Characterizing Structure Through Shape Matching and Applications to Self Assembly

TL;DR

This paper explores how shape matching techniques from computer science can be used to develop flexible structural metrics for complex self-assembled systems, extending traditional methods in condensed matter physics.

Contribution

It introduces a framework for applying shape matching to characterize structures in self-assembly, demonstrating its effectiveness through three proof-of-concept examples.

Findings

Shape matching methods can identify local and global structures.

These methods track structural transitions effectively.

Applicable to both simulated and experimental systems.

Abstract

Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist, often they are insufficient for treating problems in the emerging field of nano and microscale self-assembly, where the structures encountered may be complex and unusual. The computer science field of "shape matching" offers a robust solution to this problem by defining diverse methods for quantifying the similarity between arbitrarily complex shapes. Most order parameters and correlation functions used in condensed matter apply a specific measure of structural similarity within the context of a broader scheme. By substituting shape matching quantities for traditional quantities, we retain the essence of the broader scheme, but extend its applicability to more complex structures. Here we review some standard shape matching techniques and discuss how they might be used to create highly flexible structural metrics for diverse systems such as self-assembled matter. We provide three proof-of-concept example problems applying shape matching methods to identifying local and global structures, and tracking structural transitions in complex assembled systems. The shape matching methods reviewed here are applicable to a wide range of condensed matter systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.