Chemical reaction Belousov-Zhabotinskii

B-Z reaction (Belousov-Zhabotinskii reaction) A chemical reaction that shows a periodic colour change between magenta and blue with a period of about one minute, it occurs with a mixture of sulphuric acid, potassium bromatefV), cerium sulphate, and... 

The existence of chaotic oscillations has been documented in a variety of chemical systems. Some of tire earliest observations of chemical chaos have been on biochemical systems like tire peroxidase-oxidase reaction [12] and on tire well known Belousov-Zhabotinskii (BZ) [13] reaction. The BZ reaction is tire Ce-ion-catalyzed oxidation of citric or malonic acid by bromate ion. Early investigations of the BZ reaction used tire teclmiques of dynamical systems tlieory outlined above to document tire existence of chaos in tliis reaction. Apparent chaos in tire BZ reaction was found by Hudson et a] [14] aiid tire data were analysed by Tomita and Tsuda [15] using a return-map metliod. Chaos was confinned in tire BZ reaction carried out in a CSTR by Roux et a] [16, E7] and by Hudson and... 

The Belousov-Zhabotinskii reaction is a typical oscillating chemical reaction. Spiral structures form periodically, disappear and reappear as the result of an autocatalytic reaction, the oxidation of Ce3+ and Mn2+ by bromate (lessen, 1978). 

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. 

Fig. 1.19. Complex, but strictly periodic, oscillations in a chemical reaction showing bursting in a model of the Belousov-Zhabotinskii reaction. (Reprinted with permission from Bar-Eli, K and Noyes, R. M. (1988). J. Chem. Phys., 88, 3636-54. American Institute of Physics.)...

Tyson, J. J. (1976). The Belousov-Zhabotinskii reaction. Springer, Berlin. Field, R. J. and Burger, M. (eds) (1985). Oscillations and travelling waves in chemical systems. Wiley-Interscience, New York. 

Another form of behaviour exhibited by a number of chemical reactions, including the Belousov-Zhabotinskii system, is that of excitability. This concerns a mixture which is prepared under conditions outside the oscillatory range. The system sits at the stationary state, which is stable. Infinitesimal perturbations decay back to the stationary state, perhaps in- a damped oscillatory manner. The effect of finite, but possibly still quite small, perturbations can, however, be markedly different. The system ultimately returns to the same state, but only after a large excursion, resembling a single oscillatory pulse. Excitable B-Z systems are well known for this propensity for supporting spiral waves (see chapter 1). 

Waves of chemical reaction may travel through a reaction medium, but the ideas of important stationary spatial patterns are due to Turing (1952). They were at first invoked to explain the slowly developing stripes that can be exhibited by reactions like the Belousov-Zhabotinskii reaction. This (rather mathematical) chapter sets out an analysis of the physically simplest circumstances but for a system (P - A - B + heat) with thermal feedback in which the internal transport of heat and matter are wholly controlled by molecular collision processes of thermal conductivity and diffusion. After a careful study the reader should be able to ... 

As we have already commented, mappings of the type discussed above are not in any way easily related to a given set of reaction rate equations. Such mappings have, however, been used for chemical systems in a slightly different way. A quadratic map has been used to help interpret the oscillatory behaviour observed in the Belousov-Zhabotinskii reaction in a CSTR. There, the variable x is not a concentration but the amplitude of a given oscillation. Thus the map correlates the amplitude of one peak in terms of the amplitude of the previous excursion. 

In an open system such as a CSTR chemical reactions can undergo self-sustained oscillations even though all external conditions such as feed rate and concentrations are held constant. The Belousov-Zhabotinskii reaction can undergo such oscillations under isothermal conditions. As has been demonstrated both by experiments [1] and by calculations 12,3] this reaction can produce a variety of oscillation types from simple relaxation oscillations to complicated multipeaked periodic oscillations. Evidence has also been given that chaotic behavior, as opposed to periodic or quasi-periodic behavior, can take place with this reaction [4-12]. In addition, it has been shown in recent theoretical studies that chaos can occur in open chemical reactors [11,13-17]. 

Tyson, J. J. (1985) A quantitative account of oscillations, bistability, and travelling waves in the Belousov-Zhabotinskii reaction. In R. J. Field and M. Burger, eds. Oscillations and Traveling Waves in Chemical Systems (Wiley, New York). 

Another point of interest to the reader is that except the review articles, only those contributions where the original chemical observations and advances are presented will be reviewed. The remaining articles are considered as relevant to areas outside the scope of the present review. This explanation is necessary because under the name of, e.g. Belousov-Zhabotinskii, the literature is inundated beyond reach, obviously contributing to other areas of this reaction scheme not necessarily focusing on its oscillatory solutions. Furthermore, the terminology used in the referenced sources is preserved wherever possible. 

Cerium (III, IV) Ions and Ferroin in the Oscillating Belousov-Zhabotinskii Chemical Reaction Teor. Eksp. Khim. 17 (4) 493-499, (Rus.). [Theor. Exper. Chem. 17 (4) 382-387 (Engl, trans.)]... 

