Network Theory of the Gel Point and the ``Incestuous'' Polymerization of Diallyl Phthalate

Abstract

The status of the gel point equation, advanced by Flory, Stockmayer, and Walling for polyfunctional reactions, is briefly discussed. Two complicating factors in the chain polymerization of divinyl compounds, to which this equation has been applied, are reviewed: the admixture of a monovinyl compound of comparable reactivity, and the ``incestuous'' tendency for the two double bonds in a divinyl compound to enter the same polymerization chain. Contrary to the treatment by Simpson and co-workers, these two factors are found to demand different theoretical approaches. The progress of polymerization enriches the monomer mixture in the monovinyl compound, while the incestuous tendency remains constant. Kinetic derivations are given for the gel point condition in both cases. The gel point in the ``incestuous'' polymerization of diallyl phthalate is calculated to lie at conversions 40 percent higher than estimated by Simpson and co-workers, and much better agreement is thus achieved with their experimental measurements. A simple network theory suffices to predict the gel point in two chain polymerization reactions. Substantial delays of the gel point, predicted by Walling's theory of diffusion control in such reactions, are not encountered.