The Linear Viscoelastic Relaxation Modulus Related to the MWD of Linear Homopolymer Blends

Abstract

This work analyzes the relation between the shear relaxation modulus of entangled, linear and flexible homopolymer blends and molecular weight distribution (MWD). The theory employed is based on the double reptation mixing rule and a law for the relaxation time of chains in a polydisperse matrix. It is shown that chain reptation with contour length fluctuations and tube constraint release are the relevant mechanisms of chain relaxation, when the polydispersity is high. The effect of the last mechanism is to decrease chain relaxation times. Calculations are carried out with rheometric data of linear viscoelasticity for polystyrene, polybutadiene, polypropylene and high density polyethylene. The model predictions are compared with experimental data of gel permeation chromatography (GPC). In homopolymer blends with a wide molecular weight distribution, only chains of relatively low molecular weight relax by reptation with contour length fluctuations. A relaxation law for chains in a polydisperse polymer matrix is suggested and validated with GPC data. The theory verifies that the zero-shear rate viscosity of a polydisperse polymer, is proportional to the mass average molecular weight raised to a power greater than that found for the near monodisperse counterpart.