Zero- and One-Dimensional Systems

The primary objective of this chapter is to develop low-dimensional representations of chemically reacting flow situations. Specifically these include batch reactors (corresponding to homogeneous mass-action kinetics), plug-flow reactors (PFR), perfectly stirred reactors (PSR), and one-dimensional flames. The derivations also serve to illustrate the approach that is taken to derive appropriate systems of equations for other low-dimensional circumstances or flow situations. 

Three ideal reactors—the batch reactor, the plug-flow reactor and the perfectly stirred reactor—are mathematical approximations to corresponding laboratory reactors that are used regularly to study chemical kinetics (Section 13.3.2). The batch reactor (or static reactor) is particularly useful to characterize explosion limits [241] and kinetic behavior at temperatures below 1000 K (e.g., [304,351]), while stirred reactors (e.g., [151,249,296, 367,397]) and flow reactors (e.g., [233,442]) have proved highly valuable in the study of chemical kinetics at higher temperatures. 

Even for systems with highly complex fluid dynamics, where the flow cannot adequately be approximated by a single chemical reactor, a network of ideal reactors may form the basis of a useful approximation. Because of the computational difficulties of handling mixing and chemical reaction in the complex flow patterns encountered in industrial applications, 

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In Chapter 11, Molecular Electron Transfer, the broad and deep field of electron-transfer reactions of metal complexes is surveyed and analyzed. In Chapter 12, Electron Transfer From the Molecular to the Nanoscale, the new issues arising for electron-transfer processes on the nanoscale are addressed this chapter is less a review than a toolbox for approaching and analyzing new situations. In Chapter 13, Magnetism From the Molecular to the Nanoscale, the mechanisms and consequences of magnetic coupling in zero- and one-dimensional systems comprised of transition-metal complexes is surveyed. Related to the topics covered in this volume are a number addressed in other volumes. The techniques used to make the measurements are covered in Section I of Volume 2. Theoretical models, computational methods, and software are found in Volume 2, Sections II and III, while a number of the case studies presented in Section IV are pertinent to the articles in this chapter. Photochemical applications of metal complexes are considered in Volume 9, Chapters 11-16, 21 and 22. 

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