A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit

Abstract

We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts that deformation-induced orientation leads to tube dilation. In contrast, for deformed polymers in which chain stretch does not relax we find tube compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome (a force imbalance) by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance is found to occur at a stress of order the equilibrium shear modulus and thus a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.

Dynamically Heterogeneous Relaxation of Entangled Polymer Chains

“…The tube model relies on a mean-field approximation by considering a single polymer chain moving or reptating through a confinement potential due to obstacles created by neighboring chains [3,4]. Recent work has considered topological entanglements in a self-consistent manner at the level of microscopic forces [5], which avoids the ad hoc assumptions of a confining tube while fundamentally deriving an effective confinement potential for entanglements.A fundamental question underlying polymer solutions and melts focuses on how stress relaxes in topologically entangled systems. Following a large deformation, the original Doi-Edwards model (D-E) assumes that polymers undergo a fast chain retraction along the confining tube, followed by a slow stress relaxation via reptation to relax non-equilibrium orientations due to the deformation.…”

“…Interestingly, these results showed that the fast initial chain retraction step predicted by the D-E model following a step strain was absent from experiments. These findings and recent theoretical advances [5,20,21] have brought into question some of the fundamental assumptions of the classic D-E theory and have highlighted the need for new molecular-level studies of entangled polymer solutions [22]. Despite their utility in probing polymer dynamics, bulk experimental methods tend to average over large ensembles of molecules, thereby obscuring the role of molecular sub-populations.…”

“…The tube model relies on a mean-field approximation by considering a single polymer chain moving or reptating through a confinement potential due to obstacles created by neighboring chains [3,4]. Recent work has considered topological entanglements in a self-consistent manner at the level of microscopic forces [5], which avoids the ad hoc assumptions of a confining tube while fundamentally deriving an effective confinement potential for entanglements.…”

Tube Model Under Tension

“…There is no easy answer to this question. Despite the recent herculean effort by Sussman and Schweizer [141][142][143][144][145] to model the topological constraints in a self-consistent manner, their theory has not yet produced any predictions about SAS behavior for us to compare with our experiments. At this moment, the only available option for us to quantitatively explore the "constraint release" effect is the GLaMM model, in which the CR can be controlled by tuning the model parameter c ν .…”

“…Second, is it possible that the chain retraction does take place, but some other nonlinear effects, unanticipated by the original Doi-Edwards theory, are responsible for the absence of the scattering signature of retraction in SANS? For example, the interplay between test chain motion and topological constraints has been widely recognized [16,20,[141][142][143][144][145]. Could constraint release (CR) during retraction lead to the observed scattering patterns?…”