Oscillatory heterogeneous

Dynamic Monte Carlo simulations of oscillatory heterogeneous catalytic reactions. 

R. J. Gelten, R. A. van Santen and A. P. J. Jansen, Dynamic Monte Carlo Simulations of Oscillatory Heterogeneous CatcJytic Reactions in Molecular Dynamics From Classical to Quantum Methods, Elsevier Amsterdam (1999). 

Slin ko, M.M., Jaeger, N.I., 1994. Oscillatory Heterogeneous Catalytic Systems. Elsevier, Amsterdam. 

Slinko, M. M. and N. Jaeger (1994). Oscillatory Heterogeneous Catalytic Systems. Amsterdam, Elsevier. 

Imbihl R and ErtI G 1995 Oscillatory kinetics in heterogeneous catalysis Chem. Rev. 95 697-733... 

R. Imbhil, G. Ertl. Oscillatory kinetics in heterogeneous catalysis. Chem Rev 95 697-733, 1995. 

R. D. Vigil, F. T. Willmore. Oscillatory dynamics in a heterogeneous surface reaction Breakdown of the mean-field approximation. Phys Rev E 54 1225-1231, 1996. 

V.F. Buldakov et al, FizAerodispersnykh-Sist, No 5, 77-82 (1971) CA 77, 64195 (1972) The results of an exptl study of the burning of 2-component (finely ground oxidizer with a high-polymer compd or a ballistic proplnt) heterogeneous systems under low pressure are presented. At a constant pressure, oscillatory burning was used... 

A careful analysis of the current portfolio of one major pharmaceutical company indicates that about 60% of the chemistry is suitable for continuous processing. About 50% of this chemistry is homogeneous and therefore readily transferable to existing continuous processing technology. The remaining 50% is heterogeneous and will therefore require implementation of some of the current advances in continuous flow equipment such as oscillatory flow reactors [13]. Technically, the transfer of these processes from batch to continuous could happen within... 

Chang, H. C., 1983, The domain model in heterogeneous catalysis. Chem. Engng ScL 38,535-546. Cohen, D. S. and Neu, J. C., 1979, Interacting oscillatory chemical reactors. In Bifurcation Theory and Applications in Scientific Disciplines. N.Y. Acad. Sci., New York. 

We have shown computer simulations from all these different levels First, we modeled the time course of affective disorders and showed that clinical observation can be mimicked in remarkable details with a combination of oscillatory dynamics and noise. Second, we presented an initial, still very basic, model of circadian cortisol release which nevertheless provided new insights also into eventual disease relevant alterations. Third, we showed single neuron and neuronal network simulations to elucidate the relevant interdependencies between ionic conductances and network interactions with regard to neuronal synchronization at different dynamic, also heterogeneous states. 

If a chemical reaction is operated in a flow reactor under fixed external conditions (temperature, partial pressures, flow rate etc.), usually also a steady-state (i.e., time-independent) rate of reaction will result. Quite frequently, however, a different response may result The rate varies more or less periodically with time. Oscillatory kinetics have been reported for quite different types of reactions, such as with the famous Belousov-Zha-botinsky reaction in homogeneous solutions (/) or with a series of electrochemical reactions (2). In heterogeneous catalysis, phenomena of this type were observed for the first time about 20 years ago by Wicke and coworkers (3, 4) with the oxidation of carbon monoxide at supported platinum catalysts, and have since then been investigated quite extensively with various reactions and catalysts (5-7). Parallel to these experimental studies, a number of mathematical models were also developed these were intended to describe the kinetics of the underlying elementary processes and their solutions revealed indeed quite often oscillatory behavior. In view of the fact that these models usually consist of a set of coupled nonlinear differential equations, this result is, however, by no means surprising, as will become evident later, and in particular it cannot be considered as a proof for the assumed underlying reaction mechanism. 

Oscillatory kinetics in heterogeneous catalysis, first reported about two decades ago, stimulated extensive study of this interesting phenomenon. G. Ertl gives us an indepth review of this subject in the article Oscillatory Catalytic Reactions at Single Crystal Surfaces. ... 

