Molecular Entanglement Theory of Flow Behavior in Amorphous Polymers

Abstract

An approximate molecular theory of steady flow in amorphous polymers has been developed by considering the properties of a deforming entanglement network. The dynamics of entanglement formation between pairs of molecules and its influence on the density of entanglements during steady deformation were examined. From a simple model for these processes, apparent viscosity was calculated as a function of the shear rate. An approximate calculation of the normal-stress differences was also made. The viscosity was found to be dependent on the rate of deformation, and at sufficiently high shear rates it approached proportionality with (shear rate)−¾. The onset of non-Newtonian behavior occurs in the same region of shear rates as that predicted by the coil-distortion theory of steady flow. However, unlike the predictions of the latter theory, dynamic-viscosity frequency curves and apparent-viscosity shear-rate curves should not necessarily superimpose, because the dispersion mechanisms are fundamentally different in the two cases. Comparison with experimental results reported in the literature showed generally satisfactory agreement in both the shape of the viscosity master curves and in the order of magnitude of the normal-stress differences.