Period chemical oscillator

Simple periodic chemical oscillation may now be said to be reasonably well understood. More complex behavior can arise when a single oscillator is pushed into new realms or when it is coupled either to other oscillators or to external influences. Some chemical oscillators that are simply periodic under one set of conditions can exhibit complex, multi-peaked, periodic or even aperiodic, chaotic (14) behavior at other concentrations and flow rates in an open reactor. Some examples of chaotic oscillations in the chlorite-thiosulfate system are shown in Figure 4. Coupling two or more reactions together can result in the... 

Periodic chemical oscillations may be complex, and complex oscillations need not always be periodic. These observations are illustrated for the chlorite-thiosulfate reaction in Figures 10 and 11, where we see first complex periodic and then aperiodic or chaotic oscillation. 

Oscillations have been observed in chemical as well as electrochemical systems [Frl, Fi3, Wol]. Such oscillatory phenomena usually originate from a multivariable system with extremely nonlinear kinetic relationships and complicated coupling mechanisms [Fr4], Current oscillations at silicon electrodes under potentio-static conditions in HF were already reported in one of the first electrochemical studies of silicon electrodes [Tul] and ascribed to the presence of a thin anodic silicon oxide film. In contrast to the case of anodic oxidation in HF-free electrolytes where the oscillations become damped after a few periods, the oscillations in aqueous HF can be stable over hours. Several groups have studied this phenomenon since this early work, and a common understanding of its basic origin has emerged, but details of the oscillation process are still controversial. 

Schneider, F. W. (1985). Periodic perturbations of chemical oscillators experiments. Ann. Rev. Phys. Chem., 36, 347-78. 

For a chemical reaction system, the characteristics of the periodic solutions are uniquely determined by the kinetic constants as well as by the concentrations of the reactants and final products. Starting from the neighborhood of steady state as an initial condition, the system asymptotically attains a closed orbit or limit cycle. Therefore, for long times, the concentrations sustain periodic undamped oscillations. The characteristics of these oscillations are independent of the initial conditions, and the system always approaches the same asymptotic trajectory. Generally, the further a system is in the unstable region, the faster it approaches the limit cycle. 

Another example of an oscillating reaction is provided by the Bray reaction, the first identified homogeneous isothermal chemical oscillator, which is a complex reaction of iodate, iodine, and hydrogen peroxide. As hydrogen peroxide decomposes to oxygen and water, the resulting rate of the evolution of oxygen and I2 vary periodically. 

Relaxation limit of a chemical oscillator) Analyze the model for the chlorine dioxide-iodine-malonic acid oscillator, (8.3.4), (8.3.5), in the limit b i. Sketch the limit cycle in the phase plane and estimate its period. 

IIIL) Orban, M., Epstein, I. R. Systematic Design of Chemical Oscillators, Part 13 1982-1 Complex Periodic and Aperiodic Oscillations in the Chloride Thiosulphate Reaction. J. Phys. Chem. 86, 3907-3910... 

As a certain concentration of CHBr (C02H)2 is needed for reaction 9 to occur long induction period for oscillations is expected, a phenomenon, which is also observed experimentally. During this induction period, the concentration of Br" is small and mechanism II dominates due to the slow conversion of Ce4+ into Ce3+ and the accumulation of brommalonic acid (reaction 8). Step 9 (8.71) results in the change of the blue color of solution to red resetting the chemical clock for the next oscillation. In fact, the oxidized form of the catalyst can also react directly with malonic acid, so there may be less than one bromide ion per cerium (III) ion produced. 

What is the link between chemical oscillations and periodic phenomena observed in living systems Is it possible to uncover the molecular... 

The peroxidase reaction provides another prototype for periodic behaviour and chaos in an enzyme reaction. As noted by Steinmetz et al. (1993), in view of its mechanism based on free radical intermediates, this reaction represents an important bridge between chemical oscillations of the Belousov-Zhabotinsky type, and biological oscillators. In view of the above discussion, it is noteworthy that the model proposed by Olsen (1983), and further analysed by Steinmetz et al. (1993), also contains two parallel routes for the autocatalytic production of a key intermediate species in the reaction mechanism. As shown by experiments and accounted for by theoretical studies, the peroxidase reaction possesses a particularly rich repertoire of dynamic behaviour (Barter et al, 1993) ranging from bistability (Degn, 1968 Degn et al, 1979) to periodic oscillations (Yamazaki et al, 1965 Nakamura et al, 1969 ... 

