Belousov-Zhabotinski Oscillatory Reaction

Korbs and co-workers 304, 305) have studied the behavior of the Belousov-Zhabotinsky oscillatory reaction in the presence of thal-lium(III), which in this context functions as a bromide-removing agent. Korbs et al. have explained their results by assuming that the ligand exchange occurs according to the following reactions ... 

We now turn to our application of MSIMPC to examine the behavior of an oscillatory reaction. To compare experimental kinetic results to theoretical chemical mechanisms, the differential equations derived from the mechanism must be solved. The Oregonator model, which is a simple model proposed to explain the oscillatory behavior of the Belousov-Zhabotinsky (BZ) reaction, is a typical case. It involves five coupled differential equations and five unknown concentrations. We do not discuss details of this mechanism or the overall BZ reaction here, since it has received considerable attention in the chemical literature. 

Although some of the fimdamental discoveries in nonlinear chemical dynamics were made at the beginning of the twentieth century and arguably even earlier, the field itself did not emerge until the mid-1960 s, when Zhabotinsky s development (1) of the oscillatory reaction discovered by Belousov (2) finally convinced a skeptical chemical community that periodic reactions were indeed compatible with the Second Law of Thermodynamics as well as all other known rules of chemistry and physics. Since the discovery of the Belousov-Zhabotinsky (BZ) reaction, nonlinear chemical dynamics has grown rapidly in both breadth and depth (3). 

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. 

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. 

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.

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

Figure 8.3 Experimental synchronization patterns in the oscillatory Belousov-Zhabotinsky reaction in a cellular flow. The horizontal direction is along an annulus, so that there are periodic boundary conditions at the ends of the images, (a) Phase waves, (b) Co-rotating synchronization. (c) Global synchronization. From Paoletti et al. (2006).

V. K. Vanag, A. M. Zhabotinsky, and I. R. Epstein. Oscillatory Clusters in the Periodically Illuminated, Spatially Extended Belousov-Zhabotinsky Reaction. Phys. Rev. Lett, 86 552, 2001. 

Examples of self-sustained oscillatory systems are electronic circuits used for the generation of radio-frequency power, lasers, Belousov-Zhabotinsky and other oscillatory chemical reactions, pacemakers (sinoatrial nodes) of human hearts or artificial pacemakers that are used in cardiac pathologies, and many other natural and artificial systems. An outstanding common feature of such systems is their ability to be synchronized. 

The Belousov-Zhabotinsky reaction is not the only one which displays oscillatory behavior. For instance the Bray-Liebhafsky reaction discovered in the 1920s by W. C. Bray and H. Liebhafsky is the decomposition of H2C>2 in O2 and H2O with I03 . 

The spiral or concentric waves observed for the spatial distribution of cAMP (fig. 5.6) present a striking analogy with similar wavelike phenomena found in oscillatory chemical systems, of which the Belousov-Zhabotinsky reaction (fig. 5.7) provides the best-known example (Winfree, 1972a). 

By now we know a large number of oscillatory reactions, not only in chemistry - as exemplified by the famous Belousov-Zhabotinsky reaction - but also in biochemical and cellular systems. It is interesting to observe that in oscillations in inorganic chemistry the molecules are simple but the mechanisms are highly complex, whereas in biochemistry the molecules responsible for rhythmic phenomena possess a complex structure (enzymes or receptors. ..) whereas the mechanisms often are simple. 

The rich variety of this type of temporal self-organization was mainly explored in detail with the famous Belousov-Zhabotinsky reaction [6,7], but with heterogeneously catalyzed reactions the oscillatory kinetics were first reported only aroimd 1970 for the oxidation of CO on Pt catalysts [8,9]. Since then oscillatory kinetics have been found with more than a dozen catalytic reactions, and this field has also been extensively reviewed [10,17]. 

Figure L Control of the spiral shape in the oscillatory Belousov-Zhabotinsky reaction. Ru(bpy)3 was used as catalyst. Ar laser beam was irradiated (illustrated by white arrow) at the core of the rotating spiral to increase the size of the core region. The morphology of spiral changed reversibly from Archimedean to logarithmic, and the wave profile from trigger-wave to phase-wave. Controlling global structure by local control of singular region is characteristic in dissipative structures.

Self-oscillatory patterns can be created by repeating swelling and de-swelling of the polymer network in a closed system, i.e., without any external stimuU. In comparison to stimuli-induced patterns (summarized above), self-oscillatory patterns have no on-off switch, and can repeat itself periodically, such as a beating heart (Fig. 9.9). The idea was based on Belousov-Zhabotinsky (BZ) type reaction [66] to induce spontaneous temporal change in the redox potential to control swelling... 

Ruof, P. and Noyes, R.M., Phase response behaviors of different oscillatory states in the Belousov-Zhabotinsky reaction, J. Chem. Phys., 89, 6247-6254, 1988. 

The Belousov-Zhabotinsky (BZ) system is a methodically characterized chemical oscillation and provides an archetype scheme for smdy of wide ranges of patterning features in oscillatory chemical reactions [47-53]. This consists of bromination reaction initially and auto-oxidation of organic substrates is takes place in sequential processes by bromate ions. Overall, the reaction is catalyzed by redox catalysts in a concentrated water-acidic solution. 

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