Termination Radical Paths

Because radicals are in minute concentration, the usual radical mechanisms involve a radical colliding with an even electron molecule in a chain process. A common error is to have a termination step instead of creating a regenerating loop. The three common radical path combinations, Sh2, Adn2, and radical polymerization, all have propagation steps in which radicals collide with an even electron species, creating a new radical. 

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 pinacol formation reaction follows a radical mechanism. Benzopinacol, benzophenone and the mixed pinacol are formed jointly with many radical species [72, 74]. In the course of the reaction, first a high-energy excited state is generated with the aid of photons. Thereafter, this excited-state species reacts with a solvent molecule 2-propanol to give two respective radicals. The 2-propanol radical reacts with one molecule of benzophenone (in the ground state, without photon aid) to lengthen the radical chain. By combination of radicals, adducts are formed, including the desired product benzopinacol. Chain termination reactions quench the radicals by other paths. 

Because there are two positive terms in the denominator of equation 4.2.85 (either of which may be associated with the dominant termination process), this equation leads to two explosion limits. At very low pressures the mean free path of the molecules in the reactor is quite long, and the radical termination processes occur primarily on the surfaces of the reaction vessel. Under these conditions gas phase collisions leading to chain breaking are relatively infrequent events, and fst fgt. Steady-state reaction conditions can prevail under these conditions if fst > fb(a — 1). 

As the pressure in the reaction vessel increases, the mean free path of the gaseous molecules will decrease and the ease with which radicals can reach the surfaces of the vessel will diminish. Surface termination processes will thus occur less frequently fst will decline and may do so to the extent that fst + fgt becomes equal to fb oc — 1). At this point an explosion will occur. This point corresponds to the first explosion limit shown in Figure 4.1. If we now jump to some higher pressure at which steady-state reaction conditions can again prevail, similar... 

Photoinitiated free radical polymerization is a typical chain reaction. Oster and Nang (8) and Ledwith (9) have described the kinetics and the mechanisms for such photopolymerization reactions. The rate of polymerization depends on the intensity of incident light (/ ), the quantum yield for production of radicals ( ), the molar extinction coefficient of the initiator at the wavelength employed ( ), the initiator concentration [5], and the path length (/) of the light through the sample. Assuming the usual radical termination processes at steady state, the rate of photopolymerization is often approximated by... 

In most reactions addition of acetone (when used as a photoinitiator) to the double bond took place. This addition has been shown to follow the same path as the formamide addition, leading to methyl ketones resulting from terminal addition in the case of terminal olefins, and to a mixture of two methyl ketones in the case of nonterminal olefins. The ratio of the two isomeric methyl ketones were the same as those of the appropriate amides obtained in these reactions. These ketones are assumed to be produced from addition of acetonyl radicals to the double bond ... 

The aziridination works for both aromatic and aliphatic olefins, including less active linear terminal olefins. Most reactions proceed in good yield at room temperature. The use of ci.v-stilbene at 0°C gives predominately cis aziridine product in about 90 10 cis trails ratio (Table 6.1). The conservation of cis structure suggests that a discrete silver nitrene intermediate is involved in the reaction path. Because of the unique disilver structure and unlikely formation of a silver(III) species, the authors suspect that a bridged nitrene intermediate between the two silver atoms may be responsible for this transformation in which each silver atom donates one electron to the nitrenoid. However, further research is necessary to prove this hypothesis and a fast radical reaction mechanism cannot be eliminated on the basis of current evidence. 

Now for most gases Dq/c is approximately equal to the mean free path and is very close to lO cm at STP (Table VIII.3), so that in a 500-cc flask (ro = 5 cm), P must be of the order of 0.002/c mm Hg or higher for diffusion to be important in controlling wall termination. Thus if a radical is captured on every collision (c = 1), diffusion control is important at pressures above 0.002 mm Hg. If, however, e = 10 , then the range is 20 mm Ilg or higher. Below these pressures radicals disappear at the walls, but there are no appreciable gradients present. 

The measured reaction orders support the proposed mechanism. Path A is certainly first order in reactant. Paths B and C may be 1/2, first, or 3/2 order, depending on the termination reaction (15). Most likely, termination involves combination or disproportionation of small chain carrying radicals (CH3, C2H5 ). With first-order initiation, this would result in 3/2-order kinetics. The overall reaction order would then be somewhere between first (Mechanism A) and 3/2 (Mechanisms B and C). The measured order of 1.33 for dodecene agrees with this prediction. The fact that propylene and nonene are formed with reaction orders of 1.10 and 1.16 with respect to dodecene (Table III) supports the hypothesis that they are formed largely by a first-order decomposition. 

Analytic solutions for Eq. (5) provide the most direct path of the prediction of PSD evolution. For batch polymerizations in Interval II, however, analytic solutions have only been achieved for the so-called zero-one system (Lichti et al., 1981). These are systems wherein negligibly few particles contain two or more free radicals because of the rapidity of the bimolecular termination reaction (e.g., in styrene emulsion polymerizations with small latex particles). In this case, Eq. (5) may be written as follows ... 

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