Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings

TL;DR

This paper presents a Monte Carlo method to analyze the free-energy and scaling behavior of globular ring polymers, revealing deviations from hyperscaling relations in the collapsed phase.

Contribution

It introduces a new simulation scheme for interacting elastic lattice polymers, enabling detailed study of long, compact globular configurations and their free energies.

Findings

Estimated bulk and surface free energies of globular rings.

Provided evidence that hyperscaling relation does not hold for globular rings.

Analyzed the entropic exponent in the collapsed phase.

Abstract

We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of "interacting elastic lattice polymers" and allows a sufficiently good sampling of long and compact configurations, an essential prerequisite to study the scaling behaviour of free energies. By simulating interacting self-avoiding rings at several temperatures in the collapsed phase, we estimate both the bulk and the surface free energy. Moreover from the corresponding estimate of the entropic exponent $\alpha-2$ we provide evidence that, unlike for swollen and $\Theta$-point rings, the hyperscaling relation is not satisfied for globular rings.