Typical chemical oscillator

Equation rates A typical chemical oscillator consists of numbers of transitory reactions which can be explained with their differential equations. It is suggesting that the rate of change is taken place for all associated reactants, intermediates, and products during the oscillations. 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

The majority of chemical reactions exhibit a monotonic time course, but it is not unusual for concentrations of intermediates in a series of coupled reactions, such as the concentration of B in the sequence A —> B —> C, to rise and fall. Less often, but still in quite a number of well-documented cases, concentrations go up and down more than once, and reactions that exhibit this behavior are called oscillatory. Typically, such oscillations will eventually die out once some or all of the starting material has been consumed. However, some reactions can be kept to oscillate indefinitely by keeping their initial concentrations constant, i.e., by replenishing any reagent lost. 

We discuss below a few representative systems where (i) only bistability occurs and (ii) both bistability and oscillations occur. Bistability results for some typical chemical systems are discussed below. Quite a few different cases [6, 7] have earlier been discussed by Field and Burger [8]. 

Biological and physiological systems are typical complex systems, which provide examples of aperiodicity and chaos [1-7]. Aperiodic cardiac oscillations are reflected in ECG for different cases of arrhythmia Fig. (12.1). Similarly, chaotic, aperiodic and noisy oscillations are observed in EEC in specific cases as shown in Fig. (12.2). Closely allied with chemical oscillations are membrane oscillations which have considerable relevance in physiological processes including neurological and cardiac disorders in the context of detection and control. 

The sensitivity of the furan ring to acid-catalyzed hydrolysis must finally be mentioned as one of its typical chemical features. Its intervention in the context of this monograph must be seen as an undesired event to be avoided, or at least minimized, since its mechanism leads to the destruction of the heterocycle with the formation of aliphatic carbonyl compounds, as illustrated in the simplified Scheme 6.9. It is therefore clear that any polymerization system requiring the preservation of the furan or cognate structures in the final product would be marred by side reactions caused by the presence of moisture in an acidic medium. Curiously, the acid-catalyzed hydrolysis of 2,5-dimethyfuran in a water-ethanol medium shows self-oscillating features [8]. 

The chemical oscillations start with a short induction period that undergoes for few second to minutes. Depending upon the conditions and the nature of the reactions, specific method has been used to measure the oscillating behaviors. Typical example of a reaction system with different oscillating property has been presented in Fig. 1.4. 

How can oscillations, in particular chemical oscillations, be explained within the mathematical dynamic theory Unfortunately, there is still no rigorous theory for distinguishing multidimensional models of self-sustained oscillations. A typical strategy is first finding the models and parametric domains in which these oscillations do not exist. For instance, according to the so-called Poincare-Bendixson criterion (which is only valid for systems with two variables), if the sum... 

Now the question is how to construct the simplest model of a chemical oscillator, in particular, a catalytic oscillator. It is quite easy to include an autocatalytic reaction in the adsorption mechanism, for example A+B—> 2 A. The presence of an autocatalytic reaction is a typical feature of the known Bmsselator and Oregonator models that have been studied since the 1970s. Autocatalytic processes can be compared with biological processes, in which species are able to give birth to similar species. Autocatalytic models resemble the famous Lotka-Volterra equations (Berryman, 1992 Valentinuzzi and Kohen, 2013), also known as the predator-prey or parasite-host equations. 

The chemical oscillator is nowadays a typical oscillator. A respectable number of them are now known, and this is continually on the increase. It constitutes a dissipative oscillator (i.e. limit cycle), whose motion must be maintained by a constant supply of fresh reactants. Its amplitude and period are extremely sensitive to the conditions. An amusing application of this is the setting up of a real chemical clock (26). The observed oscillations usually have a very marked relaxational character. They frequently comprise a single arch. There is, however, also a series that results from the periodic repetition of a basic motif comprising... 

Figure 5- Bistability and oscillation in a typical chemical system (see text), a) Simple bistability b) Effect (- -) of adding a feedback species c) Behavior of the system in b) as function of time d) Cross-shaped phase diagram.

Typical results for a semiconducting liquid are illustrated in figure Al.3.29 where the experunental pair correlation and structure factors for silicon are presented. The radial distribution function shows a sharp first peak followed by oscillations. The structure in the radial distribution fiinction reflects some local ordering. The nature and degree of this order depends on the chemical nature of the liquid state. For example, semiconductor liquids are especially interesting in this sense as they are believed to retain covalent bonding characteristics even in the melt. 

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

Figure 14.9 (a) Schematic illustration of the experimental set-up used for Au electrodeposition at a liquid/air interface, (b) Typical example of the potential oscillation during Au electrodeposition. (Reprinted from Ref [53] with permission from the American Chemical Society.)... 

The Belousov-Zhabotinskii reaction is a typical oscillating chemical reaction. Spiral structures form periodically, disappear and reappear as the result of an autocatalytic reaction, the oxidation of Ce3+ and Mn2+ by bromate (lessen, 1978). 

An associated technique which links thermal properties with mechanical ones is dynamic mechanical analysis (DMA). In this, a bar of the sample is typically fixed into a frame by clamping at both ends. It is then oscillated by means of a ceramic shaft applied at the centre. The resonant frequency and the mechanical damping exhibited by the sample are sensitive measurements of the mechanical properties of a polymer which can be made over a wide range of temperatures. The effects of compositional changes and methods of preparation can be directly assessed. DMA is assuming a position of major importance in the study of the physico-chemical properties of polymers and composites. 

The main disadvantage of direct sine-wave testing is that it can be very time-consuming when applied to typical large time-constant chemical process equipment. The steadystate oscillation must be established at each value of frequency. It can lake days to generate the complete frequency-response curves of a slow process. 

Figure 3.24 — Typical system for piezoelectric crystal detector incorporating reference (C,) and test (CJ crystal sensors individually held in oscillating circuits (Or and 0 respectively) serviced by separate frequency counters (FC, and FCj, respectively) interfaced to a common microprocessor or other readout device. (Reproduced from [167] with permission of the American Chemical Society).

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