Macromolecules 1999, 32, 181-185
181
Onset of Entanglement Y.-H. Lin* and J.-H. Juang Department of Applied Chemistry, National Chiao Tung University, Hsinchu, Taiwan Received November 26, 1997; Revised Manuscript Received April 23, 1998
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 Me ()4FRT/5GN), whereas that of component two being greater than Me (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, W2, 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 W2. According to the study, entanglement starts to occur in the close neighborhood of Me′ (the entanglement molecular weight of the blend solution and Me′ ) MeW2-1) for the polymer blend solution or equivalently Me for the monodisperse polymer melt well below Mc′ or Mc (Mc′ ) McW2-1, where Mc is the critical molecular weight of the zero shear viscosity of the polymer melt).
Introduction Polymer viscoelastic properties are strongly influenced by chain entanglement.1,2 Chain entanglement in a polymeric liquid occurs naturally when both the concentration and molecular weight are high enough. A strong indication of chain entanglement is the modulus plateau that can be observed for nearly monodisperse high molecular weight samples. The entanglement molecular weight Me can be calculated from the measured plateau modulus GN according to3,4
Me ) 4FRT/5GN
(1)
Another strong indication of chain entanglement is the steep increase of the zero shear viscosity with increasing molecular weight (the η0 ∝ M3.4 relation) above the critical molecular weight, Mc.1,2,5 For many different kinds of linear flexible polymers, the ratio of Mc/Me is about 2.4, which indicates the close relation between Mc and Me. In the molecular weight region,
