LDPE melt rheology and the pom-pom model

In their original contribution, McLeish and Larson [J. Rheol. 42 (1998) 81- 110] established a constitutive sketch for a particular branched polymer, t he 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. Sec. Faraday Trans, Part 2, 11(74) (1978a) 1802-1817]. Mo re recently, Inkson et al. [J. Rheol. 43 (1999) 873-896] succeeded in predi cting the melt rheology of longchain-branched low-density polyethylenes at start-up of extensional and shear flows, using a multi-mode pom-pom model a nd a differential approximation of the original Doi-Edwards model for the o rientation contribution. We compare the transient viscosity predictions, wh en using the original Doi-Edwards strain measure (in the independent alignm ent approximation) and the differential approximation. We conclude that the differential approximation is a crude approximation of the Doi-Edwards mod el for high Deborah number flows and for planar extension. In the case of t he pom-pom model, the differential approximation introduces a strong relaxa tion process for shear flow that is not present in the full model. Using th e original Doi-Edwards strain measure for the orientation contribution, we show that the pom-pom model predicts a strain hardening behaviour in the ca se 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 thin ning. We also analyse the pom-pom model predictions for stress relaxation a fter a step strain. The multi-mode pom-pom model does not show the time-str ain separability observed experimentally for polymer melts over several dec ades of relaxation time. (C) 2000 Elsevier Science B.V. All rights reserved .