Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses

摘要

Elucidating the physics of a concentrated suspension of ring polymers, or ofan ensemble of ring polymers in a complex environment, is an importantoutstanding question in polymer physics. Many of the characteristic features ofthese systems arise due to topological interactions between polymers, orbetween the polymers and the environment, and it is often challenging todescribe this quantitatively. Here we review recent research which suggeststhat a key role is played by inter-ring threadings (or penetrations), whichbecome more abundant as the ring size increases. As we discuss, the physicalconsequences of such threadings are far-reaching: for instance, they lead to atopologically-driven glassy behaviour of ring polymer melts under pinningperturbations, while they can also account for the shape of experimentallyobserved patterns in two-dimensional gel electrophoresis of DNA knots.