Heterogeneous catalysis oscillations

Growth of oscillations for heterogeneous catalysis model with poisoning A = amplitude, Tp = period... 

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

Since the development of nonequilibrium thermodynamics in the late 1940s, initiated by the work of Prigogine (7), numerous reports have appeared dealing with the possibility of oscillations in reaction systems far from equilibrium. Initially the main focus of these studies was the Belouzov-Zhabotinskii liquid-phase reaction (2), but since the discovery of oscillating reactions in heterogeneous catalysis in the late 1960s (3-7), over 300 publications have described research in this field as well. This review focuses on this emerging and important area of research. 

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. 

It is therefore appropriate to give an updated and extensive review on oscillations in heterogeneous catalysis. This work will focus mainly on the mechanisms that explain oscillations, considering both experimental support for these mechanisms as well as the mathematical models that describe them. The last section will consider work on spatial patterns and synchronization. 

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. 

Chaotic behavior and synchronization in heterogeneous catalysis are closely related. Partial synchronization can lead to a complex time series, generated by superposition of several periodic oscillators, and can in some cases result in deterministically chaotic behavior. In addition to the fact that macroscopically observable oscillations exist (which demonstrates that synchronization occurs in these systems), a number of experiments show the influence of a synchronizing force on all the hierarchical levels mentioned earlier. Sheintuch (294) analyzed on a general level the problem of communication between two cells. He concluded that if the gas-phase concentration is the autocatalytic variable, then synchronization is attained in all cases. However, if the gas-phase concentration were the nonautocatalytic variable, then this would lead to symmetry breaking and the formation of spatial structures. When surface variables are the model variables, the existence of synchrony is dependent upon the size scale. Only two-variable models were analyzed, and no such strict analysis has been provided for models with two or more surface concentrations, mass balances, or heat balances. There are, however, several studies that focused on a certain system and a certain synchronization mechanism. 

Oscillations are possible on all levels in a catalytic reactor, from the single-crystal plane to the crystallite to the catalyst pellet to the packed-bed reactor, and each level adds another degree of complexity. Thus it is necessary to isolate the major influences at each level and to separate the characteristics of the oscillations on one level from the effects caused by coupling with other levels. Only when each level is well understood is it possible to fully understand the overall oscillatory behavior. Oscillations in heterogeneous catalysis will therefore remain an intriguing and demanding problem for many years to come. 

To study a class of mechanisms for isothermal heterogeneous catalysis in a CSTR, Morton and Goodman (1981-1) analyzed the stability and bifurcation of simple models. The limit cycle solutions of the governing mass balance equations were shown to exist. An elementary step model with the stoichiometry of CO oxidation was shown to exhibit oscillations at suitable parameter values. By computer simulation limit cycles were obtained. 

IIIE) Morton, W., Goodman, M. G. Transients and Oscillations in Heterogeneous Catalysis, 1981-2 In Modelling of Chemical Reaction Systems, K. H. Ebert, P. Deuflhard, and W. Jager (Eds.). Springer Ser. Chem. Phys. 18, 253-260... 

HIE) Wicke, E., Kummann, P., Keil, W., Schiefler, J. Unstable and Oscillatory Behavior in 1980 Heterogeneous Catalysis. Ber. Bunsenges. Phys. Chem. 84(4) 315-323 (IIID) Wirges, H. P. Experimental Study of Self-sustained Oscillations in a Stirred Tank Reactor. 1980 Chem. Eng. Sci. 35(10) 2141-2146... 

This section will illustrate how one can use the implicit method to simulate several interesting kinetic schemes, such as an autocatalytic reaction, and heterogeneous catalysis. Then we will see the ramifications of an often used (and sometimes misused) simplification, the steady-state assumption. Finally, we will simulate a prototypical oscillating reaction. 

In category 1, the order of the autocatalytic species in the cycle reaction is equal to one (and equal to the order of X in the exit reaction). Category 2 oscillators include mechanisms with autocatalytic reaction of a higher (effective) order in X than the order of X in the removal reaction, and the type X species need not necessarily be chemical species. Rather, they may include vacant surface sites in heterogeneous catalysis, or temperature in thermokinetic oscillation. 

A rate-law of the form ) may arise in enzyme reactions, or in heterogeneous catalysis obeying a Langmuir-Hinshelwood law. The oxidation of carbon monoxide at low pressures displays sustained oscillations under isothermal conditions in an open system [15], and results indicate that an important role is played by the state of the reactor surface. This, and other features of the observed behaviour, are readily correlated qualitatively with this simple, two-step model. 

Self-oscillations of the surface concentrations are a rather widespread phenomenon in a heterogeneous catalysis. Following mechanism has been proposed for an oxidation reaction of hydrogen on the platinum catalyst ... 

An exhaustive review is not possible here and information will have to be given in a rather superficial manner. The intent is to give an overview of the field, pointing out current directions and concepts concerning oscillations and spatial effects in heterogeneous catalysis. Extensive reviews are available elsewhere [1 - 6]. 

As we have seen, the need for chemical simulations at a variety of levels is quite clearly demonstrated in the broad class of systems in which molecular and supermolecular interactions lead to macroscopic cooperativity, self-organization, and evolution. Although this class extends far beyond the domain of "classical" chemistry as well, it nevertheless covers the chemical spectrum, from combustion and explosions in gaseous mixtures to biochemical regulation of metabolism and biosynthesis, and from adsorption/ chemisorption and heterogeneous catalysis to chemical oscillations, spatial structures, and travelling chemical waves in condensed phase chemistry and biology. 

This ratio is vahd when the system operates close to thermodynamic equihbrium. It is, however, typical for heterogeneous catalysis to occur far from equihbrium in an open, nonlinear, dissipative, distributed, and multiparametric medium. Thus heterogeneous catalytic reactions exhibit diverse nonlinear phenomena the multiplicity of steady states (stable and unstable) hysteresis phenomena the ignition and extinction of the process critical phenomena phase transitions a high sensitivity of the process to changes in the parameters oscillations and wave phenomena chaotic regimes the formation of dissipative structures and seh organization phenomena. 

Self-sustained oscillations in heterogeneous catalysis were discovered in the early 1970s by groups led by P. Hugo, E. Wicke, and M.G. Slinko. 

Werner, H., Herein, D., Schulz, G. et al. (1997) Catalysis Letters, 49, 109-119. Slin ko, M.M. and Jaeger, N.I. (1994) Physicochemical Basis for the Appearance of Self-Sustained Oscillations in Heterogeneous Catalytic Systems, Elsevier. 

M. M.Slin ko and N. I. Eaeger, Oscillating Heterogeneous Catalytic Systems. Studies in Surface Science and Catalysis, v.86, Elsevier, 1994. 

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