On the Effect of High Energy Radiation to Polymers I. Cross-linking and Degradation

Integro-differential equations are obtained, which describe the variation of molecular weight distributions in a polymer substance caused by irradiation. The solutions of these equations give the gel point and the average molecular weights. In the case of cross-linking without cyclization, the results agree with those obtained by other authors. The problems involving cyclization and branching are also solved, showing that the gel formation is retarded by cyclization and that the weight average branching number diverges at the gel point, while the number average branching number does not. As for degradation, the molecular weight distributions for an arbitrary radiation dose are obtained, and it is shown that for any initial distribution the final molecular weight distribution becomes Poisson-like. The problem which deals with the case where cross-linking and degradation coexist is also discussed, and it is shown that for any initial distribution the gel formation occurs only when the ratio of the two probabilities concerning degradation and cross-linking is smaller than 4.