Assembly of hard spheres in a cylinder: a computational and experimental study

TL;DR

This study combines experiments and simulations to explore how hard spheres assemble inside cylinders, revealing structural crossovers, the influence of compression rate, and the consistency between sedimentation and compression pathways.

Contribution

It provides new insights into the assembly process of hard spheres in cylindrical confinement, highlighting the effects of compression rate and boundary conditions on structure formation.

Findings

Structural crossovers are observed without phase transitions.

Slow compression yields equilibrium-like structures.

Fast compression and sedimentation produce similar assembly pathways.

Abstract

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter $\sigma$ within cylinders of diameter $\sigma\leq D\leq 2.82\sigma$. Although in such a system phase transitions formally do not exist, marked structural crossovers are observed. In simulations, we find that the resulting pressure-diameter structural diagram echoes the densest packing sequence obtained at infinite pressure in this range of $D$. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the source of this difference. Results from colloidal sedimentation experiments at high P\'eclet number are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used. The similitude between compression and sedimentation results suggests that the assembly pathway does not here sensitively depend on the nature of the out-of-equilibrium dynamics.