Oxidation/reduction models, oscillatory reactions

In a review article on oscillatory reactions (294), Sheintuch discusses the effect of introducing a heat balance for the catalyst rather than a mass balance for the reactor into the differential equation system for a surface reaction with oxidation/reduction cycles. Although the coverage equations alone can yield oscillatory behavior, as was the case for the models discussed in the previous section, Sheintuch s model is discussed in this section because introduction of the heat balance adds qualitatively new features. In this extended system complex, multiple peak behavior and quasiperiodicity was observed as shown in Fig. 8. Sheintuch also investigated the interaction of two oscillators. This work, however, will be treated in detail in Section V, were synchronization and chaos are discussed. 

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. 

Sales et al. (1982) presented a simple physical model to explain oscillatory oxidation of carbon monoxide over Pt, Pd, and Ir catalysts. The model is based on a kinetic model incorporating a Langmuir-Hinshelwood reaction mechanism and the alternate oxidation and reduction of the catalyst. Simulation results of these three coupled differential equations (of oxidation of CO) model are shown to fit experimental observations. 

In 1972, Field, Koros, and Noyes (FKN group investigated the kinetic details which characterized the entire aspects of BZ reaction, illuminating the essential constiments of reaction and their roles in oscillations [31, 53]. The kinetic model composed three consecutive reaction processes as, (A), (B), and (C). The process A is a fast reaction step, the process (B) is an autocatalytic set of reaction, and C is the process where (Br ) ions are consumed. The oxidation of metal catalyst ions has also been taken place in the processes (A) and (B), respectively. A recovery step (process C) involves for the reduction of metal catalysts and regenerates the necessary reactant (Br ) ions for re-initiating the oscillatory-phase reaction from beginning. A schematic model for description of the chemistry of BZ reaction is shown in Fig. 1.3. 

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