Entangled dynamics and melt flow of branched polymers

One of the most puzzling properties of branched polymers is their unusual v iscoelasticity in the melt state. We review the challenges set by both non- linear experiments in extension and shear of polydisperse branched melts, a nd by the growing corpus of data on well-characterised melts of star-, comb - and H- molecules. The remarkably successful extension of the de Gennes/Do i-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 appl y it to more complex architectures and to blends of star-star and star-line ar composition. Treating linear polymers as "2-arm stars" for the early flu ctuation-dominate stages of their stress-relaxation successfully accounts f or the relaxation spectrum and "3.4-law" viscosity-molecular weight relatio nship. The model may be generalised to strong flows in the form of molecula r constitutive equations of a structure not found in the phenomenological l iterature. A model case study, the "pom-pom" polymer, exhibits strong simul taneous extension hardening and shear softening, akin to commercial branche d polymers. Computation with such a constitutive equation in a viscoelastic flow-solver reproduces the large corner vortices in contraction flows char acteristic of branched melts and suggests possible future applications of t he modelling tools developed to date.