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Modeling nonlinear rheology of polydisperse polymer melts

Wagner M. H.

International Journal of Applied Mechanics and Engineering

2006

Vol. 11, no 2

255-267

Melt rheology of polydisperse polymers is reviewed with special emphasis on the separation of effects of chain orientation and chain stretch, as described consistently by the Molecular Stress Function (MSF) theory. Based on energy balance considerations, first the Free Energy of a tube segment with a strain-dependent tube diameter is established, and it is demonstrated that the molecular stress is a function of the orientational free energy under these conditions. Then constraint release is introduced as a dissipative process, which modifies the energy balance of tube deformation, and leads to a strain-dependent evolution equation for the molecular stress function. For simple shear and extensional flows, the predictions of the MSF model consisting of a history integral for the stress tensor and a differential evolution equation for the molecular stress function with only one (extensional flows) or two (shear flow) nonlinear material parameters, are in excellent agreement with experimental data of HDPE, LDPE, LLDPE, PS, and PP melts. The concept of a strain-dependent tube diameter, which decreases with increasing deformation, explains consistently the strain hardening of linear as well as of long-chain branched polymer melts.