Mechanics of slide-ring gels: novel entropic elasticity of a topological network formed by ring and string

Slide-ring (SR) gels are polymer networks with movable cross-links that are prepared by cross-linking polyrotaxane (PR) in which many cyclic molecules are threaded into a linear polymer chain. The elastic modulus E of SR gels shows a unique dependence on cross-linking density: at a high cross-linking density, E decreases with increasing cross-linking density. This tendency is not in agreement with conventional rubber elasticity theory. In order to explain this abnormal dependence, we propose a novel molecular theory for SR gels, which considers the alignment entropy of cyclic molecules on polymer networks. The alignment yields new entropic elasticity of the slidable network in SR gels.