Chain reactions with degenerate branching

The oxidation of hydrocarbons at low temperatures, between 500 and 900 K, is of great importance as these reactions are responsible for the engine knock in spark-ignition engines and the autoignition of diesel fuel in Diesel engines and contribute to the formation of pollutants. 

Besides the straight chains and branched chains seen previously, the mechanisms of these oxidations include degenerate branching reactions, which are in fact secondary initiations. This confers a very wide variety of behaviour patterns to these reactions cool flames, autoignitions, to which must be added a particular phenomenon, the negative temperature coefficient, which consists in a lowering of the rate when the temperature is increased in a region situated around 700 K. 

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Semenov put forward the concept of slow hydrocarbon oxidation as the chain reaction with degenerate branching N. N. Semenov [49]... 

It is customarily believed that carbon chain polymers are oxidized according to the mechanism of chain reactions with degenerate branches, proposed by Semenov [3]. Initiation occurs as a result of attack on the RH molecule by oxygen according to the reaction... 

The presence of induction periods in the thermooxidative destruction of epoxide resins indicates an autocatalytic character of the reaction. By analogy with other polymers, the authors proposed that the oxidation of epoxide resins is a chain reaction with degenerate branches, which are related to decomposition of the hydroperoxides formed during the oxidation process. 

The process of oxidation of polycarbonate, as was shown in [26], is characterized by autoacceleration (Fig. 156) and is a chain reaction with degenerate branches. The process is accompanied by considerable gas evolution and is appreciably accelerated in the presence of impurities when the starting materials are insufficiently thoroughly purified, as well as in the presence of an excess of unreacted 4,4 -dihydr03qrdi-phenyl-2,2 -propane. Considerable amounts of CO and CO2, traces of H2, as well as water and formaldehyde were detected among the gaseous oxidation products of polycarbonate. 

In the Soviet Union, the concepts of Academician N. N. Semenov on chain reactions with degenerate branches have become the starting point of theoretical studies of the stabilization and destruction of polymers. Soviet scientists have developed a theory of critical concentrations of antioxidants and have shown that the processes of stabilization have a very complex chemical character. The nature of the polymers themselves greatly affects these processes and consequently, different stabilizers are required for polymers of different structures. In addition, it has been shown that the antioxidants used thus far can not only cause chain termination, but can also initiate oxidation and give rise to degenerate branches. 

Isotactic polypropylene, just like other polyolefins, is oxidized according to a radical chain mechanism with degenerate branches. Evidence of this is the presence of a well-defined induction period and autoacceleration of the reaction, which occurs according to the law w = Ae i . Hydroperoxides are the branching products [47]. The introduction of peroxide into the polymer reduces the induction period in proportion to JPer, which gives evidence of the presence of quadratic chain termination. 

Increase in oxidation rate caused by radical chain reactions with degenerated chain branches,... 

As already noted (see Chapter 4), autoxidation is a degenerate branching chain reaction with a positive feedback via hydroperoxide the oxidation of RH produces ROOH that acts as an initiator of oxidation. The characteristic features of inhibited autoxidation, which are primarily due to this feedback, are the following [18,21,23,26,31-33] ... 

The development of studies along this line entered a new phase after N. N. Semenov formulated the theory of chain reactions with branches [3], and especially after the creation of the theory of degenerate explosions [4]. 

The reaction with sulfides occurs efficiently only when the resulting carbon-centered radicals are further stabilized by a a-heteroatom. Indeed, (TMSfsSiH can induce the efficient radical chain monoreduction of 1,3-dithiolane, 1,3-dithiane, 1,3-oxathiolane, 1,3-oxathiolanone, and 1,3-thiazolidine derivatives. Three examples are outlined in Reaction (12). The reaction of benzothiazole sulfenamide with (TMS)3SiH, initiated by the decomposition of AIBN at 76 °C, is an efficient chain process producing the corresponding dialkylamine quantitatively. However, the mechanism of this chain reaction is complex as it is also an example of a degenerate-branched chain process. 

If it is accepted that the activation energy of a chain reaction is largely that of the process generating chains, then the parallelism in the behavior of the energies of activation for the ethylene and formaldehyde oxidations may be interpreted on the basis of the degenerate-branching reaction the former is identical with the initiation reaction for the latter. Two possible reactions were suggested... 

The relative importance of different channels of further transformations of peroxy radicals determines the overall rate of reaction and selectivities to certain products. Reactions with any H-containing substance (first of all—with parent alkane) finally lead to degenerate chain-branching and exponential growth of the reaction rate... 

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