Theory of main-chain scission

The analysis developed here is based in the assumption that chain scission occurs at random. A fracture density is defined as 

For any initial distribution, the number average degree of polymerization u of a degraded polymer is related to its initial value by 

If the initial distribution is not random, the theoretical treatment to derive u 2 and u 3 is complicated when the number of scissions per chain is small [2]. It has, however, been theoretically demonstrated that u 2/u = 2 if the number of scissions per chain is equal to or larger than 4 or 5. 

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