From atomistic simulations to slip-link models of entangled polymer melts: Hierarchical strategies for the prediction of rheological properties

Chain entanglements are thought to govern the rheology of long-chain polymer melts and the large-deformation properties of solid polymers. Although they have been invoked in tube and slip-link theories of polymer dynamics, their precise definition and their direct experimental observation have been elusive. Recently, algorithms enabling the full equilibration of long-chain polymer melt models on all length scales opened up the way to the detection and identification of entanglements by computer simulation, using topological reduction of configurations or dynamical analysis of simulation trajectories.After a reference to the tube model and to coarse-graining strategies for simulating polymers, this brief review discusses slip-link models that have been developed for the mesoscopic analysis and simulation of rheological properties of polymer melts. It then presents algorithms for the reduction of model melt configurations sampled in the course of atomistic or coarse-grained molecular simulations to networks of entanglements comparable to those invoked in slip-link models. Estimates of the molar mass between entanglements and of the Kuhn length of primitive paths obtained through topological analysis and through dynamical analyses of simulation trajectories are compared against experimental evidence. Statistical descriptors are then developed for the entanglement network structure, as obtained by simulation. Entanglement analysis is shown to be an important missing link in quantitatively relating the detailed chemical constitution of polymers to their rheological and large-scale deformation properties through a hierarchy of atomistic, coarse-grained, and mesoscopic slip-link model simulations.