Key takeaways
ANN ARBOR—Complexity may seem subjective, but a quantitative measure of the complexity of nanomaterials was recently developed by a team of researchers from the University of Michigan Engineering, the University of Southern California Viterbi School of Engineering and the University of Illinois Urbana-Champaign.
Their metric promises to take nanomaterials engineering from a process of discovery to one of design, enabling engineers to produce combinations of properties not seen in natural or existing man-made materials.
The findings also take nanomaterials beyond randomly distributed coatings of nanoparticles or tightly packed crystals, in which building blocks are arranged with a uniform pattern and spacing. Instead, a tunable combination of ordered crystals and randomness—considered the essence of complexity—provides a new knob for designing material properties.
"It's like a structure that has clusters and some bridges that connect these clusters throughout the system, and these interconnected communities of particles give you something new," said Nick Kotov , the Irving Langmuir Distinguished University Professor of Chemical Sciences and Engineering and co-corresponding author of the study recently published in Science. He is also the principal investigator of the $30 million Center for Complex Particle Systems , or COMPASS, which was funded by the National Science Foundation to harness nanoparticles to build materials with properties rarely, if ever, found in nature.
The team demonstrated the power of their network structures in several nanoparticle systems. In one example, they assembled gold nanoparticles into loose networks of crystal clusters that strongly reflect infrared light—something that suspensions of gold nanoparticles can't do and that gold nanoparticle crystals do poorly. The team also laid out how other researchers can harness complexity in the same way, providing a framework to quantify order and disorder and predict the resulting material properties.
"We show that graph-based measures strongly correlate with material properties and can serve as a new guiding principle for designing future materials for emerging technologies," said Xiaoming Mao , a U-M professor of physics and mechanical engineering in COMPASS and a co-corresponding author of the study. "It allows engineers to harness complexity as a powerful design parameter, opening pathways to capabilities that cannot be achieved with simple materials."
Measuring complexity
The idea that complexity is a metric related to a material's capabilities was first proposed by physics Nobel laureate Murray Gell-Mann . He defined complex structures as combinations of order and randomness, or disorder, while simple structures contain just one or the other.
Gell-Mann also described how complexity at small scales cascaded up through many larger scales. Bones, for instance, are made up of curved nanocrystals that merge into twisted plates. These further combine into larger aggregates that weave between tangled filaments of the protein collagen. The patterns within patterns make bone hard but not brittle, which is difficult to achieve.
To bring the complexity of living systems into synthetic materials, the researchers needed to introduce the right level of complexity for a given application. But there weren't any existing methods to calculate complexity.
"Gell-Mann drew a notional curve of functionality and complexity," Kotov said. "There were no numbers, and if you don't have numbers, you cannot engineer complexity in real materials. Now we can."
Charting a network
To put a number on complexity, the researchers turned to graph theory—a discipline already used to understand interactions in large systems, including ecosystems and social networks. In the graphs, each particle is represented by a node. When the particles are close enough to interact, a line is drawn between the nodes.
"By using graph theory metrics, we can measure how particles organize across multiple scales, from tiny local clusters to larger self-organizing and global networks," said Paul Bogdan , the Jack Munushian Early Career Chair associate professor in the University of Southern California's Viterbi School of Engineering and a co-corresponding author of the study.
In the bone example, researchers could draw the nanocrystals as interconnected nodes, with clusters of nodes representing plates. This graph could be nested inside another that describes how the plates merge into larger aggregates.
The researchers drew such graphs for several nanoparticle systems, in which tightly packed crystals formed from nanoparticles mixed into a liquid. Using a transmission electron microscope, the researchers imaged hundreds of nanoparticles forming crystals. The pictures served as guides to draw the graphs, and computer simulations allowed the researchers to scale up to larger systems with over 10,000 nanoparticles.
The series of graphs allowed the researchers to condense the network of nodes into metrics that quantified how interactions between neighboring nanoparticles spread out through the larger group, as well as how easily the structures could be reconfigured.
The metric for complexity closely correlated with how much and what kinds of light the gold nanoparticles could reflect. The gold particles could only weakly reflect green light when randomly distributed in liquid, but they began to reflect infrared light as the loosely packed crystal networks emerged. As the crystals formed more ordered structures and complexity decreased, they reflected less infrared light. The same metric of complexity was also correlated with how strongly nanoparticles made from tin-doped indium oxide—a material commonly used in touchscreens—absorbed and reflected light.
"The next steps for me and others in the center are to develop new ways to design functional materials with targeted levels of structural complexity, and to understand how those structures enable new combinations of properties," said Thomas Truskett , the Vennema Professor of Chemical Engineering and a co-corresponding author of the study.
Other co-corresponding authors include:
The research was also funded by the U.S. Army Research Office, DARPA, the National Institutes of Health, the Office of Naval Research and the Welch Foundation.
Researchers from the University of Texas at Austin also contributed to the study.
Kotov is also the Joseph B. and Florence V. Cejka Professor of Engineering, a professor of macromolecular science and engineering and materials science and engineering, and a member of the U-M Biointerfaces Institute. Truskett is also a member of the Biointerfaces Institute. Milliron is also the James and Judith Street Professor of Chemical Engineering.
Study: Decoding collective dynamics and complexity in nanoparticle assemblies using graph theory (DOI: 10.1126/science.aeb5134)
Science