Characterizing Complex Particle Morphologies Through Shape Matching: Descriptors, Applications, and Algorithms

TL;DR

This paper explores advanced shape matching algorithms and descriptors to characterize complex particle structures in nano and microscale systems, extending traditional methods for better analysis of intricate assemblies.

Contribution

It introduces novel shape descriptors and demonstrates their application in structural characterization, phase mapping, and correlation analysis for complex particle systems.

Findings

Shape matching algorithms effectively classify complex structures.

Descriptors improve structural analysis beyond traditional metrics.

Methods are applicable to both simulated and experimental data.

Abstract

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for characterizing the unique and highly complex structures often encountered in the emerging field of nano and microscale self-assembly, or other disciplines involving complex structures such as computational biology. Computer science algorithms known as "shape matching" methods pose a unique solution to this problem by providing robust metrics for quantifying the similarity between pairs of arbitrarily complex structures. This pairwise matching operation, either implicitly or explicitly, lies at the heart of most standard structural characterization schemes for particle systems. By substituting more robust "shape descriptors" into these schemes we extend their applicability to structures formed from more complex building blocks. Here, we describe several structural characterization schemes and shape descriptors that can be used to obtain various types of structural information about particle systems. We demonstrate the application of shape matching algorithms to a variety of example problems, for topics including local and global structure identification and classification, automated phase diagram mapping, and the construction of spatial and temporal correlation functions. The methods are applicable to a wide range of systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.