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Random close packing from hard-sphere Percus-Yevick theory.

Eytan Katzav1, Ruslan Berdichevsky2, Moshe Schwartz2

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Summary
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The Percus-Yevick theory fails for hard spheres at high densities, predicting unphysical negative values for the pair distribution function. This indicates a breakdown of the theory beyond the liquid phase, potentially related to random close packing.

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Area of Science:

  • Statistical mechanics
  • Computational physics
  • Condensed matter physics

Background:

  • The Percus-Yevick theory accurately models hard sphere systems within the liquid phase.
  • Beyond liquid densities, the theory yields unphysical predictions, lacking a mechanism for phase transitions.

Purpose of the Study:

  • Investigate the validity of the Percus-Yevick hard-sphere pair distribution function in higher dimensions.
  • Identify the critical volume fraction where the theory's predictions become unphysical.

Main Methods:

  • Analysis of the Percus-Yevick hard-sphere pair distribution function, g₂(r).
  • Examination of g₂(r) across various spatial dimensions and volume fractions (η).

Main Results:

  • The pair distribution function, g₂(r), becomes negative at certain distances beyond a critical volume fraction, ηc.
  • The calculated critical ηc values align with reported onsets of random close packing across different dimensions.

Conclusions:

  • The Percus-Yevick theory breaks down for hard spheres at high densities, indicated by unphysical negative pair distribution functions.
  • The critical volume fraction suggests a connection between the theory's limitations and the phenomenon of random close packing.
  • Findings may impact other systems modeled by Percus-Yevick theory.