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Hard sphere packings within cylinders.

Lin Fu1, William Steinhardt2, Hao Zhao1

  • 1Department of Chemistry, Duke University, Durham, NC 27708, USA. patrick.charbonneau@duke.edu.

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Researchers explored dense sphere packing in cylinders, discovering 17 new chiral structures for larger diameters (D > 2.873σ). These complex arrangements reveal interplay between inner cores and outer shells, expanding knowledge of geometric packing problems.

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Area of Science:

  • Physics
  • Materials Science
  • Geometry

Background:

  • Hard sphere packing in cylinders models systems like fullerenes in nanotubes.
  • Dense packing configurations (close packings) are geometrically complex, especially for larger cylinder-to-sphere diameter ratios (D/σ).
  • Knowledge of close packings is limited for D/σ > 2.873.

Purpose of the Study:

  • To extend the identification of close-packed structures of hard spheres in cylinders up to D = 4.00σ.
  • To investigate the geometric complexity and resulting structures in the largely unexplored regime of D/σ > 2.873.

Main Methods:

  • Adaptation of Torquato-Jiao's adaptive-shrinking-cell formulation.
  • Application of sequential-linear-programming (SLP) technique.

Main Results:

  • Identification of 17 new close-packing structures for D up to 4.00σ.
  • Discovery that almost all new structures are chiral.
  • Observation of core-shell structures competing for density beyond D ≈ 2.85σ.
  • Characterization of diverse packing geometries, including quasiperiodic, periodic, and exotic structures.

Conclusions:

  • The study significantly expands the known catalog of hard sphere close packings in cylinders.
  • New structures exhibit complex behaviors, including competing core-shell interactions and 3D extensions of 2D disk packing.
  • Findings provide insights into geometric packing principles relevant to materials science and nanotechnology.