![]() The entropic bonds are where that concentration is highest. As the nanoparticles become more ordered, the excluded volume around them becomes smaller, and the concentration of pseudoparticles in those regions increases. Vo: The pseudoparticles move around the system and fill in the spaces that are hard for another nanoparticle to fill-we call this the excluded volume around each nanoparticle. And that gave us the mathematical analogue of the electrons. Thi’s big insight was that we could count that space using fictitious point particles. Glotzer: Entropy is related to the free space in the system, but for years I didn’t know how to count that space. Image credit: Thi Vo, Glotzer Group, University of Michigan This new way of understanding how entropy creates attractive forces between nanoparticles could accelerate the development of nanomaterials with designed properties. Nanoparticles in the shape of a dodecahedron. How did you do this when no particles mediate the interactions between your nanoparticles? This is both fundamentally important for our understanding of matter and practically important for making new materials.Įlectrons are the key to those chemical equations though. Mathematically speaking, it puts chemical bonds and entropic bonds on the same footing. I’m amazed that it’s even possible to do that. While we’ve known that entropic interactions can be directional like bonds, 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. ![]() With our new theory, we can calculate the strength of those entropic bonds. 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. Glotzer: Entropy’s contribution to creating order is often overlooked when designing nanoparticles for self-assembly, but that’s a mistake. That directionality simulates a bond, and since it’s driven by entropy, we call it entropic bonding. Large entropic forces arise when the particles become close to one another.īy 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 structure gives the system the most options, and thus the highest entropy. 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. Oftentimes, entropy is associated with disorder, but it’s really about options. Instead, the attraction arises because of entropy. But unlike atoms, there aren’t electron interactions holding these nanoparticles together. ![]() It’s analogous to the chemical bonds formed by atoms. Glotzer: Entropic bonding is a way of explaining how nanoparticles interact to form crystal structures. The density of the pseudoparticles around nanoparticle shapes resembles the electron density in the electron orbitals of atoms.
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