) is crucial phase has been included.5,7 The use of SO1×1,f 2 because it maintains a nonvanishing oxygen sticking in a coverage range between 0.3 and 0.5, which is the average coverage on the (1 × 1) phase during the oscillatory CO + O2 reaction. The model leads to temporal oscillatory behavior at temperatures and reactant pressures which agree very well with experimental findings. Computation of the extent of the surface
phase transition, all adsorbate coverages, net sticking probabilities, and the reaction rate provides very complete information concerning the process of the reaction. Calculations begin with the condition that the surface is in the hex phase, the most stable phase (i.e., with θhex ) 1). Only CO can adsorb on the surface at this stage. A calculated example with T ) 500 K, pCO ) 1 × 10-5 mbar, and pO2 ) 1.6 × 10-4 mbar is shown in Figure 2a. Temporal oscillations, with a period tosc ≈ 62 s, are shown for each of the following: the fraction of the surface in hex , the (1 × 1) phase θ1×1; the local adsorbate coverages θCO 1×1 1×1 θCO , and θO and the net sticking probabilities SCO (net) and SO2 (net); the reaction rate of CO2 formation rCO2. The surface structure oscillates between 21 and 75% (1 × 1) phase. A steady state analysis greatly improves the understanding of the temporal behavior. Steady states are calculated by freezing the surface structure (i.e., under the constraint dθ1×1/ dt ) 0. θ1×1 is increased in 0.01 increments from 0 to 1, and then decreased again to 0) to reveal hysteresis in the reactivity. Figure 2b illustrates the steady state behavior for T ) 500 K, pCO ) 1 × 10 mbar, and pO2 ) 1.6 × 10-4 mbar, corresponding
Microscopic Origins of Oscillatory CO Oxidation exactly to the parameters used in Figure 2a. A bistability regime with two stable rate branches is clearly demonstrated. The two rate branches exhibit higher reactivity on a predominantly (1 × 1)-like surface phase and lower reactivity on a predominantly hex-like surface phase. For θ1×1 e 0.20, only the lower rate 1×1 is high and θO1×1 close to 0, the branch is stable. When θCO reaction is CO poisoned. For θ1×1 g 0.76, only the upper rate branch is stable; SO2 (net) is then significantly increased and the reaction rate is correspondingly high. For 0.21 e θ1×1 e 0.75, both rate branches are stable which leads to a hysteresis loop in this range. Which of the two rate branches obtained is history dependent. The oscillatory behavior is governed by this hysteresis, over the range of θ1×1 between 0.21 and 0.75. The reaction oscillates between the high and the low rate branches. One period in the temporal oscillations is equivalent to one cycle in the steady state hysteresis. The time plot sections marked A, B, C, and D in Figure 2a correspond to the steady state hysteresis marked A, B, C, and D in Figure 2b. The lower rate branch is followed (up to C) as the hex f (1 × 1) phase transition proceeds. The reaction rate of CO2 formation rCO2 slowly increases (path AB) with a slowly increasing rate of dissociative O2 adsorption. At θ1×1 ≈ 0.74 (B), an autocatalytic reaction involving the reaction steps in eqs 5-7 starts, leading to a rapid consumption of almost all of the adsorbed CO and to a transition to the upper rate branch (path BC). At θ1×1 ≈ 0.75 (C), the local coverage on the (1 × 1) phase is less than the critical coverage required to stabilize the (1 × 1) phase, and the (1 × 1) f hex phase transition occurs. The upper rate branch is followed with decreasing θ1×1 (path CD). With decreasing θ1×1, the O2 net sticking falls signifi1×1 can slowly increase until, at θ1×1 ≈ 0.22 (D), cantly and θCO a fast transition to the lower rate branch takes place (path DA). hex starts to induce the hex f (1 × The increasing amount of θCO 1) phase transition again, which closes the repeating cycle necessary for oscillatory behavior. The transitions between the upper and the lower rate branch (paths BC and DA) are always very fast, whereas the time spent on the lower (path AB) or on the upper rate branch (path CD) depends on actual parameters for T, pCO, and pO2. As θ1×1 increases, the rate of increase in θ1×1 decreases; the hex f (1 × 1) phase transition is slowed down. Thus, the time spent on the lower rate branch is long because the highest value in the hysteresis (θ1×1 ) 0.75) is only approached very slowly. However, the reaction on the upper rate branch proceeds very quickly. This can be explained by the high efficiency of the autocatalytic reaction leading to an apparently low