Model for a scission-crosslinking process with both H and Y crosslinks

We present a mathematical model that may predict average molecular weights and weight fraction of solubles for polymer chains subjected to irradiation, where both scission and crosslinking are present. Two types of crosslinks are allowed: four-armed or H crosslinks, and three-armed or Y crosslinks. This is a departure from the more traditional models for irradiation, where only H crosslinks are allowed. The model is valid both in the pregel and postgel regions, and may be applied to chains with any known distribution of molecular weights. We compare predictions from the model with experimental data on polydimethylsiloxane treated with electron beams at different doses, and show that the introduction of Y crosslinks leads to a marked improvement in the quality of the predictions as compared with a more traditional model where only H type crosslinks are allowed.