Knots as Topological Order Parameter For Semi-Flexible Polymers

TL;DR

This study explores how bending stiffness influences the conformational phases of semi-flexible polymers, revealing stable knotted phases and phase coexistence without significant energy change, using advanced Monte Carlo simulations.

Contribution

It introduces a topological order parameter based on knots to characterize phases in semi-flexible polymers, expanding understanding of their conformational diversity.

Findings

Identification of stable knotted phases in semi-flexible polymers

Discovery of phase coexistence with minimal energy change

Development of a pseudo-phase diagram for the entire stiffness range

Abstract

Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase diagram for the complete range of semi-flexible polymers, from flexible to stiff. Although a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Changing the internal bending stiffness, the model exhibits different pseudo phases like bent, hairpin or toroidal. In particular, we find thermodynamically stable knots and transitions into these knotted phases with a clear phase coexistence, but almost no change in the mean total energy.