Fluctuations in catalytic surface reactions

The internal reaction-induced fluctuations which occur in catalytic CO oxidation on a Pt field emitter tip have been studied using field electron microscopy (FEM) as a spatially resolving method. The structurally heterogeneous Pt tip consists of facets of different orientations with nanoscale dimensions. The FEM resolution of roughly 2 nm corresponds to a few hundred reacting adsorbed particles whose variations in the density are imaged as brightness fluctuations. In the bistable range of the reaction one finds fluctuation-induced transitions between the two stable branches of the reaction kinetics. The fluctuations exhibit a behaviour similar to that of an equilibrium phase transition, i.e. the amplitude diverges upon approaching the bifurcation point terminating the bistable range of the reaction. Simulations with a hybrid Monte Carlo/mean-field model reproduce the experimental observations. Fluctuations on different facets are typically uncorrelated but within a single facet a high degree of spatial coherence is found

Synchronization and spatiotemporal self‐organization in the NO+CO reaction on Pt(100). II. Synchronized oscillations on the hex‐substrate

The NO+CO reaction exhibits sustained rate oscillations on Pt(100) under conditions where the surface is mostly hex‐reconstructed. These rate oscillations have been investigated in the 10−6 mbar range using photoemission electron microscopy as a spatially resolving method. During the rate oscillations which appear in a temperature‐window ranging from 490 to 478 K, the surface reacts in a spatially homogeneous way. At the upper T‐boundary of the oscillatory range, the oscillations develop via a Feigenbaum scenario leading from chaotic small amplitude oscillations at high T to regular period‐1 oscillations at lower T. At the lower T‐boundary of the oscillatory range, at T=478 K, target patterns appear, causing the collapse of the amplitude of the rate oscillations. As the temperature is lowered further, the parallel wave trains become increasingly irregular. Spiral waves form, and finally one observes only local reaction outbursts. A model for the synchronization mechanism in the rate oscillations is proposed based on the 1×1⇔hex‐phase transition, while the origin of the chaotic oscillations in this reaction system is discussed in terms of a transition from unsynchronized to synchronized oscillations

Imbihl and Mikhailov Reply

A reply to the comment by A. A. Zvyagin and P. Schlottmann

Synchronization in oscillatory surface reactions on single crystal surfaces

In oscillatory surface reactions on single crystal surfaces the partial pressure variations that accompany the oscillations in the reaction rate represent a global interaction between the local oscillators. The NO+CO reaction on Pt(100) exhibits both synchronized and unsynchronized oscillatory behavior depending on the substrate phase. Unsynchronized oscillations occur on the 1×1 phase but on the hex phase one finds synchronized oscillatory behavior. The mechanism leading to synchronization in the oscillations on Pt(100)‐hex can be traced back to a critical dependence of the 1×1⇄hex phase transition on the partial pressures of NO and CO. At both ends of the temperature window for rate oscillations one finds well‐defined transitions to a stationary reaction rate. These bifurcations are discussed in terms of a transition from synchronized to unsynchronized behavior. In particular, the occurrence of deterministic chaos in connection with a Feigenbaum scenario is interpreted as being due to such a transition

Pulse propagation and oscillatory behavior in the NO+H₂ reaction on a Rh(110) surface

Target patterns, rotating spiral waves and solitary pulses have been found in the NO+H2 reaction under nonoscillatory conditions, i.e., when the system was an excitable medium. Using photoelectron emission microscopy (PEEM) as spatially resolving method the parameter dependence of the front velocities, the width of the pulses and the rotational period of the spiral waves were studied for fixed pNO=1.8×10−6 mbar in a T‐ range 520–620 K. The front velocities were strongly anisotropic with the degree of anisotropy depending on the pH2, T parameters. Under reaction conditions close to the high pH2 boundary for pattern formation, gas‐phase coupling becomes efficient, thus, oscillations in the N2 production rate can be observed

Synchronization and spatiotemporal self‐organization in the NO+CO reaction on Pt(100). I. Unsynchronized oscillations on the 1×1 substrate

