Non-branching chain reactions

The hydrogen-chlorine chain reaction has proved to be one of the most controversial systems yet studied. After thirty years of investigation Bodenstein43 was able to say in 1931 that every worker on the photochemical synthesis of HC1 had produced his own mechanism even as late as 1940 little positive information had been obtained. However, the accumulated techniques and experience had firmly established the importance of atom chain reactions. The mechanism of photo-initiation and propagation is the same as for the hydrogen bromide photosynthesis, a non-branching chain reaction... 

Elementary probabilistic theory for non-branching chain reactions. An active intermediate being generated in an non-branching chain reaction has two chances (i) enter into a chain propagation reaction with a probability valued or (ii) to be lost with a probability value P, such that a + fi =. ... 

The equation (1.6) describes the rate of non-branching chain reaction, which is accurate... 

Then the fundamental relationship for a non-branching chain reaction may be derived from (1.6) and (1.7) ... 

It follows from expressions (1.16) and (1.17) that two reaction regimes are typical, both for the degenerate branching and non-branching chain reactions ... 

Formal Kinetics of Multicentered Non-Branching Chain Reactions... 

Let us pass to a brief description of the formal kinetics of multicentered chain reactions. A multicentered non-branching chain reaction with linear steps of transformation of the active reactive centers (chain carriers) may be represented in the form of a formal scheme [9], as some kind of a flow graph for the dynamic process (see Section 4.5). 

Figure 5. 1. Schematic illustration of a multicentered non-branching chain reaction. R, is an active reaction center (atom, free radical, excited particle, etc.). Arrows between active reaction centers, chain carriers, R, and R , denote the reactions resulting in mutual transformations ky is the effective rate constant for the formation of the R reaction center with participation of the R reaction center A, is the...

Figure 5.3. Schematic pattern of a non-branching chain reaction with participation of four types of chain carriers. r° is the rate of initiation of the Ri chain carrier.

In the stationary regime where g>f, the kinetics of the branched chain reaction resembles the kinetics of the non-branched chain reaction and... 

Kinetic study of straight chain or non-branch chain reactions... 

The reaction rate of non-branching-chain reactions therefore follows Arrhenius law the activation energy is the sum of the activation energies of the initiation and propagation steps. 

We again note that the thesis of the decisive role of the chemical reaction in the zone of highest temperatures, which lies at the basis of the combustion theory developed here, remains fully applicable to chain reactions with both branching and non-branching chains. It is precisely this fact which has allowed us to successfully apply the general laws of the theory of combustion to interesting, non-artificial, and practically important systems. 

This expression coincides quite well with the equation for a reversible bimolecular reaction, which we used earlier. In particular, the rate of decomposition remains proportional to the square of the nitric oxide concentration, and the reaction rate is zero at the equilibrium concentration. The latter statement follows direction from the theory of non-branching chains, since for such chains the chemical energy of the centers cannot be utilized... 

Now let us derive the analytie dependence for the rate of the P product formation and the chain length component vj, on the quantitative characteristics of individual steps (r°, ku, ki), for the multicentered non-branching chain process [9]. In accordance with the reaction scheme illustrated in Figure 5.1 the rates of the chain carrier formation are ... 

We will return to branching chain reactions in a non-pseudo-steady state mode with

0, in Chapter 15, in order to explain explosions of gaseous media. 

The cobalt-catalysed reaction between aryl bromides and Grignard reagents assisted by IMes HCl is also known, however the substrate scope is quit narrow and good yields are only obtained when non-branched long chain alkyl magnesium chlorides are used as coupling reagents [80] (Scheme 6 19)... 

Comparison of conjugated and usual dehydrogenation results indicates the desirability of the oxidation method. Each consecutive reaction described by the chain non-branched scheme represents a combination of initiation, propagation and chain termination stages. 

A reaction mechanism is a sequence of elementary processes proposed to account for experimental kinetic results. Pure chemical kinetics proposes a classification of various types of mechanism (non-chain mechanisms, straight-chain and branched-chain mechanisms, etc.), establishes relationships between the properties of a global reaction and those of the elementary processes involved in the corresponding mechanism, and provides rules for writing a priori a reaction mechanism from a knowledge of the thermochemical and kinetic characteristics of the... 

The first two represent the high-temperature chemistry and the second two the branch chain of the low-temperature chemistry. Griffiths [85] has criticized the model for losing the essential feature of alkane autoignition chemistry, a switch from radical branching to non-branching reactions as the temperature increases, which is responsible for the negative temperature coefficient. The model relies on thermal feedback mechanisms only. 

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