Entangled Melts of Branched PS Behave Like Linear PS in the Steady State of Fast Elongational Flows

The classical Doi-Edwards theory for the steady-state stress of entangled linear polymers in uniaxial elongational flow is here extended to entangled branched polymers, specifically to stars and pompoms, both symmetric and asymmetric. The arm withdrawal idea advanced long ago by McLeish and Larson is also fully exploited. Non-Gaussian corrections are considered. Aside from quantitative details, the theory for branched polymers predicts that they behave similarly to linear ones in the steady state (as opposed to the startup stage) of fast elongational flows. The theoretical predictions are then successfully compared, both qualitatively and quantitatively, to data collected by Hassager and co-workers on polystyrene (PS) melts of a pompom and of an asymmetric star. These are, to the authors' knowledge, the only published data for branched polymers of known architecture that, during startup of the elongational flow, extend in time long enough to allow determination of steady-state values of the elongational stress.