Belousov-Zhabotinskii reactions

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. 

Halc enation of Acids - The Belousov-Zhabotinskii Reaction... 

For the catalytic oxidation of malonic acid by bromate (the Belousov-Zhabotinskii reaction), fimdamental studies on the interplay of flow and reaction were made. By means of capillary-flow investigations, spatio-temporal concentration patterns were monitored which stem from the interaction of a specific complex reaction and transport of reaction species by molecular diffusion [68]. One prominent class of these patterns is propagating reaction fronts. By external electrical stimulus, electromigration of ionic species can be investigated. 

This reaction, widely known as the Belousov-Zhabotinskii reaction, can proceed in an oscillatory fashion [68]. For overall slow conversion, the concentrations of intermediates and the catalyst undergo cyclic changes. By this means, many pulselike reaction zones propagate in a spatially distributed system. Ferroin/ferriin can be applied as an optically detectable catalyst... 

Figure 4.97 Global changes of the Belousov-Zhabotinskii reaction behavior in the capillary reactor under electrical field. (A) Reversal of the direction of the reaction zone (white stripe) propagation (0.5 mm capillary reactor) ...

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). 

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... 

J- J. Tyson. The Belousov-Zhabotinskii Reaction, Lecture Notes in Biomathematics, vol 10. Springer-Verlag, New York, 1976. 

Fig. 1.1. Typical experimental records of oscillatory behaviour in the Belousov-Zhabotinskii reaction (a) platinum electrode which responds primarily to the Ce3+/Ce4+ couple (b) bromide-sensitive electrode measuring In [Br ].

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. 

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 ... 

Ye, Q.-X. and Wang, M.-X. (1987). Traveling wave front solutions of Noyes-Field system for Belousov-Zhabotinskii reaction. Nonlinear Anal. Theor. Methods. Appl., 11, 1289-302. 

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... 

Secondly, it is necessary to interpret critical effects recently discovered experimentally and which are of common interest. In the adjacent field, i.e. homogeneous catalysis, a great number of such facts have been accumulated for Belousov-Zhabotinskii reactions. These facts can be interpreted only in terms of the non-linear unsteady-state models. 

Kenney in England and Luss, Takoudis, Schmidt, Ray, Jensen over here spring to mind in addition to those already mentioned. The Belousov-Zhabotinskii reaction has of course generated a minor industry of experimental and theoretical studies, dissipative systems and locus-ators which it would be rash to rush into here. 

The Belousov-Zhabotinskii reaction in an isothermal CSTR can undergo a series of transitions among periodic and chaotic states. One segment of this series of transitions is investigated in detail. Liapunov characteristic exponents are calculated for both the periodic and chaotic regions. In addition, the effect of external disturbances on the periodic behavior is investigated with the aid of a mathematical model. 

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... 

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