A thermodynamically consistent constitutive equation describing polymer disentanglement under flow

We derive a thermodynamically consistent framework for incorporating entanglement dynamics into constitutive equations for flowing polymer melts. We use this to combine the convected constraint release (CCR) dynamics of Ianniruberto-Marriccui into a finitely-extensible version of the Rolie-Poly model, and also include an anisotropic mobility as in the Giesekus model. The reversible dynamics are obtained from a free energy that describes both a finitely-extensible conformation tensor and an ideal gas of entanglements along the chain. The dissipative dynamics give rise to coupled kinetic equations for the conformation tensor and entanglements, whose coupling terms describe shear-induced disentanglement. The relaxation dynamics of the conformation tensor follow the GLaMM and Rolie-Poly models, and account for reptation, retraction and CCR. We propose that the relaxation time $\tau_\nu$ for entanglement recovery is proportional to the Rouse time $\tau_R$ which governs polymer stretch within the tube. This which matches recent molecular dynamics simulations, and corresponds to relaxing the entanglement number before the entire polymer anisotropy has relaxed on the longer reptation time $\tau_d$. Our model suggests that claimed signatures of slow re-entanglement on the reptation time in step-strain experiments may be interpreted as arising from anisotropies in reptation dynamics.Comment: 26 pages, 14 figure