Chemical reaction oscillatory

IIIK, C, K) Nair, P. K. R., Mittal, A., Srinivasulu, K. Chemical Oscillatory Reactions with and... 

Chemical reaction network is a typical example of complexity, where the reactants can interact in a variety of ways depending on the nature of interaction (chemical as well as non-chemical). Oscillatory reactions involve a number of steps, including positive and negative feedbacks. The complexity leads to periodic as well as aperiodic oscillations (multi-periodic, bursting/intermittency sequential oscillations separated by a time pause, relaxation and chaotic oscillations). The mechanism is usually determined by non-linear kinetics and computer modelling. Once the reaction mechanism has been postulated, the non-linear time-dependent kinetic equation can be formulated in terms of concentrations of different reactants, which would yield a multi-variable equation. Delay differential equations are sometimes used to characterize oscillatory behaviour as in economics (Chapter 14). 

Tomasi, R., Noel, J.M., Zenati, A., Ristori, S., Rossi, F., Cabuil, V., Kanoufi, F., Abou-Hassan, A. Chemical communication between liposomes encapsulating a chemical oscillatory reaction. Chem. Sci. 5(5), 1854-1859 (2014)... 

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

Gray, B. F. (1974). Kinetics of oscillatory reactions. In Reaction kinetics specialist periodical reports, (ed, P. G. Ashmore), pp. 309-86. The Chemical Society, London. 

This chapter introduces the simplest chemical kinetic scheme for an isothermal oscillatory reaction in a closed system. This model scheme is used to illustrate concepts of very general importance and applicability. A mathematically deeper analysis is given in chapter 3. 

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. 

The wide range of reaction systems, catalysts, and reactors that exhibit oscillatory reaction rates reinforces the motivation for research in this field. Oscillations may be lurking in every heterogeneous catalytic system (one might speculate that every heterogeneously catalyzed reaction might show oscillations under the appropriate conditions), and it is crucial to know about this possibility when engineering a chemical process. 

V.Gaspar and K.Showalter, The Oscillatory Reaction. Empirical Rate Law Model and Detailed Mechanism, Journal of the American Chemical Society,... 

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. 

Classification of oscillations in chemical systems will be made in terms of three groupings chemical reactions, chemical elements, and oscillatory mathematical solutions. In the first grouping an enumeration of different reactions , are considered. In the second, a listing of those chemical elements which take part in oscillatory reactions are considered. Finally, the oscillatory solutions of the mathematical model represented by the rate equations are classified on the basis of known examples. 

A number of chemical reactions were recognized in the early part of the century. Some of these have inspired chemists to reevaluate the oscillatory reactions. 

III A) 1967 Lindblad, P., Degn, H. A Compiler for Digital Computation in Chemical Kinetics and its Application to Oscillatory Reaction Schemes, Acta Chem. Scand. vol. 21, 791-800 (III H) 1910-1 Lotka, A. Contribution to the Theory of Periodic Reactions, J. Phys. Chem. vol. 14, 271-274... 

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. ... 

The references pertaining to chemical reactions will be given in Chapters 5 and 6. An exception, apart from a paper by Swinney, is the cited article by Winfree, describing the history of the Belousov-Zhabotinskii oscillatory reaction. The remaining references deal with philosophical problems. 

We discussed some aspects of the responses of chemical systems, linear or nonlinear, to perturbations on several earlier occasions. The first was the responses of the chemical species in a reaction mechanism (a network) in a nonequilibrium stable stationary state to a pulse in concentration of one species. We referred to this approach as the pulse method (see chapter 5 for theory and chapter 6 for experiments). Second, we studied the time series of the responses of concentrations to repeated random perturbations, the formulation of correlation functions from such measurements, and the construction of the correlation metric (see chapter 7 for theory and chapter 8 for experiments). Third, in the investigation of oscillatory chemical reactions we showed that the responses of a chemical system in a stable stationary state close to a Hopf bifurcation are related to the category of the oscillatory reaction and to the role of the essential species in the system (see chapter 11 for theory and experiments). In each of these cases the responses yield important information about the reaction pathway and the reaction mechanism. 

We now turn to our application of MSIMPC to examine the behavior of an oscillatory reaction. To compare experimental kinetic results to theoretical chemical mechanisms, the differential equations derived from the mechanism must be solved. The Oregonator model, which is a simple model proposed to explain the oscillatory behavior of the Belousov-Zhabotinsky (BZ) reaction, is a typical case. It involves five coupled differential equations and five unknown concentrations. We do not discuss details of this mechanism or the overall BZ reaction here, since it has received considerable attention in the chemical literature. 

The differential equations are stiff that is, several processes are going on at the same time, but at widely differing rates. This is a common feature of chemical kinetic equations and makes the numerical solution of the differential equations difficult. A steady state is never reached, so the equations cannot be solved analytically. Traditional methods, such as the Euler method and the Runge-Kutta method, use a time step, which must be scaled to fit the fastest process that is occurring. This can lead to large number of iterations even for small time scales. Hence, the use of Stella to model this oscillatory reaction would lead to an impossible situation. 

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. 

The use of microemulsions or reverse micelles as media for chemical and enzymatic reactions has been reviewed in recent years [20,37,38]. Microemulsions, including those based on organogels, are also useful media for enzyme-catalyzed synthetic reactions [37,39-43] and for preparation of nanoparticles [44]. In a very different direction, Vanag and Hanazaki [45] showed that the ferroin-catalyzed Belousov -Zhabitinskii oscillatory reaction exhibits frequency-multiplying bifurcations in reverse AOT microemulsions in octane, A clear understanding of reactivity in microemulsions and insight into how to optimize the experimental conditions requires kinetic models with predictive power. We focus attention primarily on this problem. 

Oscillatory reactions are a typical class of phenomena, which display unusual features. After the discovery of Belousov-Zhabotinskii (B-Z) reaction, there has been a tremendous flurry of activity [1] and a large number of such reactions have been discovered during recent years. Biochemical reactions [2-10] such as glycolytic oscillations and peroxidase catalysed oxidation of nicotinamide adenosine deoxyhydrogenase (NADH) have also generated considerable interest. The interest in such reactions is stiU sustained in view of their importance in understanding cardiac and neuronal oscillations. In the case of many oscillatory chemical reactions [1], detailed reaction mechanisms have been postulated and verified with the help of numerical computation. This has also been particularly so for B-Z reaction where Field-Koros-Noyes (FKN) mechanism [11] has been invoked. 

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