Topologically Driven Swelling of a Polymer Loop

TL;DR

This study numerically investigates how the topology of trivially knotted polymer loops influences their size, revealing power-law behavior in gyration radii consistent with self-avoiding walk theories.

Contribution

It provides detailed numerical analysis of the size distribution and topology of large polymer loops, using Alexander and Vassiliev invariants for knot identification.

Findings

Gyration radii follow a power law similar to self-avoiding walks.

Probability of trivial knots decreases with loop size.

Distribution of gyration radii aligns with theoretical predictions.

Abstract

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.