Sliding dynamics of multi-rings on a semiflexible polymer in poly[]catenanes.

The sliding dynamics of one- or multi-ring structures along a semiflexible cyclic polymer in radial poly[n]catenanes is investigated using molecular dynamics simulations. The fixed and fluctuating (non-fixed) semiflexible central cyclic polymers are considered, respectively. With increasing bending energy of the central cyclic polymer, for the fixed case, the diffusion coefficient increases monotonically due to the reduction of the tortuous sliding path, while for the fluctuating case, the diffusion coefficient decreases. This indicates that the contribution of the polymer fluctuation is suppressed by a further increase in the stiffness of the central cyclic chain. Compared with the one ring case, the mean-square displacement of the multiple rings exhibits a unique sub-diffusive behavior at intermediate time scales due to the repulsion between two neighboring rings. In addition, for the multi-ring system, the whole set of rings exhibit relatively slower diffusion, but faster local dynamics of threading rings and rotational diffusion of the central cyclic polymer arise. These results may help us to understand the diffusion motion of rings in radial poly[n]catenanes from a fundamental point of view and control the sliding dynamics in molecular designs.