A note on rattlers in amorphous packings of binary mixtures of hard spheres

TL;DR

This paper discusses the properties of rattlers in amorphous binary sphere packings and clarifies a misunderstanding regarding the theoretical jamming density bounds for such systems.

Contribution

It clarifies a misunderstanding about the theoretical bounds of jamming density in binary sphere packings, specifically addressing the role of rattlers.

Findings

Theoretical bounds on jamming density are consistent with previous results.

Rattlers play a significant role in the packing structure.

Clarification resolves apparent contradictions in prior studies.

Abstract

It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our theoretical result for the jamming density of a binary mixture of hard spheres (arXiv:0903.5099) apparently violates an upper bound that is obtained by considering the limit where the diameter ratio r = DA/DB goes to infinity. We believe that this apparent contradiction is the consequence of a misunderstanding, which we try to clarify here.