Defect Motifs for Constant Mean Curvature Surfaces

TL;DR

This paper investigates defect patterns on constant mean curvature surfaces with charged particles, revealing how defect motifs depend on curvature and potential energy, and introduces a new defect motif.

Contribution

It identifies defect motifs on curved surfaces and introduces a novel defect motif of pentagon pairs, expanding understanding of surface defect structures.

Findings

Extended defects occur on surfaces with weak curvature.

Isolated defects dominate on strongly negatively curved surfaces.

A new defect motif of pentagon pairs is reported.

Abstract

The energy landscapes of electrostatically charged particles embedded on constant mean curvature surfaces are analysed for a wide range of system size, curvature, and interaction potentials. The surfaces are taken to be rigid, and the basin-hopping method is used to locate the putative global minimum structures. The defect motifs favoured by potential energy agree with experimental observations for colloidal systems: extended defects (scars and pleats) for weakly positive and negative Gaussian curvatures, and isolated defects for strongly negative Gaussian curvatures. Near the phase boundary between these regimes the two motifs are in strong competition, as evidenced from the appearance of distinct funnels in the potential energy landscape. We also report a novel defect motif consisting of pentagon pairs.