Decoding collective dynamics and complexity in nanoparticle assemblies using graph theory

Area of Science:

• Materials Science
• Nanotechnology
• Computational Chemistry

Background:

• Nanoparticles bridge molecular and colloidal scales, exhibiting complex self-assembled structures.
• Traditional symmetry-based methods struggle to quantify the order and disorder in nanoparticle assemblies.
• Understanding these structures is crucial for controlling material properties.

Purpose of the Study:

• To develop and apply novel graph theory (GT) metrics for analyzing nanoparticle assembly structures.
• To quantify local and global structural transitions in nanoparticle systems.
• To identify structure-property relationships, particularly for plasmonic applications.

Main Methods:

• Applied graph theory (GT) to analyze nanoparticle assemblies ranging from 400 to 10,000 particles.
• Utilized augmented Forman-Ricci curvature (AFRC) and Ollivier-Ricci curvature (ORC) metrics.
• Tested the approach on gold nanocubes, gold nanoprisms, and indium tin oxide nanospheres.

Main Results:

• GT metrics, AFRC and ORC, effectively capture structural transitions from clusters to networks.
• AFRC correlates with the energetic state of nanoparticle assemblies.
• ORC identifies a "Goldilocks" regime optimizing plasmonic response.

Conclusions:

• Graph theory provides a powerful, unified framework for describing complex nanoparticle assemblies.
• AFRC and ORC offer new ways to quantify structural complexity and energetic states.
• This approach enables the optimization of nanoparticle assemblies for advanced material applications.