Pore-size entropy of random hard-sphere packings

Vasili Baranau, Dzmitry Hlushkou, Siarhei Khirevich, Ulrich Tallarek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We introduce a method for calculating the entropy of random hard-sphere packings, also referred to as pore-size entropy. The method is applicable to packings of monodisperse or polydisperse spheres as well as non-spherical particles. Pore-size entropy allows us to analyze the packing microstructure and provides deep insight into the traditional concept of pore-size distribution. Specifically, the logarithm of the pore-size distribution's tail area is equal to the packing entropy. We reveal a local minimum in the plot of pore-size entropy vs. packing density (φ) for monodisperse frictionless sphere packings at a critical density of φC ≈ 0.65, independent of the employed packing generation protocol (Lubachevsky-Stillinger, Jodrey-Tory, and force-biased algorithms), which is a density with minimal number of available packing configurations. This entropy minimum is followed by an entropy increase as φ increases up to ∼0.68, corresponding to the emergence of crystalline structures in the coexistence region; beyond this packing density the entropy decreases again. In a complementary study we modify the Lubachevsky-Stillinger protocol and reproduce the random-close packing limit at φRCP ≈ 0.64. We conclude that φRCP ≈ 0.64 is the jamming point of the glassy states with the lowest density, whereas φC ≈ 0.65 is the jamming point of the densest glassy state (the ideal glass state).

Original languageEnglish (US)
Pages (from-to)3361-3372
Number of pages12
JournalSoft matter
Issue number12
StatePublished - Mar 28 2013
Externally publishedYes

ASJC Scopus subject areas

  • General Chemistry
  • Condensed Matter Physics


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