Size and Dynamics of Ring Polymers under Different Topological Constraints

The impact of ring polymer length N and the influence of interchain and intrachain interactions on the size and dynamic behaviors of ring polymers, including the structural relaxation time τR and self-diffusion coefficient D, remain poorly understood at present due to a lack of systematic studies with relatively large N values. This work addressed this issue by applying dynamic Monte Carlo simulations with independently tuned interchain and intrachain interactions to investigate the size and dynamics of the ring melts with chain lengths over a wide range of 0.2Ne≤ N≤80Ne (Ne is the entanglement length of corresponding linear chains) under different topological constraints, including all-crossing and intercrossing systems. We found that it was inappropriate to treat the unknotting constraint free energy of the ring chains in the melts as the free energy contributed by the excluded volume interactions of polymers in a good solvent. Scaling exponents of 2.5 and 1.5 reflecting the N-dependence of τR were obtained for long ring chains in non-crossing and intra-crossing systems, respectively, suggesting that the ring chains behaved as individual clusters and exhibited Zimm-like dynamics in intra-crossing systems. A single scaling exponent of −2 reflecting the N-dependence of D was obtained for ring chains in non-crossing and intra-crossing systems, indicating that the intrachain constraints affected only the value of D, and had little influence on the scaling relationship between D and N. Furthermore, the extended Stokes-Einstein relation broke down for the ring chains in the non-crossing and intra-crossing systems because the structural relaxation and translational diffusion were decoupled for the short ring systems, while both the translational diffusion and rotational relaxations, as well as diffusion at short and long time scales, were decoupled for long ring systems.