Chlorite-iodide reaction model

The ranges of various dynamic regimes are often displayed in a two-dimensional (2D) bifurcation diagram. An example is given in fig. 11.1, obtained by calculation [5] from a model of the chlorite-iodide reaction [39,40] the 2D space of constraints in... 

An example of such a comparison is seen in the modeling of the oscillating chlorite-iodide reaction. The model initially proposed by Epstein and Kustin [39] showed only fair agreement with the experimentally observed 1 evolution, and worse agreement with the experimentally observed I2 evolution, as seen in fig. 11.5(a,b). A revised mechanism proposed by Citri and Epstein [40] predicts oscillations quite similar in shape to the experimentally observed 1 and I2 oscillations (fig. 11.5c). In many oscillatory systems the temporal variation of only a few species (essential or nonessential) can be measured. The comparison of an experimental time series with a prediction of a proposed mechanism can be made with regard to the period of the oscillations, but becomes subjective with regard to the shape of the variation. The comparisons do not easily lead to suggestions for improvements of the proposed reaction mechanism. 

Figure 3.3 In developing a model of the chlorite-iodide reaction, Epstein and Kustin studied the reaction in a batch reactor. (Adapted from Epstein and Kustin, 1985.)...

The first systematic design of a chemical oscillator had been achieved There remained some ambiguity, however. Since two autocatalytic reactions had been employed, it was not immediately clear which constituted the fundamental autocatalytic reaction and which provided the feedback in the model scheme. Historically, the arsenite-iodate system had been chosen for the former role, since its bistable behavior had been established first. More careful investigation revealed that, in fact, it was the chlorite-iodide reaction that provides the essential dynamical features of this system. The evidence comes in two forms. First, the chlorite-iodide reaction is also bistable in a CSTR (Dateo et al., 1982) and the relaxation to its steady states is more rapid than the relaxation behavior of the arsenite iodate system. According to our theory,... 

Only the BZ reaction has played a more central role in the development of nonlinear chemical dynamics than the chlorite-iodide reaction (De Kepper et al., 1990). This latter system displays oscillations, bistability, stirring and mixing effects, and spatial pattern formation. With the addition of malonic acid, it provides the reaction system used in the first experimental demonstration of Turing patterns (Chapter 14). Efforts were made in the late 1980s to model the reaction (Epstein and Kustin, 1985 Citri and Epstein, 1987 Rabai and Beck, 1987), but each of these attempts focused on a different subset of the experimental data, and none was totally successful. Since each model contains a different set of reactions fitted to a different set of data, individual rate constants vary widely among the different models. For example, the rate constant for the reaction between HOCl and HOI has been given as zero (Citri and Epstein, 1987), 2 x10 s (Rabai... 

Bistable chemical reactions are the object of increasing interest from the experimental and theoretical points of view. The simplest abstract example is the Schlogl model well known experimental cases of bistability are the chlorite-iodide reaction or the iodate oxydation of the arsenous acid. 

In this chapter we give an overview of our research on the chemistry of the CIMA reaction and experiments with Turing structures. We discuss the chlorite-iodide reaction and related systems, the effect of starch and its chemistry, the development of models for spatial studies and the results of experiments on Turing structures. We conclude by pointing out several unsolved mechanistic and experimental problems. 

The Citri-Epstein model of the chlorite-iodide reaction. 

The above experiments clearly show that the effect of mixing is an important bifurcation parameter in the chlorite-iodide reaction. It is likely, particularly in early experiments on this system, that stirring may be an uncontrolled parameter and a neglected factor in mechanistic and model studies. 

We first found that a simple extension of the most widely used model of the chlorite-iodide reaction [35] to include the malonic acid-iodine reaction cannot account for the oscillation in batch. One or more essential species and their reactions, which are negligible at the concentrations used in the CSTR, must be important in batch. Earlier mechanistic studies did not consider the formation of CIO2 in the chlorite-iodide reaction. The possible role of the... 

For most of the oscillating reactions, the knowledge of the reaction mechanism and rate constants is generally very sketchy. Since the details of a particular kinetic model are not relevant close to bifurcation conditions, we will consider the simplest ordinary differential equation model which accounts for the characteristic features of the chlorite-iodide reaction and of its variants [69-71], namely bistability, excitability and relaxation oscillations. Our model of the reaction term is a two-variable Van der Pol-like system [82, 83] (C = u,v)) ... 

