Mechanism self-oscillation

All the above mechanisms can be called the simplest catalytic oscillators. In all these mechanisms self-oscillations of the reaction rate are realized due to the combination of the fast system of steps (adsorption mechanism) leading to the sharp change in the number of unoccupied surface sites and of the "slow reversible step ensuring self-oscillations of their concentration. If the parameters of the "buffer step are sufficiently small compared with those of the main mechanism, all these oscillations will be typically relaxa-tional. 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

A comparative study was done by Kevrekidis and published as I. G. Kevrekidis, L. D. Schmidt, and R. Aris. Some common features of periodically forced reacting systems. Chem. Eng. Sci. 41,1263-1276 (1986). See also two papers by the same authors Resonance in periodically forced processes Chem. Eng. Sci. 41, 905-911 (1986) The stirred tank forced. Chem. Eng. Sci. 41,1549-1560 (1986). A full study of the Schmidt-Takoudis vacant site mechanism is to be found in M. A. McKamin, L. D. Schmidt, and R. Aris. Autonomous bifurcations of a simple bimolecular surface-reaction model. Proc. R. Soc. Lond. A 415,363-387 (1988) Forced oscillations of a self-oscillating bimolecular surface reaction model. Proc. R. Soc. Lond. A 415,363-388 (1988). 

The kinetic model accounting for the adsorption mechanism (119) cannot have rate self-oscillations since, in this case, Bendikson criterion is met... 

If one wants to describe the observed experimental rate self-oscillations, mechanism (119) must be completed by a step with at least one more intermediate or the rate constants for the steps must be assumed to be dependent on the concentrations [22, 23]. 

As far as the models accounting for these conceptions are concerned, their construction and investigation have just started. The development of these models is sure to be retarded by the absence of data on the detailed reaction mechanism and its parameters. The exception is ref. 147, where the authors construct an unsteady-state homogeneous-heterogeneous reaction model and analyze it with respect to the cyclohexane oxidation on zeolites. The study was aimed at the experimental interpretation of the self-oscillations found. The model constructed is in accordance with the law of mass action. 

We apply these conditions to distinguish simple catalytic mechanisms ensuring self-oscillations of reaction rates (see Chap. 5). 

Investigations with the graphs of non-linear mechanisms had been stimulated by an actual problem of chemical kinetics to examine a complex dynamic behaviour. This problem was formulated as follows for what mechanisms or, for a given mechanism, in what region of the parameters can a multiplicity of steady-states and self-oscillations of the reaction rates be observed Neither of the above formalisms (of both enzyme kinetics and the steady-state reaction theory) could answer this question. Hence it was necessary to construct a mainly new formalism using bipartite graphs. It was this formalism that was elaborated in the 1970s. 

The properties of the rate oscillations in the oxidation of CO over Pt, Pd, and Ir were examined comprehensively in experiments by Turner et al. [85] who suggested that the reaction follows an adsorption mechanism. Studies of the reaction model written in accordance with the law of acting surfaces show the existence of regions of multiplicity for the curves WCq2 (T) at a fixed ratio of reactant partial pressures Pco/Po, and WCq2(PC0IP02) at a fixed temperature T, which was already known [166, 174-176], Experimental data indicate that self-oscillations take place between two stable branches of the kinetic curves in the region of hysteresis [85],... 

The studies of Ertl and co-workers showed that the reason for self-oscillations [142, 145, 185-187] and hysteresis effects [143] in CO oxidation over Pt(100) in high vacuum ( 10 4 Torr) is the existence of spatio-temporal waves of the reversible surface phase transition hex - (1 x 1). The mathematical model [188] suggests that in each of the phases an adsorption mechanism with various parameters of CO and 02 adsorption/desorption and their interaction is realized, and the phase transition is modelled by a semi-empirical method via the introduction of discontinuous non-linearity. Later, an imitation model based on the stochastic automat was used [189] to study the qualitative characteristics for the dynamic behaviour of the surface. 

The calculations show that, at values of the parameters fitting the above conditions, the system will have self-oscillations. If in the mechanism examined, step (4) is substituted by AZ DZ, then coefficients a2 and a3 take the form... 

At the present time, the mechanisms in which the L-H mechanism is completed by the E-R mechanism are widespread. This two-route mechanism was first suggested by Heyne and Tompkins [113]. The same mechanism was offered by Stephens [118], Hori and Schmidt [119], and McCarthy et al. [123]. McCarthy et al. applied the two-route mechanism to interpret the extreme character of the kinetic dependences and the rate self-oscillations. Miniscloux et al. used the kinetic model corresponding to the two-route mechanism to calculate the catalytic reoxidation of CO in exhaust gases. 

On the other hand, it is clear that the "ideal models cannot describe the behaviour of complex catalytic reactions in complete detail. In particular, we cannot quantitatively explain the values of the self-oscillation periods obtained by Orlik et al. Secondly, for example, we have failed to describe the critical effects obtained by Barelko et al. in terms of model (2)—(3) corresponding to the two-route mechanism with the parameters taken from ref. 49 or ref. 142. Our calculated reaction rates proved to be at least two orders of magnitude higher than the experimental values. Apparently our models must be considerably modified, primarily in the region of normal pressures. It is necessary to take into account the formation of unreactive oxygen forms that considerably decrease the rate of C02 generation, the dependence of the reaction parameters on the surface composition and catalyst volume and finally the diffusion of oxygen into the catalyst. 

