Onset of entanglement

Abstract

The onset of entanglement was determined from studying the viscoelastic spectra of the blends consisting of two nearly monodisperse polystyrene polymers: component one having a molecular weight slightly less than the entanglement molecular weight M-e (=4 rho RT/5G(N)), whereas that of component two being greater than M-e (such a blend is referred to as the blend solution). It is shown that because of the absence of the hydrodynamic interaction the viscoelastic spectrum of the blend solution can be described by applying the Rouse theory to both components in the entanglement-free region. As entanglements among the chains of component two occur, when its weight fraction, W-2, increases above a critical point, the viscoelastic response of component one remains described by the Rouse theory. With the Rouse viscoelastic response of component one as the internal reference, the onset of chain entanglement among the chains of component two can be determined by monitoring the deviation of the viscoelastic response of component two from being described by the Rouse theory as a function of increasing mil. According to the study, entanglement starts to occur in the close neighborhood of M-e' (the entanglement molecular weight of the blend solution and M-e' = MeW2-1) for the polymer blend solution or equivalently M-e for the monodisperse polymer melt well below M-c' or M-c (M-c' = McW2-1, where M-c is the critical molecular weight of the zero shear viscosity of the polymer melt).