Imaging of spatial pattern formation in an oscillatory surface reaction by scanning photoemission microscopy

Rotermund, Harm Hinrich; Jakubith, S.; Oertzen, Alexander von; Ertl, G.

doi:10.1063/1.456735

Cited by 96 publications

(27 citation statements)

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“…For higher p CO and lower p O2 , θ tot O ahead of the front is lower and θ 1×1 and θ tot CO behind it are higher, so there is less phase relaxation. 1D front speeds are 0.13-14µm s −1 compared with 2-50 µm s −1 in experiments (at higher partial pressures and for 420K ≤ T ≤ 540K) [4,6]. CO fronts are slower at higher p O2 and lower p CO where the phase change is most marked, in accord with the argument [6] that the phase transition slows them.…”

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confidence: 69%

“…Ours is the first reaction-diffusion model to reproduce this pattern formation on physically feasible length and time scales, faithfully incorporating the available experimental data. Numerical simulations show patterns made up of CO and oxygen fronts moving at similar speeds to those seen in experiments [4][5][6].…”

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confidence: 65%

“…The surface orientation has a decisive effect on pattern formation: in the [111] orientation there is no phase change and hence no patterns, on Pt{110} classical spirals and targets are seen (e.g. [3]), while on Pt{100} the patterns are typically more irregular [4][5][6], though circular wavefronts are also seen [5].…”

mentioning

confidence: 99%

“…The diffusion terms take account of both these observations. D hex and D 1×1 are half the diffusion coefficients for CO on clean hex and 1 × 1 phases; we set them both to be 10 −6 cm 2 s −1 [4]. At the temperatures we consider oxygen is essentially immobile.…”

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Pattern Formation during the Oxidation of CO onPt{100}: A Mesoscopic Model

et al. 2007

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Constantly changing irregular patterns of carbon monoxide (CO) and oxygen are seen during CO oxidation on platinum crystals in the [100] orientation. Ours is the first reaction-diffusion model to reproduce this pattern formation on physically feasible length and time scales, faithfully incorporating the available experimental data. Numerical simulations show patterns made up of CO and oxygen fronts moving at similar speeds to those seen in experiments [4][5][6].PACS numbers: 68.43. Bc,68.47.De,82.40.Ck Spatiotemporal pattern formation occurs in a number of catalytic reactions, such as the Belousov-Zhabotinsky reaction where oscillating spirals and targets are seen [1]. Similar structures form during the catalytic oxidation of carbon monoxide on the surface of single platinum crystals, where patterns comprise areas of different surface phase or covered by different adsorbates. During the reaction oxygen and CO are adsorbed onto the platinum surface. At high enough temperatures and for certain orientations of the surface relative to the bulk crystal, the presence of adsorbates leads to a phase change, i.e. a rearrangement of the surface platinum atoms. When the oxygen and CO react, carbon dioxide gas is released and the surface reverts to its original configuration. This cycle can lead to kinetic oscillations in the surface phase. If communication between different areas on the crystal is very rapid compared with the rate of oscillation, the whole surface oscillates in phase; otherwise there can be phase lags across the surface and spatial patterns arise [2]. There are two main spatial coupling mechanisms: diffusion of CO across the surface, important at low pressures, and global coupling through the gas phase, which dominates at high pressures. The surface orientation has a decisive effect on pattern formation: in the [111] orientation there is no phase change and hence no patterns, on Pt{110} classical spirals and targets are seen (e.g. [3]), while on Pt{100} the patterns are typically more irregular [4-6], though circular wavefronts are also seen [5].In this Letter, we model pattern formation in CO oxidation on a single platinum crystal in the [100] orientation. The kinetic mechanism for this reaction is well established and has been modelled extensively [7][8][9]. Spatial modelling has concentrated on Pt{110} using a simplified representation of the kinetic mechanism, extended to include diffusion terms (and sometimes gas global coupling) [10]. These models produce results that qualitatively resemble experimentally observed patterns, but they cannot be used for detailed quantitative comparison since both the kinetic and diffusion mechanisms are simplified. Monte Carlo methods are also used, but at present these must assume unrealistically low diffusion coefficients in order to allow pattern formation on computationally accessible length and time scales [11]. We present a mesoscopic spatial model based on the detailed kinetic mechanism [9] together with diffusion terms derived from a careful consideration of...

