Key Findings
Researchers have developed a quantitative metric for complexity in nanomaterials, defining complexity as a mix of order and randomness measurable via graph theory. This breakthrough enables the engineering of materials with entirely new property combinations.
Methodology
The team used graph theory to represent nanoparticle assemblies as networks of nodes (particles) and edges (interactions). Graphs were constructed from transmission electron microscope images and computer simulations of nanoparticle crystals. Metrics derived from these graphs quantified how interactions propagate through the network and measured network reconfigurability.
Results
- The complexity metric directly correlated with the optical properties of gold and indium tin oxide nanoparticles.
- Gold nanoparticles formed loose networks of crystal clusters that reflected infrared light—a property not exhibited by random suspensions or dense crystals.
- The framework allows researchers to predict material properties based on structural complexity.
Impact
This work moves nanomaterial engineering from discovery-based to design-based. It provides a new design parameter—complexity—for creating materials with properties not found in nature. The study is part of the NSF-funded Center for Complex Particle Systems (COMPASS).
Statements
"It's like a structure that has clusters and some bridges that connect these clusters... interconnected communities of particles give you something new. "
— Nick Kotov, University of Michigan
"Graph-based measures strongly correlate with material properties and can serve as a new guiding principle for designing future materials."
— Xiaoming Mao, University of Michigan
"By using graph theory metrics, we can measure how particles organize across multiple scales. "
— Paul Bogdan, University of Southern California
Funding
The research was supported by the National Science Foundation (NSF), U.S. Army Research Office, DARPA, NIH, Office of Naval Research, and the Welch Foundation.