Revisiting the Viscosity of Moderately Entangled Ring Polymer Melts

The absence of free ends is known to impart unique properties in ring polymers. Using critically fractionated samples (polystyrenes, polyisoprenes and polybutadienes), that are as pure (free from unlinked or double chains) as currently possible, it has been shown that moderately entangled ring melts (2 < Z < 22, where Z is the number of entanglements based on the established entanglement molar mass for linear chains) do not exhibit a rubbery plateau but a power-law stress relaxation instead. The power-law exponent conforms to the prediction of the fractal loopy globule model (-3:7). However, the exact dependence of zero-shear viscosity on molar mass remains controversial, with different experimental and simulation studies, sometimes with the same samples, suggesting different values and, overall, a power-law exponent that ranges between 1 and 1.7. Here, we re-examine published linear viscoelastic data and present some new data on polystyrene melts, all being critically fractionated. We discuss the different experimental issues and analyze the data in a consistent manner, using different approaches. Our results indicate that the experimental power-law exponent is clearly and universally larger than 1, complying with a value of 1.3. With increasing molar mass, ring-ring threading events appear to contribute significantly to the zero-shear viscosity.