A tube-based constitutive equation for polydisperse entangled linear polymers

We present a tube-based constitutive model for polydisperse entangled linear polymers. The model is constructed as the non-linear extension of a linear model [A. Leygue, C. Bailly, R. Keunings, A differential tube-based model for predicting the linear viscoelastic moduli of polydisperse entangled linear polymers, J. Non Newton. Fluid Mech., in press] capable of predicting quantitatively the linear viscoelasticity of polydisperse linear systems. The constitutive equation accounts for the major linear and non-linear phenomena thought to be important in the description of entangled linear polymers: reptation, contour-length fluctuations, thermal constraint release, convective constraint release and chain stretch effects. In the non-linear regime convective constraint release couples the relaxation of the different masses and provides a non-linear mixing rule for the model. The predictive capabilities of the model are tested on published results for mono- and bi-disperse entangled solutions [C. Pattamaprom, R.G. Larson, Constraint release effects in monodisperse and bidisperse polystyrenes in fast transient shearing flows, Macromolecules 34 (2001) 5229–5237; X. Ye, R.G. Larson, C.J. Pattamaprom, T. Shridar, Extensional properties of monodisperse and bidisperse polystyrene solutions, J. Rheol. 47 (2) (2003) 443–468], both in shear and extension.