The oscillatory NO+CO reaction on Pt(100) has been investigated in the 10−6 mbar range using photoemission electron microscopy (PEEM) as a spatially resolving method. The existence ranges for kinetic oscillations have been mapped out in (pCO,T)‐parameter space with fixed pNO=4×10−6 mbar. Kinetic oscillations occur within a partial pressure range of 0.8NO/p CO <1.9. In the lower lying of two temperature windows for oscillatory reaction behavior, the oscillations proceed unsynchronized on a 1×1 substrate without exhibiting macroscopic rate variations. Instead, one observes spatiotemporal pattern formation which has been studied in detail. These patterns are dominated by periodic wave trains, which become unstable at lower temperatures, giving rise to spiral waves and irregularly shaped reaction fronts. With decreasing temperature, the front velocity increases, while simultaneously the spatial periodicity of the wave trains becomes larger. In agreement with theoretical predictions by a three‐variable model, the local oscillations terminate at the upper T boundary via a Hopf bifurcation and at the lower T boundary via a bifurcation of the saddle‐loop type

Tuning excitability by alloying: the Rh(111)/Ni/H2 + O2 system

The dynamic behavior of the O2 + H2 reaction on a Rh(111) surface alloyed with Ni has been studied in the 10(-5) mbar range using photoemission electron microscopy (PEEM) as a spatial resolving method. For T = 773 K and p(O2) = 5 x 10(-5) mbar the bifurcation diagram has been mapped out as a function of the Ni coverage in a range of 0 ML /= 1.3 ML. A critical Ni coverage of Theta(Ni,crit) = 0.13 monolayers (ML) is required for excitability. In the excitable parameter range pulse trains and irregular chemical wave patterns are found. Whereas the propagation speed of the pulses exhibits no clear-cut dependence on the Ni coverage, the frequency of the local PEEM intensity oscillations increases linearly with Ni coverage in the range from Theta(Ni) = 0.13 ML to Theta(Ni) = 1.3 ML.DF

Surface Structure and Catalytic COCO Oxidation Oscillations

A cellular automaton model is used to describe the dynamics of the catalytic oxidation of $CO$ on a $Pt(100)$ surface. The cellular automaton rules account for the structural phase transformations of the $Pt$ substrate, the reaction kinetics of the adsorbed phase and diffusion of adsorbed species. The model is used to explore the spatial structure that underlies the global oscillations observed in some parameter regimes. The spatiotemporal dynamics varies significantly within the oscillatory regime and depends on the harmonic or relaxational character of the global oscillations. Diffusion of adsorbed $CO$ plays an important role in the synchronization of the patterns on the substrate and this effect is also studied.Comment: Latex file with six postscript figures. To appear in Physica

Turbulence and standing waves in oscillatory chemical reactions with global coupling

Using the model of the complex Ginzburg–Landau equation with global coupling, the influence of long‐range interactions on the turbulent state of oscillatory reaction–diffusion systems is investigated. Experimental realizations of such a system are, e.g., oscillatory reactions on single crystal surfaces where some of the phenomena we simulate have been observed experimentally. We find that strong global coupling suppresses turbulence by transforming it into a pattern of standing waves or into uniform oscillations. Weaker global coupling gives rise to an intermittent turbulent state which retains partial synchrony

The role of adsorbate–adsorbate interactions in the rate oscillations in catalytic CO oxidation on Pd (110)

The CO+O2 reaction on Pd(110) exhibits kinetic oscillations above pO2 ≊ 10−3 Torr and bistability below this pressure. Based on the reversible formation of subsurface oxygen and the Langmuir Hinshelwood mechanism of catalytic CO oxidation, a mathematical model had been developed which described the occurrence of rate oscillations and most of the qualitative features of the oscillations. This model, however, failed to reproduce the change from bistability to oscillatory behaviour with increasing pO2. In this paper we demonstrate that by introducing repulsive interactions between COad and Oad, the subsurface oxygen model correctly reproduces the experimentally determined stability diagram in pO2,pCO parameter space. The effect of the repulsive interactions is to reduce the activation barrier for penetration of chemisorbed oxygen into the subsurface region, thus facilitating the formation of subsurface oxygen at high coverages. For the improved subsurface oxygen model a bifurcation analysis has been conducted in pO2,pCO parameter space. The influence of the constants in the model has been analyzed likewise with bifurcation theory