The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release

The molecular stress function theory for polymer melts is extended to inclu de a new, dissipative convective constraint release process. First the Helm holtz free energy of tube segments with strain-dependent tube diameter is e stablished neglecting constraint release, and it is demonstrated that the m olecular stress is a function of the average logarithmic stretch under thes e conditions. Then convective constraint release is introduced as a dissipa tive process in the energy balance of tube deformation, which leads to a st rain-dependent evolution equation for the molecular stress function. Constr aint release is considered to be the consequence of different convection me chanisms for tube orientation and tube cross section. Our new, dissipative constraint release model emphasizes that tube kinematics are fundamentally different for rotational and nonrotational flows, and therefore distinguish es explicitly between simple shear and pure shear (planar extension). For t he startup of simple shear and extensional flows, the predictions of our se t of constitutive equations consisting of a history integral for the stress tensor and a differential evolution equation for the molecular stress func tion with only two nonlinear material parameters are in excellent agreement with experimental data of a polydisperse high-density polyethylene (HDPE) and a polydisperse low-density polyethylene (LDPE) melt. Also, stress relax ation after step-shear strain is described for both the HDPE and the LDPE m elt. (C) 2001 The Society of Rheology.