Belousov-Zhabotinskii reaction Oscillating reactions

An acidic bromate solution can oxidize various organic compounds and the reaction is catalyzed by species like cerous and manganous ions that can generate 1-equivalent oxidants with quite positive reduction potential. Belousov (1959) first observed oscillations in Celv]/[Cem] during Ce (III) catalysed oxidation of citric acid by bromate ion. Zhabotinskii made extensive studies of both temporal and spatial oscillations and also demonstrated that instead of Ce (III), weak 1- equivalent reductants like Mn(II) and Fe (II) can also be used. The reaction is called Belousov-Zhabotinskii reaction. This reaction, most studied and best understood, can be represented as... 

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... 

In the Belousov-Zhabotinskii reaction, beautiful regular patterns form spontaneously as the result of the oscillating concentrations of reactants and products due to competing reactions. 

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. 

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. 

The Belousov-Zhabotinskii reaction is a cerium-catalyzed oxidation of malonic acid by bromate, in which the quotient [Ce3+]/[Ce4+] oscillates by a factor of 10 to 100.8... 

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]. 

We have investigated the transitions among the types of oscillations which occur with the Belousov-Zhabotinskii reaction in a CSTR. There is a sequence of well-defined, reproducible oscillatory states with variations of the residence time [5]. Similar transitions can also occur with variation of some other parameter such as temperature or feed concentration. Most of the oscillations are periodic but chaotic behavior has been observed in three reproducible bands. The chaos is an irregular mixture of the periodic oscillations which bound it e.g., between periodic two peak oscillations and periodic three peak oscillations, chaotic behavior can occur which is an irregular mixture of two and three peaks. More recently Roux, Turner et. al. 

We have therefore made a preliminary investigation of the effects of such disturbances using the model of Ganapathisubramanian and Noyes (3). This is a seventh order model for the Belousov-Zhabotinskii reaction in a CSTR. The equations and all necessary parameters are given in their paper. The model predicts a periodic 2-3 oscillatory region bracketed by a two peak and a three peak periodic oscillation (for constant feed rates). The transition points predicted by the model have been calculated to two or three significant figures by numerical simulation. The transition between 11(2) and n(2,3) occurs at... 

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). 

IIIC) 1978 Wegmann, K., Rossler, O. E. Different Kinds of Chaotic Oscillations in the Belousov-Zhabotinskii Reaction, Z. Naturforschung A, vol. 33A, no. 10, 1170-1183 (III J) 1980 Willamowski, Rossler, O. E. Irregular Oscillations in a Realistic Abstract Quadratic Mass Action System, Z, Naturforsch., vol. 35a, 317-318 (IIIG) 1965 Yamazaki, L., Yokoya, K., Nakajima, R. Oscillatory Oxidations of Reduced Pyridine Nucleotide by Peroxidase, Biochim. Biophys. Res. Commun., vol. 21, 582-586 (IIIG) 1967 Yamazaki, I., Yokota, K. Analysis of the Conditions Causing the Oscillatory Oxidation of Reduced Nicotinamide-Adenine Dinucleotide by Biochem. Biophys. Acta, vol. 132, 310-320... 

Briggs-Rauscher) and bromate oscillators (Belousov-Zhabotinskii), these new reactions are chlorite oscillators. For the chlorite oscillators, Orban et al. (1982-3) have also given a preliminary classification. 

Oscillations in Belousov-Zhabotinskii Reactions. Teor. Eksp. Khim. 16(3) 409-415. 

IIIC) Pikovskii, A. S. A Dynamical Model for Periodic and Chaotic Oscillations in the 1981 Belousov-Zhabotinskii Reaction. Phys. Lett. 85A, 13-16... 

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.

Fig. 95. Chaotic oscillations of the [Ce4+] concentration in the Belousov-Zhabotinskii reaction.

The experimental phenomena observed in the Belousov-Zhabotinskii reaction, such a doubling of the oscillation period, chaotic oscillations or alternate periodical and chaotic oscillations, can be modelled still more exactly by the recurrent equation... 

Tyson J J 1979 Oscillations, bistability and echo waves in models of the Belousov-Zhabotinskii reaction Ann. New York Acad. Sci. 316 279-95... 

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,... 

Oscillations in the Belousov-Zhabotinskii reaction are easily produced. A convenient recipe is given by Field (1972). Ingredients ... 

This phenomenon is often called "hard self-excitation" because there exists a self-excited (i.e. orbitally asymptotically stable) limit cycle, but to reach the self-excited oscillation requires a "hard" (i.e. finite) perturbation from the steady state. (In contrast, a "soft self-excitation" is illustrated in Fig. I.l.) There is some experimental indication of hard self-excitation in the Belousov-Zhabotinskii reaction. Notice in Fig. II. 1 that after a short induction period the oscillations appear suddenly with large amplitude. This is to be expected for hard self-excitation during the induction period the system is trapped in a locally stable steady state until the kinetic parameters change such that the steady state loses its stability and the system jumps to large amplitude stable oscillations. In the case of soft self-excitation it is expected that as the steady state loses stability, small amplitude stable oscillations first appear and then grow in size. 

Murray, J, D, (1974a), "On a model for temporal oscillations in the Belousov-Zhabotinskii reaction," J, Chern, Phys, 61, 3610-3613,... 

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. 

Hudson, J. L., Hart, M. Marinko, D. (1979). An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinskii Reaction. 

Wolfe, R. J. (1978). Temporal oscillation in a kinetic model of the Belousov-Zhabotinskii reaction. Arch. Rati. Mech. Anal., 67, 225-50. 

Srivastava, P.K., Mori, Y., Hanazaki, I. Photo-inhibition of chemical oscillation in Ru(bpy )2+-catalyzed Belousov-Zhabotinskii reaction. Chem. Phys. Lett. 190, 279 (1992)... 

Belousov-Zhabotinskii reaction (B-Z reaction) An oscillating chemical reaction in which there are periodic oscillations in the color of a mixture of sulfuric acid, potassium bromate, cerium (or iron) sulfate, and propanedioic acid. The period of oscillation is about one minute. The color changes are caused by repeated oxidations and reductions of cerium (or iron) ions. The reaction was first observed by the Russian chemist B. P. Belousov in the case of cerium and modified to iron by A. M. Zhabotinskii in 1963. The mechanism of the B-Z reaction is highly complicated and involves a large number of individual steps. 

Figure 8.2 Schematic representation of a slow manifold in the concentration space of a chemical reaction that exhibits mixed-mode oscillations. The trajectory shown has one large and three small extrema in X and Y for each cycle of oscillation. (Reprinted with permission from Barkley, D. 1988. Slow Manifolds and Mixed-Mode Oscillations in the Belousov-Zhabotinskii Reaction, . /. Chem. Phys. 89, 5547-5559. 1988 American Institute of...

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