(4cz) Molecules That Tangle: Polymer Entanglement and Melt Structure
Linear polymers are flexible chain molecules containing many chemical repeat units. The motion of individual polymers in a dense polymer liquid (molten plastic) is severely constrained by surrounding chains, and by the fact that chains cannot cut through one another. Effectively, polymers may be considered as being confined inside a tube-like region. The tube diameter, or the entanglement length, is the key parameter needed by the standard molecular theory for polymer rheology. But a molecular understanding of the origin of the tube diameter is still lacking. We approach this problem by closing polymers into rings, in order to obtain a system with well-defined, permanent topology, and using tools from the mathematical theory of knots to identify and count topological entanglements. For simulated polymer melts, this approach enables us to get a tube diameter value that is based on topological considerations alone, and that agrees with values obtained by more heuristic methods. We use this approach to study the effects of chain flexibility and addition of diluents upon the tube diameter.
Another consequence of the unique chain-like structure of polymers is the presence of composition fluctuations at the length scale of a polymer coil size. These composition fluctuations can be measured by small angle neutron and X-ray scattering. Understanding these fluctuation phenomena is important for understanding the structure and self-assembly behavior of multi-component polymeric systems. We show that composition fluctuations in systems of diblock copolymers can be accurately described by a statistical mechanical theory that we developed, by comparing its predictions with simulation results.