Chemically coupled Oscillators

Chemically coupled oscillation in batch reactor involving the use of two or more organic substrates in case of B-Z oscillator and Briggs-Rauscher [58] have been studied. Both systems exhibited a bust of oscillations, characteristic of one substrate followed by a quiescent period and then a bust of oscillations characteristic of the other substrate. 

To what extent are we justified in thinking of a chemically coupled oscillator system as consisting of the two independent subsystems plus a set of cross-reactions that provide the coupling A partial answer can be found in a mechanistic investigation of the bromate-chlorite-iodide reaction (Citri and Epstein, 1988). The mechanisms that had been derived for the bromate-iodide and chlorite-iodide systems in independent studies of these reactions are shown, respectively, in Tables 12.1 and 12.2. 

It is not difficult to understand why a chemically coupled oscillator system can display birhythmicity for some range of parameters. If the coupling is not too strong, it may distort the shape and location of the limit cycle and the range of... 

Chemically coupled oscillators can also give rise to chaotic behavior. Again, we choose an example from the bromate-chlorite-iodide system. Although this system may well show isolated regions of chaos, the best characterized chaotic behavior in this reaction occurs as part of a period-adding sequence in which, as the... 

The range of new reactions available offers the possibility of creating systems of chemically coupled oscillators [48]. For example. Fig. 8 illustrates the phenomenon of birhythmicity in the C102 -Br03 -r reaction [12], where the C102 -I" and Br03"-I oscillatory subsystems are coupled via the common species I". The phase diagram in Fig. 9 demonstrates some of the complexity possible in the dynamics of such systems. 

The concept of coupled oscillators is important from the viewpoint of understanding oscillatory phenomena in biochemical systems where the basic question relates to the type of dynamic behaviour when two are more such systems are coupled together. The concept of coupling is quite relevant in the context of spatial dissipative structures in cases where chemical oscillators are coupled through diffusion. 

Figure 12.2 Schematic diagram of an apparatus consisting of two CSTRs for studying physically coupled oscillating reactions. A needle valve controls the flow between the reactors. Inputs to the reactors are independently controlled. Drop detectors ensure that liquid flows out of the two reactors at the same rate so that there is no net mass transfer from one to the other. Reprinted, in part, with permission from Crowley, M. F. Epstein, I. R. 1989. Experimental and Theoretical Studies of a Coupled Chemical Oscillator Phase Death, Multistability, and In-Phase and Out-Of-Phase Entrainment, J. Phys. Chem. 93, 2496-2502. CC 1989 American Chemical Society.)...

A fascinating example of complex oscillation occurs in the bromate-chlorite-iodide chemically coupled system, where we observe periodic behavior consisting of one compound oscillation followed by n small amplitude oscillations. Trajectories for two of these C animals are shown in Figure 12.19. 

FitzHugh, R. (1969) Mathematical models of excitation and propagation in nerve. In Biological Engineering ed. by H. P. Schwan (McGraw-Hill, New York) p. 1 Fujii, H., Sawada, Y. (1978) Phase difference locking of coupled oscillating chemical systems. J. Chem. Phys. 69, 3830... 

Moreover, in this linear-response (weak-coupling) limit any reservoir may be thought of as an infinite number of oscillators qj with an appropriately chosen spectral density, each coupled linearly in qj to the particle coordinates. The coordinates qj may not have a direct physical sense they may be just unobservable variables whose role is to provide the correct response properties of the reservoir. In a chemical reaction the role of a particle is played by the reaction complex, which itself includes many degrees of freedom. Therefore the separation of reservoir and particle does not suffice to make the problem manageable, and a subsequent reduction of the internal degrees of freedom in the reaction complex is required. The possible ways to arrive at such a reduction are summarized in table 1. 

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". 

The vibrational motions of the chemically bound constituents of matter have fre-quencies in the infrared regime. The oscillations induced by certain vibrational modes provide a means for matter to couple with an impinging beam of infrared electromagnetic radiation and to exchange energy with it when the frequencies are in resonance. In the infrared experiment, the intensity of a beam of infrared radiation is measured before (Iq) and after (7) it interacts with the sample as a function of light frequency, w[. A plot of I/Iq versus frequency is the infrared spectrum. The identities, surrounding environments, and concentrations of the chemical bonds that are present can be determined. 

RAIRS spectra contain absorption band structures related to electronic transitions and vibrations of the bulk, the surface, or adsorbed molecules. In reflectance spectroscopy the ahsorhance is usually determined hy calculating -log(Rs/Ro), where Rs represents the reflectance from the adsorhate-covered substrate and Rq is the reflectance from the bare substrate. For thin films with strong dipole oscillators, the Berre-man effect, which can lead to an additional feature in the reflectance spectrum, must also be considered (Sect. 4.9 Ellipsometry). The frequencies, intensities, full widths at half maximum, and band line-shapes in the absorption spectrum yield information about adsorption states, chemical environment, ordering effects, and vibrational coupling. 

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