Tag Archives: Sharon C. Glotzer

Entropic bonding for nanoparticle crystals

A January 19, 2022 University of Michigan news release (also on EurekAlert) is written in a Q&A (question and answer style) not usually seen on news releases, Note: Links have been removed),

Turns out entropy binds nanoparticles a lot like electrons bind chemical crystals

ANN ARBOR—Entropy, a physical property often explained as “disorder,” is revealed as a creator of order with a new bonding theory developed at the University of Michigan and published in the Proceedings of the National Academy of Sciences [PNAS]. 

Engineers dream of using nanoparticles to build designer materials, and the new theory can help guide efforts to make nanoparticles assemble into useful structures. The theory explains earlier results exploring the formation of crystal structures by space-restricted nanoparticles, enabling entropy to be quantified and harnessed in future efforts. 

And curiously, the set of equations that govern nanoparticle interactions due to entropy mirror those that describe chemical bonding. Sharon Glotzer, the Anthony C. Lembke Department Chair of Chemical Engineering, and Thi Vo, a postdoctoral researcher in chemical engineering, answered some questions about their new theory.

What is entropic bonding?

Glotzer: 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.

Why is this important?

Glotzer: Entropy’s contribution to creating order is often overlooked when designing nanoparticles for self-assembly, but that’s a mistake. 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.

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. 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.

Electrons are the key to those chemical equations though. How did you do this when no particles mediate the interactions between your nanoparticles?

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

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. 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. 

In crowded conditions, the entropy lost by increasing the order is outweighed by the entropy gained by shrinking the excluded volume. As a result, the configuration with the highest entropy will be the one where pseudoparticles occupy the least space.

The research is 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 also 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 U-M.

Here’s a link to and a citation for the paper,

A theory of entropic bonding by Thi Vo and Sharon C. Glotzer. PNAS January 25, 2022 119 (4) e2116414119 DOI: https://doi.org/10.1073/pnas.2116414119

This paper is behind a paywall.

The physics of melting in two-dimensional systems

You might want to skip over the reference to snow as it doesn’t have much relevance to this story about ‘melting’, from a Feb. 1, 2017 news item on Nanowerk (Note: A link has been removed),

Snow falls in winter and melts in spring, but what drives the phase change in between?
Although melting is a familiar phenomenon encountered in everyday life, playing a part in many industrial and commercial processes, much remains to be discovered about this transformation at a fundamental level.

In 2015, a team led by the University of Michigan’s Sharon Glotzer used high-performance computing at the Department of Energy’s (DOE’s) Oak Ridge National Laboratory [ORNL] to study melting in two-dimensional (2-D) systems, a problem that could yield insights into surface interactions in materials important to technologies like solar panels, as well as into the mechanism behind three-dimensional melting. The team explored how particle shape affects the physics of a solid-to-fluid melting transition in two dimensions.

Using the Cray XK7 Titan supercomputer at the Oak Ridge Leadership Computing Facility (OLCF), a DOE Office of Science User Facility, the team’s [latest?] work revealed that the shape and symmetry of particles can dramatically affect the melting process (“Shape and symmetry determine two-dimensional melting transitions of hard regular polygons”). This fundamental finding could help guide researchers in search of nanoparticles with desirable properties for energy applications.

There is a video  of the ‘melting’ process but I have to confess to finding it a bit enigmatic,

A Feb. 1, 2017 ORNL news release (also on EurekAlert), which originated the news item, provides more detail about the research,

o tackle the problem, Glotzer’s team needed a supercomputer capable of simulating systems of up to 1 million hard polygons, simple particles used as stand-ins for atoms, ranging from triangles to 14-sided shapes. Unlike traditional molecular dynamics simulations that attempt to mimic nature, hard polygon simulations give researchers a pared-down environment in which to evaluate shape-influenced physics.

“Within our simulated 2-D environment, we found that the melting transition follows one of three different scenarios depending on the shape of the systems’ polygons,” University of Michigan research scientist Joshua Anderson said. “Notably, we found that systems made up of hexagons perfectly follow a well-known theory for 2-D melting, something that hasn’t been described until now.”

