Other Oscillatory Reactions

Add 5 cm 1 M sulphuric acid to 20 cm acetone followed by 20 cm O.I M potassium iodate, S cm of 100 volume hydrogen peroxide and 5 cm 0.075 M manganese sulphate solution. Use a magnetic stirrer and note the oscillation of the colour from yellow to colourless. Otherwise record the mV meter output when it is connected to the platinum and the calomel electrode as above. 

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Since the discovery of the Belousov-Zhabotinskii (B-Z) reaction a large number of variations of this reaction has been investigated by numerous researchers. Both experimental and theoretical investigations outnumber those for any other oscillatory reaction. The reason for this extensive interest comes from the fact that the B-Z reaction is very rich in its interesting dynamical behavior and its variations are quite extensive. In this section research done during the period of 1980-82 is discussed briefly. 

The relative fluctuations in Monte Carlo simulations are of the order of magnitude where N is the total number of molecules in the simulation. The observed error in kinetic simulations is about 1-2% when lO molecules are used. In the computer calculations described by Schaad, the grids of the technique shown here are replaced by computer memory, so the capacity of the memory is one limit on the maximum number of molecules. Other programs for stochastic simulation make use of different routes of calculation, and the number of molecules is not a limitation. Enzyme kinetics and very complex oscillatory reactions have been modeled. These simulations are valuable for establishing whether a postulated kinetic scheme is reasonable, for examining the appearance of extrema or induction periods, applicability of the steady-state approximation, and so on. Even the manual method is useful for such purposes. 

Searching for other oscillatory autoxidation reactions led Druliner and Wasserman to use cyclohexanone as a substrate instead of benzalde-hyde (168). Unlike the simple stoichiometry found for the benzaldehyde reaction, the ketone gives at least six or more products, and the relative amounts of these vary substantially with the experimental conditions (Scheme 7). 

In chapters 2-5 two models of oscillatory reaction in closed vessels were considered one based on chemical feedback (autocatalysis), the other on thermal coupling under non-isothermal reaction conditions. To begin this chapter, we again return to non-isothermal systems, now in a well-stirred flow reactor (CSTR) such as that considered in chapter 6. 

Finally, the quest to develop mechanistic explanations for these varied and fascinating phenomena can succeed only if more data become available on the component processes. Kinetics studies of the reactions which make up a complex oscillatory system are essential to its understanding. In some cases, traditional techniques may be adequate, though in many others, fast reaction methods will be required. There also appears to be some promise in developing an analysis of the relaxation of flow systems in non-equilibrium steady states as a technique to complement equilibrium relaxation techniques. 

The vast body of literature on electrochemical oscillations has revealed a quite surprising fact dynamic instabilities, manifesting themselves, for example, in bistable or oscillatory reaction rates, occur in nearly every electrochemical reaction under appropriate conditions. An impressive compilation of all the relevant papers up to 1993 can be found in a review article by Hudson and Tsotsis. This finding naturally raises the question of whether there are common principles governing pattern formation in electrochemical systems. In other words, are there universal mechanisms leading to self-organization phenomena in systems with completely different chemical compositions, and thus also distinct rate laws ... 

In the literature there is a small number of reactions exhibiting oscillations, observed experimentally, which motivated a vast number of studies either devising a model for the reaction scheme or analyzing the small variations thereof. Although oscillatory behavior has been recognized in the past by a handful of chemists, it is recently that oscillatory behavior of chemical systems attracted considerable attention. As a result, studies carried out by various groups of researchers have been reviewed and summarized in review articles. Some of these reviews are more comprehensive than others and cover multiple examples of oscillatory reactions. A partial list of these articles is given in Table II with some annotations. 

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

Examples of self-sustained oscillatory systems are electronic circuits used for the generation of radio-frequency power, lasers, Belousov-Zhabotinsky and other oscillatory chemical reactions, pacemakers (sinoatrial nodes) of human hearts or artificial pacemakers that are used in cardiac pathologies, and many other natural and artificial systems. An outstanding common feature of such systems is their ability to be synchronized. 

Oscillatory reactions require a separate analysis, which is presented in detail. Responses of nonlinear systems to pulses or other perturbations are treated in some generality. The concluding chapter gives a brief introduction to bioinformatics, including several methods for determining reaction mechanisms. 

Most of the methods outlined above are suitable for obtaining information on oscillatory reaction networks. As pointed out in several other chapters in this book, related methods can be used for determination of causal connectivities of species and deduction of mechanims in general nonoscillatory networks. Pulses of species concentration by an arbitrary amount have been proposed (see chapter 5) and experimentally applied to glycolysis (see chapter 6). Random perturbation by a species can be used and the response evaluated by means of correlation functions (see chapter 7) this correlation metric construction method has also been tested (see chapter 8). Another approach to determining reaction mechanisms by finding Jacobian matrix elements is described in Mihaliuk et al. [69]. 

In this section the whole field of exotic dynamics is considered this term includes not merely oscillating reactions but also oligo-oscillatory reactions, multiple steady states, spatial phenomena such as travelling reaction waves, and chaotic systems. All of these have common roots in autocatalytic processes. This area has continued to expand, and there is a case for treatment in future volumes by a specialist reviewer. An entry into the literature can be gained from a recent series of articles in a chemical education joumal, and in a festschrift issue in honor of Professor R. M. Noyes. Other useful sources are a volume of conference proceedings, and a volume of lecture preprints of a 1989 conference. The present summary is concerned with the chemical rather than the mathematical aspects of the topic. 

