The Belousov-Zhabotinsky Reaction

Pour solutions A and B into a 2-L flask equipped with a magnetic stir bar. The solution will become brown from bromine formation. After the solution clears, add solution C and 30 mL of 25 mM ferroin (Fisher). The solution will change from green to blue to violet and then to red over a period of about 1 min. These oscillations will persist for about 20 min. 

A smaller version can be prepared using appropriately scaled volumes. 

Substituting solution D for C will produce an oscillator with an initial period of 3-5 min that will continue oscillating for 8 h The period will gradually lengthen to 15 min. 

Bromates are strong oxidizing agents and should be treated with caution. Spills of sulfuric acid should be neutralized with bicarbonate. 

The completed reaction can be neutralized with bicarbonate and flushed down the drain with copious amounts of water. 

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Gyorgyi L and Field R J 1992 A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction Nature 355 808-10... 

An example of the application of J2-weighted imaging is afforded by the imaging of the dynamics of chemical waves in the Belousov-Zhabotinsky reaction shown in figure B 1.14.5 [16]. In these images, bright... 

The 1970s saw an explosion of theoretical and experimental studies devoted to oscillating reactions. This domain continues to expand as more and more complex phenomena are observed in the experiments or predicted theoretically. The initial impetus for the smdy of oscillations owes much to the concomitance of several factors. The discovery of temporal and spatiotemporal organization in the Belousov-Zhabotinsky reaction [22], which has remained the most important example of a chemical reaction giving rise to oscillations and waves. 

At the same time as the Belousov-Zhabotinsky reaction provided a chemical prototype for oscillatory behavior, the first experimental studies on the reaction catalyzed by peroxidase [24] and on the glycolytic system in yeast (to be discussed in Section 111) demonstrated the occurrence of biochemical oscillations in vitro. These advances opened the way to the study of the molecular bases of oscillations in biological systems. 

Despite the fact that from a principal point of view a problem of concentration oscillations could be considered as solved [4], satisfactory theoretical descriptions of experimentally well-studied particular reactions are practically absent. Due to very complicated reaction mechanism (in order to describe the Belousov-Zhabotinsky reaction even in terms of standard chemical kinetics several tens of concentration equations for intermediate products should be written down and solved numerically [4, 9, 10]) these equations contain large number of ill-defined parameters - reaction rates [10]. 

As it follows from the above-said, nowadays any study of the autowave processes in chemical systems could be done on the level of the basic models only. As a rule, they do not reproduce real systems, like the Belousov-Zhabotinsky reaction in an implicit way but their solutions allow to study experimentally observed general kinetic phenomena. A choice of models is defined practically uniquely by the mathematical formalism of standard chemical kinetics (Section 2.1), generally accepted and based on the law of mass action, i.e., reaction rates are proportional just to products of reactant concentrations. 

Hudson, J. L., Hart, M. and Marinko, D., 1979, An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinski reaction. J. Chem. Phys. 71,1601-1606. 

One of the well-studied systems that illustrates this successive-bifurcation behavior is the Belousov-Zhabotinski reaction. Let me briefly show you the results of some experiments done at the University of Texas at Austin,8 referring for further details to the discussion by J. S. Turner in this volume. The experimental setup of the continuously stirred reactor... 

Fig. 7. Mixed mode oscillations in the Belousov-Zhabotinski reaction when it is farther from equilibrium than it is in Fig. 6.

Fig. 8. When the Belousov-Zhabotinski reaction is sufficiently far from equilibrium it shows a chaotic behavior. This is reflected in the power spectrum being flat in comparison with the spectrum of the more orderly oscillatory behavior.

Fig. 9. A schematic representation of the different types of nonequilibrium behavior in the Belousov-Zhabotinski reaction.

COMPLEX PERIODIC AND NONPERIODIC BEHAVIOR IN THE BELOUSOV-ZHABOTINSKI REACTION... 

