Belousov-Zhabotinskii oscillating reactions

Effects of added salts on the Belousov-Zhabotinskii oscillating reaction have also been attributed to solvent structural factors, through the influence of the cations (Li+, Na+, K+, Me4N+) on the water structure. Specific effects of added salts on transition states have been proposed for the reactions of cobalt(ii) with chlorophyllic acid (in methanol) and the conversion of / - into -dodeca-molybdosilicate. In the former case added lithium nitrate is thought to inhibit solvation of the transition state, but in the latter added ions are believed actually to enter the transition state. Salt effects on the kinetics and mechanism of formation of monofluoro-complexes of a range of M + and Al + cations in aqueous media are described in a conference report comprehensible only to readers of Russian. 

Salter, L.F., Sheppard, J.G. A duel frequency Belousov-Zhabotinskii oscillating reaction with ethylacetoaceatate as organic substrate. Int J. Chem. Kinett 14, 815 (1982)... 

Ce(IV) sulfate is widely used as a catalyst for various reactions, for instance grafting acrylamide on alkali lignin (Meister et al., 1984) and the Belousov-Zhabotinskii oscillating reaction (Winfree, 1984). It can be also used as a strong oxidant for several classes of organic compounds (Rao et al., 1983). 

Zhuravlev, A.I., and V.M. Trainin. Chemiluminescent Reactions in the Belousov-Zhabotinskii Oscillating System. J Biolumin Chemilumin (October 1990) 227-34. 

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.)]... 

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). 

Brusa, M. A. Perissinotti, L. J. Colussi, A. J. 1985. Electron Spin Resonance Kinetic Studies of Malonyl Radical Self-Decay and Oxidation Reactions by Cerium(IV) and Bromate in Acid Aqueous Media. The Role of Free Radicals in the Belousov-Zhabotinskii Oscillator, J. Phys. Chem. 89, 1572-1574. 

Noszticzius, Z. Bodiss, J. 1979. A Heterogeneous Chemical Oscillator. The Belousov-Zhabotinskii-Type Reaction of Oxalic Acid, J. Am. Chem. Soc. 101, 3177—3182. 

The most curious process in which Ru(bpy)3 " plays the role of LES is an oscillating reaction. It is well established that certain types of chemical reactions, under appropriate experimental conditions, organize themselves spontaneously to give rise to regular spacial patterns or to periodic rate fluctuations (see, e.g. ref. 59). The best studied among the oscillating homogeneous processes is the classical Belousov-Zhabotinskii (BZ) reaction[60], in which a crucial role is played by a redox catalyst. The usual catalyst of the BZ reaction is the couple, but polypyridine... 

Any systematic analysis of the literature of oscillating chemical reactions (see., e.g., BURGER and BUJDOSO [1]), would show at least two clear trends. First, there has been a rapid expansion in both the number of papers published annually and in the number of groups working on such problems. Second, and more recent has been a diversification in the set of chemical systems studied an ever increasing fraction of work is being devoted to systems other than the classic Belousov-Zhabotinskii (BZ) reaction. 

The development first of belief and then of interest on the part of chemists in oscillating reactions was spurred by two major developments, one theoretical, the other experimental. Studies in the field of nonequilibrium thermodynamics (Glansdorff and Prigogine, [1 ]. see Procaccia and Ross, [2 ] for a review) established that, sufficiently far from equilibrium, chemical oscillation was indeed consistent with the laws of thermodynamics. The accidental discovery in the Soviet Union (Belousov, [ 3 ] ) of a reaction which gave easily observable oscillations at room temperature evoked the interest of several chemists, first as an amusing lecture demonstration and then as a subject of serious research. It is interesting that the first homogeneous chemical oscillator (Bray, [4 ]), also discovered by serendipity almost 4o years before the Belousov-Zhabotinskii (bz) reaction, received little attention until after the BZ system had become a major focus of research. 

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. 

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... 

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... 

Even more intriguing is the Belousov-Zhabotinskii class of oscillating reactions some of which can continue for hours. Such a reaction was first observed in 1959 by B. P. Belousov who noticed that, in stirred sulfuric acid solutions containing initially KBr03, cerium(IV) sulfate and malonic acid, CH2(C02H)2, the concentrations of Br and Ce" " underwent repeated oscillations of major proportions (e.g. tenfold changes on a time-scale which was constant but which could be varied from a few seconds to a few minutes depending on concentrations and temperature). These observations were extended by... 

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