Investigation of the nonlinear mixing rule for its adequacy in viscosity to molecular weight distribution transforms

Abstract

While the molecular weight distribution (MWD) model of Bersted and Slee, and later Malkin and Teishev, has been widely used in viscosity to MWD transformation, a fundamental assumption in the model—the empirical nonlinear mixing rule for homologous blends η1/α=∑wiηi1/α—has not been examined as a function of deformation rate and MWD. In this study of the nonlinear mixing rule, we evaluated the influence of deformation rate and MWD, both experimentally and theoretically, by using real polymers. Direct experimental results indicate that the nonlinear mixing rule exponent can be a function of deformation rate. According to the theory-based quadratic mixing rule, the exponent α depends on both the deformation rate and the MWD of blends, suggesting that the nonlinear mixing rule is fundamentally invalid. However, for moderately wide distributions (Mw/Mn<2), the nonlinear mixing rule with a constant α of 3.4 for all shear rates and MWDs, is almost equivalent to the quadratic mixing rule. Thus the simplified mixi...