Ring polymers with topological constraints

TL;DR

This paper reviews recent experimental and theoretical work on topologically constrained polymer rings, introduces new simulation techniques for modeling polymer knots, and explores how topology influences their thermal properties.

Contribution

It presents novel methods for preserving knot topology during Monte Carlo simulations and demonstrates the application of parallelized Wang-Landau algorithms to large polymer knots.

Findings

Topology affects thermal properties of polymer knots

New techniques ensure knot preservation during simulations

Parallelized algorithms enable study of large polymer systems

Abstract

In the first part of this work a summary is provided of some recent experiments and theoretical results which are relevant in the research of systems of polymer rings in nontrivial topological conformations. Next, some advances in modeling the behavior of single polymer knots are presented. The numerical simulations are performed with the help of the Wang-Landau Monte Carlo algorithm. To sample the polymer conformation a set of random transformations called pivot moves is used. The crucial problem of preserving the topology of the knots after each move is tackled with the help of two new techniques which are briefly explained. As an application, the results of an investigation of the effects of topology on the thermal properties of polymer knots is reported. In the end, original results are discussed concerning the use of parallelized codes to study polymers knots composed by a large number of segments within the Wang-Landau approach.