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, ΔE, which depends on the three characteristic parameters of the PR system, ΔE = ΔE(α, μ, ρring), where α is the ratio of the rod to the coil strand length, μ is a quantity of measuring the stretching degree of the coil block, and ρring 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.