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  3. Analytical Interaction Potentials For Disks In Two Dimensions.

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Analytical interaction potentials for disks in two dimensions.

Binghan Liu1,2,3, Junwen Wang2,3,4, Gary S Grest5

  • 1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA.

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|March 17, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

Researchers derived analytical forms for interactions between thin disks in 2D systems. Simulations revealed order transitions in disk packing and stratification phenomena during drying.

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Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • Interactions between disk-shaped objects are crucial in various 2D systems.
  • Existing models often rely on numerical methods, limiting analytical insights.
  • The Lennard-Jones potential is a standard for inter-particle interactions.

Purpose of the Study:

  • To derive compact analytical forms for interactions involving thin disks in 2D.
  • To validate these analytical potentials against numerical integrations.
  • To apply the derived potentials in simulations of 2D disk suspensions.

Main Methods:

  • Integration of the Lennard-Jones 12-6 potential for pairwise interactions.
  • Development of analytical expressions for potentials and forces between disks, points, and walls.
  • Implementation of analytical potentials in LAMMPS for simulating disk suspensions with explicit solvent.

    • Main Results:

    • Validated analytical forms for disk-point, disk-disk, and disk-wall interactions.
    • Observed a disorder-to-order transition in monodisperse disk suspensions with increasing area fraction or solvent evaporation.
    • Identified "small-on-top" stratification in bidisperse disk suspensions during rapid drying, mirroring 3D colloidal behavior.

    Conclusions:

    • The derived analytical potentials provide efficient tools for modeling 2D disk systems.
    • The study demonstrates key phenomena like phase transitions and stratification in 2D suspensions.
    • These findings have implications for understanding and designing 2D materials and soft matter systems.