Gel formation in polymers resulting from simultaneous crosslinking and scission

Abstract

An equation giving the gel fraction of polymers undergoing simultaneous crosslinking and scission is derived for an arbitrary initial molecular-size distribution. Application is made to the case where the initial distribution is the generalized Poisson type. For an initial distribution which is either very broad or very narrow as compared with the Poisson type and for a moderate value of the ratio of the scission rate to the crosslinking rate, considerable deviations from the Charlesby-Pinner relationship (derived for an initial random distribution) occur.