Harmonic Order Parameters for Characterizing Complex Particle Morphologies

TL;DR

This paper introduces harmonic order parameters based on shape matching techniques to characterize complex particle morphologies, extending traditional methods to more intricate nanoscale structures.

Contribution

It develops a novel approach using shape matching for creating specialized order parameters for complex particle shapes, enhancing analysis of nanoscale self-assembly.

Findings

Harmonic descriptors can identify unknown structures effectively.

Symmetry properties of harmonic descriptors can be exploited for problem-solving.

Techniques are applicable to both simulated and experimental particle systems.

Abstract

Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to more complex shapes, such as those encountered in nanoscale self-assembly applications. To do so, we build on a powerful set of techniques that originate in the computer science field of "shape matching." We demonstrate how shape matching techniques can be applied to identify unknown structures and create highly-specialized \textit{ad hoc} order parameters. Additionally, we investigate the special symmetry properties of harmonic descriptors, and demonstrate how they can be exploited to provide optimal solutions to certain classes of problems. Our techniques can be applied to particle systems in general, both simulated and experimental, provided the particle positions are known.