Scaling behavior of topologically constrained polymer rings in a melt

TL;DR

This study uses GPU-based molecular dynamics simulations to analyze how topological constraints like knots affect the size scaling of ring polymers in melts, confirming the crumpled globule model for large rings.

Contribution

It provides the first large-scale simulation analysis of topologically constrained ring polymers, revealing how knot complexity influences size scaling.

Findings

Ring sizes scale as N^{1/3} for large N, consistent with the crumpled globule model.

Knots occupy a significant fraction of small rings, affecting their size scaling.

Scaling exponents vary with knot type for small ring sizes.

Abstract

Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and the exponent is generally larger than 0.4.