Diffusion of a Ring Threaded on a Linear Chain

A mesoscopic simulation is applied to investigate the effects of hydrodynamic interactions and axial chains on the dynamics of threaded rings. The hydrodynamic interactions significantly speed up the diffusion and relaxation of both free and threaded rings. The decoupled diffusion and relaxation dynamics indicate the broken of the Einstein-Stokes relationship. The diffusion of a ring threaded on a flexible chain exhibits a synergism effect compared to that on an axial rod, which originates from the self-diffusion of the ring and the reptation-like motion of the axial chain. Meanwhile, hydrodynamic interactions significantly improve the synergism effect, leading to an enhanced sliding motion of the threaded ring. The faster sliding of threaded rings suggests that the entropic barrier is negligible, which agrees well with the basic assumption of barrier-less confining tube at equilibrium in tube theory. Our results provide a new perspective on analysis of the effects of topology constraints on polymer dynamics.