A differential tube-based model for predicting the linear viscoelastic moduli of polydisperse entangled linear polymers

We present a simple tube theory for topologically linear entangled polymers that accounts for reptation, contour-length fluctuations and thermal constraint release. This theory is based on a new differential formulation of the thermal constraint release phenomenon proposed by the authors [A. Leygue, C. Bailly, R. Keunings, A differential formulation of thermal constraint release for entangled polymers, J. Non Newtonian Fluid Mech. 128 (1) (2005) 23–28] which is extended here to account for contour-length fluctuations. We apply the theory to mono- and poly-disperse polystyrene melts and demonstrate its ability to produce quantitative predictions. Additionally, we discuss a mathematically linear approximation of our approach that preserves the structure of the model. While most quantitative tube theories for predicting linear viscoelasticity are mathematically non-linear, our approach allows one to address the linear viscoelastic response of a polydisperse entangled system with a mathematically linear theory.