Molecular rheology and statistics of long chain branched metallocene-catalyzed polyolefins

We derive the theologically relevant "priority" and "seniority" distributions of entangled segment topology from a kinetic model of long chain branch formation in metallocene-catalyzed polyolefins. For the model considered, the chemistry results in a two-parameter family of molecular distributions; convenient parameters are the typical strand molecular weight between cross-links and a branching probability. Only the branching probability controls the chain topologies. We comment on the different nature of the metallocene ensemble from the usual gelation ensemble that is a candidate model for standard low-density polyethylene. We calculate the extensional rheology of a model system within a decoupling approximation that permits a partial mapping onto the "multimode pompom" constitutive scheme.