Nonlinear Rheology of Unentangled Polymer Melts

Nonlinear rheology of polymers has been extensively studied from both experimental and theoretical points of view. Transient stress overshoot followed by thinning, commonly observed for entangled melts and solutions under fast shear, is well described by advanced molecular models based on the tube/slip-spring concept. Nevertheless, under fast extension, strain-hardening is observed for entangled solutions but not for entangled melts, and those models cannot explain this difference between the solution and melt. This problem has been resolved by Ianniruberto and coworkers who developed a concept of segmental friction (ζ) reduction occurring in a highly co-aligned environment in melts. The rapidly moving solvents are not oriented, which allows the entangled solutions to be free from the ζ-reduction thereby exhibiting the strain hardening.

Obviously, the ζ-reduction is a local phenomenon occurring in a length scale well below the entanglement length. Thus, we have investigated details of ζ-reduction and other non-equilibrium features for unentangled melts being free from any nonlinearity of entanglement dynamics. Specifically, the extensional viscosity η_E of an unentangled polystyrene melt was found to exhibit hardening at the Weissenberg number Wi ~ 0.5 and then softening at Wi > 1. The standard Rouse model and its modification for the finite extensible nonlinear elasticity (FENE) cannot reproduce this hardening-softening crossover. However, the model with FENE and ζ-reduction can describe the data given that ζ is chosen to properly decrease with increasing stress. This result demonstrates importance of FENE and ζ-reduction in the non-equilibrium dynamics of chains in unentangled melt (and in entangled melt, too). An additional feature is found for the viscosity η and the first normal stress difference coefficient Ψ₁ under fast shear. The Rouse analysis with FENE and ζ-reduction indicates that a factor (η/η₀)² should agree with the Ψ₁/ Ψ_1,0 ratio if ζ and the mean-square Brownian force intensity B satisfy the fluctuation-dissipation theorem, B = 2ζk_BT. However, the unentangled PS melt does not show this agreement, and thus the non-equilibrium behavior emerges also for B. Further information obtained from rheo-dielectric experiments will be presented on site.