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Lattice-based random jammed configurations for hard particles.

F H Stillinger1, H Sakai, S Torquato

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2003
PubMed
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This study enumerates jammed packings derived from crystal structures. It identifies jamming categories and vacancy limits, finding that distinct jammed packings increase exponentially with system size.

Area of Science:

  • Condensed matter physics
  • Materials science
  • Statistical mechanics

Background:

  • Jammed packings, particularly those derived from crystalline structures, are crucial in understanding disordered materials.
  • Sequential particle removal from periodic arrays generates a subset of these jammed packings.

Purpose of the Study:

  • To enumerate jammed packings originating from triangular disk and cubic sphere lattices.
  • To categorize packings based on their response to geometric constraints and virtual displacements.
  • To determine the maximum vacancy concentration for different jamming types.

Main Methods:

  • Analysis of packings derived from triangular disk, face-centered cubic, and body-centered cubic lattices.
  • Distinguishing between locally jammed, collectively jammed, and strictly jammed categories.

Related Experiment Videos

  • Identifying critical vacancy clusters that disrupt jamming.
  • Utilizing local attrition factors for approximate enumeration.
  • Main Results:

    • Three categories of jammed packings (locally, collectively, strictly jammed) were defined.
    • Upper limits for vacancy concentration were established for each packing type.
    • Specific vacancy clusters causing local jamming failure were identified.
    • The number of distinct jammed packings is expected to grow exponentially with system size.

    Conclusions:

    • The study provides a framework for enumerating jammed packings from crystalline structures.
    • Understanding vacancy concentrations and cluster formations is key to predicting packing stability.
    • Future work may benefit from lattice-gas/Ising-model representations for further analysis.