Global coupling in the presence of defects: Synchronization in an oscillatory surface reaction

Veser, Götz; Mertens, F.; Mikhailov, Alexander S.; Imbihl, R.

doi:10.1103/physrevlett.71.935

Cited by 88 publications

(79 citation statements)

References 12 publications

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“…Subsequently, this reaction became subject of extended investigations with Pt(100) in the 10 -7 to 10 -5 mbar pressure regime [142][143][144][145][146][147][148]. No oscillations were observed on Pt (111) and Pt (110), which planes were found to be much less reactive in dissociating NO, in accordance with findings made with the cylindrical Pt single crystal sample [146].…”

Section: Other Isothermal Systems With Oscillatory Kineticssupporting

confidence: 73%

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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Section: Other Isothermal Systems With Oscillatory Kineticssupporting

confidence: 73%

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

Ertl

2008

Handbook of Heterogeneous Catalysis

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“…In heterogeneous catalysis mixing in the gas phase produces a global coupling because a consumption of reactants at one location causes changes in conditions at all locations of the system. [24][25][26][27] Global coupling through an external control or an integral constraint has also been a͒ Electronic mail: eiswirth@fhi-berlin.mpg.de investigated in heterogeneous catalytic systems. [28][29][30] Pattern formation in semiconductors is to a large extent due to local diffusion and global constraints due to the current circuit.…”

Section: Introductionmentioning

confidence: 99%

Negative coupling during oscillatory pattern formation on a ring electrode

Christoph

Otterstedt

Eiswirth

et al. 1999

The Journal of Chemical Physics

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“…In surface chemical reactions [3], reaction elements are however additionally interacting through the gas phase where instantaneous complete mixing occurs. As a result, global coupling between chemical oscillators arises [4]. Moreover, global delayed feedbacks through the gas phase could be artificially introduced to control turbulence in surface reactions [17,18,19,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

Birhythmicity, synchronization, and turbulence in an oscillatory system with nonlocal inertial coupling

Casagrande

Mikhailov

2005

Physica D: Nonlinear Phenomena

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We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial coupling, the system exhibits birhythmicity with two oscillation modes at largely different frequencies. Stability of uniform oscillations in the birhythmic region is analyzed by means of the phase dynamics approximation. Numerical simulations show that, depending on its parameters, the system has irregular intermittent regimes with local bursts of synchronization or desynchronization.

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Global coupling in the presence of defects: Synchronization in an oscillatory surface reaction

Cited by 88 publications

References 12 publications

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

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

Negative coupling during oscillatory pattern formation on a ring electrode

Birhythmicity, synchronization, and turbulence in an oscillatory system with nonlocal inertial coupling

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