Abstract

The spanning tree model' (utilising Gaussian-flight statistics) for the kinetics of simultaneous ring-chain competition in linear and branched polycondensation reactions has been extended by the use of the path weighting method of cascade statistics to the system glycerol/adipic acid. In this system there is no single fixed increment in ring sizes as more units are added to the ring-closing path, since a glycerol unit incorporated through the reaction of its two primary hydroxyls contributes a longer increment to the path length than when one primary and one secondary hydroxyl are involved. A computational method has been developed to count, as the reaction proceeds, the mean number of paths of all lengths available for forming a cycle back to a given root functionality, with each path receiving the correct Gaussian weight according to its length.

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