Energetically favoured defects in dense packings of particles on spherical surfaces

TL;DR

This study explores the stability and defect structures of particle packings on spheres, revealing that small icosahedral arrangements are most thermally stable and that short-range interactions further enhance structural stability.

Contribution

It provides a comprehensive analysis of defect stability in spherical particle packings, comparing Lennard-Jones and Morse potentials, and highlights the role of defects in energetic and entropic stabilization.

Findings

Small icosahedral structures are most robust against thermal fluctuations.

Excess defects lower potential energy but increase entropy at low temperatures.

Short-range potentials stabilize structures and reduce thermal defect excitation.

Abstract

The dense packing of interacting particles on spheres has proved to be a useful model for virus capsids and colloidosomes. Indeed, icosahedral symmetry observed in virus capsids corresponds to potential energy minima that occur for magic numbers of, e.g., 12, 32 and 72 identical Lennard-Jones particles, for which the packing has exactly the minimum number of twelve five-fold defects. It is unclear, however, how stable these structures are against thermal agitation. We investigate this property by means of basin-hopping global optimisation and Langevin dynamics for particle numbers between ten and one hundred. An important measure is the number and type of point defects, that is, particles that do not have six nearest neighbours. We find that small icosahedral structures are the most robust against thermal fluctuations, exhibiting fewer excess defects and rearrangements for a wide temperature range. Furthermore, we provide evidence that excess defects appearing at low non-zero temperatures lower the potential energy at the expense of entropy. At higher temperatures defects are, as expected, thermally excited and thus entropically stabilised. If we replace the Lennard-Jones potential by a very short-ranged (Morse) potential, which is arguably more appropriate for colloids and virus capsid proteins, we find that the same particle numbers give a minimum in the potential energy, although for larger particle numbers these minima correspond to different packings. Furthermore, defects are more difficult to excite thermally for the short-ranged potential, suggesting that the short-ranged interaction further stabilises equilibrium structures.