Radical chain branching reactions

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... 

During the polymeriza tion process the normal head-to-tad free-radical reaction of vinyl chloride deviates from the normal path and results in sites of lower chemical stabiUty or defect sites along some of the polymer chains. These defect sites are small in number and are formed by autoxidation, chain termination, or chain-branching reactions. Heat stabilizer technology has grown from efforts to either chemically prevent or repair these defect sites. Partial stmctures (3—6) are typical of the defect sites found in PVC homopolymers (2—5). 

The second explosion limit must be explained by gas-phase production and destruction of radicals. This limit is found to be independent of vessel diameter. For it to exist, the most effective chain branching reaction (3.17) must be overridden by another reaction step. When a system at a fixed temperature moves from a lower to higher pressure, the system goes from an explosive to a steady reaction condition, so the reaction step that overrides the chain branching step must be more pressure-sensitive. This reasoning leads one to propose a third-order reaction in which the species involved are in large concentration [2], The accepted reaction that satisfies these prerequisites is... 

More generally, low-temperature combustion relies heavily on the tendency of radical propagation to yield chain-branching reactions, a phenomenon first explored... 

In the reaction steps for H2 oxidation the first two reactions are chain branching reactions, with one radical species producing two other radicals every time a reaction event occurs. The first of these probably proceeds by the steps... 

Note that this reaction produces two reactive See radicals from one. We call these chain branching reactions because the propagation steps produce more radical species than... 

Figure 10-9 Sketch of chain branching reactions where the propagation steps produce more than one radical so that the process taids to grow exponentially, leading to a rapid acceleration of the reaction and possibly a chain-branching explosion.

For conditions with a constant temperature of 500°C, the mixture is nonexplosive at pressures below about 1.5 Torr. Under these conditions of very low pressure, radical diffusion to the walls of the vessel is fast, and termination at the wall efficiently removes radicals formed in the initiation and chain-branching reactions, thereby breaking the chain. Since the first limit of explosion is surface dependent, it will depend on the size and the surface material/treatment of the vessel. 

As the pressure increases above 1.5 Torr, explosion occurs. The higher pressure causes radical diffusion to the walls to become slower and the heterogeneous loss of radicals can no longer compete with the chain-branching reaction sequence (R19) to (R22). 

High-Temperature Oxidation The high-temperature oxidation of methane has been studied extensively, and the mechanism is better established than that of the low temperature oxidation. At high temperatures the methylperoxy radical (CH302) is no longer stable, and the low-temperature oxidation pathway initiated by reaction (R15) is not active. Furthermore the chain-branching reaction... 

The fuel and oxygen are consumed primarily by a sequence of chain-branching reactions that yield a net production of active free radicals ... 

The HCO dissociation reaction is fast for a dissociation reaction, because the H-CO bond in the formyl (HCO) is very weak. These reactions are sufficiently fast to compete with the H + O2 OH + O chain-branching reaction, and thus produce the mole-number overshoot. Under some circumstances pressure-dependent dissociation of small hydrocarbon free radicals can also contribute to the mole-number overshoot. These reactions can include... 

A sufficiently high inlet velocity will cause the flame to be extinguished [270]. There are two reasons for the extinction. One is heat loss to the wall, which reduces the flame temperature and hence the chemical reaction rates. The second, and perhaps less obvious, is strain extinction. As the inlet velocity increases and the boundary layer thins, the radial velocity increases (the general shape of the radial velocity profiles are shown in Fig.6.6). As the radial velocity increases, the residence time in the flame zone also decreases. The reduced residence time, in turn, limits the time available for the relatively slow radical-recombination reactions to keep the flame temperature high. Reduced temperature and residence time limit the relatively slow the chain-branching reaction H + O2 OH + O, which is needed to sustain a flame. Ultimately a flame cannot be sustained [214],... 

Rate of chain branching reactions giving multiple free radicals (ending the Ti induction period). 

Equation (XIV.G.3) represents, of course, one special case among many possible examples of chain-branching reactions. Variations of this equation may be obtained by adding terms that represent homogeneous first-order termination ka C) to Eq. (XIV.6.3) or wall-initiation terms to the auxiliary boundary equation (XIV.6.4). The addition of terms which are second-order in radicals, such as second-order recombination in the gas phase, or second-order branching leads to equations which are nonlinear and which may only be solved cither numerically or by approximation. 

It is apparent that the fate of the H atom (radical) is crucial in determining the rate of the H2-O2 reaction or, for that matter, the rate of any hydrocarbon oxidation mechanism. From the data in Appendix B one observes that at temperatures encountered in flames the rates of reaction between H atoms and many hydrocarbon species are considerably larger than the rate of the chain branching reaction (17). Note the comparisons in Table 1. Thus, these reactions compete very effectively with reaction (17) for H atoms and reduce the chain branching rate. For this reason. 

In the absence of chain-branching reactions, which are not discussed here, radicals X are generated only by photolysis, reaction (16). 

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. 

Free Radical Trap Theories. Combustion vapor-phase reactions have been studied using premixed gas flames such as methane. Considerable information concerning the mechanism of flame propagation has resulted from this work 40, 49, 50). Basically the process occurs predominantly by branching chain reactions among free radicals. The major chain branching reactions are... 

Thus the inhibitive effect results from the removal of active oxygen atoms (O ) from the vapor phase. Additional inhibition can result from removal of OH radicals in the chain-branching reactions ... 

Radicals are consumed during the reaction by bimolecular chain termination steps such as eq. (5). Replacement radicals are produced by chain branching reactions such as eq. (4). The new radicals (e. g., alkoxy radicals see below) can abstract hydrogen to start new chains. At steady state, the radical generation rate is essentially equal to the radical consumption rate. There have been lively debates in the literature on the sources of the original radicals this question is essentially unresolved [8, 10, 14]. 

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