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weight of the sample. The use of isotopically labeled initiators such as 14C-labeled AIBN and benzoyl peroxide and 35S-labeled potassium persulfate is a sensitive method for determining the number of initiator fragments [Bonta et al., 1976]. Isotopically labeled initiators also allow a quantitative analysis of the initiator radicals in systems where their identities are not clear-cut. For example, the use of benzoyl peroxide with 14C in the carbonyl carbon shows that fCOO is responsible for 98% of initiation of styrene polymerization at 80 C, but this drops to about 60% (with f initiating 40% of the propagating chains) at 30 C [Berger et al., 1977]. A third method involves the use of radical scavengers, which count the number of radicals in a system by rapidly stopping their growth. Three groups of radical scavengers are used [Bamford, 1988; Koenig and Fischer, 1973]. The rst group consists of stable radicals such as 2,2-diphenylpicrylhydrazyl (DPPH) obtained by oxidation of diphenylpicrylhydrazine:
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NO2 NO2 2N N NO2 NO2
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The DPPH radical terminates other radicals, probably by the reaction
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NO2 R + 2N N NO2 NO2 R N NO2 NH NO2
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The reaction can be easily followed spectrophotometrically, since the DPPH radical is deep violet and the product is usually light yellow or colorless. Other stable radicals include TEMPO (2,2,6,6-tetramethyl-1-piperidinyloxy), 1,3,5-triphenylverdazyl, and galvinoxyl [Areizaga and Guzman, 1988; Braun and Czerwinski, 1987]. A second group reacts by fast hydrogen or halogen transfer and consists of thiols, iodine, bromine, and dihydroanthracene. The third group, consisting of molecules that react with radicals, includes duroquinone and pbenzoquinone [Janzen, 1971]. Nitroso and nitrone compounds have been found to be highly useful [Evans, 1979; Sato et al., 1977]. These compounds, called spin traps, react with radicals to form stable radicals. 2-Methyl-2-nitrosopropane (XIII) and phenyl-N-t-butylnitrone (XIV) have been used extensively:
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(CH3)3C N O + R XIII O CH N C(CH3)3 + R
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Electron spin resonance (ESR) spectroscopy can be advantageously used to measure the radical concentrations of the nitroxide radicals (XV and XVI) produced, since these are much more stable then the R radicals. Of greater importance, ESR can be used to determine the structure of R, since the ESR of the nitroxide radical is quite sensitive to the structure of R. (For this purpose, nitroso spin traps are more useful, since the R group in the nitroxide radical is nearer to the lone electron.) This can allow a determination of the structures of radicals rst formed in initiator decomposition, the radicals that actually initiate polymerization (if they are not identical with the former) as well as the propagating radicals [Rizzardo and Solomon, 1979; Sato et al., 1975]. The radical scavenging methods require the general caution that the stoichiometry of the reaction between scavenger and radical must be established. A problem with some scavengers is that their reaction with radicals may not be quantitative. The DPPH radical is an extremely ef cient scavenger in many systems. It completely stops vinyl acetate and styrene polymerizations even at concentrations below 10 4 M [Bartlett and Kwart, 1950]. However, the scavenging effect of DPPH is not universally quantitative for all monomers. A fourth method is the dead-end polymerization technique, which allows the simultaneous determination of kd [Catalgil and Baysal, 1987; Reimschuessel and Creasy, 1978; Stickler, 1979]. Dead-end polymerization refers to a polymerization in which the initiator concentration decreases to such a low value that the half-life of the propagating polymer chains approximates that of the initiator. Under such circumstances the polymerization stops short of completion, and one observes a limiting conversion of monomer to polymer at in nite reaction time. Consider a dead-end polymerization initiated by the thermal homolysis of an initiator. Equations 3-28a and 3-32 can be combined and rearranged to yield
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where p is the extent of conversion of monomer to polymer and is de ned by M 0 M = M 0 . At long reaction times (t ! 1), [M] and p reach the limiting values of M 1 and p1 , respectively, and Eq. 3-92 becomes
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