The topological glass in ring polymers

¹ Department of Physics, National Central University - Taoyuan 32001, Taiwan
² Department of Physics, University of Warwick - Coventry, CV4 7AL, UK
³ Centre for Complexity Science, University of Warwick - Coventry, CV4 7AL, UK

Received: 7 April 2013
Accepted: 30 May 2013

Abstract

We study the dynamics of concentrated, long, semi-flexible, unknotted and unlinked ring polymers embedded in a gel by Monte Carlo simulation of a coarse-grained model. This involves the ansatz that the rings compactify into a duplex structure where they can be modelled as linear polymers. The classical polymer glass transition involves a rapid loss of microscopic freedom within the polymer molecule as the temperature is reduced toward T_g. Here we are interested in temperatures well above T_g where the polymers retain high microscopic mobility. We analyse the slowing of stress relaxation originating from inter-ring penetrations (threadings). For long polymers an extended network of quasi-topological penetrations forms. The longest relaxation time appears to depend exponentially on the ring polymer contour length, reminiscent of the usual exponential slowing (e.g., with temperature) in classical glasses. Finally, we discuss how this represents a universality class for glassy dynamics.