Belousov-Zhabotinsky oscillating reaction

The famous Oregonator model (ref. 9) is a highly simplified (but very successful) description of the Belousov - Zhabotinsky oscillating reaction ... 

Several groups have developed cellular automata models for particular reaction-diffusion systems. In particular, the Belousov-Zhabotinsky oscillating reaction has been examined in a number of studies.84-86 Attention has also been directed at the A + B —> C reaction, using both lattice-gas models 87-90 and a generalized Margolus diffusion approach.91 We developed a simple, direct cellular automaton model92 for hard-sphere bimolecular chemical reactions of the form... 

Non-traditional applications of NMR imaging to studies of chemical reactions including polymerization reactions and the Belousov-Zhabotinsky oscillating reaction are considered. Publications concerning applications of NMR imaging to studies of the temperature and electric current density distributions in various specimens are discussed. NMR studies of hyperpolarized gases and gases... 

Ganapathisubramanian, N. Noyes, R. M. 1982b. Additional Complexities during Oxidation of Malonic Acid in the Belousov-Zhabotinsky Oscillating Reaction, J. Phys. Chem. 86, 5158-5162. 

The Runge-Kutta algorithm cannot handle so-called stiff problems. Computation times are astronomical and thus the algorithm is useless, for that class of ordinary differential equations, specialised stiff solvers have been developed. In our context, a system of ODEs sometimes becomes stiff if it comprises very fast and also very slow steps and/or very high and very low concentrations. As a typical example we model an oscillating reaction in The Belousov-Zhabotinsky (BZ) Reaction (p.95). 

The major characteristics of excitable media, such as oscillating chemical reactions, and some important concepts necessary for understanding their behaviour have been discussed. The capacity of Belousov-Zhabotinsky (BZ) reactions for spontaneous spatiotemporal auto-organization is described 289... 

The easily visualized Belousov Zhabotinsky (BZ) reaction is now a classic example of the emergence of temporal and spatio temporal dissipative struc tures in homogeneous chemical systems. The reaction was discovered by Soviet military chemist B. P. Belousov in 1951 when he was studying homo geneous oxidation of citric acid by potassium bromide, KBrOq, in the presence of cerium sulfate Ce(S04)2 as the catalyst for redox processes. In the dissolved mixture of these compounds under certain process conditions, Belousov discovered a time-oscillating synchronous reduction of cerium(4+) ions ... 

Despite the importance of the chlorite-iodide systems in the development of nonlinear chemical dynamics in the 1980s, the Belousov-Zhabotinsky(BZ) reaction remains as the most intensively studied nonlinear chemical system, and one displaying a surprising variety of behavior. Oscillations here were discovered by Belousov (1951) but largely unnoticed until the works of Zhabotinsky (1964). Extensive description of the reaction and its behavior can be found in Tyson (1985), Murray (1993), Scott (1991), or Epstein and Pojman (1998). There are several versions of the reaction, but the most common involves the oxidation of malonic acid by bromate ions BrOj in acid medium and catalyzed by cerium, which during the reaction oscillates between the Ce3+ and the Ce4+ state. Another possibility is to use as catalyst iron (Fe2+ and Fe3+). The essentials of the mechanisms were elucidated by Field et al. (1972), and lead to the three-species model known as the Oregonator (Field and Noyes, 1974). In this... 

Figure 8.23. Color oscillations in Belousov - Zhabotinsky (BZ) reaction...

The Ce(IV)/Ce(III) (Br /BrOj ) system is one of several redox systems in which oscillating oxidation-reduction cycles can be observed. This particular system, with organic substrates like malonic acid (among others), is known as the Belousov-Zhabotinsky oscillator. This system has been studied for more than 15 years and has been the subject of several reviews and a number of symposia. The Ce--Br oscillating reaction system has been described in terms of a seven-step rate process (all reversible reactions), the Field-Koros-Noyes (FKN) mechanism (Field et al. 1972). 

The best known oscillating reaction is without a doubt the Belousov-Zhabotinsky (BZ) reaction, the oxidation of an organic substrate, typically malonic acid, CH2(C00H)2, by bromate, Br03, in an acidic medium in the presence of a metalion catalyst. It was discovered by Belousov in the early 1950s [32], and modified by Zhabotinsky [497]. The mechanism of the BZ reaction was elucidated by Field, Koros, and Noyes in 1972 [326, 130, 325] and reduced to five essential steps by Field and Noyes [131]. This model is called the Oregonator and in the version presented by Tyson and Fife [442] it is given by... 

Studies carried out by Yoshida and coworkers have coupled this phenomena with oscillating chemical reactions (such as the Belousov-Zhabotinsky, BZ, reaction) to create conditions where pseudo non-equilibrium systems which maintain rhythmical oscillations can demonstrated, in both quiescent (4) and continuously stirred reactors (5). The ruthenium complex of the BZ reaction was introduced as a functional group into poly(N-isopropyl acrylamide), which is a temperature-sensitive polymer. The ruthenium group plays it s part in the BZ reaction, and the oxidation state of the catalyst changes the collapse temperature of the gel. The result is, at intermediate temperature, a gel whose shape oscillated (by a factor of 2 in volume) in a BZ reaction, providing an elegant demonstration of oscillation in a polymer gel. This system, however, is limited by the concentration of the catalyst which has to remain relatively small, and hence the volume change is small. 

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

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. 

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