Chemical reaction dynamic behavior

Theory may play two particularly important roles in rationalizing and predicting chemical reaction dynamics. As noted in the last section, the first step to understanding the dynamical behavior of a complex chemical system is breaking down the overall system into its constituent elementary processes. From a theoretical standpoint, the likely importance of various processes may be qualitatively assessed from the potential energy surfaces of putative reactions. Reactions with very high barriers will be less likely to play an important role, while low-barrier reactions will be more likely to do so. 

The robust existence of a skeleton composed of a NHIM and its spherical invariant cylinders in the phase space should play their essential roles not only to help us understand the physical origin of observed nonstatistical, dynamical behavior but also to provide us with a new scope to control chemical reaction dynamics in terms of geometrical feature of the phase space. Here, let us articulate some of the subjects we have to confront in the immediate future ... 

Recent computational efforts to understand SCF solvent effects have focused on (i) determining the behavior of pure SCF solvents, as such information provides a backdrop against which to understand solvation in these fluids, (ii) predicting solvation energies and structure in SCFs, as these properties critically affect solute reaction, and (iii) examining how such SCF solvent effects alter chemical reaction dynamics. Recent advances in these areas are discussed in Sections 2, 3, and 4, respectively. Close attention is paid to what has been learned about the unique behaviors of SCF solvents and to how these effects have been treated computationally. 

Models for description of liquids should provide us with an understanding of the dynamic behavior of the molecules, and thus of the routes of chemical reactions in the liquids. While it is often relatively easy to describe the molecular structure and dynamics of the gaseous or the solid state, this is not true for the liquid state. Molecules in liquids can perform vibrations, rotations, and translations. A successful model often used for the description of molecular rotational processes in liquids is the rotational diffusion model, in which it is assumed that the molecules rotate by small angular steps about the molecular rotation axes. One quantity to describe the rotational speed of molecules is the reorientational correlation time T, which is a measure for the average time elapsed when a molecule has rotated through an angle of the order of 1 radian, or approximately 60°. It is indirectly proportional to the velocity of rotational motion. 

The extension of generic CA systems to two dimensions is significant for two reasons first, the extension brings with it the appearance of many new phenomena involving behaviors of the boundaries of, and interfaces between, two-dimensional patterns that have no simple analogs in one-dimension. Secondly, two-dimensional dynamics permits easier (sometimes direct) comparison to real physical systems. As we shall see in later sections, models for dendritic crystal growth, chemical reaction-diffusion systems and a direct simulation of turbulent fluid flow patterns are in fact specific instances of 2D CA rules and lattices. 

The point of this terse introduction is that cellular automata represent not just a formalism for describing a certain particular class of behaviors (lattice gas simulations of fluid dynamics, models of chemical reactions and diffusion processes, etc.), but a much more general template for original and heretofore untapped ways of looking at a large class of unsolved or only poorly understood fundamental problems. 

Steady state models of the automobile catalytic converter have been reported in the literature 138), but only a dynamic model can do justice to the demands of an urban car. The central importance of the transient thermal behavior of the reactor was pointed out by Vardi and Biller, who made a model of the pellet bed without chemical reactions as a onedimensional continuum 139). The gas and the solid are assumed to have different temperatures, with heat transfer between the phases. The equations of heat balance are ... 

Cross-sections for reactive scattering may exhibit a structure due to resonance or to other dynamical effects such as interference or threshold phenomenon. It is useful to have techniques that can identify resonance behavior in a system and distinguish it from other sorts of dynamics. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the sub-picosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

The transition state theory provides a useful framework for correlating kinetic data and for codifying useful generalizations about the dynamic behavior of chemical systems. This theory is also known as the activated complex theory, the theory of absolute reaction rates, and Eyring s theory. This section introduces chemical engineers to the terminology, the basic aspects, and the limitations of the theory. 

The dynamic behavior of reactions in liquids may differ appreciably from that of gas phase reactions in several important respects. The short-range nature of intermolecular forces leads to several major differences in the macroscopic properties of the system, often with concomitant effects on the dynamics of chemical reactions occurring in the liquid phase. 

Reaction dynamics is the part of chemical kinetics which is concerned with the microscopic-molecular dynamic behavior of reacting systems. Molecular reaction dynamics is coming of age and much more refined state-to-state information is becoming available on the fundamental reactions. The contribution of molecular beam experiments and laser techniques to chemical dynamics has become very useful in the study of isolated molecules and their mutual interactions not only in gas surface systems, but also in solute-solution systems. 

Besides the two most well-known cases, the local bifurcations of the saddle-node and Hopf type, biochemical systems may show a variety of transitions between qualitatively different dynamic behavior [13, 17, 293, 294, 297 301]. Transitions between different regimes, induced by variation of kinetic parameters, are usually depicted in a bifurcation diagram. Within the chemical literature, a substantial number of articles seek to identify the possible bifurcation of a chemical system. Two prominent frameworks are Chemical Reaction Network Theory (CRNT), developed mainly by M. Feinberg [79, 80], and Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83]. An analysis of the (local) bifurcations of metabolic networks, as determinants of the dynamic behavior of metabolic states, constitutes the main topic of Section VIII. In addition to the scenarios discussed above, more complicated quasiperiodic or chaotic dynamics is sometimes reported for models of metabolic pathways [302 304]. However, apart from few special cases, the possible relevance of such complicated dynamics is, at best, unclear. Quite on the contrary, at least for central metabolism, we observe a striking absence of complicated dynamic phenomena. To what extent this might be an inherent feature of (bio)chemical systems, or brought about by evolutionary adaption, will be briefly discussed in Section IX. 

The dynamic relationships discussed thus far in this book were determined from mathematical models of the process. Mathematical equations, based on fundamental physical and chemical laws, were developed to describe the time-dependent behavior of the system. We assumed that the values of all parameters, such as holdups, reaction rates, heat transfer coeflicients, etc., were known. Thus the dynamic behavior was predicted on essentially a theoretical basis. 

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