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An Introduction to Nonlinear Chemical DynamicsOscillations, Waves, Patterns, and Chaos$
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Irving R. Epstein and John A. Pojman

Print publication date: 1998

Print ISBN-13: 9780195096705

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195096705.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 January 2022

Analysis of Chemical Oscillations

Analysis of Chemical Oscillations

(p.83) 5 Analysis of Chemical Oscillations
An Introduction to Nonlinear Chemical Dynamics

Irving R. Epstein

John A. Pojman

Oxford University Press

Many of the most remarkable achievements of chemical science involve either synthesis (the design and construction of molecules) or analysis (the identification and structural characterization of molecules). We have organized our discussion of oscillating reactions along similar lines. In the previous chapter, we described how chemists have learned to build chemical oscillators. Now, we will consider how to dissect an oscillatory reaction into its component parts—the question of mechanism. A persuasive argument can be made that it was progress in unraveling the mechanism of the prototype BZ reaction in the 1970s that gave the study of chemical oscillators the scientific respectability that had been denied it since the discovery of the earliest oscillating reactions. The formulation by Field, Körös, and Noyes (Field et al., 1972) of a set of chemically and thermodynamically plausible elementary steps consistent with the observed “exotic” behavior of an acidic solution of bromate and cerium ions and malonic acid was a major breakthrough. Numerical integration (Edelson et al., 1975) of the differential equations corresponding to the FKN mechanism demonstrated beyond a doubt that chemical oscillations in a real system were consistent with, and could be explained by, the same physicochemical principles that govern "normal" chemical reactions. No special rules, no dust particles, and no vitalism need be invoked to generate oscillations in chemical reactions. All we need is an appropriate set of uni- and bimolecular steps with mass action kinetics to produce a sufficiently nonlinear set of rate equations. Just as the study of molecular structure has benefited from new experimental and theoretical developments, mechanistic studies of complex chemical reactions, including oscillating reactions, have advanced because of new techniques. Just as any structural method has its limitations (e.g., x-ray diffraction cannot achieve a resolution that is better than the wavelength of the x-rays employed), mechanistic studies, too, have their limitations. The development of a mechanism, however, has an even more fundamental and more frustrating limitation, sometimes referred to as the fundamental dogma of chemical kinetics. It is not possible to prove that a reaction mechanism is correct. We can only disprove mechanisms.

Keywords:   Lotka-Volterra model, Oregonator, chlorite-iodide reaction, diffusion-controlled macromolecular reactions, empirical rate law models, flow control (negative feedback), limit cycle, mechanisms vs. models, network stability

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