Nonlinear viscoelastic behavior of polymer melts

Abstract

With the aid of Eyring's rate theory a set of equations is derived describing the nonlinear viscoelastic behavior of a generalized Maxwell liquid in simple shear. It is shown that this behavior may be completely described by a stress- and temperature-dependent relaxation spectrum which, in a first approximation, becomes independent of stress if the latter tends to zero. Each term of the discrete relaxation spectrum is characterized by a relaxation time, a shear modulus, and a dimensionless parameter Γ equal to the limiting value of a recoverable strain at infinitely high stress. All Γi's disappear from the relevant equations if the stress tends to zero. Similar expressions describing nonlinear behavior of a generalized Kelvin-Voigt solid may be derived from Schwarzl and Brinkman's diffusion theory. The theory is used to interpret the observed nonlinear flow and relaxation behavior of a number of various polymer melts. The polymers have been studied under well-defined hydrodynamical and thermal conditions in a cone-and-plate viscometer. In a first approximation, all Γi's have been supposed equal to 1. The theoretical flow and relaxation curves calculated from the observed relaxation spectrum are in fair agreement with the experimental ones. Finally it is shown that the observed behavior may also be interpreted in terms of the transient network theory if the activated state of a flow unit is identified with the strained state of more or less voluminous parts of the molecular network in a polymer melt.