Phase Transitions in Pressurised Semiflexible Polymer Rings

TL;DR

This paper investigates the phase behavior of pressurised semiflexible polymer rings, revealing a continuous transition between collapsed and inflated phases through simulations and theoretical analysis.

Contribution

It introduces a comprehensive model combining pressure, semiflexibility, and self-intersections, and derives the phase diagram and scaling laws for the area.

Findings

Identifies a continuous phase transition between collapsed and inflated states.

Derives scaling laws for the average area as a function of ring size.

Shows good agreement between simulations and analytical results.

Abstract

We propose and study a model for the equilibrium statistical mechanics of a pressurised semiflexible polymer ring. The Hamiltonian has a term which couples to the algebraic area of the ring and a term which accounts for bending (semiflexibility). The model allows for self-intersections. Using a combination of Monte Carlo simulations, Flory-type scaling theory, mean-field approximations and lattice enumeration techniques, we obtain a phase diagram in which collapsed and inflated phases are separated by a continuous transition. The scaling properties of the averaged area as a function of the number of units of the ring are derived. For large pressures, the asymptotic behaviour of the area is calculated for both discrete and lattice versions of the model. For small pressures, the area is obtained through a mapping onto the quantum mechanical problem of an electron moving in a magnetic field. The simulation data agree well with the analytic and mean-field results.