Entropy-Induced Localization and Sliding Dynamics of Rings on Polyrotaxane

Regulating the position and sliding dynamics of rings on the polyrotaxane (PR) backbone plays a crucial role in determining the properties and/or functions of PR and PR-based soft materials. In this work, we use molecular dynamics simulations to reveal that the features of localization and sliding dynamics of rings on a PR modeled by a rod-coil-rod triblock copolymer are regulated by the entropy effect of the coil block. The distribution of the rings along the rod-coil-rod PR backbone is found to be highly heterogeneous and can be described by a two-state model characterized by a (free) energy gap, Delta E, which depends on the three characteristic parameters of the PR system, Delta E = Delta E(alpha, mu, rho(ring)), where alpha is the ratio of the rod to the coil strand length, mu is a quantity of measuring the stretching degree of the coil block, and rho(ring) is the overall ring coverage along the PR backbone. A theoretical model is proposed to describe the origin of this universality, the prediction of which is quantitatively consistent with simulation results for the single-ring rod-coil-rod PR system. The existence of an energy gap also gives a model for the dynamics of ring sliding along the PR backbone.