A hierarchical algorithm for predicting the linear viscoelastic properties of polymer melts with long-chain branching

The "hierarchical model" proposed earlier [Larson in Macromolecules 34:4556-4571, 2001] is herein modified by inclusion of early time fluctuations and other refinements drawn from the theories of Milner and McLeish for more quantitative prediction. The hierarchical model predictions are then compared with experimental linear viscoelastic data of well-defined long chain branched 1,4-polybutadienes and 1,4-polyisoprenes using a single set of parameter values for each polymer, which are obtained from experimental data for monodisperse linear and star polymers. For a wide range of monodisperse branched polymer melts, the predictions of the hierarchical model for monodisperse melts are very similar to those of the Milner-McLeish theories, and agree well with experimental data for many, but not all, of the branched polymer samples. Since the modified hierarchical model accounts for arbitrary polydispersity in molecular weight and branching distributions, which is not accounted for in the Milner-McLeish theories, the hierarchical algorithm is a promising one for predicting the relaxation of general mixtures of branched polymers.