Topological effects in ring polymers: A computer simulation study

TL;DR

This study uses computer simulations to investigate the topological effects in ring polymers, revealing their compactness, dynamics, and scaling behavior, which differ from linear chains and show no signs of entanglement effects.

Contribution

It provides detailed simulation data on the size, dynamics, and scaling laws of unknotted ring polymers in the melt, highlighting topological constraints' influence.

Findings

Ring polymers are more compact than Gaussian chains.

The size scales as R ∝ N^{0.39}, consistent with topological interactions.

The dynamics show a single characteristic time scale with no crossover to entangled behavior.

Abstract

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction \Phi=0.5 and show that rings in the melt are more compact than gaussian chains. A careful finite size analysis of the average ring size R \propto N^{\nu} yields an exponent \nu \approx 0.39 \pm 0.03 in agreement with a Flory-like argument for the topologica interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale \tau_{ee} \propto N^{2.0(2); this is shown by the collapse of several mean-square displacements and correlation functions onto corresponding master curves. Because of the shrunken state of the chain, this scaling is not compatible with simple Rouse motion. It applies for all sizes of ring studied and no sign of a crossover to any entangled regime is found.