2026-05-21 ミシガン大学
＜関連情報＞
- https://news.umich.edu/complexity-isnt-subjective-the-right-amount-results-in-new-nanomaterial-properties/
- https://www.science.org/doi/10.1126/science.aeb5134
グラフ理論を用いたナノ粒子集合体における集団ダイナミクスと複雑性の解読 Decoding collective dynamics and complexity in nanoparticle assemblies using graph theory
Jonas Hallstrom, Puquan Pan, Jayson Sia, Sangwok Bae, […] , and Nicholas A. Kotov
Science Published:14 May 2026
DOI:https://doi.org/10.1126/science.aeb5134
Graph curvature measures quantify disorder and complexity for self-assembled particle systems.
NP assemblies can be viewed as a series of graphs or networks in which nodes represent NPs and edges represent strong interparticle interactions. ORC and AFRC can be found for every edge in these graphs, quantifying the structural order and complexity in the local area around those edges. Scale bars, 200 nm.
Abstract
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.
