Topological effects in the thermal properties of knotted polymer rings

TL;DR

This study uses Monte Carlo simulations to explore how knot topology influences the thermal properties of polymer rings, revealing significant effects especially in short-length polymers and identifying three temperature regimes affecting energy growth.

Contribution

Introduces a fast method to verify knot topology during thermal fluctuations and applies it to analyze thermal properties of various knotted polymers.

Findings

Topological effects significantly influence thermal properties in short polymers.

Three distinct temperature regimes affect the internal energy growth.

Knot topology preservation is efficiently checked during simulations.

Abstract

The topological effects on the thermal properties of several knot configurations are investigated using Monte Carlo simulations. In order to check if the topology of the knots is preserved during the thermal fluctuations we propose a method that allows very fast calculations and can be easily applied to arbitrarily complex knots. As an application, the specific energy and heat capacity of the trefoil, the figure-eight and the $8_1$ knots are calculated at different temperatures and for different lengths. Short-range repulsive interactions between the monomers are assumed. The knots configurations are generated on a three-dimensional cubic lattice and sampled by means of the Wang-Landau algorithm and of the pivot method. The obtained results show that the topological effects play a key role for short-length polymers. Three temperature regimes of the growth rate of the internal energy of the system are distinguished.