Kinetics of chain reactions

The overall rate of a chain process is determined by the rates of initiation, propagation, and termination reactions. Analysis of the kinetics of chain reactions normally depends on application of the steady-state approximation (see Section 4.2) to the radical intermediates. Such intermediates are highly reactive, and their concentrations are low and nearly constant throughout the course of the reaction ... 

Exercise 2.6 Steady State Assumption in the Kinetics of Chain Reactions... 

Oxidation of organic compounds by dioxygen is a phenomenon of exceptional importance in nature, technology, and life. The liquid-phase oxidation of hydrocarbons forms the basis of several efficient technological synthetic processes such as the production of phenol via cumene oxidation, cyclohexanone from cyclohexane, styrene oxide from ethylbenzene, etc. The intensive development of oxidative petrochemical processes was observed in 1950-1970. Free radicals participate in the oxidation of organic compounds. Oxidation occurs very often as a chain reaction. Hydroperoxides are formed as intermediates and accelerate oxidation. The chemistry of the liquid-phase oxidation of organic compounds is closely interwoven with free radical chemistry, chemistry of peroxides, kinetics of chain reactions, and polymer chemistry. 

Some chain reactions can be initiated photochemically [3]. In fact, most of the early work on kinetics of chain reactions was done with photochemical initiation. For example, in the hydrogen-bromide reaction (see next section), initiation Br2 — 2 Br can be achieved with ultraviolet light. Such initiation allows the reaction to be conducted at a lower temperature at which thermal initiation is ineffective. This may be an advantage in an industrial process, and also offers opportunities for elucidation of reaction mechanisms. 

The discovery of the unimolecular reactions which depend upon collisions blurred the classification in terms of orders, and the complex kinetics of chain reactions stiU further lessened its utility as a... 

The kinetics of chain-reaction polymerization is illustrated in Fig. 3.28 for a free radical process. Analogous equations, except for termination, can be written for ionic polymerizations. Coordination reactions are more difficult to describe since they may involve solid surfaces, adsorption, and desorption. Even the crystallization of the macromolecule after polymerization may be able to influence the reaction kinetics. The rate expressions, as given in Appendix 7, Fig. A7.1, are easily written under the assumption that the chemical equations represent the actual reaction path. Most important is to derive an equation for the kinetic chain length, v, which is equal to the ratio of propagation to termination-reaction rates. This equation permits computation of the molar mass distribution (see also Sect. 1.3). The concentration of the active species is very small and usually not known. First one must, thus, ehminate [M ] from the rate expression, as shown in the figure. The boxed equation is the important equation for v. 

The kinetics of chain reactions of small molecules is much harder to follow (and prove) than chain-reaction polymerization. Once the reaction is over, the sttucture of the produced macromolecule can be studied as permanent documentation of the reaction (see Chaps. 1 and 3). 

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. 

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. 

Condensation reactions follow kinetic schemes similar to those of small molecule reactions. They are simple first-order, second-order, etc. reactions. In contrast, the kinetics of chain reactions, such as free-radical polymerization or ionic polymerization, are much more complicated. 

Chain reactions provide energetically favorable reaction routes for reactions between stable molecules. The kinetics of chain reactions can be solved with the steady-state approximation. 

Atomic chlorine is generated under the action of light. This scheme was confirmed experimentally, and its particular steps were thoroughly studied. A new science, viz., kinetics of chain reactions, thus appeared in 1913—1918. 

Methods for studying chain reactions appeared and were improved in parallel with their discovery and study. Experimental evidence for the chain mechanism of the process and participation in it of free atoms and radicals gained significance at the first stage of development of the kinetics of chain reactions (1920-1940). It seems reasonable to consider briefly these proofs. 

The study of the kinetics of chain reactions in the stationary regime allows one to determine a combination of the rate constants for bimolecular chain termi-... 

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