Oscillating reaction systems

Using the ability to displace the trajectory of a limit cycle across a fixed boundary (the separatrix) as a measure of sensitivity to an external perturbation, it can therefore be seen that nonlinear oscillating reaction systems are able to respond most sensitively to a range of externally applied frequencies close to their endogenous frequency. 

Experimenting with the combined catalytic action of Ce(III, IV) and ferroin on the oscillating reaction system bromate/malonic acid/H2S04 for different ratios... 

The Ce(IV)/Ce(III) (Br /BrOj ) system is one of several redox systems in which oscillating oxidation-reduction cycles can be observed. This particular system, with organic substrates like malonic acid (among others), is known as the Belousov-Zhabotinsky oscillator. This system has been studied for more than 15 years and has been the subject of several reviews and a number of symposia. The Ce--Br oscillating reaction system has been described in terms of a seven-step rate process (all reversible reactions), the Field-Koros-Noyes (FKN) mechanism (Field et al. 1972). 

The key species in the FKN mechanism is BrO, which functions as both oxidant for Ce(III) and reductant for Ce(IV). This species is formed in the reaction between BrOj (bromate) and HBrOj (bromous acid). Neither BrOj nor HBrOz are stable in aqueous media and thus are produced and consumed in the FKN mechanism as intermediate species. A lucid description of the specifics of the oscillating reaction system has been provided by Barkin et al. (1977). A more recent contribution from Bar-Eli (1985) indicates that in a continuously stirred tank reactor (CSTR) only four or five of the total 14 reaction rate constants are required to describe the oscillations. Yoshida and Ushiki (1982) studied the oxidation of Ce(III) by Br03 found an induction period precedes a burst of Ce(IV) production, followed by continued slow generation of Ce(IV). The length of the induction period was highly dependent on the age of the reactant solution. 

In this section we will focus our attention on the chemical mechanism of the Belousov-Zhabotinsky (B-Zh) reaction. As mentioned above, the B-Zh reaction is one of the most extensively studied among the oscillating chemical reactions [15-47], The classical B-Zh oscillating reaction system presents the oxidation of malonic acid (MA) by bromate ion (potassium bromate) in an acid medium (sulfuric acid), catalyzed by the single-electron Ce /Ce redox couple. The oxidized form of the catalyst, the Ce" ion, is yellow colored, and the reduced one, Ce, is colorless. The periodicity of the B-Zh reaction is detected as a periodic yellow coloring of the solution. 

Autocatalysis can cause sustained oscillations in batch systems. This idea originally met with skepticism. Some chemists believed that sustained oscillations would violate the second law of thermodynamics, but this is not true. Oscillating batch systems certainly exist, although they must have some external energy source or else the oscillations will eventually subside. An important example of an oscillating system is the circadian rhythm in animals. A simple model of a chemical oscillator, called the Lotka-Volterra reaction, has the assumed mechanism ... 

How relevant are these phenomena First, many oscillating reactions exist and play an important role in living matter. Biochemical oscillations and also the inorganic oscillatory Belousov-Zhabotinsky system are very complex reaction networks. Oscillating surface reactions though are much simpler and so offer convenient model systems to investigate the realm of non-equilibrium reactions on a fundamental level. Secondly, as mentioned above, the conditions under which nonlinear effects such as those caused by autocatalytic steps lead to uncontrollable situations, which should be avoided in practice. Hence, some knowledge about the subject is desired. Finally, the application of forced oscillations in some reactions may lead to better performance in favorable situations for example, when a catalytic system alternates between conditions where the catalyst deactivates due to carbon deposition and conditions where this deposit is reacted away. 

As mentioned in the introduction, it is difficult to explain the characteristics of the oscillation based on the mechanisms which have been proposed so far for the potential oscillations with systems similar to Eq. (16) [4,7,35-38]. A precise investigation on individual ion transfers and adsorptions at two interfaces is necessary for the elucidation of the oscillation mechanism, although the spontaneous oscillation might be realized by the combination of a much larger number of ion transfer reactions and adsorptions than those in the case of the oscillation under the applied potential or current. 

The last unconventional approach considered in this chapter is low-pressure analyte pulse perturbation-CL spectroscopy (APP-CLS). This approach is highly dynamic as it relies on the combination of an oscillating reaction, which is a particular case of far-from-equilibrium dynamic systems, and a CL reaction. 

We demonstrate the use of Matlab s numerical integration routines (ODE-solvers) and apply them to a representative collection of interesting mechanisms of increasing complexity, such as an autocatalytic reaction, predator-prey kinetics, oscillating reactions and chaotic systems. This section demonstrates the educational usefulness of data modelling. 