In some experiments performed with some variants of the chlorite-iodide reaction, the oscillating front patterns have been observed to invade one of the end CSTRs [32, 33]. Henceforth the two CSTRs cannot be considered to be in a steady state during the experimental run as before. In order to account for the interplay of the dynamics inside the Couette reactor and in the CSTRs, we have performed subsequent numerical simulations [59,64] of our reaction-diffusion model (3)Avith the CSTR boundary conditions defined in Equation (5). We give here a short description of the patterns observed when considering the slow-manifold (6). The following parameters are kept fixed e = 10 , a = 0.5, uq = 2,ui = —4, Vi = f ui), i = 0,1. D = hg is our control parameter. 

The Lengyel-Epstein model is a more realistic chemical reaction scheme. The Lengyel-Epstein model is a two-variable model for the chlorite-iodide-malonic acid (CIMA) reaction scheme and its variant, the chlorine dioxide-iodine-malonic acid (CDIMA) reaction scheme. In the model, the oscillatory behavior is related with ... 

LengyeI, I., and Epstein, I. R. (1991) Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction. Science 251, 650. 

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... 

Epstein and Kustin [39] set up a first reaction mechanism for the chlorite-iodide oscillator and reported a (diagonal) cross-shaped diagram in the species [CIO2 ]o-[I ]o- Later, Citri and Epstein [40] revised the first suggestion for the mechanism by reducing the original model considerably. Flere we employ the revised mechanism proposed by Citri and Epstein. The elementary steps are as follows ... 

Lengyel, 1., Epstein, I.R. Modeling of Turing stmctures in the chlorite-iodide-malonic acid-starch reaction system. Science 251(4994), 650-652 (1991). http //dx.doi.org/10. 1126/science.251.4994.650... 

Thus, we have two autocatalytic reactions that have the species 1 and I2 in common. In late 1980, Patrick De Kepper, who had developed the cross-shaped phase diagram model while working with Jacques Boissonade at the Paul Pascal Research Center in Bordeaux, arrived at Brandeis University to join forces with Irving Epstein and Kenneth Kustin, who had independently come to the conclusion that chemical oscillators could be built from autocatalytic reactions and had targeted the chlorite iodide and arsenitc iodate systems as promising candidates. The collaboration quickly bore fruit. 

Figure 19.10 (a) Turing structure in a one-dimensional Brusselator model, (b) Turing structures observed in chlorite-iodide-malonic acid reaction in an acidic aqueous solution (Courtesy Harry L. Swinney). The size of each square is nearly 1 mm. 

With the single exception of the chlorite-bromate-reductant systems [14], for which a mechanism has been developed by joining the NFT model [26] with THOMPSON S [42] mechanism for the BrOj -ClOo reaction, no mechanism has been published for any chlorite oscillator. In Table 2, we give a recently developed mechanism [43] for the minimal chlorite-iodide oscillator. Of special significance is the fact that it contains no radical species, but rather the binuclear intermediate CIO,. Calculations with this mechanism give excellent agreement with a wide variety of experimental results. One example is given in Fig. 5. 

Recent unpublished work at Brandeis suggests that the fundamental chlorite-iodide oscillator (Dateo et al.,[31] ) can be understood in terms of a mechanism involving the key binuclear intermediate IC102 In contrast to the mechanism for the BZ reaction, this model would require only singlet, non-radical species, thus constituting a fundamentally different pathway to oscillation. 

Two different reactions have presently been studied in the Couette flow reactor, namely the variants of the Belousov-Zhabotinsky [27-30, 32] and chlorite-iodide [29-33] reactions. The BZ reaction has revealed a rich variety of steady, periodic, quasi-periodic, frequency-locked, period-doubled and chaotic spatio-temporal patterns [27, 28], well described in terms of the diffusive coupling of oscillating reactor cells, the frequency of which changes continuously along the Couette reactor as the result of the imposed spatial gradient of constraints. This experimental observation has been successfully simulated with a schematic model of the BZ kinetics [68] and the recorded bifurcation sequences of patterns resemble those obtained when coupling two nonlinear oscillators. 

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