Rheology of highly entangled linear and branched polymers using flow birefringence and mechanical rheometry

Rheology of highly entangled linear polystyrene solutions was studied using both birefringence polarimetry and mechanical rheometry. A phase modulated flow birefringence apparatus was developed which is capable of measuring time-dependent changes in the optical equivalents of shear stress (σ) and first normal stress difference (N₁) in a planar-Couette shear flow geometry. Several new findings were reported. Step shear experimental results show that the damping function h(γ) = G(t,γ)/G(t) in entangled polymer liquids continuously varies with polymer molecular weight and concentration. In weak to moderately entangled solutions, experimental results for h(γ) are in accord with the Doi-Edwards (1986) theoretical prediction, h_DE-IA . At higher entanglement densities, h(γ) becomes progressively softer than h_DE-IA, particularly at low strains. Step shear observations can be explained in terms of coupled relaxation of polymer segment orientation and tube equilibration following step shear. In steady shear flow, a plateau steady-state orientation angle was observed for well entangled polymer solutions over a range of flow rates between inverse terminal relaxation time and inverse Rouse relaxation time. In start-up of fast shear flows a transient undershoot in orientation angle was observed. A differential constitutive model was developed incorporating convective constraint release and an expression for molecular drag that explicitly depends on number of entanglements (N/N_e). The predictions of this model in steady and start-up of steady shear flows are in fair accord with experimental observations.; Low amplitude oscillatory shear and step shear dynamics of various model entangled six-arm (A₃-A-A₃) and eight-arm (A₃-A-A₂-A-A ₃) polybutadiene melts were investigated to understand the effects of branching. Several new results were reported. First, the mean segmental relaxation time of multi-arm polymers was found to be a function of cross-bar molecular weight and polymer architecture. Second, the plot of longest relaxation time and zero shear viscosity rescaled with monomeric scale properties against dilated cross-bar length indicated a power law dependence closer to the value expected for reptation. Finally, the slowest relaxation mode of eight-arm materials was found to be dominated by Rouse-like fluctuation modes of the branch points. The relaxation spectra of six-arm polymers were modeled using a hierarchy of relaxation events.