Molecular distributions in polycondensations involving unlike reactants. I. Gelation

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Abstract
A general criterion for gelation in polycondensations having like groups of unequal reactivity has been formulated. In its simplest form, the criterion is that, for gelation, the expectation that a given structure will be propagated is unity, or greater. Several specific cases are treated, and literal expressions relating the gelation point to the reaction probabilities are derived. Included are treatments of systems involving anhydrides and mixtures of acids and glycols. The manner in which kinetic calculations may be used to determine reaction probabilities is summarized. It is found that the inclusion of unsymmetrical reactants significantly increases the degree of polymerization necessary for gelation. However, when anhydrides are used, depending on the relative reaction rates of the anhydride and the acid formed when the anhydride reacts, the degree of reaction necessary for gelation may be either greater or less than that for a similar system using only symmetrical reactants.

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