Blending laws for high-molecular-weight polymer melts

Abstract

Blending laws have been previously proposed to describe the effects of molecular weight distribution (MWD) on the viscoelastic properties of polymer melts. The blending laws represent the relaxation spectrum of a blend HB(τ) as a weighted sum of the relaxation spectra of the individual components, each shifted in time by an amount characteristic of the interactions between the molecular species. In general, the binary blending law is (Remark: Graphics omitted.) The weighing factor Vij, and shift factors λij may be obtained directly from the calculated relaxation spectra of blends of narrow MWD fractions. These parameters are used to test the applicability of two types of blending laws: (1) The quadratic blending law, Vij=wiwj, where wk is the weight fraction of the k-th component; (2) The simple blending law, Vij=viδij. The experimental results give qualified support to the quadratic blending law but place strong restrictions on the magnitude and shape of the cross relaxation spectra term Hij. These require that Hij≠Hji, Hij/Hii=constant, and λij=λii. In addition, the restrictions imply that the simple and the quadratic blending laws are equivalent representations of HB(τ). © 1973, The Society of Polymer Science, Japan. All rights reserved.