Chemical oscillators systematic design

Prior to our systematically designed oscillators, the inorganic oscillator most intensively studied was the BZ reaction. Examination of this reaction and the FKN mechanism reveals several features helpful to achieving an appreciation for the construction of a chemical oscillator. The driving force for the BZ reaction is the reduction of bromate and the associated oxidation of malonic acid (MA) to carbon dioxide. The stoichiometry is not that simple, however, since bromomalonic acid is also produced in the reaction, and can be oxidized to formic acid. A possible stoichiometry is... 

IIIL) De Kepper, P., Epstein, I. R., Kustin, K. Systematic Design of Chemical Oscillators... 

Iodate-Chlorite System, J. Am. Chem. Soc. 103, 2133-2134 (IIIL) De Kepper, P., Epstein, I. R., Kustin, K. Systematic Design of Chemical Oscillators 1981-2 Part 3. Bistability in the Oxidation of Arsenite by Iodate in Stirred Flow Reactor, J. Am. Chem. Soc. 103, 6121-6127... 

M. Orban, Ch. Dateo, P. De Kepper, and I. R. Epstein. Systematic design of chemical oscillators. 11. Chlorite oscillators new experimental examples, tristability, and preliminary classihcation. J. Am. Chem. Soc., 104 5911-5918, 1982. 

Citri, O. Epstein, I. R. Systematic design of chemical oscillators. 42. Dynamic behavior in the chlorite-iodide reaction a simplified mecfianism. J. Phys. Chem. 1987, 91, 6034—6040. 

Luo, Y Epstein, 1. R. Systematic design of chemical oscillators. 38. Stirring and premixing effects in the oscillatory chlorite-iodide reaction. J. Chem. Phys. 1986, 85, 5733-5740. 

Figure 4.8 Systematic design of a chemical oscillator, (a) The fundamental bistable system, with the steady-state concentration of. v shown as a function of the parameter X. Steady states SSI and SSII are two distinct, stable steady states. Dashed line shows third, unstable steady state, (b) The system in part a perturbed by a feedback species z. The actual value of X is A.Q. The arrows indicate effective increase in X caused by the perturbation, (c) Time course followed by x corresponding to the values of Xq and z illustrated in part b. (d) Phase diagram obtained when experiments like that shown in part b are performed at different levels of i. Panel (a) corresponds to r = 0.

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,... 

In Chapter 4, we discussed the role played by the cross-shaped phase diagram in the systematic design of chemical oscillators. A key element in that effort was the two-variable ODE model (Boissonade and De Kepper, 1980) ... 

Before I980, the only chemical oscillators of nonbio-logical origin had been discovered by chance or were variants of the two accidentally discovered systems. Since that time, experimental and theoretical advances have made it possible to systematically design new oscillating chemical reactions. 

The first system on which this approach was tried (De Kepper, Epstein and Kustin, [ 18]) employed two coupled autocatalytic reactions, chlorite plus iodide, and arsenite plus iodate, which have key intermediates in common. As Figure h shows, the chlorite-iodate-arsenite system did indeed prove to oscillate, constituting the first systematically designed chemical oscillator. More recently, by starting from the fundamental or minimal chlorite-iodide bistable system and adding different feedback species, it has been possible to generate a family of nearly 20 different chlorite-iodine species oscillators (Orb n et al., [19]). In addition, two iodine free chlorite oscillators involving thiosulfate (Orban, De Kepper and Epstein, [ 20] ) and bromate (Orban and Epstein, [21]) have been found. 

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