Molecular distributions in polycondensations involving unlike reactants. II. Linear distributions

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Abstract
A general procedure is developed for the treatment of the molecular distributions arising from linear polycondensations involving more than one monomer. The distributions actually arising are rather complex, and are usually represented by several series. A method is elucidated by which the number average molecular weight may be derived directly and by which normalizing factors for the number and weight fraction distributions may be determined. The general expression for the number fraction of a given species of molecule is found to be a product of several probabilities. The weight fraction distribution and the weight average molecular weight may be derived in a straightforward manner from the number fraction distribution. A number of molecular distributions are worked out in detail. These include reactions of diacids with glycols, reactions of acid anhydrides with glycols, reactions involving asymmetric reactants, and reactions of mixtures of the above types of reactants. Certain polycondensations of interest are treated by the methods of this work. The results are the following: (1) The distribution of AB self‐condensing is identical to the condensation of AA with BB only if all have identical molecular weights and equivalent amounts of AA and BB are used. (2) In the condensation of AA with BB, the more unequal the proportions, the broader the molecular weight distribution. (3) In the above condensation, the greater the difference in molecular weights, the broader the distribution. (4) For all distributions, as M̄N → ∞ M̄W/M̄N → 2. (5) The distributions for anhydrides or unsymmetrical reactants are narrower than for symmetrical reactants, and are different from each other.