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confidence: 65%

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Pattern Formation during the Oxidation of CO onPt{100}: A Mesoscopic Model

et al. 2007

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“…1,[16][17][18] However, in certain pressure regimes, spatial structure and self-organization have been observed by various surface imaging techniques to accompany the oscillations in the macroscopic reaction rate. [2][3][4]19 This typically takes the form of continuously varying patches of predominantly oxygen-and CO-covered surface whose arrangement changes in time through the passage of traveling reaction waves. These waves are of two types: relatively slowmoving CO fronts, at which the 1 ϫ 1 to hex phase relaxation occurs, and faster oxygen fronts not accompanied by phase change.…”

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Theoretical study of pattern formation during the catalytic oxidation of CO on Pt{100} at low pressures

Anghel

Hoyle

Irurzun

et al. 2007

The Journal of Chemical Physics

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Theoretical studies have thus far been unable to model pattern formation during the reaction in this system on physically feasible length and time scales. In this paper, we derive a computational reaction-diffusion model for this system in which most of the input parameters have been determined experimentally. We model the surface on a mesoscopic scale intermediate between the microscopic size of CO islands and the macroscopic length scale of pattern formation. In agreement with experimental investigations ͓M. Eiswirth et al., Z. Phys. Chem., Neue Folge 144, 59 ͑1985͔͒, the results from our model divide the CO and O 2 partial pressure parameter space into three regions defined by the level of CO coverage or the presence of sustained oscillations. We see CO fronts moving into oxygen-covered regions, with the 1 ϫ 1 to hex phase change occurring at the leading edge. There are also traveling waves consisting of successive oxygen and CO fronts that move into areas of relatively high CO coverage, and in this case, the phase change is more gradual and of lower amplitude. The propagation speed of these reaction waves is similar to those observed experimentally for CO and oxygen fronts ͓H. H. Rotermund et al., J. Chem. Phys. 91, 4942 ͑1989͒; H. H. Rotermund et al., Nature ͑London͒ 343, 355 ͑1990͒; J. Lauterbach and H. H. Rotermund, Surf. Sci. 311, 231 ͑1994͔͒. In the two-dimensional version of our model, the traveling waves take the form of target patterns emitted from surface inhomogeneities.

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Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

Ertl

2008

Handbook of Heterogeneous Catalysis

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The rate of a catalytic reaction is governed by the underlying mechanism, i.e. the sequence of elementary reaction steps, and depends on the external control parameters such as the concentrations (= partial pressures) p j of educt and product species and temperature T, if transport processes are excluded in this context. More specifically, usually the adsorbed species are assumed to be randomly distributed over the surface, and their concentrations (= coverages) θ i are described within a mean-field approximation so that the reaction rate (= number of molecules r formed per unit time, dn r /dt t ) is given by dn r dt = f θ i , T ( ) (1) whereby the coverages θ i are in turn determined by a set of differential equations (modeling the individual steps of adsorption, desorption and surface reaction) of the typeProper treatment then requires that additional constraints given by heat and mass balance are taken into consideration.Under flow conditions with the external control parameters being kept fixed, usually the reaction proceeds at steady state with constant rate, i.e., dn r /dt = constant and dθ i /dt = 0. Due to the nonlinear character of the quoted differential equations, this has, however, not necessarily to be the case; the kinetics may -for certain ranges of parameters -become oscillatory or even irregular (chaotic). Such systems are typically far away from equilibrium, and (i) By far the most detailed insights into the underlying mechanisms and the general phenomenology of spatio-temporal self-organization were obtained in studies with well-defined single crystal surfaces by applying the arsenal of modern surface physical methods.(ii) Single crystal studies are usually conducted with bulk samples under low pressure conditions (≤ 10 -4 mbar)where the temperature changes associated with varying reaction rate are negligible. In addition, the mean-free path of gaseous molecules is comparable or even larger than the dimensions of the reaction vessel, which is operated as a continuous flow reactor. Hence, concentration gradients in the gas phase are practically instantaneously (≤ 10 -3 s)transmitted. Analysis of such experiments is thus appreciably simplified.(iii) Experiments with polycrystalline, i.e. "real", catalysts are usually conducted at elevated partial pressures (≥ 1 mbar) under which the heat released by the reaction may lead to noticeable temperature variations. The resulting thermokinetic effects may become dominating, so that even the nonuniformity of the surface chemistry is masked and quite novel phenomena may arise. Ideally, the reaction is conducted in a way, which may be described by a continuously stirred tank reactor (CSTR), i.e., perfect mixing ensures that the concentrations are everywhere identical.However, frequently a concentration profile exists along the reactor, which is hence rather of the plug-flow type. It is thus evident that heat and mass transfer limitations may play important roles with such systems.Generally, an extended system such as a single crystal surface, or even more ...

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Imaging of spatial pattern formation in an oscillatory surface reaction by scanning photoemission microscopy

Cited by 96 publications

References 28 publications

Pattern Formation during the Oxidation of CO onPt{100}: A Mesoscopic Model

Pattern Formation during the Oxidation of CO onPt{100}: A Mesoscopic Model

Theoretical study of pattern formation during the catalytic oxidation of CO on Pt{100} at low pressures

Non‐Linear Dynamics: Oscillatory Kinetics and Spatio‐Temporal Pattern Formation

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