Before we leave this topic, it would be wise to note the results of some recent research on heterogeneously catalysed gas reactions. Here finite rates of adsorption and desorption had to be introduced into the reaction scheme in order to explain the occurrence of multiple steady states and oscillatory phenomena. This observed exotic behaviour could be reproduced by solving a set of coupled equations for the rates of adsorption/desorption, the rate of the surface reaction, and the mass balance relations [22, 23], Adsorption steps (ii) and (iv) may therefore need to be invoked for any heterogeneously catalysed solution reactions that are found to exhibit similar dynamic behaviour. 

Heterogeneous solid propellants possess additional mechanisms with potentials for producing oscillatory burning. For example, certain metalized composite propellants have been observed to burn in the laboratory with identifiable ranges of frequencies of oscillation [118] in this case, the mechanism may involve chemical interactions between the metal and the oxidizer. It was indicated in Section 9.1.5.5 that heterogeneities introduce at least local periodicities and that, in the presence of a mechanism for synchronizing the phases of the oscillations over the surface of the propellant, sustained coherent oscillations of the combustion will occur. A review is... 

The examples above illustrate the benefits gained by unsteady operation. They are, however, only partially related to the phenomena dealt with in this review. The instabilities described above are externally introduced by forcing operation parameters, whereas oscillatory states in heterogeneous catalysis are inherently unstable. Because these autonomous oscillations usually arise as a Hopf bifurcation, wherein the stable state is completely lost. 

The wide range of reaction systems, catalysts, and reactors that exhibit oscillatory reaction rates reinforces the motivation for research in this field. Oscillations may be lurking in every heterogeneous catalytic system (one might speculate that every heterogeneously catalyzed reaction might show oscillations under the appropriate conditions), and it is crucial to know about this possibility when engineering a chemical process. 

The effects discussed here demonstrate that oscillations in heterogeneous catalysis are very complex phenomena. The closer an experimental system is to an industrial catalytic process, the more factors there are that have to be taken into account in order to truly understand the mechanisms leading to oscillatory reaction rates. Table II shows which factors influence the macroscopically observed oscillatory behavior of a catalytic system in different pressure regimes. 

As early research on oscillatory reactions in heterogeneous catalysis began, little attention was given to the state of the catalyst surface. These first studies recorded the reaction rate by analysis of the product concentrations (see, e.g.. Refs. 3,81) or by measurement of catalyst temperatures 3,162). Later, however, attempts were also made to monitor the catalyst surface during the oscillations, first by measurement of the work function 81), and later by methods such as infrared (IR) spectroscopy 108) and low-energy electron diffraction (LEED) for HV oscillations 245). Table III lists methods employed to study oscillations. 

Although many oscillating reactions have been studied experimentally, as many or perhaps even more models describing the oscillatory behavior have been discussed. At present there is no universal mechanism that explains oscillations in all heterogeneously catalyzed reactions. Every reaction has to be thoroughly investigated to discover its specific oscillation mechanism. There are, nevertheless, certain classes of models under which several oscillating systems can be considered. 

Fig. 6. General representations of heterogeneous oscillatory mechanisms, (a) Buffer-step model (b) coverage-dependent activation energy (c) empty-site model (d) Sales-TUrner-Maple model (e) Pt(lOO) phase transition model (f) Dagonnier model (g) blocking/ reactivation model (h) bulk-phase transition model.

A similar model was analyzed by Pikios and Luss (283). They analyzed the same set of reaction steps with the coverage-dependent activation energy interpreted in terms of surface heterogeneity. They derived criteria for the occurrence of oscillations as did Belyaev et al. (154,162). They also found a singular steady state, which became a limit cycle for values of the surface heterogeneity lying above a certain threshold value, and they performed numerical analyses of these oscillatory states. 

Nearly all models discussed so far have one feature in common they are not distributed models and can describe only spatially uniform systems. Many of the mathematical models use ordinary differential equations, and the resultant time series are nearly always simply periodic. This approach, however, describes only part of the experimentally observed behavior there is a great deal of experimental evidence for spatial heterogeneity and chaotic oscillatory behavior in heterogeneously catalyzed systems. 

As more research is done in this field, it becomes clearer that there is probably no single mechanism explaining all oscillatory behavior in heterogeneous catalysis, but rather that every single system has to be studied in detail in order to elucidate a mechanism on the microscopic scale. 

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