How unconcatenated ring polymers relax stress in a melt
In plain words
Ring-shaped polymers have no ends, so they cannot slide out of entanglements end-first as linear chains do. How a melt of rings flows and relaxes stress is still unclear.
Precise statement
For melts of nonconcatenated, unknotted rings of N monomers with $N / N_e >> 1$ ($N_e$ the entanglement length), determine the scaling of the zero-shear viscosity $\eta_0(N)$ and of the stress-relaxation modulus $G(t)$ (power law $G(t) \sim t^{-\alpha}$ versus a plateau), the role of ring-ring threading, and whether threading produces a topological glass for large N. An answer is a theory agreeing with simulations to $N / N_e > 50$ and with experiments on purified rings.
What would settle it
Consistent $\eta_{0}(N)$ exponents and $G(t)$ shapes from purified-ring experiments and long-ring simulations, explained by a theory that predicts or excludes a threading-induced glass.
Status in the literature
Unverified note
Simulations and experiments on purified rings report power-law stress relaxation; whether threading produces a topological glass at large N remains disputed (2026).