Sliding dynamics of ring chain on a knotted polymer in rotaxane

Abstract

Rotaxane is a supramolecule in which ring chains are threaded on an axial chain, showing a fascinating sliding dynamics of ring chains along the axial chain. In this study, we investigated the sliding dynamics of ring chains on a knotted polymer chain in rotaxane, exhibiting a sub-diffusion at the intermediate time range resulting from the intra-strand interaction between the ring chains and the knotted axial chain in the knot crossing region. Meanwhile, the non-monotonous dependence of sliding diffusion coefficient D of ring chains on ring size Nring indicates that there exist two competing effects: one is the friction effect between the ring chains and the axial chain in which the ring chains slide fast along the knotted axial chain for large Nring, and another is the knot effect in which the ring chains move slowly along the knotted axial chain for large Nring because the knot crossing hinders ring chains to pass through for large Nring. Based on the unique sliding sub-diffusion behaviour of the threaded ring chains, we also proposed a new approach to estimate the average knot size of the knotted axial chain, and our estimation about the average knot size is in good agreement with the result according to the Alexander polynomial calculation using the free python package TOPOLY. These results may provide a fundamental view for understanding the dominant factors of the sliding dynamics of ring chains in complex polymer-based rotaxane.