Sliding dynamics of ring chain on graft polymer in rotaxane

Rotaxane is a mechanically interlocked molecule in which rings are threaded on the axial linear polymer chain, and a characteristic feature of rotaxane is that ring can slide along the axial chain. In this study, molecular dynamics simulations are performed to investigate the sliding dynamics of ring on a regular/random graft polymer with graft density f and side chain length Ns. The mean-square displacement g3(t) of ring exhibits a novel sub-diffusion behavior in the intermediate time range due to the interaction between the branches and ring, and the sub-diffusive regime occurs at g3(t)∼((Nc−1)*b2)2, qualitatively, where Nc is the number of monomers between two adjacent side chains and b is bond length. For ring chain sliding along either a regular graft polymer or a random one, the sliding dynamic of ring relies strongly on the side chain length Ns、graft density f、ring size as well as the distribution of branches in the graft polymer. The diffusion coefficient D of ring decreases with the increase of Ns or f. However, ring slides faster along the regular graft polymer than that random one, because the dense side chains in the random graft polymer greatly hinder the ring's mobility. The effect of regular distribution on the improved diffusion gets most obvious when the side-chain length is middle. These results may provide a fundamental view for the understanding the effect of topological structure of axial graft polymer chain on the sliding dynamics of ring in rotaxane.