Topological defects of dipole patchy particles on a spherical surface

TL;DR

This study explores how dipole patchy particles assemble on spherical surfaces, revealing defect formations and defect-related structures influenced by topological constraints through Brownian dynamics simulations.

Contribution

It provides new insights into the defect structures and assembly patterns of dipole patchy particles confined to spherical surfaces, highlighting the influence of topology.

Findings

Four +1/2 defects satisfy Euler characteristic.

Eight grain boundary scars proliferate with sphere size.

Defect positions are correlated with scar orientations.

Abstract

We investigate the assembly of the dipole-like patchy particles confined to a spherical surface by Brownian dynamics simulations. The surface property of the spherical particle is described by the spherical harmonic $Y_{10}$, and the orientation of the particle is defined as the uniaxial axis. On a flat space, we observe a defect-free square lattice with nematic order. On a spherical surface, defects appear due to the topological constraint. As for the director field, four defects of winding number $+1/2$ are observed, satisfying the Euler characteristic. We have found many configurations of the four defects lying near a great circle. Regarding the positional order for the square lattice, eight grain boundary scars proliferate linearly with the sphere size. The positions and orientations of the eight grain boundary scars are strongly related to the four $+1/2$ defect cores.