Free-radical addition polymerization average chain lengths

As in step-growth polymerization, a distribution of chain lengths is always obtained in a free-radical addition polymerization because of the inherently random nature of the termination reaction with regard to chain length. Expressions for the number-average... 

The quantity Fi, the instantaneous copolymer composition, is analogous to x , the instantaneous number-average chain length in free-radical addition polymerization. Like x , it depends on the conditions in the reactor at a particular instant. It, too, is really an average, since not all the copolymer formed at a particular instant has exactly the same composition. However, the instantaneous distribution of compositions is normally much narrower than the instantaneous distribution of chain lengths, and because the fact that it is an average is not normally of great practical importance and cannot be controlled anyhow, the overbar is left off of Fj. 

For quantitative analysis, it is assumed that termination by initiator free radicals is negligibly small. In addition, termination should result solely from the recombination of two polymer free radicals. The number-average degree of polymerization is then equal to twice the kinetic chain length ... 

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