Optimal packing of polydisperse hard-sphere fluids

TL;DR

This paper investigates how intermolecular interactions influence the optimal size distribution of polydisperse hard spheres, revealing a transition to bi-modal distributions at higher densities through simulations and theoretical analysis.

Contribution

It demonstrates the limitations of the Percus-Yevick approximation and highlights the emergence of non-monotonic size distributions in dense systems.

Findings

No solutions beyond volume fraction ~0.260 in Percus-Yevick approximation.

Monte Carlo simulations show bi-modal distributions at higher densities.

Finite size effects are crucial for understanding distribution behavior.

Abstract

We consider the effect of intermolecular interactions on the optimal size-distribution of $N$ hard spheres that occupy a fixed total volume. When we minimize the free-energy of this system, within the Percus-Yevick approximation, we find that no solution exists beyond a quite low threshold ($\eta \thickapprox 0.260$). Monte Carlo simulations reveal that beyond this density, the size-distribution becomes bi-modal. Such distributions cannot be reproduced within the Percus-Yevick approximation. We present a theoretical argument that supports the occurrence of a non-monotonic size-distribution and emphasizing the importance of finite size effects.