This example shows that mixed-mode oscillations, while arising from a torus attractor that bifurcates to a fractal torus, give rise to chaos via the familiar period-doubling cascade in which the period becomes infinite and the chaotic orbit consists of an infinite number of unstable periodic orbits. Mixedmode oscillations have been found experimentally in the Belousov-Zhabotin-skii (BZ) reaction 2.84 and other chemical oscillators and in electrochemical systems, as well. Studies of a three-variable autocatalator model have also provided insights into the relationship between period-doubling and mixedmode sequences. Whereas experiments on the peroxidase-oxidase reaction have not been carried out to determine whether the route to chaos exemplified by the DOP model occurs experimentally, the DOP simulations exhibit a route to chaos that is probably widespread in the realm of nonlinear systems and is, therefore, quite possible in the peroxidase reaction, as well. 

Oscillatory States in the CSTR limit Cycles.— The nature of the diemically open system makes it an ideal vehicle for studying reactions which odiibit chemical oscillations. The continuous supply of reactants diminates damping from reactant depletion inevitable in closed systems and permits the experimental establishment of true limit-cycle behaviour. However, not all oscillations in the CSTR need be kinetically interesting in their origin (e.g. the periodic variations in temperature and concentrations in reactors run with feedback control More importantly from the combustion researcher s viewpoint, oscillations may arise between multiple stable steady states of any normal exothermic reaction because of restric-... 

The study of nonlinear chemical dynamics begins with chemical oscillators - systems in which the concentrations of one or more species increase and decrease periodically, or nearly periodically. While descriptions of chemical oscillators can be found at least as far back as the nineteenth century (and chemical oscillation is, of course, ubiquitous in living systems), systematic study of chemical periodicity begins with two accidentally discovered systems associated with the names of Bray (2) and of Belousov and Zhabotinsky (BZ) 3,4), These initial discoveries were met with skepticism by chemists who believed that such behavior would violate the Second Law of Thermodynamics, but the development of a general theory of nonequilibrium thermodynamics (5) and of a detailed mechanism 6) for the BZ reaction brought credibility to the field by the mid-1970 s. Oscillations in the prototypical BZ reaction are shown in Figure 1. 

In these experiments, the volume of the confined gel is constant its main role is to damp hydrodynamical motions that would otherwise perturb the chemical intrinsic patterns. More recently it has been shown experimentally that the coupling of a volume phase transition with a chemical oscillator can generate a self-oscillating gel (i, 4). More precisely, if one of the chemical species taking part in the chemical reaction modifies the threshold for the phase transition, then the time periodic variation of this concentration can generate autonomous swelling-deswelling cycles of the gel even in absence of any external stimuli (5, 6). This device thus provides a novel biomimetic material with potential biomedical and technical applications. 

In the physical sciences, many natural and man-made systems exhibit instabilities, in particular, dampened, indefinitely periodic and undampened oscillations. Such oscillations are found in mechanical systems, electrical systems, biological systems and indeed chemical systems. Perhaps the most well-known chemical oscillations are those associated with the liquid phase redox systems, the Belousov-Zhabotinsky system which is cerium catalysed and the Briggs-Rauscher system which is manganese catalysed and their related chemistries [81], which, in addition to showing temporal oscillations, may show spatio-temporal oscillations as well in both 3D and 2D environments. Most of the conceptual foundations for this area can be traced back to the mathematician and computer scientist Alan Turing and his seminal paper in which he proposed the existence of aU these classes of chemical oscillations [82]. 

Another interesting feature is the failure to achieve a 100 % Sq population by exogenous redox compounds. Numerous chemicals have been tested. Among different substances NH2OH and NH2NH2 are widely used because they do permit a two digit phase shift of the period four oscillation of flash induced oxygen evolution (11). 

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