Molecular weight distribution in random crosslinking of polymers: Modality of the molecular weight distribution

Abstract

AbstractThe molecular weight distribution (MWD), formed during random crosslinking of polymers whose initial molecular weight distribution is given by the Schulz‐Zimm distribution, is proposed. The obtained equation can be considered as a good approximation even for nonrandom crosslinking reactions such as free‐radical and living crosslinking copolymerizations. When the initial molecular weight distribution is very narrow, namely, the polydispersity index (Pw/Pn) is smaller than about 1,1, a multimodal distribution can be obtained. Quite often the MWD is represented solely by the average molecular weights such as number‐ and weight‐average molecular weights in conventional approaches; however, such types of measure can not give enough description for multimodal distributions. Multimodal distributions may be obtained for the primary polymer molecules formed via living polymerizations. On the other hand, for the primary polymer molecules formed by free‐radical polymerization whose polydispersity index must be larger than 1,5, it is impossible to form a bimodal distribution as long as nonideal kinetics such as the size and structure dependence of crosslinking reactions are neglected.