In fact, Oregonator (reaction mechanism for B-Z reaction proposed for the first time) provides only a skeleton mechanism which was improved and modified at later stages. Although the subject has advanced considerably, one is still interested in predicting and understanding other features of oscillatory reaction such as bistability, multiperiodicity and chaos including its generation and control. 

As in other cases of study of elementary or slightly complex reactions, it is also necessary to confirm the existence of the intermediate in oscillatory reactions by using various techniques such as UV, IR Mass, ESR, Spectra and HPCL. An acceptable test of the level of understanding of a mechanism is by computer simulation. Such a test is by no means unequivocal, but can often reveal gross deficiencies in assumption about a mechanism [38]. More rigorous test of the mechanism would be its capability to predict other characteristic features such as the bifurcation point, aperiodicity and chaos. 

The net stoichiometric equation can be the same for several pathways in the other more complex system. Such kind of reaction mechanism possesses the model of the mechanism for the Bray-Liebhafsky oscillatory reaction, which will be considered later. 

Although some of the fimdamental discoveries in nonlinear chemical dynamics were made at the beginning of the twentieth century and arguably even earlier, the field itself did not emerge until the mid-1960 s, when Zhabotinsky s development (1) of the oscillatory reaction discovered by Belousov (2) finally convinced a skeptical chemical community that periodic reactions were indeed compatible with the Second Law of Thermodynamics as well as all other known rules of chemistry and physics. Since the discovery of the Belousov-Zhabotinsky (BZ) reaction, nonlinear chemical dynamics has grown rapidly in both breadth and depth (3). 

Guided by this model study, we can summarize the steps that one should take in constructing a mechanism for an oscillatory, or other complex, reaction system. While it may not be feasible to follow this recipe step-by-step in every case, adhering to the spirit of this route will help prospective mechanism builders to avoid pitfalls and to come up with plausible schemes for further testing in a relatively expeditious fashion. Here is our recommended approach ... 

Appendix A) for the Ginzburg-Landau system is very suggestive this inequality may be viewed as a condensed expression of the universal mechanism of the phase instability in oscillatory reaction-diffusion systems not restricted to the vicinity of the Hopf bifurcation point. Remember that Ci measures the degree to which the diffusion matrix of the starting reaction-diffusion equations deviates from a scalar. On the other hand, C2 represents how strongly the frequencies of the individual local oscillators depend on their amplitudes this is obvious if one expresses (2.4.15) as... 

In oscillatory reactions the Gibbs free energy of the overall reaction is oscillatory, the rate is oscillatory, and so is the dissipation. There now appears a new quantity, the phase relation between the oscillatory Gibbs free energy and the oscillatory rate. The dissipation, which is the product of these two quantities (see (13.1) and (13.6) in Chap. 13) depends critically on this phase relation and is controlled by it. There is an analogy here between DC and AC circuits on the one hand, and reactions in time-independent stationary states and in oscillatory states, on the other. We return to that in-... 

The evolution of a. star after it leaves the red-giant phase depends to some extent on its mass. If it is not more than about 1.4 M it may contract appreciably again and then enter an oscillatory phase of its life before becoming a white dwarf (p. 7). When core contraction following helium and carbon depletion raises the temperature above I0 K the y-ray.s in the stellar assembly become sufficiently energetic to promote the (endothermic) reaction Ne(y,a) 0. The a-paiticle released can penetrate the coulomb barrier of other neon nuclei to form " Mg in a strongly exothermic reaction ... 

A mechanical system, typified by a pendulum, can oscillate around a position of final equilibrium. Chemical systems cannot do so, because of the fundamental law of thermodynamics that at all times AG > 0 when the system is not at equilibrium. There is nonetheless the occasional chemical system in which intermediates oscillate in concentration during the course of the reaction. Products, too, are formed at oscillating rates. This striking phenomenon of oscillatory behavior can be shown to occur when there are dual sets of solutions to the steady-state equations. The full mathematical treatment of this phenomenon and of instability will not be given, but a simplified version will be presented. With two sets of steady-state concentrations for the intermediates, no sooner is one set established than the consequent other changes cause the system to pass quickly to the other set, and vice versa. In effect, this establishes a chemical feedback loop. 

In this short initial communication we wish to describe a general purpose continuous-flow stirred-tank reactor (CSTR) system which incorporates a digital computer for supervisory control purposes and which has been constructed for use with radical and other polymerization processes. The performance of the system has been tested by attempting to control the MWD of the product from free-radically initiated solution polymerizations of methyl methacrylate (MMA) using oscillatory feed-forward control strategies for the reagent feeds. This reaction has been selected for study because of the ease of experimentation which it affords and because the theoretical aspects of the control of MWD in radical polymerizations has attracted much attention in the scientific literature. 

An important class of cycles with non-linear behavior is represented by situations when coupling occurs between cycles of different elements. The behavior of coupled systems of this type has been studied in detail by Prigogine (1967) and others. In these systems, multiple equilibria are sometimes possible and oscillatory behavior can occur. There have been suggestions that atmospheric systems of chemical species, coupled by chemical reactions, could exhibit multiple equilibria under realistic ranges of concentration (Fox et ai, 1982 White, 1984). However, no such situations have been confirmed by measurements. 

The harmonic oscillator is an important system in the study of physical phenomena in both classical and quantum mechanics. Classically, the harmonic oscillator describes the mechanical behavior of a spring and, by analogy, other phenomena such as the oscillations of charge flow in an electric circuit, the vibrations of sound-wave and light-wave generators, and oscillatory chemical reactions. The quantum-mechanical treatment of the harmonic oscillator may be applied to the vibrations of molecular bonds and has many other applications in quantum physics and held theory. 

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