Two Catalysts in the Belousov-Zhabotinskii Oscillatory Chemical Reaction Dokl. Akad. 

The references pertaining to chemical reactions will be given in Chapters 5 and 6. An exception, apart from a paper by Swinney, is the cited article by Winfree, describing the history of the Belousov-Zhabotinskii oscillatory reaction. The remaining references deal with philosophical problems. 

In Chapter 2 we have shown that the equation of type (3.80) may appear in models describing the dynamics of a chemical reaction (see also remarks in Section 3.7). The model (3.80) will be employed in Chapter 6 for the description of changes in the dynamics of the Belousov-Zhabotinskii reaction. 

We will also investigate models corresponding to specific chemical systems. Most of the attention will be devoted to the largely examined Belousov-Zhabotinskii reaction (see Chapter 1 and Section 6.2). 

The Belousov-Zhabotinskii (BZ) reaction has been selected as an example illustrating diverse dynamical states observable in chemical systems. The BZ reagent is very convenient both for experimental and theoretical investigations, since the BZ reaction has many dynamical states of interest, which will be described below. In the BZ reaction one may observe the steady state, the time periodic state (concentration oscillations), the spatially periodic state, the stationary state (dissipative structures), the time and spatially periodic state (propagating chemical waves) and turbulent states (chaotic oscillations, stochastic spatial structures, stochastic chemical waves). 

Fig. 92. Concentration oscillations in the Belousov-Zhabotinskii reaction. Reprinted with permission from R.J. Field, E. Kotos and R.M. Noyes, Journal of American Chemical Society, 94 (1972), 8649.

At the end of this chapter we will now briefly discuss a theoretical approach to the description of chaotic processes encountered in chemical kinetics, see Section 1.3 and Sections 6.2.2.4, 6.3.2.4. In Section 6.2.2.4 we described the method of generation and physical meaning of a chaotic state of the Belousov-Zhabotinskii reaction carried out in a flow reactor. 

Fig. 104. Chemical chaos in the Belousov- Zhabotinskii reaction. Reprinted with permission from C. Vidal, page 49, Springer Series in Synergetics, H. Haken (Ed.), Vol. 12. Nonlinear Phenomena in Chemical Dynamics.

The Belousov-Zhabotinskii reaction has been described and analysed in books by Zhabotinskii and Tyson, as well as by Murray. Much information on the models of chemical reactions is provided in books by Prigogine and coworkers and by Chernavskii, Romanovskii and Stepanova. Chemical chaos is described in a paper by Agladze and Krinsky, Simoyi et al. and in collections of papers edited by Kadomcev, Vidal and Pacault, as well as a book by Berge. The collections also contain a number of interesting papers dealing with other non-linear phenomena, such as multistability, dissipative... 

W. Jahnke, W. Skaggs, and A. Winfree. Chemical vortex dynamics in the Belousov-Zhabotinskii reaction and in the two-variable Oregonator model. 

An understanding of chemical oscillations and wave patterns in the Belousov-Zhabotinskii reaction requires some familiarity with the language and methods of chemical kinetics on one hand and some facility with the mathematics of differential equations on the other. Since not every reader can be expected to know both fields to the extent which we will need later,... 

I present in this chapter a short discussion of chemical reaction rate laws and mechanisms, and of nonlinear ordinary and partial differential equations. To strengthen the connection between this review material and the later chapters, I have drawn the examples and problems here from literature relevant to the Belousov-Zhabotinskii reaction. 

In 1958 B.P. Belousov discovered that the oxidation of citric acid by brornate in the presence of cerium ions does not proceed to equilibrium methodically and uniformly, like most chemical reactions, but rather oscillates with clocklike precision between a yellow and colorless state. See Fig. II.1, p. 50 A.M. Zhabotinskii followed up on Belousov s original observation and in 1964 his first investigations appeared in the Russian journal Biofizika. 

The Belousov-Zhabotinskii reaction has also caught the attention of chemical engineers who, in the study of chemical reactor design, have been interested for some time now in chemical instabilities, multiple steady state behaviour and sustained oscillations (Schmitz, 1974). 

Let me encourage those who have not yet experimented with the Belousov-Zhabotinskii reaction to give it. a try. For your convenience I have given recipes for producing homogeneous oscillations (p. 50) propagating waves (pp. 70f ). The chemicals and glassware are readily available in almost any wet-chemistry laboratory. Just ask ... 

Oscillatory reactions are a typical class of phenomena, which display unusual features. After the discovery of Belousov-Zhabotinskii (B-Z) reaction, there has been a tremendous flurry of activity [1] and a large number of such reactions have been discovered during recent years. Biochemical reactions [2-10] such as glycolytic oscillations and peroxidase catalysed oxidation of nicotinamide adenosine deoxyhydrogenase (NADH) have also generated considerable interest. The interest in such reactions is stiU sustained in view of their importance in understanding cardiac and neuronal oscillations. In the case of many oscillatory chemical reactions [1], detailed reaction mechanisms have been postulated and verified with the help of numerical computation. This has also been particularly so for B-Z reaction where Field-Koros-Noyes (FKN) mechanism [11] has been invoked. 

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