Bzs systems

The behaviour of the BZ system ean be modelled semi-quantitatively by the oregonator model [15] ... 

Figure A3.14.9. Reaction-diflfiision structures for an excitable BZ system showing (a) target and (b) spiral waves. (Courtesy of A F Taylor.)...

In order to understand the BZ system Field, Koros and Noyes developed the so-called FKN mechanism. From this, Field and Noyes later derived the Oregonator model, an especially convenient kinetic model to match individual experimental observations and predict experimental conditions under which oscillations might arise. 

The unbounded domain causes difficulties, on the one hand, via continuous spectrum which may - and does - interfere with the pure point spectrum required for our bifurcation analysis. The unbounded domain is necessary, on the other hand, to correctly incorporate the Euclidean symmetry of the problem under translations and rotations. In section 3.2 below we will specifically address competing and coexisting pinning and drifting phenomena. Such phenomena are predicted for the light-sensitive BZ system, when full Euclidean symmetry is broken towards a mere translational lattice symmetry, by choosing a spatially periodic lighting. 

Application of one-channel feedback control to spiral waves in the light-sensitive BZ system allows to observe the discrete set of stable resonant attractors experimentally [21, 30, 43, 46]. Note, that Eq. (9.23) for the radius of the resonance attractor contains only one medium dependent parameter (p, which specifies the direction of the resonance drift. To avoid a rather complicated experimental procedure to determine this value, the obtained experimental data were fitted to the theoretically predicted linear dependence (9.23) using p = —0.31. The results are shown in Fig. 9.3 by dashed lines. Then, the boundaries of the basin of attraction were specified in accordance with Eq. (9.24) (solid lines in Fig. 9.3). 

Single or periodic pulse perturbation effects on the BZ reaction, and the influence of delay time in a BZ system in a CSTR when the concentration of the input is controlled by the concentration of a reaction species have been studied. The BZ reaction has been studied using CH3COCH2COCH3 as substrate in a pair of CSTR coupled by mass flow between them. Ferroin and Ce are often used together in BZ systems. A study of the kinetics of reaction between Ce and ferroin shows that [Fe(II)(bipy)l ] decreases to a minimum, then increases to a maximum before finally decreasing. A mechanism involving an iron(IV) species is proposed. The effect of added Ag" has been a topic of controversy. Further work has appeared, and the dispute has been resolved. The problem concerned the value to be assigned (10 -10 s ) to the rate constant for the... 

The BZ system may be viewed as a medium that can process information for instance, an excess of a chemical species at a point of die reactor may be treated as 1 (or true"), while its deficit as 0 (or false"). 

Pelle et al. have examined how water-soluble alcohols affect the BZ system (4S). Lombardo et al. studied the effects of polyethylene glycol on the BZ system (chapter 21 of this volume). 

The present work is the next step where we have undertaken a systematic study of the perturbed BZ system with an alcoholic and a nonalcoholic polymer, namely polyethylene glycol with different molecular weights and polyethyleneglycol dimethyletiier (MPEG), respectively. The dynamical behaviour of the BZ system has been monitored by means of CO2 evolution rate and spectrophotometric measurements. Moreover, for the sake of comparison we have also performed spectrophotometric measurements in the presence of etiiylene glycol. 

The current study utilizes two complementaiy techniques to monitor the behaviour of the BZ system in the absence and presence of additives CO2 evolution rate measurements (6), which reflects the rate of the overall reaction, and UV-vis spectrophotometric measurements. 

Figure 1 shows typical spectrophotometric and CO2 evolution measurements of an unperturbed and a polymer-perturbed BZ system. The experimental results obtained with the two different techniques are in fair agreement. 

These findings suggest that there should be certain reaction(s) of the polymer which does not take place with the monomer in the BZ reaction. In that case PEG perturbs the BZ system not only by its reactive side groups, Le. the... 

Figure 2. Plot of the length of the induction period (IP) as a function of the additive concentration for the perturbed BZ system with (V and W) EG, (A and A) PEG-400, (O) PEG-900, and M) PEG-2000, (O and MPEG-2000, Open andfilled symbols refer to Ce(IV) absorbance and CO2 evolution...

What type of reactions of die polymer backbone can we expect in a BZ system First of all it is known (7, 8) that Ce(IV) can react with PEG. The reaction leads to the formation of free radicals... 

This reaction scheme implies that an extra source for the intermediates HOBr and HBr02 appears in the BZ system. As HBr02 is the autocatalytic intermediate its production enhances the positive feedback loop, which would lead to an increase in the IP. (This is because turning off the autocatalytic HBr02 production at the end of the IP becomes more difficult.) On the other hand the inflow of HOBr would decrease the IP since HOBr brominates the malonic acid (R31, for the reactions of the unperturbed BZ system we follow the notations of the MBM model) ... 

Presently we have no exact values for the rate constants of the polymeric reactions (P2)-(P5) however, these measurements are in progress. Also some modifications in the MBM mechanism can be expected 1,4), Nevertheless, the present semiquantitative calculations applying estimated rate constants prove that the assumed mechanism of the polymeric perturbations qualitatively predicts the observed perturbation effects due to the polymers. Simulation results are shown in Figure 4. In Figure 4A Ce(IV) oscillations of the unperturbed BZ system are depicted. The perturbation effect due to the polymer backbone reaction is shown separately in Figure 4B. It causes a shortening of the induction... 

Figure 4, Ce(IV) concentration vs. time diagrams in a BZ system calculated with the MBM mechanism. A) Unperturbed system. Initial concentrations [MA] = 0.1 moldm [KBrOs] = 0.03 moldm, [Ce(lV)J = 410 moldm [H2SO4] = / mohdm (See Fig. lA for comparison). B) The same system as in A) but perturbed with 0.015 mol dm polymer (regarding backbone reactions only). kp2= 400 dm mot s It is assumed that the rate determining step of process (P3)+(P4) leading to HOBr is a diffusion controlled radical-radical recombination reaction (kp3=l(f dm mol s ). C) The same system as in A) but perturbed with the alcoholic endgroup reaction exclusively. Bromous acid inflow = 6 10 dm mor s due to (P5) was regarded to be independent of time. D) Combination of the two perturbations shown in B) and C).

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