Ranking knots of random, globular polymer rings

TL;DR

This study uses extensive simulations to analyze the distribution and growth of knots in random, collapsed polymer rings, revealing power-law frequency decay and exponential knot diversity growth.

Contribution

It provides new insights into the statistical distribution of knots and their growth behavior in collapsed polymer rings through large-scale simulations.

Findings

Knot frequencies decrease as a negative power of rank.

Number of different knots grows exponentially with chain length.

Relative knot frequencies converge to fixed values.

Abstract

An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and suggests that the total number of different knots realized grows exponentially with the chain length. Relative frequencies of specific knots converge to definite values because the free energy per monomer, and its leading finite size corrections, do not depend on the ring topology, while a subleading correction only depends on the crossing number of the knots.