adsorbate coverage on the (1 × 1) phase, which in turn speeds up the (1 × 1) f hex phase transition. For the CO + NO and the NO + H2 reaction, the adsorbate coverage remaining after the autocatalytic reaction is higher than that for the CO + O2 reaction leading to a slower (1 × 1) f hex phase transition and therefore to a longer time spent on the upper rate branch.20,23 It can be concluded that the driving force for the modeled oscillations is a combination of (a) the hex T (1 × 1) phase transition, particularly the nonlinearity in (1 × 1) island growth, (b) low reactivity on the hex phase and high reactivity on the (1 × 1) phase leading to hysteresis between the two rate branches, and (c) an autocatalytic reaction enabling a fast switch from the lower to the higher rate branch. We emphasise that both the surface structural phase transition and the autocatalytic reaction play important roles in the production of sustained oscillations. This combination of roles also applies to the CO + NO system in the high-temperature regime20 and to the NO + H2 system,23 which is discussed below. In our preliminary report on this model,16 we demonstrated the critical importance of the nonlinear term expressed in the
J. Phys. Chem., Vol. 100, No. 34, 1996 14421
Figure 3. The fraction of the surface in the (1 × 1) phase and the local CO coverage on the hex phase as a function of time for three different reaction orders n in the power law for the Pt{100} hex f (1 × 1) phase transition. From top to bottom: n ) 4.1, n ) 3.5, and n ) 3.0, with pCO ) 1 × 10-5 mbar, pO2 ) 1.6 × 10-4 mbar, and T ) 500 K.
(1 × 1)-CO island growth rate power law. In order to do this, the power factor n was varied in a set of computations. Figure 3 shows the results of these simulations with temporal variations hex in θ1×1 and θCO for different values of n. The period of the oscillations decreases with decreasing reaction order n and completely vanishes for n e 3. As explained in detail below, a reaction order of n implies that nCO molecules on the hex phase are involved in a concerted conversion to an area of (1 × 1) phase (see Figure 4). Consequently, a high reaction order of n ≈ 4 leads to an extremely slow hex f (1 × 1) hex . θ1×1 increases much more slowly transformation at low θCO hex than θCO , as can be seen for n ) 4.1 in Figure 3. With decreasing n, this changes significantly. For n ) 3.5, θ1×1 increases faster than for n ) 4.1, but oscillations are still maintained (tosc ≈ 8 s). The relative time spent on the upper rate branch as compared to the time spent on the lower rate branch increases with decreasing n. For n e 3.0, the θ1×1 hex growth approaches the rate of θCO growth and the oscillations disappear. Again, an interpretation of the temporal behavior can be given with the help of the corresponding steady state hysteresis (Figure 2b). The steady state curves comply with the condition dθ1×1/dt ) 0 and are therefore identical for all reaction orders n. For n ) 3, the phase transformation, and hence the (1 × 1)-CO island growth, is relatively fast. The rate of (1 × 1) formation prevents the system from reaching a value of θ1×1 as low as 0.22 (point D), the critical value on the hysteresis curve, required to switch from the upper rate branch to the lower rate branch (path D,A) before a single cycle can be completed. The system therefore remains on the upper, more reactive, rate branch, and oscillations are not observed. Point D is never reached. Evidently, a slow phase transition with a high reaction order above n ) 3 is crucial to obtain oscillatory behavior; the new model shows that this is perfectly met by the experimentally determined power law expression (eq I). Although the model as described in section 2 is of purely kinetic character, valuable information about the actual dynamic processes underlying the CO + O2 reaction on Pt{100} can be concluded. The nonlinear expression for the CO-induced hex
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Figure 4. Schematic illustration of subsequent dynamical processes during the CO + O2 reaction on an initial Pt{100} hex surface in a plan view (A-D). Light gray circles: first-layer Pt atoms in the hex phase. Dark gray circles: first-layer Pt atoms in a growing (1 × 1) island. Black circles: Pt atoms forced up from the first layer by the transformation. Hatched circles: chemisorbed CO molecules on top of the first Pt atom layer. Open circles: chemisorbed oxygen atoms on top of the first atom layer. For further explanation see the text.
