Slow Dynamics of Ring Polymer Melts by Asymmetric Interaction of Threading Configuration: Monte Carlo Study of a Dynamically Constrained Lattice Model.

Abnormally slower diffusional processes than its internal structure relaxation have been observed in ring polymeric melt systems recently. A key structural feature in ring polymer melts is topological constraints which allow rings to assume a threading configuration in the melt phase. In this work, we constructed a lattice model under the assumption of asymmetric diffusivity between two threading rings, and investigated a link between the structural correlation and its dynamic behavior via Monte Carlo simulations. We discovered that the hierarchical threading configurations render the whole system to exhibit abnormally slow dynamics. By analyzing statistical distributions of timescales of threading configurations, we found that the decoupling between internal structure relaxation and diffusion is crucial to understand the threading effects on the dynamics of a ring melt. In particular, in the limit of small but threaded rings, scaling exponents of the diffusion coefficient D and timescale τ diff with respect to the degree of polymerization N agree well with that of the annealed tree model as well as our mean-field analysis. As N increases, however, the ring diffusion abruptly slows down to the glassy behavior, which is supported by a breakdown of the Stokes⁻Einstein relation.