Shapes of flexible vesicles at constant volume

Abstract

A three-dimensional vesicle model on the cubic lattice with fixed surface area N and at constant volume V is analyzed using a Monte Carlo method and finite size scaling. On the entire range of volumes accessible to the vesicles, the mean square radius of gyration obeys a scaling law <R2≳∼Nνf(VN−3ν/2), where ν≊4/5. The scaling function f(x) has a minmum at the crumpling point xc≊0.177, separating the regimes of branched conformations V∼N (x≤xc) and expanded conformations V∼N3/2 (x≥xc). At the crumpling point Vc≊0.177N3ν/2, the conformations are crumpled with <R2≳c≊0.146Nν. The shapes of vesicles are spherically symmetric in the inflated regime, whereas oblate in the branched regime. The crossover is characterized by the asymmetry parameter A, which exhibits an effective power law <A≳≊(15x)−3.0. A crumpling parameter is introduced characterizing the increasing roughness of the vesicles at decreasing volume. The scaling of the mean local curvature is discussed as well.