Thermodynamic and topological properties of copolymer rings with a segregation/mixing transition

TL;DR

This paper investigates the thermodynamic and topological phase transition of two interacting ring polymers, revealing how their linking probability and properties change across segregated and mixed phases near a critical point.

Contribution

It introduces a lattice model to analyze the phase transition and linking behavior of two ring polymers, highlighting the relationship between topology and thermodynamics.

Findings

Linking probability is low in the segregated phase.

Linking probability increases in the mixed phase.

Topological complexity correlates with thermodynamic properties.

Abstract

Two ring polymers close to each other in space may be either in a segregated phase if there is a strong repulsion between monomers in the polymers, or intermingle in a mixed phase if there is a strong attractive force between the monomers. These phases are separated by a critical point which has a $\theta$-point character. The metric and topological properties of the ring polymers depend on the phase, and may change abruptly at the critical point. In this paper we examine the thermodynamics and linking of two ring polymers close in space in both the segregated and mixed phases using a cubic lattice model of two polygons interacting with each other. Our results show that the probability of linking is low in the segregated phase, but that it increases through the critical point as the model is taken into the mixed phase. We also examine the metric and thermodynamic properties of the model, with focus on how the averaged measures of topological complexity are related to these properties.