Connecting packing efficiency of binary hard sphere systems to their intermediate range structure

TL;DR

This study links the packing efficiency of binary hard sphere systems to their intermediate range structural order, revealing that optimal packing correlates with maximum local disorder and specific structural symmetries depending on particle size ratio.

Contribution

It introduces a four-point correlation function to analyze 3D structures of binary sphere mixtures, connecting packing efficiency to intermediate range order and local disorder.

Findings

Maximum packing fraction occurs at a composition with maximum local disorder.

Structural correlation length varies with composition, showing a minimum at optimal packing.

Intermediate range order depends on particle size ratio, q.

Abstract

Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we reveal that this 3d structure has on intermediate and large length scales a surprisingly regular order, the symmetry of which depends on q. The related structural correlation length has a minimum at the composition at which the packing fraction is highest. At this composition also the number of different local particle arrangements has a maximum, indicating that efficient packing of particles is associated with a structure that is locally maximally disordered.