LDPE melt rheology and the pom–pom model

Abstract

In their original contribution, McLeish and Larson [J. Rheol. 42 (1998) 81–110] established a constitutive sketch for a particular branched polymer, the pom–pom model. The orientation contribution to the stress tensor of the pom–pom polymer under flow is calculated using the tube concept of Doi and Edwards [J. Chem. Soc. Faraday Trans, Part 2, 11(74) (1978a) 1802–1817]. More recently, Inkson et al. [J. Rheol. 43 (1999) 873–896] succeeded in predicting the melt rheology of longchain-branched low-density polyethylenes at start-up of extensional and shear flows, using a multi-mode pom–pom model and a differential approximation of the original Doi–Edwards model for the orientation contribution. We compare the transient viscosity predictions, when using the original Doi–Edwards strain measure (in the independent alignment approximation) and the differential approximation. We conclude that the differential approximation is a crude approximation of the Doi–Edwards model for high Deborah number flows and for planar extension. In the case of the pom–pom model, the differential approximation introduces a strong relaxation process for shear flow that is not present in the full model. Using the original Doi–Edwards strain measure for the orientation contribution, we show that the pom–pom model predicts a strain hardening behaviour in the case of the second normal stress difference in planar extension, in contrast to experimental evidence. In shear flow, it is in quantitative disagreement with the experimentally observed amount of stress overshoot and shear thinning. We also analyse the pom–pom model predictions for stress relaxation after a step strain. The multi-mode pom–pom model does not show the time-strain separability observed experimentally for polymer melts over several decades of relaxation time.