Fig. 3. Experimental traces of bromide ion concentration in closed system studies of the Belousov-Zhabotinski reaction, showing (a) quasiharmonic (i.e., sinusoidal) oscillations, (A>) and (c) increasingly nonlinear oscillations, and (

Diffusional process and chemical reaction synchronization induces oscillations of reaction product yields. This common type of synchronous reactions in the literature is referred to as the Belousov-Zhabotinsky reaction. 

Modeling of the Stirring Effect in the Autocatalytic Step of the Belousov—Zhabotinsky Reaction. 

Tsuda, Ichiro, "On the abnormality of period doubling bifurcation in connection with the bifurcation structure in. the Belousov-Zhabotinsky reaction system", preprint (1981). 

Another aspect of a very different nature also merits attention. For complex reaction schemes, it can be very cumbersome to write the appropriate set of differential equations and their translation into computer code. As an example, consider the task of coding the set of differential equations for the Belousov-Zhabotinsky reaction (see Section 7.5.2.4). It is too easy to make mistakes and, more importantly, those mistakes can be difficult to detect. For any user-friendly software, it is imperative to have an automatic equation parser that compiles the conventionally written kinetic model into the correct computer code of the appropriate language [37-39],... 

Some autocatalytic chemical reactions such as the Brusselator and the Belousov-Zhabotinsky reaction schemes can produce temporal oscillations in a stirred homogeneous solution. In the presence of even a small initial concentration inhomogeneity, autocatalytic processes can couple with diffusion to produce organized systems in time and space. 

The Belousov-Zhabotinsky reaction system is one example leading to such chemical oscillations. One of the interesting phenomena is the effect of the very narrow range of controlling parameter /x on the stability of the Belousov-Zhabotinsky reaction system. The following reactions represent the Belousov-Zhabotinsky reaction scheme ... 

The Belousov-Zhabotinsky reaction scheme can also produce moving spatial inhomogeneties in unstirred solutions. Spatial waves develop as an oxidizing region advances into a region of low but finite bromide ion concentration that falls below a critical value. The autocatalytic production of bromous acid at the interface advances the wave faster than the diffusion of any other molecules proceeds (Field et al., 1972). Nagy-Ungvarai and Hess (1991) used the electrochemical method to produce experimental data on the two-dimensional concentration profile of three variables in distributed Belousov-Zhabotinsky solutions. 

Example 13.5 The Belousov-Zhabotinsky reaction scheme Field et al. (1972) explained the qualitative behavior of the Belousov-Zhabotinsky reaction, using the principles of kinetics and thermodynamics. A simplified model with three variable concentrations producing all the essential features of the Belousov-Zhabotinsky reaction was published by Field and Noyes (1974). Some new models of Belousov-Zhabotinsky reaction scheme consist of as main as 22 reaction steps. With the defined symbols X = HBr02, Y = Br, Z = Ce4+, B = organic, A = B1O3 (the rate constant contains H+), FKN Model (Field et al., 1972) consists of the following steps summarized by Kondepudi and Priogogine (1999) ... 

The oxidation step is approximated with the reaction above. Concentration of the organic compounds (B) is assumed constant. Effective stoichiometry (/ ) is a variable, and the oscillations occur when/varies in the range 0.5-2.4. Representative kinetic equations of the Belousov-Zhabotinsky reaction scheme based on Eqs. (13.21)— (13.25) are... 

Solve the above equations and assess the structuring conditions. 13.9 The Belousov-Zhabotinsky reaction scheme is... 

Representative kinetic equations of the Belousov-Zhabotinsky reaction scheme based on Eqs. (13.21)—(13.25) are... 

Table 4.4 Elementary transformations at the Belousov-Zhabotinsky reaction with malonic acid as the oxidized substrate...

In a recent study, photoemission electron microscopy (85) was used to reveal remarkable patterns of spaciotemporal variations, as shown in Fig. 5 (86). These patterns are similar to those observed with a homogeneous solution in which the Belousov-Zhabotinsky reaction (97) is occurring. 

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