To interpret new experimental chemical kinetic data characterized by complex dynamic behaviour (hysteresis, self-oscillations) proved to be vitally important for the adoption of new general scientific ideas. The methods of the qualitative theory of differential equations and of graph theory permitted us to perform the analysis for the effect of mechanism structures on the kinetic peculiarities of catalytic reactions [6,10,11]. This tendency will be deepened. To our mind, fast progress is to be expected in studying distributed systems. Despite the complexity of the processes observed (wave and autowave), their interpretation is ensured by a new apparatus that is both effective and simple. 

Kinetic study of the self-oscillating reaction observed in a potassium iodate-hydrogen peroxide-cysteine-sulfuric acid (acid medium) system was carried out [57], It is found that according to an adequate model the feedback mechanism is associated with autocatalytic reaction... 

Based on the analysis of the obtained experimental regularities of the electrochemical process, it may be fundamentally concluded that the process at electrode displays a selfoscillation mechanism. Obviously, self-oscillations happen due to internal diffusion of the surface components of the mimetic electrode, which is not affected by solution mixing intensity. Mixing causes a strong influence on the external diffusion and OH- anion drainage from the interface layer. 

First I reproduced Belousov s results. Then I modified the system and made it much more convenient to study. I showed that it was self oscillating and determined several key steps in the reaction mechanism. After that, I wrote my first paper. However, I did not have a complete understanding of the chemical mechanism of the oscillations. Then I found the last key part of the mechanism, namely, what species was the inhibitor. It gave me a qualitative understanding of the entire chemistry involved in the mechanism (Box 2), and I was able to find a large set of similar oscillating... 

The analysis of critical phenomena, such as hysteresis and self-oscillations, gives valuable information about the intrinsic mechanism of catalytic reactions [1,2], Recently we have observed a synergistic behavior and kinetic oscillations during methane oxidation in a binary catalytic bed containing oxide and metal components [3]. Whereas the oxide component (10% Nd/MgO) itself is very efficient as a catalyst for oxidative coupling of methane (OCM) to higher hydrocarbons, in the presence of an inactive low-surface area metal filament (Ni-based alloy) a sharp increase in the rate of reaction accompanied by a selectivity shift towards CO and H2 takes place and the oscillatory behavior arises. In the present work the following aspects of these phenomena have been studied ... 

Any rhythm can be comprehended as a sequence of two phases that merge and follow each other in an autonomous manner. The first phase, of amplification, corresponds here to the onset of a peak in cAMP synthesis. The second phase, of limitation, corresponds to the decrease in cAMP synthesis, once the maximum is passed. Autonomous oscillations occur because of the regenerative process that leads to the renewal of the self-amplification phase after cAMP has reached its minimum level. To understand the mechanism of oscillations is tantamount to identifying this regenerative process as well as those responsible for self-amplification and for its limitation. 

From a dynamic point of view, we may thus see the cell cycle as driven by two self-sustained, limit cycle oscillators, one involving cdc2, and the other cdk2. The mechanism of oscillations in each case would be similar to the one described above, and would involve a cyclin and its associated cyclin-dependent kinase (cdk) and cyclin protease, as well as... 

Dynnik, V.V., E.E. Sel kov I. A. Ovtchinnikov. 1977. Self-oscillations in the lower part of the glycolytic system. Two alternative mechanisms. Studia Biophys. 63 9-23. 

The current knowledge of the CO + O2 reaction mechanism makes possible to state rather justified theoretical models giving insight to the features of spatio-temporal dynamics of reaction on the platinum surface. Carbon monoxide oxidation over Pt(lOO) single crystal has been studied comprehensively. It was shown that under certain conditions (partial pressures of reactants and temperature), the adsorbate coverages and the reaction rate undergo self-oscillations attended by the spatio-temporal pattern of COads and Oads formation on the surface [1,2,94]. The observed phenomena are associated with the reversible adsorbate-induced surface phase transition hex 1 X 1. The platinum state in unreconstructed 1x1 phase is catalytically active due to the ease of oxygen molecules dissociation S (02) 0.3—0.4 S (02) 10. The CO... 

The sensitivity of the furan ring to acid-catalyzed hydrolysis must finally be mentioned as one of its typical chemical features. Its intervention in the context of this monograph must be seen as an undesired event to be avoided, or at least minimized, since its mechanism leads to the destruction of the heterocycle with the formation of aliphatic carbonyl compounds, as illustrated in the simplified Scheme 6.9. It is therefore clear that any polymerization system requiring the preservation of the furan or cognate structures in the final product would be marred by side reactions caused by the presence of moisture in an acidic medium. Curiously, the acid-catalyzed hydrolysis of 2,5-dimethyfuran in a water-ethanol medium shows self-oscillating features [8]. 

To construct an autonomous mechanical pumping system such as intestines, we fabricated a self-oscillating gel in a tubular shape by photopolymerization (Fig. 5.1.4) [50]. Several types of tubular self-oscillating gels that exhibit autonomous peristaltic motion were... 

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