Simulating Chemical Waves and Patterns

Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M55 3H6, Canada 

Reviews in Computational Chemistry, Volume 20 edited by Kenny B. Lipkowitz, Raima Latter, and Thomas R. Cundari ISBN 0-471-44525-8 Copyright 2004 John Wiley Sons, Inc. 

The choice of theoretical tools used to analyze the behavior of these systems depends on the scales on which one wishes to model the dynamics and the questions being asked. If the phenomena of interest are truly macroscopic, for example, the chemical waves in the BZ reaction, then an appropriate level of description is through reaction-diffusion equations. This macroscopic description focuses on chemical concentrations in small (but still macroscopic) system volumes and considers how these local concentrations change as a result of reaction and diffusion. In such an approach, one bypasses the molecular level of description completely and focuses directly on phenomena occurring on macroscopic scales. 

If the phenomena of interest occur on shorter mesoscopic length and time scales, say tens to hundreds of nanometers and pico- to microseconds, then a mesoscopic description in terms of Markov processes or Markov chain 

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Raymond Kapral, Simulating Chemical Waves and Patterns. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

In this section some basic features of nonlinear wave propagation in non-reactive and RD processes will be illustrated and compared with each other. The simulation results presented are based on simple equilibrium or non-equilibrium models [51, 65] for non-reactive separations. In the reactive case, similar models are used, assuming either kinetically controlled chemical reactions or chemical equilibrium. We focus on concentration (and temperature) dynamics and neglect fluid dynamics. Consequently, for equimolar reactions constant flows along the column height are assumed. However, qualitatively similar patterns of behavior are also displayed by more complex models [28, 57, 65] and have been confirmed in experiments [41, 59, 89, 107] for non-reactive multi-component separations. First experimental results on nonlinear wave propagation in reactive columns are presented subsequently. 

Figure 18 The experimental Zr SSNMR spectrum of MIL-140A at 21.1 T is pictured in (A), while the analytical simulation of experimental data is shown in (B). Plane-wave DFT calculations on a fully geometry-optimized structure predict the powder pattern denoted (C), while calculations on the proton-optimized crystal structure result in the simulated Zr powder pattern shown in (D).The similar simulated powder XRD patterns of the reported MIL-140A crystal structure (red (light gray in the print version)) and a geometry-optimized structure (black) are shown in (E). Adapted and reprinted with permission from Ref [75]. Copyright The American Chemical Society 2014.

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