f (1 × 1) phase transition provides the starting point for a description on a microscopic scale. In the temperature range
where the power law (eq I) applies, the new phase does not grow by accretion of single adsorbates diffusing to the phase
Microscopic Origins of Oscillatory CO Oxidation boundary, the growth mechanism can rather be represented by eq 8. This equation implies that n molecules on the hex phase are involved in a concerted conversion of a patch of hex phase to the (1 × 1) phase. Assuming a constant local adsorbate fractional coverage of 1/p of a monolayer (ML) on the growing (1 × 1) phase, the number of Pt surface atoms involved in this process is n × p (m + n in eq 8). The growth mechanism is illustrated in Figure 4, with p ) 2 and n ) 4, for the (1 × 1)-CO island growth on an initial Pt hex surface. Transformation of the entire surface from a hex to a (1 × 1) phase with increasing CO coverage might proceed via nucleation and growth of (1 × 1)-CO islands of limited size. As recent scanning tunneling microscopy studies of the CO-induced phase transition at 300 K showed, small isotropic islands with diameter of 10-15 Å and larger islands strongly elongated along the [01h1] direction are formed with increasing CO exposure.24 However, the modeled kinetic temporal behavior in the oscillatory CO + O2 reaction shown in Figure 2a starts with an initial hex phase followed by the growth mechanism illustrated in Figure 4a,b. At the beginning of the reaction, the local CO coverage on the hex phase is as low as ≈0.04 ML whereas on the (1 × 1) phase it is above ≈0.4 ML. For ≈20 s, the main process is an increase in the amount of (1 × 1) phase due to the nonlinear (1 × 1)-CO island growth mechanism (Figure 4a,b); the reaction rate to form CO2 is low because the (1 × 1) phase is still predominantly occupied by CO molecules having been converted from the hex phase. With increasing time and 1×1 increasing fraction of the surface in the (1 × 1) phase, θCO falls due to desorption and reaction. Thus, the amount of vacant sites on the (1 × 1) phase increases (Figure 4c). Because of the higher O2 gas pressure and the non-zero sticking probabilities and SO1×1,f on the (1 × 1) phase, increasingly more oxygen SO1×1 2 2 is adsorbed (Figure 4d). The O2 net sticking probability SO2 (net) and the reaction rate rCO2 increase considerably, leading to the autocatalytic reaction with the rapid consumption of almost all of the adsorbed CO and oxygen after ≈60 s. It is worthwhile to mention that CO clean-off starts only when the hex f (1 × 1) conversion rate becomes negligible. Otherwise CO adsorption on the hex phase and the following (1 × 1)-CO island growth serve continuously as a reservoir for maintaining CO on the (1 × 1) phase. However, after the autocatalytic reaction, the remaining total coverage is no longer sufficient to stabilize the (1 × 1) phase and the surface reverts to a predominantly hex structure. The (1 × 1)-CO island growth can start again (Figure 4a,b) which closes the oscillatory repeating cycle. Recent He reflectivity measurements during CO adsorption and desorption in the temperature range of 350-1100 K7 strongly support the mechanism illustrated in Figure 4. It was found that by starting with an initial Pt hex surface the fraction of the surface in the (1 × 1) phase grows at a constant local coverage of ≈0.4 ML on the (1 × 1)-CO islands up to the CO saturation of the surface. A marked hysteresis in the reflectivity of the surface during desorption also confirmed the stabilization 1×1 as low as 0.25 ML. of the metastable (1 × 1) phase at θCO Withdrawal of (1 × 1)-CO islands occurs only at lower CO ) 0.25 ML. coverages than θcrit 4. Conclusions Our new model for the CO + O2 reaction on Pt{100} based on independently derived parameters reproduces the experimentally observed temporal oscillatory behavior. The inclusion of a strongly nonlinear power law for the (1 × 1)-CO island growth rate from the stable hex phase and of new independent experimental input leads to a detailed understanding of the mechanism behind the oscillatory behavior. Monitoring of all
