Two-Dimensional Packing of Soft Particles and the Soft Generalized Thomson Problem

TL;DR

This paper explores the phase behavior and structural arrangements of soft colloidal particles in two dimensions and on spherical surfaces, revealing how potential shape influences order and revisiting classical Thomson problem configurations.

Contribution

It provides a comprehensive numerical analysis of soft particle packing in 2D and on spheres, highlighting the impact of potential shape and revisiting minimal energy configurations for small N.

Findings

Multiple ordered phases emerge at low temperatures with increasing density.

Structural variety depends on the pair potential's functional form.

Minimal energy configurations for small N are identified and compared to electrostatic cases.

Abstract

We perform numerical simulations of purely repulsive soft colloidal particles interacting via a generalized elastic potential and constrained to a two-dimensional plane and to the surface of a spherical shell. For the planar case, we compute the phase diagram in terms of the system's rescaled density and temperature. We find that a large number of ordered phases becomes accessible at low temperatures as the density of the system increases, and we study systematically how structural variety depends on the functional shape of the pair potential. For the spherical case, we revisit the generalized Thomson problem for small numbers of particles N <= 12 and identify, enumerate and compare the minimal energy polyhedra established by the location of the particles to those of the corresponding electrostatic system.