Entropy is generally regarded as a force of chaos or disorder in physics. but it's entropy that researchers at the University of Michigan are using to harness and assemble nanoparticle crystals for future use in creating designer materials that could be used in high-tech applications from healthcare to materials science.

The Proceedings of the National Academy of Sciences has just published a report from these University of Michigan researchers on their work. Here's how this works, in theory. The published report explains that earlier work exploring the formation of crystal structures by space-restricted nanoparticles found that entropy could be quantified and harnessed in future efforts at particle assembly. The equations that govern nanoparticle interaction as it relates to entropy mirror those equations that describe chemical bonding.

Sharon Glotzer, the Anthony C. Lembke Department Chair of Chemical Engineering, and Thi Vo, a postdoctoral researcher in chemical engineering, are the authors of the new theory that unites why these equations look so similar. It turns out that entropy can bind nanoparticles together in a similar way to how electrons bind chemical crystals.

How Entropic Bonding Works

Glotzer says: "Entropic bonding is a way of explaining how nanoparticles interact to form crystal structures. It's analogous to the chemical bonds formed by atoms. But unlike atoms, there aren't electron interactions holding these nanoparticles together. Instead, the attraction arises because of entropy. 

"Oftentimes, entropy is associated with disorder, but it's really about options. When nanoparticles are crowded together and options are limited, it turns out that the most likely arrangement of nanoparticles can be a particular crystal structure. That structure gives the system the most options, and thus the highest entropy. Large entropic forces arise when the particles become close to one another. 

"By doing the most extensive studies of particle shapes and the crystals they form, my group found that as you change the shape, you change the directionality of those entropic forces that guide the formation of these crystal structures. That directionality simulates a bond, and since it's driven by entropy, we call it entropic bonding."

How Entropic Bonding Can Be Used to Create High-Tech Materials

Glotzer explains that "if entropy is helping your system organize itself, you may not need to engineer explicit attraction between particles—for example, using DNA or other sticky molecules—with as strong an interaction as you thought. With our new theory, we can calculate the strength of those entropic bonds." This could lead to a new way to assemble materials for a host of applications, from healthcare to high-tech materials.

"While we've known that entropic interactions can be directional like bonds," Glotzer adds, "our breakthrough is that we can describe those bonds with a theory that line-for-line matches the theory that you would write down for electron interactions in actual chemical bonds. That's profound. I'm amazed that it's even possible to do that. Mathematically speaking, it puts chemical bonds and entropic bonds on the same footing. This is both fundamentally important for our understanding of matter and practically important for making new materials."

How is it possible to create entropic bonds when no particles mediate the interactions between nanoparticles, which would be similar to what you see when electrons are the driving bonding force?

Glotzer explains: "Entropy is related to the free space in the system, but for years I didn't know how to count that space. [The] big insight was that we could count that space using fictitious point particles. And that gave us the mathematical analogue of the electrons."

Glotzer's research partner Vo says that pseudoparticles move around the system and fill spaced that are hard for another nanoparticle to fill. "We call this the excluded volume around each nanoparticle. As the nanoparticles become more ordered, the excluded volume around them becomes smaller, and the concentration of pseudoparticles in those regions increases. The entropic bonds are where that concentration is highest."

Could this be used to create new ways of assembling materials? If you would like to learn more, the study abstract can be found at A theory of entropic bonding (DOI: 10.1073/pnas.2116414119). The research was funded by the Simons Foundation, Office of Naval Research, and the Office of the Undersecretary of Defense for Research and Engineering. It relied on the computing resources of the National Science Foundation's Extreme Science and Engineering Discovery Environment. Glotzer is the John Werner Cahn Distinguished University Professor of Engineering, the Stuart W. Churchill Collegiate Professor of Chemical Engineering, and a professor of material science and engineering, macromolecular science and engineering, and physics at the University of Michigan.