Shifting Shape Scenarios

In 3-D systems such as a thinning icicle, melting takes the form of a first-order phase transition. This means that collections of molecules within these systems exist in either solid or liquid form with no in-between in the presence of latent heat, the energy that fuels a solid-to-fluid phase change . In 2-D systems, such as thin-film materials used in batteries and other technologies, melting can be more complex, sometimes exhibiting an intermediate phase known as the hexatic phase.

The hexatic phase, a state characterized as a halfway point between an ordered solid and a disordered liquid, was first theorized in the 1970s by researchers John Kosterlitz, David Thouless, Burt Halperin, David Nelson, and Peter Young. The phase is a principle feature of the KTHNY theory, a 2-D melting theory posited by the researchers (and named based on the first letters of their last names). In 2016 Kosterlitz and Thouless were awarded the Nobel Prize in Physics, along with physicist Duncan Haldane, for their contributions to 2-D materials research.

At the molecular level, solid, hexatic, and liquid systems are defined by the arrangement of their atoms. In a crystalline solid, two types of order are present: translational and orientational. Translational order describes the well-defined paths between atoms over distances, like blocks in a carefully constructed Jenga tower. Orientational order describes the relational and clustered order shared between atoms and groups of atoms over distances. Think of that same Jenga tower turned askew after several rounds of play. The general shape of the tower remains, but its order is now fragmented.

The hexatic phase has no translational order but possesses orientational order. (A liquid has neither translational nor orientational order but exhibits short-range order, meaning any atom will have some average number of neighbors nearby but with no predicable order.)

Deducing the presence of a hexatic phase requires a leadership-class computer that can calculate large hard-particle systems. Glotzer’s team gained access to the OLCF’s 27-petaflop Titan through the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program, running its GPU-accelerated HOOMD-blue code to maximize time on the machine.

On Titan, HOOMD-blue used 64 GPUs for each massively parallel Monte Carlo simulation of up to 1 million particles. Researchers explored 11 different shape systems, applying an external pressure to push the particles together. Each system was simulated at 21 different densities, with the lowest densities representing a fluid state and the highest densities a solid state.

The simulations demonstrated multiple melting scenarios hinging on the polygons’ shape. Systems with polygons of seven sides or more closely followed the melting behavior of hard disks, or circles, exhibiting a continuous phase transition from the solid to the hexatic phase and a first-order phase transition from the hexatic to the liquid phase. A continuous phase transition means a constantly changing area in response to a changing external pressure. A first-order phase transition is characterized by a discontinuity in which the volume jumps across the phase transition in response to the changing external pressure. The team found pentagons and fourfold pentilles, irregular pentagons with two different edge lengths, exhibit a first-order solid-to-liquid phase transition.

The most significant finding, however, emerged from hexagon systems, which perfectly followed the phase transition described by the KTHNY theory. In this scenario, the particles’ shift from solid to hexatic and hexatic to fluid in a perfect continuous phase transition pattern.

“It was actually sort of surprising that no one else has found that until now,” Anderson said, “because it seems natural that the hexagon, with its six sides, and the honeycomb-like hexagonal arrangement would be a perfect match for this theory” in which the hexatic phase generally contains sixfold orientational order.

Glotzer’s team, which recently received a 2017 INCITE allocation, is now applying its leadership-class computing prowess to tackle phase transitions in 3-D. The team is focusing on how fluid particles crystallize into complex colloids—mixtures in which particles are suspended throughout another substance. Common examples of colloids include milk, paper, fog, and stained glass.

“We’re planning on using Titan to study how complexity can arise from these simple interactions, and to do that we’re actually going to look at how the crystals grow and study the kinetics of how that happens,” said Anderson.

There is a paper on arXiv,

Shape and symmetry determine two-dimensional melting transitions of hard regular polygons by Joshua A. Anderson, James Antonaglia, Jaime A. Millan, Michael Engel, Sharon C. Glotzer
(Submitted on 2 Jun 2016 (v1), last revised 23 Dec 2016 (this version, v2))  arXiv:1606.00687 [cond-mat.soft] (or arXiv:1606.00687v2

This paper is open access and open to public peer review.

