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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Free energy of singular sticky-sphere clusters.

Yoav Kallus1, Miranda Holmes-Cerfon2

  • 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.

Physical Review. E
|March 17, 2017
PubMed
Summary

Sticky particle networks exhibit emergent crystalline order. Hyperstatic clusters, favored in larger systems, drive this ordering, even in small sticky-sphere assemblies.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Particle networks with spring-like interactions model diverse systems like colloids and metamaterials.
  • Zero-frequency vibrational modes (singularities) are crucial for system behavior, deviating from harmonic approximations.
  • Understanding these singularities is key to predicting emergent properties in particle systems.

Purpose of the Study:

  • To develop a theory for sticky particle systems that accounts for singularities in the sticky limit.
  • To investigate the emergence of crystalline order from small- to large-scale particle assemblies.
  • To determine the factors governing the stability and properties of sticky particle clusters.

Main Methods:

  • Directly accounting for singularities in the sticky limit of pairwise interactions.

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  • Calculating asymptotic values of partition functions for singular clusters.
  • Analyzing the geometric characterization of rigidity (second-order rigidity).
  • Computing partition functions for rigid clusters up to N=21 particles.

    • Main Results:

    • The asymptotic partition function of singular clusters depends on potential depth and range.
    • Hyperstatic clusters (with >3N-6 contacts) dominate the cluster landscape for N≤21.
    • Singular and isostatic clusters are less frequent than hyperstatic ones, despite entropic advantages.
    • Hyperstatic clusters resemble fragments of close-packed lattices.

    Conclusions:

    • The theory provides a framework for understanding sticky particle systems, including their emergent order.
    • The prevalence of hyperstatic clusters explains the emergence of crystalline order in sticky-sphere systems.
    • This work elucidates how local interactions lead to global order, even in small systems (N=10).