Depletion zones and crystallography on pinched spheres

TL;DR

This study explores how charged particles arrange themselves on a pinched sphere, revealing a depletion zone caused by the interplay of Coulomb repulsion and curvature, with implications for designing deformable charged interfaces.

Contribution

It provides a systematic analysis of the geometric and energetic factors leading to depletion zones on pinched spheres, advancing understanding of crystallography on curved surfaces.

Findings

Depletion zones form at negatively curved waist regions.

Elongated scars cleave into pleats with increased pinching.

The depletion zone is a finite size effect due to Coulomb and geometry interplay.

Abstract

Understanding the interplay between ordered structures and substrate curvature is an interesting problem with versatile applications, including functionalization of charged supramolecular surfaces and modern microfluidic technologies. In this work, we investigate the two-dimensional packing structures of charged particles confined on a pinched sphere. By continuously pinching the sphere, we observe cleavage of elongated scars into pleats, proliferation of disclinations, and subsequently, emergence of a depletion zone at the negatively curved waist that is completely void of particles. We systematically study the geometrics and energetics of the depletion zone, and reveal its physical origin as a finite size effect, due to the interplay between Coulomb repulsion and concave geometry of pinched sphere. These results further our understanding of crystallography on curved surfaces, and have implications in design and manipulation of charged, deformable interfaces in various applications.