J. Phys. Chem., Vol. 100, No. 34, 1996 14423 adsorbate coverages, reaction rates, and the surface phase provides complete information about the progress of the reaction. Calculations of steady states as a function of (1 × 1) surface area supplies a ready means of interpreting the temporal behavior. It has been found that the driving force for oscillations is a combination of (a) the hex T (1 × 1) phase transition, particularly the nonlinearity in (1 × 1) island growth, (b) a low reactivity on the hex and a high reactivity on the (1 × 1) phase leading to a hysteresis between the two rate branches, and (c) an autocatalytic reaction enabling a fast switch from the lower to the higher rate branch. It has been shown for the first time that surface structural phase transitions as well as the autocatalytic reaction play the decisive role in the oscillatory mechanism. This combination also applies to the oscillatory behavior established for the CO + NO system in the high-temperature regime20 and the NO + H2 reaction23 on the same Pt surface. The detailed understanding of the kinetic behavior during reaction gained by the presented model together with the dynamics of the recently discovered (1 × 1)-CO island growth mechanism on the Pt{100} hex phase provides an interpretation of the underlying surface processes down to a microscopic scale. Acknowledgment. We thank A. Hopkinson for discussions concerning the program used for the CO + NO model. The EC is acknowledged for a fellowship to M.G. under the Human Capital and Mobility Scheme. T.A. acknowledges the Oppenheimer Trust for a research studentship. References and Notes (1) Hopkinson, A.; Bradley, J. M.; Guo, X. C.; King, D. A. Phys. ReV. Lett. 1993, 71, 1597. (2) Hopkinson, A.; Guo, X. C.; Bradley, J. M.; King, D. A. J. Chem. Phys. 1993, 99, 8862. (3) Guo, X. C.; Bradley, J. M.; Hopkinson, A.; King, D. A. Surf. Sci. 1994, 310, 163. (4) Guo, X. C.; King, D. A. Surf. Sci. 1992, 302, L251. (5) Bradley, J. M.; Guo, X. C.; Hopkinson, A.; King, D. A. J. Chem. Phys. 1996, 104, 3810. (6) Yeo, Y. Y.; Wartnaby, C. E.; King, D. A. Science 1995, 268, 1731. (7) Pasteur, A. T.; Guo, X. C.; Ali, T.; Gruyters, M.; King, D. A. Surf. Sci., in press. (8) Heilmann, P.; Heinz, K.; Mu¨ller, K. Surf. Sci. 1979, 83, 487. (9) Norton, P. R.; Davies, J. A.; Creber, D. K.; Sitter, C. W.; Jackman, T. E. Surf. Sci. 1981, 108, 205. (10) Heinz, K.; Lang, E.; Strauss, K.; Mu¨ller, K. Appl. Surf. Sci. 1982, 11/12, 611. (11) Imbihl, R.; Ertl, G. Chem. ReV. 1995, 95, 697 and references therein. (12) Eiswirth, M.; Schwankner, R.; Ertl, G. Zeit. Phys. Chem. 1985, 144, 59. (13) Scott, S. K. Chemical Chaos; Clarendon Press: Oxford, 1991. (14) Gruyters, M.; King, D. A. Nature, to be submitted. (15) King, D. A. Surf. ReV. Lett. 1994, 1, 435. (16) Gruyters, M.; Ali, T.; King, D. A. Chem. Phys. Lett. 1995, 232, 1. (17) Andrade, R. F. S.; Deweland, G.; Borckmans, P. J. Chem. Phys. 1989, 91, 2675. (18) Eiswirth, M.; Mo¨ller, P.; Wetzl, K.; Imbihl, R.; Ertl, G. J. Chem. Phys. 1989, 90, 510. (19) Norton, P. R.; Griffiths, K.; Bindner, P. E. Surf. Sci. 1984, 138, 125. (20) Hopkinson, A.; King, D. A. J. Chem. Phys. 1993, 177, 433. (21) Jackman, T. E.; Griffiths, K.; Davies, J. A.; Norton, P. R. J. Chem. Phys. 1983, 79, 3529. (22) Griffiths, K.; Jackman, T. E.; Davies, J. A.; Norton, P. R. Surf. Sci. 1984, 138, 113. (23) Gruyters, M.; Pasteur, A. T.; King, D. A. Faraday Trans., in press. (24) Borg, A.; Hilmen, A. M.; Bergene, E. Surf. Sci. 1994, 306, 10.
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