Rate of branching

Gamer and Hailes [462] postulated a chain branching reaction in the decomposition of mercury fulminate, since the values of n( 10—20) were larger than could be considered consistent with power law equation [eqn. (2)] obedience. If the rate of nucleation is constant (0 = 1 for the generation of a new nuclei at a large number of sites, N0) and there is a constant rate of branching of existing nuclei (ftB), the nucleation law is... 

The term D3 can be expressed in terms of the relative rates of branch formation plus termination compared to propagation. 

BEI. The action of BEI, BEIIa, and BEIIb on amylopectin has also been studied by Guan and Preiss (1993). Of the three isoforms, BEI had the highest activity in branching amylose and its rate of branching amylopectin... 

As pointed out previously, an upper limit is placed upon (C) by second-order recombination processes, so that the radical concentration cannot grow without limit. At pressures near the first explosion limit this restriction is unimportant. Thus if we assume that the reaction H -f- H -f M proceeds at every tenth triple collision (that is, A = 3 X 10 liters2/mole -sec) then the lifetime of an II atom at 750 K when M = 8 mm Hg and H = 0.8 mm Hg ( ) is about 0.2 sec [t = l/fc(M)(H)]. This is much slower than the rate of branching in the H2 + O2 system (see page 457). 

For consistency, at the stationary state, the rate of loss of radicals at the walls must equal the total rate of radical initiation in the entire volume plus their total rate of branching. These two conditions must be equivalent. 

Hence the partial pressure of the peroxide was ca. 2 torr. Shtern then considered whether such small amounts of peroxide could lead to a rate of branching of the same magnitude as that given by the aldehyde, viz. branching due to either... 

He concluded, therefore, that such a small quantity of peroxide is capable of producing the same rate of branching as a quantity of aldehyde fifty times as great. 

The replacement of (5c) by (5d) has been chosen so as to recognize that as the peracid concentration becomes high attack on it by the radical present in the highest concentration is possible. For the region where the rate of branching is much greater than that of initiation this scheme leads to the instantaneous rate expression... 

The lower lines in Fig. 2 plot the conditions when the rates of branching (via RO2) and of termination (via R) are equal for two alkanes of widely differing autoignition propensities. Below the line for a particular fuel low-temperature alkyl peroxy radical chemistry is dominant. Above the line alkyl peroxy radicals are of less significance. 

Figure 11. Photooxidation rate of branched polyethylene films containing 0.1% Neotex ISO carbon black (9) and 0.1% substituted o-hydroxybenzophenone (H). Also shown are the rates of unprotected films exposed to direct radiation (A), to radiation transmitted by the black screen (O), and by the film cotaaining the...

At deep stages of oxidation the rate of decomposition of hydroperoxide increases with its concentration. The rate of quadratic chain termination is proportional to the square concentration of radicals. At this point plays an important role expenditure monomer units of the polymer. Nucleation rate of the chain compared with the rate of branching can be neglected. The reaction is carried out at a high concentration of oxygen and the contribution reaction R +R02 is negligible, [R ] [R02 ]. For these conditions, the balance equation of free radicals and hydroperoxide is ... 

The self-ignition phenomenon and its minimum temperature can be interpreted by the chain-reaction concept of burning. The resultant rate of branched chain-reactions can be derived from the difference between the branching and terminating rates of the chain ... 

This temperature, T2, is the lowest temperature at which ignition may occur. Consequently, at the self-ignition temperature, the rate of branching is equal to the rate of chain termination. 

Continuity of combustion can be interpreted on the basis of chain reaction mechanisms. It was pointed out that the resultant rate of a chain reaction depended on the difference between the rate of branching and that of termination. A combustion will... 

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