Untangling the mechanics of entanglements in slide-ring gels towards both super-deformability and toughness

Entanglement plays a critical role in determining the dynamic properties of polymer systems, e.g., resulting in slip links and pulley effects for achieving large deformation and high strength. Although it has been studied for decades, the mechanics of entanglements for stiffness-toughness conflict is not well understood. In this study, topological knot theory incorporating an extended tube model is proposed to understand the entanglements in a slide-ring (SR) gel, which slips over a long distance to achieve large deformation and high toughness via the pulley effect. Based on topological knot theory, the sliding behavior and pulley effect of entanglements among molecular chains and cross-linked rings are thoroughly investigated. Based on rubber elasticity theory, a free-energy function is formulated to describe mechanical toughening and slipping of topological knots, while the SR gel retains the same binding energy. Finally, the effectiveness of the proposed model is verified using both finite element analysis and experimental results reported in the literature.