B-Z reaction

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. 

The next two important steps in this narrative are considered to be the following (i) the description of the bruxellator by Prigogine and Lefever, who, following on from Turing s work, analyzed theoretically the ingredients that should be present in a model of chemical reactions in order to produce spatial self-organization (Prigogine and Lefever, 1968) (ii) the description of the Belousov-Zhabotinsky (B-Z) reaction. 

In the hydrogen-oxygen and B-Z reactions considered above, the autocatalytic cycles correspond to a value for n of unity. The resulting rate law, rate = klab, involves the product of two concentrations and is known as quadratic autocatalysis . In the reaction between iodate and iodide ions, I is produced through an autocatalytic cycle which, at its simplest, corresponds... 

With this identification, the stable stationary-state behaviour (found for the cubic model with 1 < A < 4) corresponds to oscillations for which each amplitude is exactly the same as the previous one, i.e. to period-1 oscillatory behaviour. The first bifurcation (A = 4 above) would then give an oscillation with one large and one smaller peak, i.e. a period-2 waveform. The period doubling then continues in the same general way as described above. The B-Z reaction (chapter 14) shows a very convincing sequence, reproducing the Feigenbaum number within experimental error. 

The uncatalysed Belousov-Zhabotinsky (B-Z) reaction between malonic acid and acid bromate proceeds by two parallel mechanisms. In one reaction channel the first molecular products are glyoxalic acid and carbon dioxide, whereas in the other channel mesoxalic acid is the first molecular intermediate. The initial reaction for both pathways, for which mechanisms have been suggested, showed first-order dependence on malonic acid and bromate ion.166 The dependence of the maximal rate of the oxidation of hemin with acid bromate has the form v = [hemin]0-8 [Br03 ] [H+]12. Bromate radical, Br02, rather than elemental bromine, is said to play the crucial role. A mechanism has been suggested taking into account the bromate chemistry in B-Z reactions and appropriate steps for hemin. Based on the proposed mechanism, model calculations have been carried out. The results of computation agree with the main experimental features of the reaction.167... 

Since the discovery of the Belousov-Zhabotinskii (B-Z) reaction a large number of variations of this reaction has been investigated by numerous researchers. Both experimental and theoretical investigations outnumber those for any other oscillatory reaction. The reason for this extensive interest comes from the fact that the B-Z reaction is very rich in its interesting dynamical behavior and its variations are quite extensive. In this section research done during the period of 1980-82 is discussed briefly. 

At the start of this three year period, Noyes (1980) presented a generalized mechanism explaining the oscillations observed in the B-Z reactions. The thermodynamic and kinetic constraints and the limitations of the mechanism were discussed in detail. The reactions discussed are ... 

Original B-Z reaction where metal ion catalyzed organic substrate is brominated by enolization and bromide is liberated when the organic bromate reacts with the oxidized form of the catalyst, [See G G]. 

B-Z reaction with phenols and anilines as substrate, [Orban, Koros, Noyes, J. Phys. Chem. 82 (1978) 1672],... 

B-Z reaction with mixed substrates Tartaric acid/acetone [Rastogi, R. P., Singh, H. J. and Singh, A. K., Kinetics of Physicochemical Oscillations, Preprints of Submitted Papers. Aachen Discussion Meeting of Deutsche Bunsengesellschaft fur Physicalisehe Chemie, (1979) 98-107], oxalic acid/acetone [Noszticzius, Mag. Kern. Foly 85 (1979) 330]. 

B-Z reaction with added silver nitrate exhibits suppressed oscillations of a bromide-specific electrode while the potential of the platinum electrode still oscillates, [Noszticzius, J. Am. Chem. Soc. 101 (1979) 3660]. 

In section C we summarize the recent contributions under subsections. The general considerations on the mechanism of the B-Z reaction are in four subsections. Following these general considerations, we have sections C.2. Mathematical models and techniques, C.3. Experiments with different substrates, C.4. Experiments with different catalysts, and C.5. Horatian oscillations in bromate oxidations. The name horatian has recently been proposed for replacing the term chaotic. Here we simply state that throughout this article instead of chaotic oscillations, the term horatian oscillations will be used. 

Orban et al. (1982-2) discovered that in a CSTR within an extremely narrow range of flow rates and input concentrations a system containing Br03, Br" and Mn(II) or Ce(III) exhibits oscillations in the potential of either a Pt redox or Br- selective electrode. Existence of oscillations was predicted by the model calculations of Bar-Eli [Bar-Eli in Vidal and Pacault (1981) 228-239]. The bromate oscillators such as the B-Z reaction were derived from this fundamental system by adding feedback species which enlarges the region of critical space in which oscillations occur. 

Investigating the role of bromomalonic acid during the induction period of the B-Z reaction Burger and Koros (1980-1, 2) found that bromomalonic acid concentration has to reach a certain level for oscillations to start. This crucial concentration in turn is affected by changes in the acid concentration of the medium. 

Observing that the feed-back role played by bromide ion in the B-Z reaction, contrary to the previous schemes, may not explain recent experimental findings, Nosticzius and Bodiss (1980) proposed the Lotka-Volterra model for a B-Z reaction with combined oxalic aeid/acetone substrate. The reaction scheme becomes, for X=HBr02, Y=HOBr,... 

Noszticzius (1981) showed that the response of the electrode potential is probably due to hypobromous acid and no information about the bromide concentration could be obtained under the given scheme. Thus it was concluded that the bromide ion is not a controlling intermediate in the B-Z reaction. The applicability of the... 

Lotka-Volterra model to the B-Z reaction with other substrates was verified by Nosticzius and Feller (1982). 

