Tubes, Topology, and Entangled Rings
This event is part of the Biophysics/Condensed Matter Seminar Series.
Long polymer chains in concentrated solutions or dense melts interpenetrate extensively. Polymer motion is severely restricted by entanglement and topological constraints, long understood in terms of a confining tube. We show that a purely topological approach can be used to compute the entanglement length Ne by establishing a direct link to the statistics of topological states in simulations of topologically equilibrated ring polymers. We determine how Ne varies with solvent dilution and chain stiffness. Another way to study entanglement is to use simulations to test tube-based theory predictions for entangled chain dynamics; this has been done extensively for entangled linear chain melts. This has been done extensively with large-scale molecular dynamics simulations for entangled linear chain melts. One might suppose the dynamics of a self-entangled ring would be uninteresting, because of the absence of free ends and the permanent confinement of the chain to the tube. In fact, a ring trapped in a tube should have four dynamical regimes, just as for entangled linear chains: free Rouse motion below the entanglement strand Rouse time taue, curvilinear Rouse motion up to tauR, reptation up to taud, stationary thereafter. Because there are no end effects, we can write analytical expressions for the monomer mean-square displacement versus time, which can be compared to simulations to determine taue and Ne.