Nonlinear Dynamics of Nonconcatenated Entangled Ring Polymers*

The steady-state shear viscosity of nonconcatenated ring polymer melts is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z≈5 and Z≈11 entanglements indicate weaker shear thinning for rings compared to linear polymers and observe power-law dependence of ring shear viscosity on shear rate with exponent -0.56±0.02 up to Weissenberg number Wi~100. Non-equilibrium molecular dynamics simulations reveal a similar shear thinning behavior with exponent -0.57±0.08 for a wider range of the number of entanglements per ring 4≤Z≤57. If the shear rate exceeds a certain threshold, shear-thinning becomes non-universal, chain length-dependent. In our experiments, we see the onset of this regime at the largest accessed Wi, and in simulations, which we extended up to Wi~10,000, it is fully developed. In this regime, viscosity decreases with increasing chain length. A simple scaling theory predicts universal regime in the sheared melt of rings with viscosity decreasing with the shear rate with exponent -0.57, in good agreement with both experiments and simulations. We develop a shear slit model explaining many subtle details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity in the non-universal regime at large shear rates. The signature feature of the model is the presence of two distinct length scales: each chain is confined in the velocity gradient direction to a shear slit of thickness dictated by the size of chain section with relaxation time on the order of reciprocal shear rate, while chains are strongly stretched in the flow velocity direction, with much smaller tension blobs. In this model, the chain length-dependent onset of non-universal behavior is set by tension blob getting as small as about one Kuhn segment.