Dense packings of geodesic hard ellipses on a sphere

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Packing problems are crucial in various scientific fields, including liquid crystals, colloids, and granular matter.
• Anisotropic particle packings are common, but most studies focus on Euclidean geometry, neglecting curved surfaces.
• Experimental systems often involve anisotropic particles on curved surfaces, like Pickering emulsions or protein-coated vesicles.

Purpose of the Study:

• To investigate random close packing configurations of elliptical particles on a spherical surface.
• To analyze the interplay between finite-size effects and surface curvature on packing behavior.
• To compare packing properties on curved surfaces with those in 2D Euclidean space.

Main Methods:

• Developed a two-dimensional model of spherical geodesic ellipses.
• Studied random close packing configurations.
• Analyzed packing fraction and mean contact number in relation to ellipse aspect ratio and curvature.

Main Results:

• Monodisperse ellipse packings on a spherical surface are inherently disordered.
• Packing fraction and mean contact number show non-monotonic dependence on ellipse aspect ratio.
• Curvature induces frustration, leading to disordered configurations even with monodisperse particles, unlike the 2D Euclidean case.

Conclusions:

• Closed curved surfaces effectively introduce disorder in particle packing systems.
• This work highlights fundamental differences between packing on curved vs. flat surfaces.
• Findings could facilitate the study of monodisperse random packings in curved geometries.