Physics Department News

To what extent do concentrated solutions, or melts, of ring polymers thread through one another at equilibrium? An analogous system is a well-shaken bucket full of very long rubber bands. If one attempts to withdraw a single rubber band it is very likely that a large tangle of interpenetrating rubber bands will instead emerge. This is to be contrasted with an attempt to withdraw a single strand from a bowl of freshly cooked spagetti, analogous to a system of linear polymers. A strand of spaghetti can easily be withdrawn via a slithering motion through it neighbours. This, seemingly trivial contrast, hides an extremely longstanding and intellectually challenging set of questions regarding the configuration and dynamics of ring polymers. In a recent publication [1] we provide the first evidence for the existence of threadings in unlinked unknotted ring polymers. Using langevin dynamics we monitor the diffusive motion of unlinked and unknotted rings in a system in which a fraction of pre-equilibrated chains are artificially immobilised (“frozen”). We find that this freezing process results in caged diffusion of rings in the unfrozen fraction, which we associate with the presence of a threading by frozen rings; caged rings exhibit an r.m.s. displacement that saturates at about the rings’ radius of gyration, even for very long times. This proves the existence of threadings in the corresponding, completely unfrozen equilibrated configuration. Intruigingly the fraction of unfrozen rings that are caged (threaded) approaches unity as the ring length is increased, even as the fraction of explicitly frozen rings approaches zero.

• Caption to Figure: A time-lapse movie of our simulations with a few of the ring polymers shown in different colours. All polymers are pre-equilibriated and then all but the red polymer are frozen. The red polymer appears as a localised "blur" because it is moving but it is trappend by threadings with the other rings, showing that such threadings would have existed, at least transiently, had none of the chains been frozen.

• Publication: D. Michieletto and M. S. Turner A topologically driven glass in ring polymers PNAS 2016 ; published ahead of print April 26, 2016
• DOI: doi:10.1073/pnas.1520665113