Statistical Mechanics of Multistability in Microscopic Shells

TL;DR

This paper explores how microscopic elastic shells and plates switch shapes spontaneously due to thermal noise, using statistical mechanics, simulations, and analytical methods, with implications for nanomaterials and biological structures.

Contribution

It introduces a simplified geometric mode approach and combines Monte Carlo and Fokker-Planck analyses to study shape transitions in microscopic shells.

Findings

Shape transitions depend on noise strength.

Stationary distributions match Fokker-Planck predictions.

Mean first passage times characterize transition kinetics.

Abstract

Unlike macroscopic multistable mechanical systems such as snap bracelets or elastic shells that must be physically manipulated into various conformations, microscopic systems can undergo spontaneous conformation switching between multistable states due to thermal fluctuations. Here we investigate the statistical mechanics of shape transitions in small elastic elliptical plates and shells driven by noise. By assuming that the effects of edges are small, which we justify exactly for plates and shells with a lenticular section, we decompose the shapes into a few geometric modes whose dynamics are easy to follow. We use Monte Carlo simulations to characterize the shape transitions between conformation minima as a function of noise strength, and corroborate our results using a Fokker-Planck formalism to study the stationary distribution and the mean first passage time problem. Our results are applicable to objects such as such as graphene flakes or protein {\beta}-sheets, where fluctuations, geometry and finite size effects are important.