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

We derive the theologically relevant "priority" and "seniority" distributio ns of entangled segment topology from a kinetic model of long chain branch formation in metallocene-catalyzed polyolefins. For the model considered, t he 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 metallocen e ensemble from the usual gelation ensemble that is a candidate model for s tandard low-density polyethylene. We calculate the extensional rheology of a model system within a decoupling approximation that permits a partial map ping onto the "multimode pompom" constitutive scheme.