The Compressibility of Minimal Lattice Knots

TL;DR

This study investigates how the topology and geometry of minimal lattice knots influence their compressibility across different cubic lattices, revealing non-monotonic behavior and topology-dependent variations.

Contribution

It provides the first systematic analysis of the compressibility of minimal lattice knots in various cubic lattices, highlighting the roles of topology and geometry.

Findings

Compressibility is generally non-monotonic with pressure.

Topology affects the compressibility of lattice knots.

Geometry of the lattice influences compressibility differences.

Abstract

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.