Polyatomic Reactive Systems

1 An Outline of the Seminal Friction Coefficient Concept of Maxwell 

Maxwell [95, 97] was the first to derive a set of diffusion equations in a form analogous to (2.397) for dilute binary gas mixtures using kinetic theory arguments. Maxwell s [95, 97] seminal idea was that concentration gradients result from the friction between the molecules of different species, hence the proportionality coefficients, Cjjt, were interpreted as inverse fliction or drag coefficients. 

To convert the system balance description into an Eulerian control volume formulation the transport theorem is employed (i.e., expressed in terms of the species s velocity, v )  

To convert the area integrals into volume integrals the Gauss theorem is used (App A) in the standard manner. 

From Chap. 1 it is known that this balance has to be valid for any volume, hence the integral argument must be equal to zero  

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In this chapter, the diverse coupling constants and MEC components identified in the combined electronic-nuclear approach to equilibrium states in molecules and reactants are explored. The reactivity implications of these derivative descriptors of the interaction between the electronic and geometric aspects of the molecular structure will be commented upon within both the EP and EF perspectives. We begin this analysis with a brief survey of the basic concepts and relations of the generalized compliant description of molecular systems, which simultaneously involves the electronic and nuclear degrees-of-freedom. Illustrative numerical data of these derivative properties for selected polyatomic molecules, taken from the recent computational analysis (Nalewajski et al., 2008), will also be discussed from the point of view of their possible applications as reactivity criteria and interpreted as manifestations of the LeChatelier-Braun principle of thermodynamics (Callen, 1962). 

Other bimolecular reactions of complex systems, such as those of benzene and iodine and acid-base reactions, have also been studied. Currently, we are examining the inelastic and reactive collision of halogen atoms with polyatomics (e.g., CH3I). Other groups at the National Institutes of Science and Technology and at the University of Southern California have studied a new class of reactions O + CH4 — [CH3OH] — CH3 + OH and H + ON2 — HO + N2 or HN + NO. 

Suppose the reactive polyatomic molecule of interest can undergo uni-molecular reaction to form several products, and we imagine carrying out a constrained reaction path analysis for each of the product channels. To carry out the analysis of a particular constrained reaction path, Zhao and Rice adopted a system-bath model [74] in which the reaction path coordinate delines the system and all other coordinates constitute the bath. The use of this representation permits the elimination of the bath coordinates, which then increases the efficiency of calculation of the optimal control field for motion along the reaction coordinate. 

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