Chemical Education Today edited by
Book & Media Reviews
Edward J. Walsh Allegheny College Meadville, PA 16335
An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos by I. R. Epstein and J. A. Pojman Oxford University Press: New York, 1998. x + 392 pp. ISBN 0-19-509670-3. $75.00. reviewed by Richard J. Field
Intense study of oscillating chemical reactions and nonlinear dynamics in chemistry is only about 30 years old, but there has been enormous progress in understanding this fascinating and important area of chemistry. This advance was triggered in the 1960s by two nearly simultaneous developments. The first was Ilya Prigogine’s theory of dissipative structures (an early form of complexity theory). The second was the discovery, with later mechanistic elucidation by Field, Köros, ˝ and Noyes, of an unequivocal chemical example, the cerium-ion-catalyzed oxidation of CH2(COOH)2 by BrO3᎑ (the Belousov–Zhabotinsky reaction), in which oscillations in [Br᎑] and in [CeIV]/[CeIII] are easily observed. This book is a comprehensive overview of the area and covers basic chemistry, underlying theory, experimental methods, and applications. The idea of oscillating chemical reactions did not find ready acceptance. It is our observation, formalized by the second law of thermodynamics, that all spontaneously occurring processes must be accompanied by an increase in the entropy of the universe. However, in a spontaneously reacting chemical system this means only that certain species, referred to as reactants, must always monotonically disappear, while other species, referred to as products, must always monotonically appear. The concentrations of intermediate species, both produced and consumed in the course of the chemical reaction and present at concentrations much smaller than those of the principal reactants, may indeed execute complex, nonmono-
450
tonic behavior, but it must be driven by the entropy increase of the overall conversion of reactants to products. Thus, in a well-stirred system, intermediate concentrations may exhibit multiple steady states, excitability, steady-state instability, temporal oscillations, and even deterministic chaos, and in an unstirred system, they may exhibit traveling waves or stationary patterns in space. The requirements for the occurrence of these behaviors are that the system be maintained far from equilibrium and that the governing dynamic equations be both nonlinear (i.e., contain terms such as ki xy or kj x2) and possess suitable feedback loops, often related to activator–inhibitor interactions or to autocatalytic generation of intermediates. The major strength of this treatment by Epstein and Pojman is a strong connection between theory and experiment. The mechanisms of many oscillating chemical reactions are described in detail. This leads into the mathematics of their governing nonlinear differential equations (e.g., simple stability and bifurcation theory, together with the dynamic structure necessary for a system to exhibit nonmonotonic behavior). Descriptive topics, such as the systematic design and major classes of chemical oscillators (e.g., the BrO3᎑- and ClO2᎑driven systems in open and closed reactors) are coupled with a careful description of experimental methods. Also included are recipes for demonstrations and undergraduate laboratory experiments, useful computational and simulation tools in chemical kinetics, and a sense of applications of these new ideas in biology and chemical technology—for example, polymerization processes and mixing and coupling effects in chemical reactors. This book belongs within easy reach of any person either working in the area or in daily contact with people, especially students, who nowadays hear of these topics from many sources and who wish to learn more about them. Richard Field is in the Department of Chemistry, The University of Montana, Missoula, MT 59812.
Journal of Chemical Education • Vol. 77 No. 4 April 2000 • JChemEd.chem.wisc.edu
