Chemical reaction Oregonator

Field, K6ros and Noyes [13] suggested to use as the basic model for the Belousov-Zhabotinsky system a rather complicated set of chemical reactions with seven intermediate products. Its more global analysis based on macrokinetic stages and retaining still the principal features of this reaction [14] has led to the simplified scheme with three intermediate products only. This model called Oregonator [9, 15] is described by the following equations ... 

Binary Chemical Weapons Chemical weapons formed from two non-lethal elements (called precursors) through a chemical reaction after the munitions are fired or launched. Binary weapons were manufactured, stored, and transported with only one of the chemical elements in the weapon. The second element was to be loaded into the weapon at the battlefield. As of November 1993, the precursors for the binary chemical weapons are stored at Aberdeen Proving Ground, Maryland Pine Bluff Arsenal, Arkansas Tooele Army Depot, Utah and Umatilla Depot Activity, Oregon. 

Levenspiel, O. Chemical Reaction Engineering, 2nd ed., Wiley, New York, 1972, 3rd ed., 1999 Chemical Reactor Omnibook, Oregon State University Bookstore, Corvallis, Or, 1993. 

The modified Oregonator model used in this chapter has been previously presented [18] and further details of the modeling can be found there. The chemical reactions comprising the model are ... 

Heller-Kallai, L. 2002. Clay catalysis in reactions of organic matter. In Organo-clay complexes and interactions, ed. S. Yariv, H. Cross, 567-613. New York Marcel Dekker. Herbelin, A. L., and J. C. Westall. 1996. FITEQL3.2, A Program for the Determination of Chemical Equilibrium Constants from Experimental Data. Corvallis Oregon State University. 

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. ... 

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... 

W. Jahnke, W. Skaggs, and A. Winfree. Chemical vortex dynamics in the Belousov-Zhabotinskii reaction and in the two-variable Oregonator model. 

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. 

In the Oregonator kinetic model the symbolic representations have specific chemical meaning. A = BrOs, B = MA are the initial reagents, X = HB1O2, Y = Bf, Z = Ce" are the intermediate species, P = HBrO is the reaction product, and/is the stoichiometric coefficient indicating how many bromine ions are formed to reduce two cerium ions. According to Tyson... 

In general, the skeletal Oregonator model or the Oregonator -like models describe the experimental data. Nevertheless the precise description of the experimental results is achieved when more extended kinetic models for the B-Zh reaction are used (see, for example [27-32]). At that the propagation of chemical waves in the reactor space (spatial periodicity) is described by the diffusion equations [48-50]. 

Now the question is how to construct the simplest model of a chemical oscillator, in particular, a catalytic oscillator. It is quite easy to include an autocatalytic reaction in the adsorption mechanism, for example A+B—> 2 A. The presence of an autocatalytic reaction is a typical feature of the known Bmsselator and Oregonator models that have been studied since the 1970s. Autocatalytic processes can be compared with biological processes, in which species are able to give birth to similar species. Autocatalytic models resemble the famous Lotka-Volterra equations (Berryman, 1992 Valentinuzzi and Kohen, 2013), also known as the predator-prey or parasite-host equations. 

Just as the BZ reaction has become the experimental prototype for nonlinear chemical dynamics, the Oregonator model (Field and Noyes, 1974b), is easily the most familiar and thoroughly studied model system in nonlinear chemical dynamics. We recall from Chapter 5 that the model equations are... 

The Gyorgyi-Field proposal called into question the source of chaotic behavior in the best characterized chaotic chemical system, the BZ reaction. After several months of occasionally heated discussion with experimentalists, Gyorgyi and Field (1992) developed several chemically plausible variants of the Oregonator model that produce chaotic behavior with perfect mixing under conditions resembling those in the experiments. Their models are derived from an initial eleven-variable Mass Action model shown in Table 15.2. The four-variable versions contain the three variables—Br, Br02, and Ce(IV)—of the standard Oregonator, supplemented with the bromomalonic acid concentration as a fourth variable. Because of the steady-state approximations used for such species as cerous ion, malonyl radical, and bromine dioxide, these models contain some nonpolynomial (non-Mass Action) terms, but they are nonetheless chemically based. It is even possible to simplify further to obtain a still chaotic, but somewhat less faithful, three-variable model. 

Jahnke, W. Skaggs, W. E. Winfree, A. T. 1989. Chemical Vortex Dynamics in the Belousov-Zhabotinsky Reaction and in the Two-Variable Oregonator Model, J. Phys. Chem. 93, 740-749. 

TYSON and FIFE [4] have presented a theory of target pattern formation in the BZ reaction, based on the assumption that at the center of each pattern there is a heterogeneity which periodically triggers waves of excitation (either oxidation or reduction) which then propagate away from the center at speeds determined by the chemical composition of the medium at the wave front. They describe the chemistry of the reaction in terms of the highly successful Oregonator model [5,6]. In suitably scaled and reduced form the Oregonator equations are... 

The detailed chemistry of the BZ reaction was first elucidated (in 1972) by FIELD, KOROS, and NOYES [60]. From the detailed mechanism, which involved more than 20 reactions and as many chemical constituents, FIELD and NOYES [61] then derived a reduced model (the "Oregonator") with only 3 variables. A modified Oregonator (with 7 variables) was then proposed and studied by SHOWALTER et al. [26], who were not successful in their attempt to simulate the observations by SCHMITZ et al. [4] of nonperiodic behavior. SHOWALTER et al. [26] concluded that the difference between experiment and simulation suggests that the chaotic behavior observed experimentally may result from fluctuations too small to measure in any other way. Similar conclusions have been reached in several other studies [27,28,62,63]. However, abstract models have been developed that display chaos and some of the transition sequences observed in experiments (e.g., see [64-66]). 

Our results and those of Ruoff /with Ag" / [41 clearly demonstrate that even in the presence of bromide-removing ions Oregonator can simulate the experimentally recorded curves, and modification neither in the Oregonator model nor in the skeleton of the chemical mechanism is necessary. This means that bromide ion should not be replaced by an, other control intermediate /e.g. HOBr, Br/ and more than one auto-catalytic reaction should not be taken into consideration. 

Belousov s reaction, the metal ion (generally Ce " ) catalyzed bromination of an organic substrate, most often malonic acid, by bromate, was developed experimentally by Zhabotlnskii (I 5 ] ). It was, however, the publication (Field, Koros and Noyes, [6 ] ) of a detailed mechanism for the system and of a simplified three-variable model (the Oregonator, Field and Noyes, [ 7 ] ) of that mechanism that spurred interest in the BZ system as a prototype o,f periodic chemical behavior. 

There is a widespread belief that exotic patterns of behaviour in chemical systems require either very complex kinetic mechanisms or non-isothermal influences. There have been many investigations of the single, irreversible, exothermic reaction [see e.g. 1 5] proceeding under well-stirred, open conditions (in a CSTR). By contrast, the isothermal systems [6] covered have tended to be rather specific enzyme rate-laws or reactions at surfaces. Models proposed for homogeneous, isothermal reactions include complicated schemes [7 58] such as the Brusselator and Oregonator . Table 1 lists some of the important historical landmarks of this subject. 

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