Thermodynamic behaviour of two-dimensional vesicles revisited

TL;DR

This paper investigates the phase transition behavior of pressurised two-dimensional vesicles, revealing a shape transition from unfaceted to polygonal forms driven by pressure, supported by simulations and theoretical models.

Contribution

It demonstrates the existence of a thermodynamic phase transition in 2D vesicles at a non-zero scaled pressure, extending previous models with new simulation and theoretical insights.

Findings

Existence of a phase transition at a critical scaled pressure.

Shape transition from unfaceted to regular polygonal form.

Area scales with the square of the number of monomers for all positive pressures.

Abstract

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4\pi$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories.