Effects of High Energy Radiation on Polymers II. End-linking and Gel Fraction

The effect of end-linking induced in polymers by high energy radiation is discussed. When cyclization does not occur, the same results are obtained as those derived by A. Charlesby, and moreover it is known that for any initial distribution the gel formation does not occur when σ is smaller than 1/4, where σ represents the probability that an end produced by a molecular scission links with a monomer unit of another molecule. The theory also gives the average molecular weights and the average end numbers. For the initial uniform distribution the weight average molecular weight has a maximum in case 1/12<σ<1/4, while for the initial Poisson distribution it has no maximum. The weight average end number becomes infinite at the gel point, but the number average end number does not. It is shown that the retardation of incipient gel formation is negligible when cyclization occurs. Beyond the gel point the gel part grows rapidly. The feature is studied in the cases of cross-linking and end-linking with or without...