A numerical technique for preserving the topology of polymer knots: The case of short-range attractive interactions

TL;DR

This paper introduces a Monte Carlo simulation method using the pivot algorithm and PAEA to study the topology-preserving conformations of polymer knots with short-range attractive interactions, analyzing their energy, size, and heat capacity.

Contribution

The authors develop a topology-preserving Monte Carlo technique for polymer knots with attractive forces, extending previous methods to include energy and size analysis.

Findings

Specific energy and heat capacity increase with knot complexity.

Polymer size varies with temperature, influenced by knot type.

Attractive interactions affect the thermodynamic properties of knots.

Abstract

The statistical mechanics of single polymer knots is studied using Monte Carlo simulations. The polymers are considered on a cubic lattice and their conformations are randomly changed with the help of pivot transformations. After each transformation, it is checked if the topology of the knot is preserved by means of a method called pivot algorithm and excluded area (in short PAEA) and described in a previous publication of the authors. As an application of this method the specific energy, the radius of gyration and heat capacity of a few types of knots are computed. The case of attractive short-range forces is investigated. The sampling of the energy states is performed by means of the Wang-Landau algorithm. The obtained results show that the specific energy and heat capacity increase with increasing knot complexity as in the case of repulsive interactions. The data about the gyration radius allow to estimate the size of the polymer knots at different temperatures.