Digital alchemy from the University of Michigan (US)

Describing this work as ‘digital alchemy’ seems like a bit of a stretch as lead is not being turned into gold digitally or otherwise, from an Oct. 30, 2015 news item on Azonano,

Alchemy left the mainstream centuries ago, but one of its core concepts, transmuting the elements, is experiencing a revival in nanotechnology.

Researchers at the University of Michigan are charting a path toward materials with new properties by cleverly altering the nanoparticles used to build them.

An Oct. 27, 2015 University of Michigan news release, which originated the news item, provides more details from the scientists,

“Today, scientists achieve something akin to alchemy when we change materials’ building blocks by adding atoms or molecules to them, or even changing their shape. Such changes affect how the building blocks fit together, which in turn controls material’s behavior and properties,” said Sharon Glotzer, the John Werner Cahn Distinguished University Professor of Engineering and the Stuart W. Churchill Collegiate Professor of Chemical Engineering.

“We’ve developed a new theoretical tool that can be used by computers to carry out ‘alchemy’ on the fly, rapidly searching for the best building block for a given application. Digital alchemy will transform the way we design materials.”

Nanoparticles have the potential to redefine the “elements” available to materials scientists, going from the 90 stable elements to an infinite palette of tiny synthetic particles, just a few hundred times the size of the atoms themselves. The researchers propose a way to navigate the new frontier of nanoscale building blocks not by making and measuring each particle, but by exploring why particles build certain types of structures. Then, the important attributes can be identified and applied to design particles that will produce those structures.

“It seems like having an infinitude of new ‘elements’ to make materials from is a great thing. But if we don’t know the rules they use to organize themselves, and we can’t determine the rules by trial and error because we can’t make all the different elements, then we need to approach developing materials in a new way,” said Greg van Anders, a research fellow in the Glotzer group and first author of the study.

“Rapidly scanning through building blocks is not just a useful way of finding good candidates for new materials, but a necessary step to deal with the tremendous flexibility we now have in making particles.”

To demonstrate the concept, the team used a computer simulation that arranged a set of particles into a structure and then allowed the shape of the particles to change.

“We just stick the particles into a structure and say ‘find a shape that you’re happy with if you have to sit in that structure,'” van Anders said.

It had been assumed that the best shape for self-assembling into a particular structure is the one that packs into that structure most efficiently, leaving very little empty space. To test this, the team simulated the self-organization of four-sided pyramids (known as tetrahedra). They pack efficiently into a diamond structure—the structure produced by carbon atoms in a diamond—if their points are cut off. But if the diamond structure is the goal, how much of the points should be removed?

Not as much as needed for the closest packing, van Anders said. The shapes self-assembled best if the points were left a little longer, better preserving the tetrahedral character.

The team also explored what happens when ripples of attraction and repulsion run through a collection of spherical particles. This causes the particles to arrange themselves with respect to their neighbors. When these ripples are timed in a certain way, the particles form an icosahedral quasicrystal, an intricate structure that is symmetrical but doesn’t have a repeating structural unit.

“It’s one of the most complicated structures we know,” van Anders said. “If we could understand how to control the interactions so that this structure forms better, then chances are, we could also figure out how to make less complicated structures in systems that use a different set of interactions.”

This could help researchers build structures by exposing a fluid containing nanoparticles to forces such as light, electric fields and magnetic fields. These capabilities could lead to many interesting advances. One of Glotzer’s particular interests is in materials that can change color on command, creating the ultimate camouflage.

Here’s a link to and a citation for the paper,

Digital Alchemy for Materials Design: Colloids and Beyond by Greg van Anders, Daphne Klotsa, Andrew S. Karas, Paul M. Dodd, and Sharon C. Glotzer. ACS Nano, 2015, 9 (10), pp 9542–9553 DOI: 10.1021/acsnano.5b04181 Publication Date (Web): September 24, 2015

Copyright © 2015 American Chemical Society

This paper is behind a paywall.