Statistical chain-scission reactions

Depolymerization, elimination, and statistical chain-scission reactions can be used for polymer analysis. When the monomer is the main degradation product obtained, it can easily be identified by boiling point and refractive index. 

Thus, transesterification causes branching as well as chain scission Let us consider the branching statistics for the case of a polycarboxylic acid and polyepoxide with groups of independent reactivity. The use of the statistical method is justified because neither the substitution effect nor the initiated chain growth are operative. If only addition esterification occurs (and indeed this reaction can be selectively accelerated by special catalysts the statistics is analogous to the polyamine-polyepoxide addition and even simpler because the substitution effect is here absent. The pgf s for the number of bonds issuing from polyacid (C) and polyepoxide (E) units read ... 

The model chosen to describe the degradation of polyethylene was random chain scission. Lenz (3,) in his section on degradation reactions of polymers cites work which supports the contention that polyethylene does thermally degrade in a random chain scission manner as opposed to depolymerization. For this model a statistical treatment has been developed by Montroll and Simha (). The extent of reaction may be related to the number average molecular weight by ... 

In ideal random crosslinking polymerization or crosslinking of existing chains, the reactivity of a group is not influenced by the state of other groups all free functionalities, whether attached or unattached to the tree, are assumed to be of the same reactivity. For example, the molecular weight distribution in a branched polymer does not depend on the ratio of rate constants for formation and scission of bonds, but only on the extent of reaction. Combinatorial statistics can be applied in this case, but use of the p.g.f. simplifies the mathematics considerably. 

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