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

We propose a method of obtaining all three key "tube" model parameters, namely, the plateau modulus G_N0, the entanglement molecular weight, M_e, and the frictional equilibration time τ_e, from the molecular weight per backbone bond of ethene/α -olefin copolymers with longer comonomers, ranging from C4 (butylene) to C26 (hexacosene). G_N⁰ is obtained from a correlation by Fetters [Macromolecules 35, 10096-10101 (2002)] and M_e is obtained from this using the standard tube-model formula, M_e = (4/5) (ρ _RT/ G_N⁰). The equilibration time τ_e is obtained from a remarkable finding by Stadler and Münstedt [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 G _N⁰ and M_e, we use the tube theory to construct a method for obtaining τ_e from the comonomer type and content. We show that these a priori values of the tube model parameters, when used in two publicly available models ("hierarchical model" and "branch-on-branch" model) for predicting linear rheology, yield accurate predictions for a wide range of polydisperse copolymers. These results show that a priori predictions of linear rheology of complex commercial polyolefin copolymers are now possible.