Mh. Wagner et al., The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J RHEOL, 45(6), 2001, pp. 1387-1412
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.