Hard Spheres: Crystallization and Glass Formation

TL;DR

This paper uses molecular dynamics simulations to study how polydispersity and concentration affect crystallization and glass formation in hard sphere assemblies, revealing distinct nucleation regimes and the impact of polydispersity.

Contribution

It provides new insights into the effects of polydispersity on crystallization and identifies three nucleation regimes in hard sphere systems, including a novel high-concentration mechanism.

Findings

No crystallization for polydispersity s > 0.07

Polydispersity slows down crystal nucleation at intermediate levels

Identification of three nucleation regimes with distinct behaviors

Abstract

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition.