Decoding collective dynamics and complexity in nanoparticle assemblies using graph theory

• 成果类型: Article
• 署名作者: Hallstrom, Jonas; Pan, Puquan; Sia, Jayson; Bae, Sangwok; Qian, Dingwen; Qian, Chang; Liu, Sindy; Yao, Lehan; Truskett, Thomas M.; Milliron, Delia J.; Chen, Qian; Mao, Xiaoming; Bogdan, Paul; Kotov, Nicholas A.
• 署名单位: University of Michigan System; University of Michigan; University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign; University of Southern California; University of Michigan System; University of Michigan; University of Michigan System; University of Michigan; University of Michigan System; University of Michigan; University of Texas System; University of Texas Austin
• 刊物名称: SCIENCE
• ISSN/ISSBN: 0036-8075; 1095-9203
• DOI: 10.1126/science.aeb5134
• 发表日期: 2026-05-14
• 页码: eaeb5134
• 关键词: growth

摘要

Being intermediate in scale between molecules and colloids, nanoparticles combine characteristics of both. The structure of their self-assembled states combining order and disorder is difficult to quantify using traditional symmetry-based descriptors. Here, we applied graph theory (GT) to analyze assemblies of 400 to 10,000 nanoparticles across three material systems. We show that GT metrics, augmented Forman-Ricci curvature (AFRC) and Ollivier-Ricci curvature (ORC), capture local and global structural transitions from small clusters to extended networks. AFRC reflects the energetic state of the assembly, whereas ORC quantifies structural complexity and reveals a Goldilocks regime that maximizes plasmonic response. The generality of this approach is demonstrated for gold nanocubes, gold nanoprisms, and indium tin oxide nanospheres, providing a unified framework for describing and optimizing complex nanoparticle assemblies.