The reputation idea of de Gennes and the tube model theory of Doi and Edwards for monodisperse polymers are extended to explain the viscoelastic properties of highly entangled linear polymers with molecular weight distribution (MWD).
A modified tube model theory, the equivalent primitive chain model, is proposed with the consideration of the significance of constraint release by local tube renewal in accounting for the relaxation process of a model chain in the binary blend of two monodisperse species of the same polymer. Its relaxation by concurrent reputation and constraint release is remodeled as the pure reptational disengagement process of an equivalent primitive chain. Including the effect of contour-length fluctuation at chain ends, the longest relaxation time of the model chain is related to the component relaxation times in pure state, molecular weights (MW``s) of blend components and composition.
The proposed model is then extended to multicomponent blends. Based on the interpretation for the binary blend case, the longest relaxation times of the components are obtained.
From the knowledge of the equivalent chain parameters during relaxation, the stress equation for polydisperse polymers is formulated and reduced to the constitutive equation for the shear stress relaxation modulus G(t)incorporating the effects due to fast intramolecular chain dynamics. Blending laws for other linear viscoelastic properties are then deduced from G(t).
In order to test the theory, G(t) and the dynamic moduli $G^*(ω)$ for the binary and ternary blends of standard polystyrene fractions are measured with a parallel plate rheometer in a linear deformation regime. Details of MWD for the fractions are obtained by a gel permeation chromatography method. Both the fractions and their blends are observed to obey the time-temperature superposition principle, based on which master curves of G(t) and $G^*(ω)$ can be constructed.
The time and frequency dependence of the G(t) and $G^*...