Effect of topology on dynamics of knots in polymers under tension

TL;DR

This study uses computer simulations to compare how different knot topologies in polymers affect their diffusion and relaxation dynamics under tension, revealing topology-dependent differences in behavior.

Contribution

It provides a comparative analysis of torus and even-twist knots' dynamics, highlighting the influence of topology on diffusion and relaxation in polymer knots.

Findings

Torus knots diffuse faster than even-twist knots of similar complexity.

Friction coefficients grow linearly with average knot length.

Relaxation times vary with knot type, longer for torus knots.

Abstract

We use computer simulations to compare the dynamical behaviour of torus and even-twist knots in polymers under tension. The knots diffuse through a mechanism similar to reptation. Their friction coefficients grow linearly with average knot length for both knot types. For similar complexity, however, the torus knots diffuse faster than the even twist knots. The knot-length auto-correlation function exhibits a slow relaxation time that can be linked to a breathing mode. Its timescale depends on knot type, being typically longer for torus than for even-twist knots. These differences in dynamical behaviour are interpreted in terms of topological features of the knots.