An entanglement constraint model of topological knot in highly entangled gel towards ultra-high toughness

Abstract Highly entangled gels have gained extensive attention due to their excitingly large deformation and high toughness. To understand the toughening mechanism of these highly entangled gels, an entanglement constraint model has been established, based on the spatially prismatic constraint and Gaussian distribution models. A free-energy function is formulated to study the conformational dynamics, rubbery elasticity and sliding effect of topological knots in the entangled chains. Monte Carlo, molecular dynamics and finite element analysis were conducted to verify the coupling effect of inter-chain entanglement and intra-chain knot topology on the toughness behavior of highly entangled gels. Finally, experimental data available in the literature were used to verify the proposed models, providing a physical insight into the toughening mechanism of inter-chain entanglement constraint and intra-chain knot topology in the highly entangled gel.