Experimental Validation of the Hierarchical Multi-mode Molecular Stress Function Modelin Elongational Flow of Long-chain Branched Polymer Melts

The Hierarchical Multi-mode Molecular Stress Function (HMMSF) model predicts the elongational start-up viscosity of long-chain branched (LCB) polymer melts quantitatively up to the point of fracture or up to the steady-state elongational viscosity. It is based on the linear-viscoelastic relaxation modulus and only one nonlinear material parameter in extensional flows, the so-called dilution modulus GD. In addition to the concepts of hierarchical relaxation and dynamic dilution, the HMMSF model was so far based on the concept of interchain tube pressure limiting chain stretch. Here, we replace the tube pressure idea by the recently developed Enhanced Relaxation of Stretch (ERS) model, which assumes that the decreasing tube diameter with increasing deformation leads to faster stretch relaxation at smaller length scales. We also take the entropic fracture criterion into account. The modified HMMSF model is validated by comparison with elongational viscosity data of well-defined low-dispersive polystyrene Pom-Pom model systems, for which the dilution modulus GD is equal to the plateau modulus. If not preceded by fracture, branch point withdrawal will occur in LCB melts at higher Hencky strains and strain rates. This can be modeled by a stretch parameter, which expresses the characteristic backbone stretch when side arms and their branch points are withdrawn into the backbone tube. We demonstrate that the predictions of this extension of the HMMSF model, the so-called Extended Hierarchical Multi-mode Molecular Stress Function (EHMMSF) model are in excellent agreement with experimental elongational data of three commercial low-density polyethylene melts, and that the specific stretch parameter is a useful measure of the global effect of branching structure on the rheology of LCB melts.