Field, Koros, Noyes model

The basie features of the oseillatory meehanism of the BZ reaetion are given by the Field-Koros-Noyes (FKN) model [14]- This involves three proeesses —A, B and C. Proeess A involves step (8) and step (9) from seetion A3,14.2.1. leading to removal of uiliibitor bromide ion. Proeess B involves step (3) and step (4) from Seetion A3.14.1.1 and gives the autoeatalytie oxidation of the eatalyst. This growth is limited partly by the disproportionation reaetion... 

The model that we take into account has been firstly proposed by H. J. Krug and coworkers in 1990 [30], to properly account for the photochemically-induced production of inhibitor bromide in the Belousov-Zhabotinsky reaction (BZ) catalyzed with the ruthenium complex Ru(bpy)3 [31, 32]. The Oregonator model was proposed in 1974 [16] on the basis Tyson-Fife reduction of the more complicated Field-Koros-Noyes mechanism [15] for the BZ reaction, the following modified model has been derived ... 

Show that the differential equation (4.9) (the induced kinetic differential equation of the Field-Koros-Noyes mechanism model of the Belousov-Zhabotinskii reaction) does have periodic solutions at certain values of the parameters. 

The Field-Koros-Noyes (FKN) model of the Belousov-Zhabotinsky reaction consists of the following steps with A = BrO, X = HB1O2, Y = Br , Z = Ce" +, P = HBrO and B = Org. In modeling the reaction, [H+] is absorbed in the definition of the rate constant. 

In order to understand the BZ system Field, Koros and Noyes developed the so-called FKN mechanism. From this, Field and Noyes later derived the Oregonator model, an especially convenient kinetic model to match individual experimental observations and predict experimental conditions under which oscillations might arise. 

RO, Fig. 3d) (2) higher-frequency, smaller amplitude, quasi-harmonic oscillations (QHO, Fig. 3a) and (3) double-frequency oscillations containing variable numbers of each of the two previous types. By far the most familiar feature of the BZ reaction, the relaxation oscillations of type 1 were explained by Field, Koros, and Noyes in their pioneering study of the detailed BZ reaction mechanism.15 Much less well known experimentally are the quasiharmonic oscillations of type 2,4,6 although they are more easily analyzed mathematically. The double frequency mode, first reported by Vavilin et al., 4 has been studied also by the present author and co-workers,6 who explained the phenomenon qualitatively on the basis of the Field-Noyes models of the BZ reaction. 

Theory of Wave-Field Interaction in BZ Medium. A model of the mechanisms behind the BZ reaction has been set forth by Field, Koros and Noyes (33) (FKN) and more recently this mechanism has been modified to incorporate more processes (3 ). 

Field, Koros 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 ... 

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... 

Field, Koros, and Noyes (FKN) [45] developed the mechanism of BZ reaction in 1972. Basically FKN model containing a total of 11 reaction chains involving 15 different intermediates and molecules [42]. The mentioned reaction chains were additionally formulated into three major processes [46]. The first processes starts with the depletion of bromide ions by a reaction of bromate ions. During this... 

In 1972, Field, Koros, and Noyes (FKN group investigated the kinetic details which characterized the entire aspects of BZ reaction, illuminating the essential constiments of reaction and their roles in oscillations [31, 53]. The kinetic model composed three consecutive reaction processes as, (A), (B), and (C). The process A is a fast reaction step, the process (B) is an autocatalytic set of reaction, and C is the process where (Br ) ions are consumed. The oxidation of metal catalyst ions has also been taken place in the processes (A) and (B), respectively. A recovery step (process C) involves for the reduction of metal catalysts and regenerates the necessary reactant (Br ) ions for re-initiating the oscillatory-phase reaction from beginning. A schematic model for description of the chemistry of BZ reaction is shown in Fig. 1.3. 

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]). 

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. 

A more detailed model was proposed by Field, Koros, and Noyes, which included 11 steps and seven intermediates. Later, this model was expanded to include 80 reactions and involved 26 intermediates. 

In a simplified way, this Field, Koros and Noyes (FNK) model, which serves as a basis of a well known Oregonator model, splits the overall reaction... 

Field, R.J., Koros, E., Noyes, R.M. Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system. J. Am. Chem. Soc. 94(25), 8649-8664 (1972). http //dx.doi.org/10.1021/ja00780a001 Field, R.J., Noyes, R.M. Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60(5), 1877-1884 (1974). http //dx. doi.org/10.1063/1.1681288... 

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