BZ reactions

The BZ reaction involves the oxidation of an organic molecule (citric acid, malonic acid (MA)) by an... 

The reaction involving chlorite and iodide ions in the presence of malonic acid, the CIMA reaction, is another that supports oscillatory behaviour in a batch system (the chlorite-iodide reaction being a classic clock system the CIMA system also shows reaction-diffusion wave behaviour similar to the BZ reaction, see section A3.14.4). The initial reactants, chlorite and iodide are rapidly consumed, producing CIO2 and I2 which subsequently play the role of reactants . If the system is assembled from these species initially, we have the CDIMA reaction. The chemistry of this oscillator is driven by the following overall processes, with the empirical rate laws as given ... 

Figure A3.14.15. The difTerential flow-induced chemical instability (DIFICI) in the BZ reaction. (Reprinted with pennission from [44], C5 The American Physical Society.)...

The existence of chaotic oscillations has been documented in a variety of chemical systems. Some of tire earliest observations of chemical chaos have been on biochemical systems like tire peroxidase-oxidase reaction [12] and on tire well known Belousov-Zhabotinskii (BZ) [13] reaction. The BZ reaction is tire Ce-ion-catalyzed oxidation of citric or malonic acid by bromate ion. Early investigations of the BZ reaction used tire teclmiques of dynamical systems tlieory outlined above to document tire existence of chaos in tliis reaction. Apparent chaos in tire BZ reaction was found by Hudson et a] [14] aiid tire data were analysed by Tomita and Tsuda [15] using a return-map metliod. Chaos was confinned in tire BZ reaction carried out in a CSTR by Roux et a] [16, E7] and by Hudson and... 

Figure C3.6.4(a) shows an experimental chaotic attractor reconstmcted from tire Br electrode potential, i.e. tire logaritlim of tire Br ion concentration, in tlie BZ reaction [F7]. Such reconstmction is defined, in principle, for continuous time t. However, in practice, data are recorded as a discrete time series of measurements (A (tj) / = 1,...

Figure C3.6.4 Single-handed chaotic attractor and next-amplitude map reconstmcted from experimental data for tire BZ reaction, (a) The reconstmcted attractor projected onto tire + x)) plane (see tire text for a...

This map has a single quadratic extremum, similar to tliat of tire WR model described in detail earlier. Such maps (togetlier witli tire technical constraint of negative Schwarzian derivative) [23] possess universal properties. In particular, tire universal (U) sequence in which tire periodic orbits appear [24] was observed in tire BZ reaction in accord witli tliis picture of tire chemical dynamics. 

Figure C3.6.11 Defect-mediated turbulence in tire BZ reaction, (a) Spatial stmcture close to tire instability, (b) Fully developed spatio-temporal turbulence. The control parameter is tire concentration of H2SO4 in tire feed reactor. Reproduced by pennission from Ouyang and Flesselles [501.

In some cases, potassium carbonate is superior to DBU and tetramethylguanidine (TMG) in the BZ reaction. Thus 7 reacts with TosMIC (19) in the presence of K2CO3 to afford pyrrole 20 in excellent yield. The yield of 20 using DBU is 62%. 

Ono and Lash have been the two pioneers in applying the BZ reaction to the synthesis of pyrroles and, particularly, with applications to the synthesis of novel fused and other porphyrins. Although the concept was recognized by Barton and Zard, Ono and Lash independently discovered the conversion of 2-pyrrolecarbo ylates, prepared by the BZ reaction, into porphyrins by what is now a standard protocol (1. LiAlfL 2. 3. 

Other workers have employed a BZ reaction and subsequent chemistry to synthesize porphyrins. Likewise, the BZ reaction has been extended to the... 

The often inaccessible and labile isoindoles can be accessed by the BZ reaction, as can be heteroisoindoles, such as 32. " Novel pyrroles fused to rigid bicyclic skeleta are readily crafted via a BZ reaction. Certain nitroheterocycles undergo the BZ... 

There exist many different CA models exhibiting BZ-like spatial waves. One of the simplest, and earliest, described in the next section, is a model proposed by Greenberg and Hastings in 1978 [green78], and based on an earlier excitable media model by Weiner and Rosenbluth [weiner46]. One of the earliest and simplest mathematical models of the BZ reaction, called the Orcgonator, is due to Field and Noyes [field74]. 

Fig. 8.14-a Greenberg-llastings model of the BZ-reaction 320 x 200 lattice after 50 iter-a-tion steps, starting from a random initial state consisting of 5% active and 5% refractory sites. 

This subject has been reviewed by Noyes and Field,8 who give reference to the original formulation as well as a more explicit treatment. The presentation here will be given not in general terms but by means of one striking example, the oxidation of malonic acid by bromate ions catalyzed by cerium(IV). It is called the Belousov-Zhabotinsky (or BZ) reaction, after its discoverers.9 The stoichiometry of the reaction with excess malonic acid is... 

This reaction can oscillate in a well-mixed system. In a quiescent system, diffusion-limited spatial patterns can develop, but these violate the assumption of perfect mixing that is made in this chapter. A well-known chemical oscillator that also develops complex spatial patterns is the Belousov-Zhabotinsky or BZ reaction. Flame fronts and detonations are other batch reactions that violate the assumption of perfect mixing. Their analysis requires treatment of mass or thermal diffusion or the propagation of shock waves. Such reactions are briefly touched upon in Chapter 11 but, by and large, are beyond the scope of this book. 

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... 

Mox represents the metal ion catalyst in its oxidised form (Ceexperimentally determined empirical rate law and does clearly not comprise stoichiometrically correct elementary processes. The five reactions in the model provide the means to kinetically describe the four essential stages of the BZ reaction ... 

Figure 3-36. The BZ reaction as represented by the Oregonator model. The species Br, HBr02 and Mox display regular oscillations while the species BrO3, HOBr and MA change their concentrations slowly and more steadily.

The Belusov-Zhabotinsky (BZ) reaction is catalyzed by a different mechanism when low-reduction-potential couples such as [Fe(phen)3] +/[Fe(phen)3] + are employed. Experimental results for the BZ reaction with this couple in aerated conditions are compared with satisfactory agreement to a model calculation based on an 18-step skeleton mechanism, which includes reactions of organic radicals and molecular oxygen. 

Nonlinear Dynamics of the BZ Reaction A Simple Experiment that Illustrates Limit Cycles, Chaos, Bifurcations and Noise 258... 

The BZ Reaction Experimental and Model Studies in the Physical Chemistry Laboratory 259... 

In closed system studies of the BZ reaction, three principal modes of homogeneous oscillations have been identified (1) low-frequency, large amplitude, highly nonlinear (i.e., nonharmonic) relaxation oscillations... 

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. 

In order to understand such complex oscillatory modes in terms of the underlying nonequilibrium chemistry, it is convenient to begin with a simplified version of the full BZ mechanism15 which describes the main features of earlier experimental observations of the closed BZ reaction. 

Here I consider the Field-Noyes model15 of the BZ reaction. With reverse reactions included,4b it takes the form ( model F )... 

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