Belousov reaction

Fig. 5.2 Periodic behaviour in [Br ] and Celv / Celn in Belousov reaction.

Out-of-equilibrium systems (non-linear, dynamic processes), such as the Zabotinski-Belousov reaction, and other oscillating reactions bifurcation, and order out of chaos convection phenomena tornadoes, vortexes... 

A. M. Zhabotinsky, Periodic Kinetics of Oxidation of Malonic Acid in Solution (Study of the Belousov Reaction Kinetics). Biofizika 1964, 9, 306-311 A. N. Zaikin, A. M. Zhabotinsky, Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System. Nature 1970, 225, 535-537. See, also, a conversation with Anatol M. Zhabotinsky, I. Hargittai, Candid Science III More Conversions with Famous Chemists. (ed. M. Hargittai.) Imperial College Press, London, 2003, pp. 432-447. 

When I wrote my first manuscript, I encountered an ethical problem. I was unaware of Belousov s publications, and I had not received his recipe direcdy from him. So I decided to put his name in the subtitle of the paper, which read A study of kinetics of the Belousov reaction, and gave the manuscript to Shnol. I wanted him to be a co-author because it was his idea to do this study and he was my official adviser. He declined, saying that he had done nothing, but he was pleased to see the manuscript completed. I also asked him whether I could send the manuscript to Belousov before submitting it for publication. He told me that we can send it by the same route that the recipe had come. 

Fig. III.6. Oscillations of colored solution of Belousov reaction (After Zhabotinskii (1964-1))...

Reaction Mechanism. Noyes, Field, Koros (1972), Field, Koros, Noyes (1972) Noyes et al. (1972) gave a mechanism for the Belousov reaction. They proposed that in an acid solution of bromate, Br03, and malonic acid, CH2(COOH)2 containing sufficient amount of bromide ion, Br, four reactions form Process A. These reactions are (Rl, R3, and R7). 

Kopell, N. and Howard, L. N. (1973a). "Horizontal bands in the Belousov reaction." Science 180, 1171-1173. 

Othmer, H, G. (1975). "On the temporal characteristics of a model for the Zhabotinskii-Belousov reaction." Math. Biosci. 24, 205-238. 

Stanshine, J. A. (1975). "As3nnptotic solutions of the Field-Noyes model for the Belousov reaction." Thesis, Mass. Inst. Technology. 

Tilden, J. (1974). "On the velocity of spatial wave propagation in the Belousov reaction." J. Chem. Phys. 3349-3350. 

Zhabotinsky, A.M. Periodical oxidation of malonic acid in solution a study of the Belousov reaction kinetics. Biofizika 9, 1306 (1964)... 

Field, R. J. Noyes, R. M. 1972. Explanation of Spatial Band Propagation in the Belousov Reaction, Nature (London) 237, 390-392. 

Zhabotinsky, A. M. 1964a. Periodic Kinetics of Oxidation of Malonic Acid in Solution (Study of the Belousov Reaction Kinetics), Biofizika 9, 306-311. 

Kopell, N., Howard, L. N. (1973b) Horizontal bands in the Belousov reaction. Science 180, 1171 Kuramoto, Y., Tsuzuki, T. (1974) Reductive perturbation approach to chemical instabilities. Prog. Theor. Phys. 52, 1399... 

Both the Belousov-Zhabotinskii and the Bray-Liebhafsky systems have been characterized mechanistically. We consider the Belousov reaction in detail. Oscillatory behavior is not limited to a narrow range of concentrations. Initial conditions which lead to periodic concentration variation are given in Table 7.1. The period of oscillation is quite dependent upon initial concentrations, as suggested by the Lotka result (7.23) it varies from 15 to 200 sec in different experiments. Not only are there oscillations in the [Ce(IV)]/[Ce(III)] ratio but [Br ], which is present in trace quantities, oscillates as well. Typical results are shown in Fig. 7.6 the amplitudes diminish only very gradually over dozens of cycles. For the experiment il-... 

Our analysis of the Belousov reaction has just considered the oscillatory domain. Whether sequence (A) or sequence (B) is followed, initially there must be an induction period before oscillation commences since periodic behavior is triggered by replenishing [Br ], which cannot occur until [BrMa] is large enough so that (F) becomes important. The behavior illustrated in Fig. 7.6 is consistent with this interpretation. After initiation... 

Fig. 7.8. Schematic diagram showing development of concentration waves in the Belousov reaction, (a) Sequence A is triggered in central domain diffusion flows are indicated, (b) At a later time sequence B dominates in central region rings of concentration variations propagate outward.

Whereas oscillatory phenomena have been, until recently, considered chemical curiosities, they had been of great interest to biochemists for years. Metabolic pathways conform to all requirements for the observation of oscillations the systems are open—reactants constantly enter across cell walls and products are removed they are far from equilibrium there are feedback loops to maintain and reassert control even when the cell is drastically perturbed. Most biochemical oscillators are so complex that a detailed mechanistic analysis, such as that given for the Belousov reaction, is not available. The mechanism of glycolytic oscillation in yeast is the most well established. 

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