A phenomenological blending law was proposed in terms of the relaxation spectrum $H_B(τ)$ to describe the effects of blending on a mixture composed of two linear polymeric components with different molecular weights and with high entanglement density.
The blending law was established in terms of the chain relaxation processes discussed in recent tube model theories as well as of earlier experimental observations on the linear viscoelastic properties of such polydisperse polymers with bimodal molecular weight distributions. The law for $H_B(τ)$ was then extended to the binary blending laws for principal viscoelastic properties on the basis of the linear viscoelasticity theory.
The proposed blending laws were compared with available experimental data, such as the shear stress relaxation modulus, dynamic moduli and relaxation spectrum, for the binary blends of narrowly distributed polystyrenes, showing good agreement between predictions and data over a wide range of time or frequency.
The predicted compositional dependence of the representative viscoelastic constants, the zero-shear viscosity and steady-state shear compliance, was in good agreement with earlier experimental data on the binary blends of polystyrenes and linear polybutadienes if the blends are not so diluted that a high molecular weight component chain entangles with surrounding low molecular weight component chains only.
The currently proposed semi-empirical blending law for $H_B(τ)$ was also compared with those proposed by others in terms of the tube model. This showed that the current law is more applicable than those over a wide range of the component molecular-weight-ratio.
