Shapes within shapes: how particles arrange inside a cavity

TL;DR

This study calculates the configurational entropy of hard particles in cavities, revealing how entropy and particle arrangements depend on cavity shape, particle number, and boundary effects, with implications for confined systems and material design.

Contribution

It introduces a Monte Carlo integration method to analyze entropy in various particle-cavity configurations, highlighting the effects of shape and particle number on ordering and density.

Findings

Entropy decreases with cavity aspect ratio for small N.

High particle density occurs near boundaries as N increases.

Ordered regions emerge at higher particle numbers.

Abstract

We calculate the configurational entropy of hard particles confined in a cavity using Monte Carlo integration. Multiple combinations of particle and cavity shapes are considered. For small numbers of particles $N$, we show that the entropy decreases monotonically with increasing cavity aspect ratio, regardless of particle shape. As $N$ increases, we find ordered regions of high and low particle density, with the highest density near the boundary for all particle and cavity shape combinations. Our findings provide insights relevant to engineering particles in confined spaces, entropic barriers, and systems with depletion interactions.