Patterns, Belousov-Zhabotinsky reaction

In a recent study, photoemission electron microscopy (85) was used to reveal remarkable patterns of spaciotemporal variations, as shown in Fig. 5 (86). These patterns are similar to those observed with a homogeneous solution in which the Belousov-Zhabotinsky reaction (97) is occurring. 

In general, in a CSTR, the amplitude and period of an oscillation decrease if the residence is shortened. However, this decrease is not smooth. Typically, there are some preferred, relatively stable 1° oscillations at wide residence-time windows, but in between the patterns may be composites as described above. A case in point is the Belousov-Zhabotinsky reaction [40-42]. Most of the observed wave forms and pattern have been successfully reproduced by computation with a modified oregonator [43] ... 

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).

J. J. Tyson and P. C. Fife. Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J. Chem. Phys., 73 2224, 1980. 

Tyson, J.J., K.A. Alexander, V.S. Manoranjan J.D. Murray. 1989. Spiral waves of cyclic AMP in a model of slime mold aggregation. Physica 34D 193-207. Tyson, J.J. P.C. Fife. 1980. Target patterns in a realistic model of the Belousov-Zhabotinsky reaction. J. Chem. Phys. 73 2224-37. 

A common example is the Belousov - Zhabotinsky reaction [24], Beautiful patterns of chemical wave propagation can be created in a chemical reaction - diffusion system with a spatiotemporal feedback. The wave behavior can be controlled by feedback-regulated excitability gradients that guide propagation in the specified directions [25, 26]. 

Vanag, V.K. Waves and patterns in reaction-diffusion systems. Belousov-Zhabotinsky reaction in water-in-oil microemulsions. Phys. Usp. 47(9), 923-941 (2004). http //dx.doi. org/10.1070/PU2004v047n09ABEH001742... 

Vanag, V.K., Epstein, I.R. Pattern formation in a tunable medium the Belousov-Zhabotinsky reaction in an aerosol-OT microemulsion. Phys. Rev. Lett. 87, 228301 (2001)... 

Maselko, J., Reckley, J.S., Showalter, K. Regular and irregular spatial patterns in an immobilized-eatiyst Belousov-Zhabotinsky reaction. J. Phys. Chem. 93, 2774 (1989)... 

Chemical systems with complex kinetics exhibit a fascinating range of dynamical phenomena. These include periodic and aperiodic (chaotic) temporal oscillation as well as spatial patterns and waves. Many of these phenomena mimic similar behavior in living systems. With the addition of global feedback in an unstirred medium, the prototype chemical oscillator, the Belousov-Zhabotinsky reaction, gives rise to clusters, i.e., spatial domains that oscillate in phase, but out of phase with other domains in the system. Clusters are also thought to arise in systems of coupled neurons. 

Figure 1.7 Target patterns and spiral waves in the Belousov-Zhabotinsky reaction observed in a Petri dish. (Courtesy of T. Yamaguchi.)...

Pacault, A. Hanusse, P. De Kepper, P. Vidal, C. Boissonade, J. 1976. Phenomena in Homogeneous Chemical Systems far from Equilibrium, Acc. Chem. Res. 9,438-445. Pagola, A. Vidal, C. 1987. Wave Profile and Speed near the Core of a Target Pattern in the Belousov Zhabotinsky Reaction, J. Phys. Chem. 91, 501-503. 

Rovinsky, A. B. 1987. Turing Bifurcation and Stationary Patterns in the Ferroin Catalyzed Belousov-Zhabotinsky Reaction, J. Phys. Chem. 91, 4606-4613. 

Expanding target patterns in the Belousov-Zhabotinsky reaction were first discovered by Zaikin and Zhabotinsky (1970). In their experiment, they used a spontaneously oscillating thin layer of solution which was contained in a Petri dish of diameter 100 mm. The reagent contained bromate, bromomalonic acid and ferroin. With this prescription, one may observe periodic alternation of oxidized and reduced forms of the catalyst through a dramatic color change of the solution between red (reduced state) and blue (oxidized state). Some features of the pattern observed by them and by later experimenters are the following . ... 

Rotating waves with two and more arms have been observed by Agladze and Krinsky (1982) for the Belousov-Zhabotinsky reaction, and theoretically discussed by Koga (1982). We shall, however, restrict ourselves to the usual singlearmed spiral waves for which / = 1. As a further restriction, the pattern is assumed to rotate steadily (with frequency Q, Q> 0), i.e.. 

And when the chemicals are placed in a gel everyday Life in a flat dish, the colors appear as a pattern of waves in space rather than as oscillations in time. Chemists have since shown that the Belousov-Zhabotinsky reaction occurs by two different mechanisms, first by one, then by the otho-. These mechanisms are repeated in space or time, depending on the concentrations of intermediate substances. During the reaction, an indicator changes color depending on which mechanism is active. Although the complete set of elementary steps of the Belousov-Zhabotinsky reaction is complicated, the overall reaction occurs just as you would expect. The initial reactants continue to decrease ovct time and the final products increase as the substances come to equilibrium. 

This is a plate showing the wave patterns of the Belousov-Zhabotinsky reaction (in a gel). 

Experimentally, traveling waves have been observed in the Belousov-Zhabotinsky reaction (Fig. 19.12) but only recently have the Turing patterns been realized in the laboratory [31]. 

Figure 1 (a) A spiral wave formed in a thin gel layer of the Belousov-Zhabotinsky reaction (from Belmonte and Flesselles, Ref. 5. (b) Formation of a labyrinthine pattern in the bistable region of the iodine-ferrocyanide-sulfite chemical reaction in a gel reactor (from Lee and Swinney, Ref. 6). 

Another type of dynamic self-organization, so-called dissipative structure , is known as a general physical phenomenon which is generated under chemical or physical conditions far from equilibrium [238]. Many spatiotemporal patterns of the dissipative structures are formed in the dissipative processes ranging in size from sub-micrometers to hundreds of kilometers. Several types of regular patterns, e.g. spirals in the Belousov-Zhabotinsky reaction systems, the honeycomb and stripes of Rayleigh/Benard convection, are formed as spatiotemporal patterns in the dissipative processes. To utilize the dissipative structures for self-organization of molecular assemblies, the spatiotemporal patterns have to be frozen as stationary stable structures. 

The oscillations in most demonstration experiments produce periodic color changes. However, other properties of the solution, like the electrical potential, oscillate as well. This is due to changes in the concentrations of the redox active species. The electrical potential changes can be observed by measuring the potential of a platinum electrode versus a reference electrode. The voltage oscillates in phase with the color changes. The range of oscillations in the classic Belousov-Zhabotinsky reaction is about 200 mV. If the solution is poured in a petri dish and left unstirred, mosaic patterns appear as spatial oscillations. 

Welsh, B. J., Pattern Formation in the Belousov-Zhabotinsky Reaction, Thesis, Glasgow College of Technology (1984). 

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