Entangled dynamics and melt flow of branched polymers

One of the most puzzling properties of branched polymers is their unusual viscoelasticity in the melt state. We review the challenges set by both non-linear experiments in extension and shear of polydisperse branched melts, and by the growing corpus of data on well-characterised melts of star-, comb- and H- molecules. The remarkably successful extension of the de Gennes/Doi-Edwards tube model to branched polymers is treated in some detail in the case of star polymers for which it is quantitatively accurate. We then apply it to more complex architectures and to blends of star-star and star-linear composition. Treating linear polymers as "2-arm stars" for the early fluctuation-dominated stages of their stress-relaxation successfully accounts for the relaxation spectrum and "3.4-law" viscosity-molecular weight relationship. The model may be generalised to strong flows in the form of molecular constitutive equations of a structure not found in the phenomenological literature. A model case study, the "pom-pom" polymer, exhibits strong simultaneous extension hardening and shear softening, akin to commercial branched polymers. Computation with such a constitutive equation in a viscoelastic flow-solver reproduces the large corner vortices in contraction flows characteristic of branched melts and suggests possible future applications of the modelling tools developed to date.