The Runge-Kutta algorithm cannot handle so-called stiff problems. Computation times are astronomical and thus the algorithm is useless, for that class of ordinary differential equations, specialised stiff solvers have been developed. In our context, a system of ODEs sometimes becomes stiff if it comprises very fast and also very slow steps and/or very high and very low concentrations. As a typical example we model an oscillating reaction in The Belousov-Zhabotinsky (BZ) Reaction (p.95). 

Chemical mechanisms for real oscillating reactions are very complex and presently not understood in every detail. Nevertheless, there are approximate mechanisms which correctly model several crucial aspects of real oscillating reactions. In these simplified systems, often not all physical laws are strictly obeyed, e.g. the law of conservation of mass. 

The actual schemes of these reactions are very complicated the radicals involved may also react with the metal ions in the system, the hydroperoxide decomposition may also be catalysed by the metal complexes, which adds to the complexity of the autoxidation reactions. Some reactions, such as the cobalt catalysed oxidation of benzaldehyde have been found to be oscillating reactions under certain conditions [48],... 

The schemes considered are only a few of the variety of combinations of consecutive first-order and second-order reactions possible including reversible and irreversible steps. Exact integrated rate expressions for systems of linked equilibria may be solved with computer programs. Examples other than those we have considered are rarely encountered however except in specific areas such as oscillating reactions or enzyme chemistry, and such complexity is to be avoided if at all possible. 

The field of oscillating reactions, or periodic reactions, or chemical clocks, came out of this background indeed quite a number of chemical systems have been described, which show this oscillating, periodic, regular behavior (Field, 1972 Briggs and Rauscher, 1973 Shakhashiri, 1985 Noyes, 1989 Pojman etal, 1994 Jimenez-Prieto etal., 1998). 

Out-of-equilibrium systems (non-linear, dynamic processes), such as the Zabotinski-Belousov reaction, and other oscillating reactions bifurcation, and order out of chaos convection phenomena tornadoes, vortexes... 

The need for oscillations can be seen in another way if we look at electron transfer processes in the mitochondrial or chloroplast reaction systems. In both there are series of electron transfer centers. By studying the spin state of metal ions in these centers it has been shown that the metal atoms can flip rapidly between different spin states. As these states must have some difference in conformation and as the metals are bound... 

Steady states and oscillations in homogeneous-heterogeneous reaction systems (with X. Song and L.D. Schmidt). Chem. Eng. Sci. 46,1203-1215 (1991). 

In situations where the macroscopic equations tell us that a coherent state is possible, it is important to know if this coherence could withstand the destructive influence of fluctuations. For instance, the macroscopic equations of a diffusion-reaction system might have a solution that implies that the concentrations can oscillate homogeneously. We expect the in-homogenous fluctuations to have a tendency to destroy this coherence if they are strong enough. An analysis of the situation shows that the coherence can be maintained if the dimension of the system is larger than a certain critical dimension. Malek-Mansour et al.19 have shown that for chemical systems amenable to one variable, the critical dimension dc is given by... 

In the homogeneous systems at low temperatures, oscillation phenomena were also observed for this reaction system. Similar observations were made for the CO and 02 system. In order to explain the oscillation mechanism mathematically, a complicated kinetic scheme was devised which is capable of predicting the sustained oscillations [Yang (26, 27)]. Apparently a similar complicated kinetic mechanism governs the undamped oscillations in the heterogeneous system, however, a pertinent analysis has not been performed in the literature so far. 

Relaxation methods can be classified as either transient or stationary (Bernasconi, 1986). The former include pressure and temperature jump (p-jump and t-jump, respectively), and electric field pulse. With these methods, the equilibrium is perturbed and the relaxation time is monitored using some physical measurement such as conductivity. Examples of stationary relaxation methods are ultrasonic and certain electric field methods. Here, the reaction system is perturbed using a sound wave, which creates temperature and pressure changes or an oscillating electric field. Chemical relaxation can then be determined by analyzing absorbed energy (acous-... 

Synchronous processes represent the most demonstrative and unique example of chemical reaction ensembles, arranged in time and space. Interest in synchronous chemical reactions is also so much keener, because in biological systems many processes are synchronous. This means that biochemical reactions are arranged and performed in systems with molecular and permolecular structures, which is the chemist s pipe dream . Studies performed in recent decades have allowed the development of the interaction theory for synchronous chemical reactions at two levels—microscopic and macroscopic. Strictly speaking, parallel reactions may also be taken as synchronous reactions although proceeding simultaneously in the reaction system, they are characterized by the absence of any interaction between them. However, such synchronous reactions are trivial and of no special interest for chemistry. It is of much more importance when they interact and, therefore, induce oscillations in yields of synchronous reaction products. 

Kinetic study of the self-oscillating reaction observed in a potassium iodate-hydrogen peroxide-cysteine-sulfuric acid (acid medium) system was carried out [57], It is found that according to an adequate model the feedback mechanism is associated with autocatalytic reaction... 

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