Entangled chain polymer liquids under continuous shear deformation: consequences of a microscopically anharmonic confining tube

We generalize our non-classical theory for the shear rheology of entangled flexible polymer liquids to address the consequences of a deformation-modified anharmonic tube confinement field. Numerical results for stress-strain curves, orientational relaxation time, primitive path (PP) step orientational order parameter, dynamic tube diameter and transverse entropic barrier under nonequilibrium conditions are presented as a function of dimensionless shear rate, strain and degree of entanglement. Deformation-induced changes of the tube field have essentially no effect on rheology under fast deformations conditions corresponding to Rouse Weissenberg numbers Wi(R) > 1 because of the dominance of PP chain stretch. However, the scaling behavior of the effective orientational relaxation time and rheological response at low deformation rates Wi(R) < 1 are significantly modified, with the stress overshoot coordinates predicted to become shear rate and degree of entanglement dependent. Stress-assisted transverse activated barrier hopping as a new channel of orientational relaxation is found to be potentially important when Wi(R) < 1. The dynamic tube diameter and transverse entropic barrier that confines chains in a tube are rich functions of strain, shear rate and degree of entanglement. Deformation can increase or decrease the tube diameter, and non-monotonic changes with strain are possible due to competing consequences of PP orientation, chain stretch and stress. The transverse barrier is relatively high for all strains below the stress overshoot, for weaker entanglement, and for Wi(R) > 1, corresponding to a dynamically stable tube. But for high enough degrees of entanglement and Wi(R) < 1, although the barrier still exists it can become very low.