Physics of the Stress Overshoot and Chain Stretch Dynamics of Entangled Polymer Liquids Under Continuous Startup Nonlinear Shear

Abstract

We construct a new theory for transient aspects of the shear rheology of entangled chain liquids. Within an established tube model constitutive equation framework, four new physical features are introduced: a tension blob scaling derivation of the interchain grip force that generates chain stretch, a force imbalance condition for the termination of affine stretch deformation, a delayed chain retraction process that after loss of grip is accelerated for fast deformations, and a distribution of tube diameters. Nonclassical predictions are made for the stress–strain curve to just beyond the overshoot, the existence of a master curve, and fractional power law scaling of the overshoot strain and stress at high shear rates, all in good agreement with experiment and simulation. Testable new predictions are made for chain stretch dynamics.

Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics

“…We now examine support from our simulations for the intermolecular gripping force in the model of Xie and Schweizer . The Xie and Schweizer model predicts well the peak strain from our simulations (see Fig.…”

“…a) as well as the corresponding data for PS melts. In particular, the model has the correct scaling exponent, as reported in Refs . The model achieves this because the intermolecular gripping force delays chain retraction relative to the GLaMM model for moderate values of by requiring strands to exceed a critical tension.…”

“…Comparison of our MD results with experiments by Costanzo et al (PS melt and solution), Schweizer et al (PS melt), Menezes and Graessley (PBD solutions), Boukany et al (SBR melts) and Ravindranath and Wang (PBD solutions), along with the GLaMM and Xie and Schweizer models. The strain at peak stress against for PS and low Z (a) and high Z (b); the peak stress against peak strain (c); and the peak stress against for PS and low Z (d) and high Z (e).…”

From Wall Slip to Bulk Shear Banding in Entangled Polymer Solutions

“…Scenario (b) remains to be worked out for the challenging case of nonquiescent relaxation after step shear of entangled melts. In contrast to (a) and (b), the theory for scenario (c) is less quantitative and still under development . However, it may have plausibly captured the correct physics, and thus should be taken seriously.…”

“…The observations of shear strain localization in both startup shear and stepwise shear also motivated a different kind of interpretation: The termination of homogeneous deformation occurs upon localized yielding through breakdown of the entanglement network upon force imbalance between the intrachain entropic retraction force and the intermolecular grip force . While the theoretical development along this line is still at its infancy, promising progress is being made …”