Molecular Size Distribution and Gelation of Irradiated Copolymers

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Abstract
A theory is developed about the molecular size distribution in a system of copolymers which are composed of two different kinds of monomer units and undergo random crosslinking when exposed to high‐energy radiations. The radiation‐induced change in the molecular size distribution is described by an integro‐differential equation, which we solve exactly by means of Laplace transform for an arbitrary initial distribution to obtain the number‐average as well as the weight‐average degree of polymerization as a function of radiation dose. Further, the gel point, or the dose required for incipient gelation, is given as a function of concentrations of the monomer units constituting the copolymeric system. The present theory, which also involves the problem of crosslinking in a mixture of two kinds of polymers as a special case, leads to a condition for gelation of such a mixture due to irradiation when crosslinking competes with main‐chain scission. This condition proves to be completely independent of the initial distribution.

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