Belousov-Zhabotinsky BZ Reaction

The Runge-Kutta algorithm cannot handle so-called stiff problems. Computation times are astronomical and thus the algorithm is useless, for that class of ordinary differential equations, specialised stiff solvers have been developed. In our context, a system of ODEs sometimes becomes stiff if it comprises very fast and also very slow steps and/or very high and very low concentrations. As a typical example we model an oscillating reaction in The Belousov-Zhabotinsky (BZ) Reaction (p.95). 

The Belousov-Zhabotinsky (BZ) reaction involves the oxidation of an organic species such as malonic acid (MA) by an acidified aqueous bromate solution in the presence of a metal ion catalyst such as the Ce(m)/Ce(IV) couple. At excess [MA] the stoichiometiy of the net reaction is... 

The major characteristics of excitable media, such as oscillating chemical reactions, and some important concepts necessary for understanding their behaviour have been discussed. The capacity of Belousov-Zhabotinsky (BZ) reactions for spontaneous spatiotemporal auto-organization is described 289... 

The easily visualized Belousov Zhabotinsky (BZ) reaction is now a classic example of the emergence of temporal and spatio temporal dissipative struc tures in homogeneous chemical systems. The reaction was discovered by Soviet military chemist B. P. Belousov in 1951 when he was studying homo geneous oxidation of citric acid by potassium bromide, KBrOq, in the presence of cerium sulfate Ce(S04)2 as the catalyst for redox processes. In the dissolved mixture of these compounds under certain process conditions, Belousov discovered a time-oscillating synchronous reduction of cerium(4+) ions ... 

In this section, we consider the breakdown of the condition of normal hyperbolicity. First, we explain a simple example where breakdown of normal hyperbolicity leads to a bifurcation in reaction processes. In the Belousov-Zhabotinsky (BZ) reaction [40], the bifurcation from the stable fixed point to the limit cycle takes place through the breakdown of normal hyperbolicity. This is the simplest case where mathematical analyses are in progress [41]. 

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... 

Spiral waves also arise in the oxidation of carbon-monoxide on platinum surfaces [10]. In 1972 they have been discovered by Winfree [79] in the photosensitive Belousov-Zhabotinsky (BZ) reaction, see for recent investigations for example [83, 84, 87]. Both reactions are studied in the SFB 555. The classical BZ reaction is a catalytic oxidation of malonic acid, using bromate in an acidic environment. Experimentally it exhibits well reproducible drift, meander and chaotic motions of the spiral wave and its tip. 

The most studied and cited example of complex dynamic behavior in homogeneous catalysis is the Belousov - Zhabotinsky (BZ) reaction named after B. P. Belousov who discovered the reaction and A. M. Zhabotinsky who continued Belousov s early work. The reaction is theoretically important in that it shows that chemical reactions do not have to be dominated by equilibrium. These reactions are far from equilibrium and remain so for a length of time. In this sense, they provide an interesting chemical model of nonequilibrium biological phenomena, and the mathematical model of the BZ reactions themselves are of theoretical interest. 

Figure 8.23. Color oscillations in Belousov - Zhabotinsky (BZ) reaction...

As an example, let us examine the well-known Belousov-Zhabotinsky (BZ) reaction [15,16] of bromate with malonic acid catalyzed by cerium ions in acidic solution. 

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. 

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... 

Studies carried out by Yoshida and coworkers have coupled this phenomena with oscillating chemical reactions (such as the Belousov-Zhabotinsky, BZ, reaction) to create conditions where pseudo non-equilibrium systems which maintain rhythmical oscillations can demonstrated, in both quiescent (4) and continuously stirred reactors (5). The ruthenium complex of the BZ reaction was introduced as a functional group into poly(N-isopropyl acrylamide), which is a temperature-sensitive polymer. The ruthenium group plays it s part in the BZ reaction, and the oxidation state of the catalyst changes the collapse temperature of the gel. The result is, at intermediate temperature, a gel whose shape oscillated (by a factor of 2 in volume) in a BZ reaction, providing an elegant demonstration of oscillation in a polymer gel. This system, however, is limited by the concentration of the catalyst which has to remain relatively small, and hence the volume change is small. 

It is well known that the Belousov-Zhabotinsky (BZ) reaction can initiate free radical polymerisation (2) while it is less known that polymers can also affect the dynamics of the BZ reaction. Recently, we have performed preliminary experiments perturbing the BZ reaction with two different water-soluble nonionic polymers containing alcoholic end-groups, namely polypropylene glycol and polyethylene glycol (PEG) (i). It was realized that the Belousov-Zhabotinsky reaction responded to the perturbation in an unexpected way. Thus, a systematic study was undertaken to inquire whether the perturbation effect can be attributed exclusively to PEG reactive endgroups (here primary alcoholic groups) or the chemical nature of polymeric backbone plays also a relevant role. 

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