Microscopic Topology and Macroscopic Elasticity of Polymers

The viscoselastic properties of high molecular weight polymeric liquids are dominated by topological constraints on a molecular scale. Similar to entangled ropes, polymer chains can slide past but not through each other. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path. To provide a microscopic foundation for these highly successful phenomenological models, we have introduced a method for analyzing the microscopic topological state of polymeric liquids in terms of primitive paths. The resulting parameter-free predicitions for the plateau modulus agree with experiment for all major classes of synthetic polymers.