Analytical interaction potentials for disks in two dimensions

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.