Fluctuating shells under pressure

TL;DR

This paper investigates how thermal fluctuations influence the elastic behavior of pressurized spherical shells, revealing size-dependent effects and divergence near buckling, with implications for microcapsules and biological structures.

Contribution

It provides the first detailed analysis of thermal fluctuation effects on curved shells under pressure, combining perturbation theory and simulations.

Findings

Thermal fluctuations become dominant as shell size increases.

Inward pressure amplifies thermal effects and diverges near buckling.

Shape fluctuations are significantly affected by curvature and pressure.

Abstract

Thermal fluctuations strongly modify the large length-scale elastic behavior of crosslinked membranes, giving rise to scale-dependent elastic moduli. While thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic {\it shells}. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependent coupling between the in-plane stretching modes and the out-of-plane undulations. In addition, a shell can support a pressure difference between its interior and exterior. Little is known about the effect of thermal fluctuations on the elastic properties of shells. Here, we study the statistical mechanics of shape fluctuations in a pressurized spherical shell using perturbation theory and Monte Carlo computer simulations, explicitly including the effects of curvature and an inward pressure. We predict novel properties of fluctuating thin shells under point indentations and pressure-induced deformations. The contribution due to thermal fluctuations increases with increasing ratio of shell radius to thickness, and dominates the response when the product of this ratio and the thermal energy becomes large compared to the bending rigidity of the shell. Thermal effects are enhanced when a large uniform inward pressure acts on the shell, and diverge as this pressure approaches the classical buckling transition of the shell. Our results are relevant for the elasticity and osmotic collapse of microcapsules.