Chain non-branched reactions

Steps of chain non-branched reaction and conditions of its accomplishment... 

In the presence of the initiator I or under the initiating action of light or radiation, chains are generated with the rate v,-, and the oxidation of RH proceeds as a chain process including reactions (1)—(6) (see Section 13.11). Usually v, is so high that the decomposition of ROOH to radicals insignificantly contribute to initiation, so that during the experiment v,- = const, and oxidation develops as a chain non-branched reaction. 

Chain branched reactions have several substantial distinctions from chain non-branched reactions. The mechanism of these reactions was discovered by N.N. Semenov with coworkers and by S. Hinshelwood with coworkers in 1925-1928. N. N. Semenov, Yu.B. Khariton, and Z.F. Volta. Studided the conditions of ignition of phosphor vapors and established that the transition from the absence of the reaction to the blowback of vapor occurs at a rigidly specified oxygen pressure, which depends on the diameter of the vessel. In 1928 Semenov proposed the chain branched mechanism of the process involving oxygen atoms. 

In the chain non-branched reaction the concentration of active eenters n depends only on the initiation (v,) and termination rates (v, = gn, where g is the specific rate of chain termination in the presence of an inhibitor InH, g = Ai [InH]), in the quasi-stationary regime n = v/g. 

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. 

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. 

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)... 

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... 

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... 

Reaction (7) couples S2 and SH, as was noted from their fluorescence profiles. Similarly, reaction (12) links SO to S02. Reactions (13) and (14) connect oxidized and reduced species, SO with S2 and SH. The model relates all sulfur bearing species in the flames. The non-equilibrium concentrations of H and OH radicals generated in the flame front by the fast radical chain branching reactions... 

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... 

One general approach is to consider the balance between radical production and loss by the different components of a mixture. Alkanes, because of their low-temperature chemistry have active chain-branching reactions, while alkenes and aromatics have efficient termination reactions through the production of stabilized radicals, such as allyl and benzyl radicals. While the rates of the branching and termination processes arise from contributions by each of the constituents in the mixture in a way that depends linearly on their composition, the overall rate of the autoignition reactions depends on branching and termination in a non-linear fashion. 

The model also revealed the importance of non-linear interactions of chains, which determine the existence of two quasi-stationary oxidation modes. The difference in reaction rate between them is about four orders of magnitude. A critical transition between these modes is taking place due to small changes in reaction parameters, e.g., pressure. This critical transition leads to a very fast increase in the oxidation rate and an abrupt transition from the low-pressure slow oxidation to the fast high-pressure stationary chain-branching process. In the latter mode, radical generation is no more determined by a slow initiation reaction, but by very fast chain-branching reactions. It is the phenomenon... 

The same expression was obtained for non-catalytic reactions, i.e., the catalyst does not inaease the maximum rate but merely reduces the induction period. This seemingly paradoxical conclusion is based on the fact that in both cases the maximum rate is determined by the equality of catalyst-independent reaction rates of chain propagation which, in the maximum, are equal to the rate of chain branching and termination. The existence of a maximum rate was quantitatively confirmed for the oxidation of some hydrocarbons (tetralin, ethylbenzene, diphenylmethane, etc.) [14a]. 

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) ... 

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