Nonlinear rheometry of entangled polymeric rings and ring-linear blends

We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for the shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of the shear rate, as well as molecular parameters (molar mass, blend composition, and decreasing molar mass of linear component in the blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with the shear rate. The universal scaling of the strain at overshoot and fractional overshoot (the ratio of the maximum to the steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behavior of pure rings yields a slope nearly identical to predictions (−4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While N₂ is negative and its absolute value stays below that of N₁, as for linear polymers, the ratio –N₂/N₁ is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by a factor of 2), in agreement with recent nonequilibrium molecular dynamics simulations. Furthermore, –N₂ exhibits slightly weaker shear rate dependence compared to N₁ at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behavior. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading, which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This confirms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices.