Mechanical effects of topological entanglement and knotting of linear chains in a melt

The viscoelastic properties of polymer melts are affected by the entanglement of the constituent chains. However, defining/measuring entanglement remains a challenge. We use tools from topology, the Gauss linking integral and the Jones polynomial, to measure entanglement in polymer melts of linear chains using computer simulations. We use molecular dynamics simulations of coarse grained models of polymer melts of linear chains of varying molecular weight. Our results show that the self and pairwise topological entanglement complexity increases with molecular weight in equilibrium and non-equilibrium conditions. By imposing an oscillatory shear we find that both self and pairwise topological entanglement decrease with increasing loss tangent. All these results suggest that tools from topology can capture entanglement complexity relevant to material properties.