Oscillations in the potential of the B-Z reaction are found to be influenced by the addition of iodide ion to the system. By increasing the amount of iodide ion in the system Koros and Varga (1982) recorded these variations and reported that high frequency oscillations precede the expected oscillations of the B-Z reaction. Similar high frequency oscillations were also observed by addition of monoiodomalonic acid (IMA) to the B-Z system. 

Vidal and Noyau (1980) investigated the qualitative and quantitative influence of heat exchange in the B-Z reaction in a CSTR reactor and concluded that the B-Z oscillations are intrinsic and insensitive to heat exchange. 

Jorne (1980) confirmed the findings of earlier researchers that the trigger wave propagation in the ferroin catalyzed B-Z reaction is caused by the coupling between autocatalytic mechanism and diffusion. 

Ganapathisubramanian and Noyes (1982-3) studied the B-Z reaction to discover that the reaction has complexities which are hard to explain, however the interpretation of the basic mechanism is not affected by these features. 

Botre et al. (1981), using the B-Z reaction as the model reaction, studied energy... 

In addition to extensive experimental studies on the B-Z reaction several mathematical models have been discussed either as part of the experimental results or as general studies reflecting the results available in the literature. Some of the studies are discussed in this section. 

Reducing the four-dimensional scheme of Nosticzius (1981) to a three dimensional one, differential equations for the B-Z reaction were given by Noszticzius and Farkas (1981) as... 

In an attempt to explain the horatian oscillations due to the B-Z reaction in a well-stirred continuous flow reactor reported by R. A. Schmitz et al., Iwamoto and Seno (1981) proposed a reaction model and a two dimensional mathematical model. 

Working with the model of B-Z reaction, Sakanoue and Endo (1982) showed by computer simulation the coexistence of a stable and an unstable limit cycle. The existence of an unstable oscillating object between two stable objects had been... 

Treindl and Fabian (1980) studied the effect of oxygen on parameters of the B-Z reaction in the presence of Ce(IV)/Ce(III) redox catalyst and malonic acid, citric add or 2,4-pentanedione as substrates. They concluded that the effect of oxygen was in its catalytic influence on the oxidation of the substrate with Ce(IV) ion. Under this influence, the number of oscillations as well as the induction period and the first oscillation period diminished. 

Treindl and Kaplan (1981) studied the kinetics of oxidation of 2,4-pentanedione with Ce(IV) ions. The modified B-Z reaction with 2,4-pentanedione as substrate exhibited oscillations with an increasing amplitude even in the absence of stirring. 

The role of bromide ion in the B-Z reaction was questioned by Noszticzius and Bodiss (1980) while working with a B-Z reaction where combined substrate oxalic acid/acetone was used as the organic substrate. 

Habon and Koros (1979) found that pyrogallol could be a substrate in a Mn(II) catalyzed B-Z reaction. The critical Br concentrations, the effect of inhibitors such as oxygen and light were studied. 

While there are numerous studies on B-Z reactions with different substrates, there are as many investigations of reactions with different catalysts. A summary of these studies is given in Table III.C.4. 

Bolletta and Balzani (1982) observed oscillating chemiluminescence in a B-Z reaction with tris (2,2 -bipyridine ruthenium (II), Ru(bpy)3+, [First used by Demas and Diemente J. Chem. Ed. 50 (1973) 357]. This is the first example of oscillating chemiluminescence in a B-Z reaction. 

D Alba and Serravalle (1981) compared the effect of various catalysts on the B-Z reaction by using an electrochemical method, [see Botre et al. (1981)]. The catalysts compared are Ce(S04)2, ferroin and FeS04 and their various combinations. The number of oscillations, the average frequencies and the duration of oscillations were measured and tabulated for different cases. 

Yoshida and Ushiki (1982) compared the kinetics of the B-Z reaction with Ce(III) or [Fe(phen)3]2+ as catalyst, and found substantial differences in kinetic constants. Similarly, Yoshikawa (1982) studied the effects of temperature on the frequencies of oscillations in the B-Z reaction. They reported that for a reaction where Ce(III) was used as the catalyst, the activation energy range was fixed. However, when Fe(phen)3+ or Fe(bpy)3+ was used as catalyst, the apparent activation energy depended on the concentration of the catalyst. 

Bis-bipyridine-silver complexes were found to catalyze the B-Z (with malonic acid as substrate) reaction by Kuhnert and Pehl (1981-1). The reaction was shown to proceed in a heterogeneous medium due to the insolubility of the silver complexes. When organic compounds such as citric acid and 2,4-pentanedione, ethylacetoacetate and racemic malic acid were used as substrates, the oscillatory behavior was not observed. Kuhnert and Pehl (1981-2) also observed that the bipyridine complexes of chromium and osmium catalyze the B-Z reaction. 

Yatsimirskii, et al. (1981-1) studied the B-Z reaction under differeht combinations of ferroin/ferriin and Ce(III)—Ce(IV) couples used as catalyst. The changes in the amplitudes of the oscillating bromide concentrations were recorded. 

Experimenting with the B-Z reaction in a CSTR at various residence times for the same inlet concentrations and temperature, Hudson and Mankin (1981) obtained and reported horatian oscillations. The measurements of the bromide ion electrode potential and the platinum electrode potential were recorded. Calculating the time derivative of Pt, or the time delay, Pt(t-lp), three dimensional phase space plots were presented. With the time delay as the third variable a horatian solution was obtained, Fig. III.C.2. 

Ganapathisubramanian and Noyes (1982-4) constructed a model consisting of seven differential equations. The numerical solutions of these equations did not correlate with the horatian behavior observed by Hudson-Mankin (1981) in B-Z reaction in a flow reactor. 

---