Feedback species

The Landolt reaction (iodate + reductant) is prototypical of an autocatalytic clock reaction. During the induction period, the absence of the feedback species (Irere iodide ion, assumed to have virtually zero initial concentration and fomred from the reactant iodate only via very slow initiation steps) causes the reaction mixture to become kinetically frozen . There is reaction, but the intemiediate species evolve on concentration scales many orders of magnitude less than those of the reactant. The induction period depends on the initial concentrations of the major reactants in a maimer predicted by integrating the overall rate cubic autocatalytic rate law, given in section A3.14.1.1. 

A vital constituent of any chemical process that is going to show oscillations or other bifurcations is that of feedback . Some intermediate or product of the chemistry must be able to influence the rate of earlier steps. This may be a positive catalytic process , where the feedback species enhances the rate, or an inhibition through which the reaction is poisoned. This effect may be chemical, arising from the mechanistic involvement of species such as radicals, or thermal, arising because chemical heat released is not lost perfectly efficiently and the consequent temperature rise influences some reaction rate constants. The latter is relatively familiar most chemists are aware of the strong temperature dependence of rate constants through, e.g. the Arrhenius law,... 

Figure 2. Feedback mode of the SECM operation, (a) The UME tip is far from the substrate, (b) Positive feedback species R is regenerated at the substrate, (c) Negative feedback Diffusion of R to the tip is hindered by the substrate.

Orban et al. (1982-2) discovered that in a CSTR within an extremely narrow range of flow rates and input concentrations a system containing Br03, Br" and Mn(II) or Ce(III) exhibits oscillations in the potential of either a Pt redox or Br- selective electrode. Existence of oscillations was predicted by the model calculations of Bar-Eli [Bar-Eli in Vidal and Pacault (1981) 228-239]. The bromate oscillators such as the B-Z reaction were derived from this fundamental system by adding feedback species which enlarges the region of critical space in which oscillations occur. 

Feedback species (those exerting indirect inhibitory effect on the cycle species by providing negative feedback on the autocatalytic cycle), denoted Z. 

Another way of seeing this important point is shown in Figure 4.8, where we depict (a) the underlying hysteresis loop associated with the species x, (b) the effect of adding the feedback species z, (c) the oscillatory behavior for a particular... 

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.

If step 4 succeeds, continue increasing z until the bistability vanishes and oscillation appears. If it fails, go back to step 3 and try a different feedback species. 

The team first established that the arsenite iodate reaction showed bistability in a CSTR (De Kepper et aL, 1981a). They then introduced chlorite as a feedback species and obtained oscillations as shown in Figure 4.10. Note, particularly in the trace of the iodide-selective electrode, the alternation between periods of slow concentration change and rapid jumps between pseudo-steady-state levels, similar to the behavior shown schematically in Figure 4.8c. 

In this method [40], one starts from an autocatalytic reaction and seeks conditions under which the system shows bistability in a CSTR. The key step is then to find a "feedback species" which modifies the effective value of one of the system constraints (usually an input concentration) by quite different amounts on the two bistable branches. If this effect is in the right... 

In particularly fortunate cases the feedback species is generated internally, and one need only manipulate the constraints of the bistable system (e.g., the flow rate) until the bistable region closes and oscillation appears beyond the critical point. The chlorite-iodide oscillator [8] is one example of such a system. 

Figure 5- Bistability and oscillation in a typical chemical system (see text), a) Simple bistability b) Effect (- -) of adding a feedback species c) Behavior of the system in b) as function of time d) Cross-shaped phase diagram.

Our systematic search procedure may thus be summarized as a) choose an autocatalyic reaction R b) run R in CSTR and seek conditions under which the system is bistable c) choose a feedback species Z which perturbs the system by different amounts on the two branches of steady states d) by increasing the input of Z into the CSTR, seek the critical point at which bistability disappears and oscillations begin. 

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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