Monte Carlo Study of the Inflation-Deflation Transition in a Fluid Membrane

TL;DR

This study uses Monte Carlo simulations to analyze the conformational transition of a self-avoiding fluid membrane under osmotic pressure, revealing an abrupt phase change with specific scaling behaviors and critical exponents.

Contribution

It provides the first detailed Monte Carlo analysis of the inflation-deflation transition in fluid membranes, including scaling laws and critical exponents.

Findings

Abrupt conformational transition at critical pressure p*

Scaling of transition pressure with system size as p* ∝ N^(-α)

Finite size scaling of volume and radii of gyration

Abstract

We study the conformation and scaling properties of a self-avoiding fluid membrane, subject to an osmotic pressure $p$, by means of Monte Carlo simulations. Using finite size scaling methods in combination with a histogram reweighting techniques we find that the surface undergoes an abrupt conformational transition at a critical pressure $p^\ast$, from low pressure deflated configurations with a branched polymer characteristics to a high pressure inflated phase, in agreement with previous findings \cite{gompper,baum}. The transition pressure $p^{\ast}$ scales with the system size as $p^\ast \propto N^{-\alpha}$, with $\alpha = 0.69 \pm 0.01$. Below $p^\ast$ the enclosed volume scales as $V \propto N$, in accordance with the self-avoiding branched polymer structure, and for $p\searrow p^{\ast}$ our data are consistent with the finite size scaling form $V \propto N^{\beta_{+}}$, where $\beta_{+} = 1.43 \pm 0.04$. Also the finite size scaling behavior of the radii of gyration and the compressibility moduli are obtained. Some of the observed exponents and the mechanism behind the conformational collapse are interpreted in terms of a Flory theory.