Chain reaction degenerate branching

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. 

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

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] ... 

In recent years Emanuel, Neiman, and their respective schools have greatly contributed to the theory of antioxidant action by studying the phenomenon of the critical antioxidant concentration in terms of a degenerate branched chain reaction. The critical antioxidant concentration, a well-established feature of phenolic antioxidants, is one below which autoxidation is autocatalytic and above which it proceeds at a slow and steady rate. Since the theory allowed not only a satisfactory explanation of the critical antioxidant concentration itself but elucidation of many refinements, such as the greater than expected activity of multifunctional phenolic antioxidants (21), we wondered whether catalyst-inhibitor conversion could be fitted into its framework. If degenerate chain branching is assumed to be the result of... 

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 slow combustion of methylene chloride is a degenerately branched chain reaction it proceeds by a mechanism similar to that involved in the pyrolysis of the same compound which takes place at a slightly higher temperature [153]. The primary chains are the same and several of the chlorinated hydrocarbon minor products are identical. Oxygen is only involved in the conversion of the intermediate dichloroethylene to the final products hydrogen chloride and carbon monoxide. 

The initial stages of the reaction showed an exponential acceleration, according to the usual equation for degenerately branched chain reaction... 

The first steps towards an explanation of these extra modes of hydrocarbon oxidation were taken by Frank-Kamenetskii who proposed that the multiple cool flames observed were oscillatory and that the period of oscillation reflected the underlying chemistry. Experimental investigations continued to concentrate upon traditional measurements of pressure versus time, of induction period, and o establishing the identity of stable intermediates and reaction pathways. Interpretations of these results continued to be made on isothermal degenerate branched-chain reactions direct measurements of temperature were not made. These interpretations were very incomplete, and much better understanding has emerged from application of thermokinetic theory. 

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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