Fundamentals of Chemical Chain Reaction Kinetics

The difference between the kinetic behavior of conventional branching and degenerate- branching reactions is conditioned by the fact that for degenerate-branching reactions the act of branching under which the multiplication of carrier chain occurs, proceeds with the participation of a mediator , that is an intermediate molecular (nonradical) prodnct. 

Chain reactions were discovered by M. Bodenstein [1] in 1913 by the example of photochemical reaction of hydrogen chloride formation from molecular chlorine and hydrogen. 

Subsequent diseoveries in this field and formulation of the fundamentals of the chain reactions theoiy, including branching chain reactions, is linked, to a large extent, with the names of N.N. Semenov [2] and C.N. Hinshelwood [3]. So far the efforts of the seientists in this area are foeused on detailed study of the chain reactions. 

A number of original monographs and textbooks [3-31] are dedicated to chemical chain reactions. Here we provide a minimum of information on the kinetics of chain reactions, which is primarily intended to create the necessary basis for stating in subsequent Chapters the eoneept of the value description for the kinetics of chain reactions. 

Chain reaction is defined as a transformation process of initial substances into the products through periodic alternation of elementary steps with the participation of active intermediates, mostly free radicals and/or atoms. 

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As follows from a brief review of the fundamentals on the kinetics of chain reactions, an elegant one-centered model of the process, which was offered at the begiiming of the development of the chain reaction theory, provides a phenomenological description. Initiation and inhibition of reactions by small additions of compormds, critical phenomena, etc. may serve as examples. However, it should be noted that modeling a chain reaction is usually complicated, if the one-centered approximation is not justified and in the cases when consumption of initial compormds should be taken into accormt, or when the intermediates are participating in the chain process, in other words if one has to deal with chain processes of a more complicated nature. So the efforts aimed at developing the special theoretical approaches that are thought to help for a better orientation in a complex chain chemical process are justified, in particular, rmder the conditions of multi-centered, and consequently multi-routed occurrance. 

Thus, as can be inferred from the foregoing, the calculation of any statistical characteristics of the chemical structure of Markovian copolymers is rather easy to perform. The methods of statistical chemistry [1,3] can reveal the conditions for obtaining a copolymer under which the sequence distribution in macromolecules will be describable by a Markov chain as well as to establish the dependence of elements vap of transition matrix Q of this chain on the kinetic and stoichiometric parameters of a reaction system. It has been rigorously proved [ 1,3] that Markovian copolymers are formed in such reaction systems where the Flory principle can be applied for the description of macromolecular reactions. According to this fundamental principle, the reactivity of a reactive center in a polymer molecule is believed to be independent of its configuration as well as of the location of this center inside a macromolecule. 

In subsequent years, a succession of brilliant physical chemists interested in the fundamental laws of chemical kinetics began to interpret their results in terms of radical reactions. In 1918, J. A. Christiansen, K. F. Herzfeld, and M. Polanyi independently suggested a radical chain process for the H2-Br2 reaction. In 1925, H. S. Taylor postulated the occurrence of the ethyl radical to rationalize a gas-phase photolysis. In 1931, Norrish suggested that radicals occur in the photolysis of carbonyl compounds. And then in 1939, in a very influential paper, F. Paneth showed that small alkyl radicals could be produced in a flowing gas... 

Another unsolved fundamental problem of this theory concerns the correct description of copolymerization kinetics which obviously requires a well-grounded expression, from the physicochemical viewpoint, for the rate constant of the bimolecular chain termination reaction. This elementary reaction of interaction of two macroradicals proves to be diffusion-controlled beginning from the very initial conversions, and therefore, its rate in the course of the entire process is controlled by physical, rather than chemical factors. Naturally, the consideration of the kinetics of bulk copolymerization requires different approaches ... 

The subject of the equivalence of a conductive chain with a single condnctive dipole is of paramonnt importance in condnction theories and in chemical reactions modeling. In the Formal Graph theory, its fundamental importance comes from constitnting the basis for establishing from scratch the conductive relationship, allowing demonstration of many empirical or semiempirical conduction models such as the Arrhenius law in physical chemistry or transition state theories in chemical kinetics. 

First, chain chemical reactions belong to the class of reactions for which the general kinetic laws are studied in detail and the theoretical fundamentals are formulated on the whole. It is thought that the possibilities of the theoretical prerequisites of the value method will be more clearly highlighted against this background. 

A second model was developed to describe the pyrolysis kinetics on a more fundamental basis (Westerhout et al., 1997). The model accounts for the fact that both physical and chemical processes play an important role during the pyrolysis of polymers. When an apparatus, such as a TGA, is used for a kinetic study of a pyrolysis process, the rate of evaporation of pyrolysis products is measured, but not the intrinsic chemical reaction (the breaking of bonds) rate. Not every broken bond in the polymer chain leads to the evaporation of product. Only polymer chain fragments small enough to evaporate at the given reaction temperature will actually leave the polymer sample. This implies that both physical and chemical processes influence the measured rate of change of the polymer mass and hence the observed pyrolysis kinetics. 

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