A generalized differential constitutive equation for polymer melts based on principles of nonequilibrium thermodynamics

Abstract

Based on principles of nonequilibrium thermodynamics, we derive a generalized differential constitutive equation for polymer melts which incorporates terms that account for anisotropic hydrodynamic drag in the form suggested by Giesekus, finite chain extensibility with nonlinear molecular stretching, nonaffine deformation, and variation of the longest chain relaxation time with chain conformation. In the new equation, the expression for the Helmholtz free energy of deformation is defined such that the entropy remains bounded even at high deformation rates, as it should from a physical point of view. Key elements in the new constitutive model are the functions describing the dependence of the nonequilibrum free energy and the relaxation matrix on the conformation tensor. With suitable choices of these two functions, the new equation reduces to a number of well-known viscoelastic models. However, it is more general in the sense that it permits incorporating into a single constitutive differential equation more accurate expressions for the description of chain elasticity and relaxation. Restrictions on the parameters entering these two functions are obtained by analyzing the thermodynamic admissibility of the model. By analyzing the asymptotic behavior of the new constitutive equation at low and high shear rates in steady shear, one can fix all of its parameters from available rheological data for the conformation tensor except for one which should be fitted. We illustrate the procedure here where the new model is used to fit available rheological data for short polyethylene melts obtained through direct nonequilibrium molecular dynamics simulations in shear and planar elongation, with remarkable success.