Method for obtaining tube model parameters for commercial ethene/α-olefin copolymers

Abstract

We propose a method of obtaining all three key “tube” model parameters, namely, the plateau modulus GN0, the entanglement molecular weight, Me, and the frictional equilibration time τe, from the molecular weight per backbone bond of ethene/α-olefin copolymers with longer comonomers, ranging from C4 (butylene) to C26 (hexacosene). GN0 is obtained from a correlation by Fetters et al. [Macromolecules 35, 10096–10101 (2002)] and Me is obtained from this using the standard tube-model formula, Me=(4/5)(ρRT/GN0). The equilibration time τe is obtained from a remarkable finding by Stadler and Munstedt [J. Rheol. 52, 697–712 (2008)] that, at fixed weight-average molecular weight, the zero-shear viscosity of linear ethene/α-olefin copolymers is independent of comonomer type and content over a wide range of α-olefin comonomers. From this observation, and from the values of GN0 and Me, we use the tube theory to construct a method for obtaining τe from the comonomer type and content. We show that these a priori values ...