Characterizing Structure Through Shape Matching and Applications to Self Assembly

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.

19 pages, 9 figures

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• Phase Diagram of Hard Tetrahedra
• Inverse methods for design of soft materials
• Studying Rare Events using Forward-Flux Sampling: Recent Breakthroughs and Future Outlook
• A local order metric for condensed phase environments
• Activity-Enhanced Self-Assembly of a Colloidal Kagome Lattice
• Local Structure Order Assisted Two-step Crystal Nucleation in Polyethylene
• Flow-induced Density Fluctuation assisted Nucleation in Polyethylene
• Strong Orientational Coordinates and Orientational Order Parameters For Symmetric Objects
• The Role of Polytetrahedral Structures in the Elongation and Rupture of Gold Nanowires
• Rotation-equivariant Graph Neural Networks for Learning Glassy Liquids Representations
• Symmetry-specific orientational order parameters for complex structures
• Geometric Frustration Directs the Self-Assembly of Nanoparticles with Crystallized Ligand Bundles