Comparing the structure and dynamics of single and catenated partially active ring polymers

Active ring polymers exhibit complex nonequilibrium dynamics due to the interplay between their topology and active forces. In this work, we use Langevin dynamics simulations with the Kremer-Grest model to investigate semiflexible active rings with tangential forces applied along the polymer backbone. We focus on relatively small ring sizes (N ≤ 200) and low activity strengths (primarily Pe = 5). We change the number and spatial distribution of active monomers, considering both active block copolymers and active random copolymers. We calculate the average radius of gyration (Rg) and observe a non-monotonic behavior: introducing activity into an initially passive ring causes polymer shrinkage, followed by swelling as the number of active monomers increases. Maximal shrinkage scales with chain length for block copolymers but becomes length-independent for random activation. We report scaling laws for fully passive, fully active, and maximally compact states. We also observe that short fully active rings (N ≲ 100) become more aspherical compared to their passive counterparts, whereas long fully active rings (N ∼ 200) are more spherical than their passive state. We extend our analysis to two-catenated rings under two scenarios: (i) a symmetric system with two randomly activated polymer rings with the same activity fraction, and (ii) an asymmetric system consisting of a permanently passive ring and a randomly activated ring. We observe that catenation causes fully active rings to exhibit less swelling compared to the isolated fully active rings, indicating that the catenation imposes a mechanical constraint on both rings. Furthermore, in the asymmetric system, we find that physically linking an active ring to a passive ring makes the passive ring slightly more elongated than an isolated passive ring. Apart from these effects, in the absence of hydrodynamic interactions, catenation does not significantly influence the dynamics of either ring, and the two rings behave almost independently.