Oscillating chemical reaction oscillators

Only a very few experimental studies have been made for detection of mnlti-plicities of steady states to check on theoretical predictions. The studies of multiplicities and of oscillations of concentrations have similar mathematical bases. Comprehensive reviews of these topics are by Schmitz (Adv. Chem. Sen, 148, 156, ACS [1975]), Razon and Schmitz (Chem. Eng. Sci., 42, 1,005-1,047 [1987]), Morbidelli, Vamia, and Aris (in Carberry and Varma, eds.. Chemical Reaction and Reacton Engineering, Dekker, 1987, pp. 975-1,054). 

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. 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

This approximation is not valid, say, for the ohmic case, when the bath spectrum contains too many low-frequency oscillators. The nonlocal kernel falls off according to a power law, and kink interacts with antikink even for large time separations. We assume here that the kernel falls off sufficiently fast. This requirement also provides convergence of the Franck-Condon factor, and it is fulfilled in most cases relevant for chemical reactions. 

Transition metal coordination compounds in oscillating chemical reactions. K. B. Yatsimirskii and L. P. Tikhonova, Coord. Chem. Rev., 1985, 63,241 (90). 

Belouzov-Zhabotinsky reaction [12, 13] This chemical reaction is a classical example of non-equilibrium thermodynamics, forming a nonlinear chemical oscillator [14]. Redox-active metal ions with more than one stable oxidation state (e.g., cerium, ruthenium) are reduced by an organic acid (e.g., malonic acid) and re-oxidized by bromate forming temporal or spatial patterns of metal ion concentration in either oxidation state. This is a self-organized structure, because the reaction is not dominated by equilibrium thermodynamic behavior. The reaction is far from equilibrium and remains so for a significant length of time. Finally,... 

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. 

The oscillations observed with artificial membranes, such as thick liquid membranes, lipid-doped filter, or bilayer lipid membranes indicate that the oscillation can occur even in the absence of the channel protein. The oscillations at artificial membranes are expected to provide fundamental information useful in elucidating the oscillation processes in living membrane systems. Since the oscillations may be attributed to the coupling occurring among interfacial charge transfer, interfacial adsorption, mass transfer, and chemical reactions, the processes are presumed to be simpler than the oscillation in biomembranes. Even in artificial oscillation systems, elementary reactions for the oscillation which have been verified experimentally are very few. 

The voltammetry for ion transfer at an interface of two immiscible electrolyte solutions, VITIES, which is a powerful method for identifying the transferring ion and for determining the amount of ion transferred, must be helpful for the elucidation of the oscillation process [17 19]. The VITIES was also demonstrated to be useful for ion transport through a membrane, considering that the membrane transport of ions is composed of the ion transfers at two aqueous-membrane interfaces and the mass transfers and/or chemical reactions in three phases [2,20,21]. 

The chemical reactions induced by ultrasonic irradiation are generally influenced by the irradiation conditions and procedures. It is suggested that ultrasound intensity , dissolved gas , distance between the reaction vessel and the oscillator and ultrasound frequency are important parameters to control the sonochemical reactions. 

Subsequent to a fire in a teaching laboratory, it was discovered that a mixture of equal weights of the three dry solids, itself stable, reacted violently when wetted with up to two parts of water and was capable of igniting paper. All components (which exhibit an oscillating chemical reaction in solution) were necessary for this effect. 

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). 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

A chemical reaction can be designated as oscillatory, if repeated maxima and minima in the concentration of the intermediates can occur with respect to time (temporal oscillation) or space (spatial oscillation). A chemical system at constant temperature and pressure will approach equilibrium monotonically without overshooting and coming back. In such a chemical system the concentrations of intermediate must either pass through a single maximum or minimum rapidly to reach some steady state value during the course of reaction and oscillations about a final equilibrium state will not be observed. However, if mechanism is sufficiently complex and system is far from equilibrium, repeated maxima and minima in concentrations of intermediate can occur and chemical oscillations may become possible. 

First model for oscillating system was proposed by Volterra for prey-predator interactions in biological systems and by Lotka for autocatalytic chemical reactions. Lotka s model can be represented as... 

TNC. 18. R. Lefever, G. Nicolis and I. Prigogine, On the occurrence of oscillations around the steady state in systems of chemical reactions far from equilibrium, J. Chem. Phys. 47, 1045-1047 (1967). 

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]. 

The 1970s saw an explosion of theoretical and experimental studies devoted to oscillating reactions. This domain continues to expand as more and more complex phenomena are observed in the experiments or predicted theoretically. The initial impetus for the smdy of oscillations owes much to the concomitance of several factors. The discovery of temporal and spatiotemporal organization in the Belousov-Zhabotinsky reaction [22], which has remained the most important example of a chemical reaction giving rise to oscillations and waves. 

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