Diffusion of a ring polymer in good solution via the Brownian dynamics

TL;DR

This study uses Brownian dynamics with hydrodynamic interactions to compare the diffusion constants of ring and linear polymers, finding a universal ratio close to 1.11, and examines knotting probabilities under good solvent conditions.

Contribution

It provides the first quantitative estimate of the diffusion constant ratio for ring and linear polymers in good solvents using Brownian dynamics.

Findings

The diffusion constant ratio C is approximately 1.11 for large N.

Knotting probability of ring polymers is very low.

Bond crossings occur frequently despite the low knotting probability.

Abstract

Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same molecular weight in a good solvent, respectively, have been evaluated through the Brownian dynamics with hydrodynamic interaction. The ratio $C=D_{R}/D_{L}$, which should be universal in the context of the renormalization group, has been estimated as $C= 1.11 \pm 0.01$ for the large-N limit. It should be consistent with that of synthetic polymers, while it is smaller than that of DNAs such as $C \approx 1.3$. Furthermore, the probability of the ring polymer being a nontrivial knot is found to be very small, while bond crossings may occur at almost all time steps in the present simulation that realizes the good solvent conditions.