Entropy can nudge particles to form organized structures

Entropy can nudge particles to form organized nano-structures.

ANN ARBOR, Mich.—Researchers trying to herd tiny particles into useful ordered formations have found an unlikely ally: entropy, a tendency generally described as "disorder."

Computer simulations by University of Michigan scientists and engineers show that the property can nudge particles to form organized structures. By analyzing the shapes of the particles beforehand, they can even predict what kinds of structures will form.

The findings, published in this week's edition of Science, help lay the ground rules for making designer materials with wild capabilities such as shape-shifting skins to camouflage a vehicle or optimize its aerodynamics.

Physicist and chemical engineering professor Sharon Glotzer proposes that such materials could be designed by working backward from the desired properties to generate a blueprint. That design can then be realized with nanoparticles—particles a thousand times smaller than the width of a human hair that can combine in ways that would be impossible through ordinary chemistry alone.

Shapes can arrange themselves into crystal structures through entropy alone, new research from the University of Michigan shows. Image credit: P. Damasceno, M. Engel, S. Glotzer

One of the major challenges is persuading the nanoparticles to create the intended structures, but recent studies by Glotzer's group and others showed that some simple particle shapes do so spontaneously as the particles are crowded together. The team wondered if other particle shapes could do the same. "We studied 145 different shapes, and that gave us more data than anyone has ever had on these types of potential crystal-formers," Glotzer SAID. "With so much information, we could begin to see just how many structures are possible from particle shape alone, and look for trends." Using computer code written by chemical engineering research investigator Michael Engel, applied physics graduate student Pablo Damasceno ran thousands of virtual experiments, exploring how each shape behaved under different levels of crowding. The program could handle any polyhedral shape, such as dice with any number of sides.

Left to their own devices, drifting particles find the arrangements with the highest entropy. That arrangement matches the idea that entropy is a disorder if the particles have enough space: they disperse, pointed in random directions. But crowded tightly, the particles began forming crystal structures like atoms do—even though they couldn't make bonds. These ordered crystals had to be the high-entropy arrangements, too.

Glotzer explains that this isn't really disorder creating order—entropy needs its image updated. Instead, she describes it as a measure of possibilities. If you could turn off gravity and empty a bag full of dice into a jar, the floating dice would point every which way. However, if you keep adding dice, eventually space becomes so limited that the dice have more options to align face-to-face. The same thing happens to the nanoparticles, which are so small that they feel entropy's influence more strongly than gravity's.

"It's all about options. In this case, ordered arrangements produce the most possibilities, the most options. It's counterintuitive, to be sure," Glotzer said.

The simulation results showed that nearly 70 percent of the shapes tested produced crystal-like structures under entropy alone. But the shocker was how complicated some of these structures were, with up to 52 particles involved in the pattern that repeated throughout the crystal.

"That's an extraordinarily complex crystal structure even for atoms to form, let alone particles that can't chemically bond," Glotzer said.

The particle shapes produced three crystal types: regular crystals like salt, liquid crystals as found in some flat-screen TVs and plastic crystals in which particles can spin in place. By analyzing the shape of the particle and how groups of them behave before they crystallize, Damasceno said that it is possible to predict which type of crystal the particles would make.

"The geometry of the particles themselves holds the secret for their assembly behavior," he said.

Why the other 30 percent never formed crystal structures, remaining as disordered glasses, is a mystery.

"These may still want to form crystals but got stuck. What's neat is that for any particle that gets stuck, we had other, awfully similar shapes forming crystals," Glotzer said.

In addition to finding out more about how to coax nanoparticles into structures, her team will also try to discover why some shapes resist order.

This research was supported by the U.S. departments of Defense and Energy, the Deutsche Forschungsgemeinschaft and the National Science Foundation. The paper is titled "Predictive Self-Assembly of Polyhedra into Complex Structures."

Glotzer is the Stuart W. Churchill Collegiate Professor of Chemical Engineering and a professor of chemical engineering, materials science and engineering, macromolecular science and engineering, and physics in College of Literature, Science, and the Arts.

Contact: Nicole Casal Moore ncmoore@umich.edu 734-647-7087 University of Michigan

The amount of structural damage that radiation causes in electronic materials at the atomic level may be at least ten times greater than previously thought

The amount of structural damage that radiation causes in electronic materials at the atomic level may be at least ten times greater than previously thought.

That is the surprising result of a new characterization method that uses a combination of lasers and acoustic waves to provide scientists with a capability tantamount to X-ray vision: It allows them to peer through solid materials to pinpoint the size and location of detects buried deep inside with unprecedented precision.

The research, which was conducted by post-doctoral fellow Andrew Steigerwald under the supervision of Physics Professor Norman Tolk, was published online on July 19 in the Journal of Applied Physics.

"The ability to accurately measure the defects in electronic materials becomes increasingly important as the size of microelectronic devices continues to shrink," Tolk explained. "When an individual transistor contains millions of atoms, it can absorb quite a bit of damage before it fails. But when a transistor contains a few thousand atoms, a single defect can cause it to stop working."

Silicon wafer with radiation damage. (Meroli Stefano / CERN)

Previous methods used to study damage in electronic materials have been limited to looking at defects and deformations in the atomic lattice. The new method is the first that is capable of detecting disruption in the positions of the electrons that are attached to the atoms. This is particularly important because it is the behavior of the electrons that determine a material's electrical and optical properties.

"An analogy is a thousand people floating in a swimming pool. The people represent the atoms and the water represents the electrons," said Steigerwald. "If another person – representing an energetic particle – jumps into the pool, the people in his vicinity change their positions slightly to make room for him. However, these shifts can be fairly subtle and difficult to measure. But the jumper will also cause quite a splash and cause the level of the water in the pool to rise. Much like the water in the pool, the electrons in a material are more sensitive to defects than the atoms."

To detect the electron dislocations, the physicists upgraded a 15-year-old method called coherent acoustic phonon spectroscopy (CAPS).

"CAPS is similar to the seismic techniques that energy companies use to search for underground oil deposits, only on a much smaller scale," said Steigerwald.

Oil explorers set off a series of small explosions on the surface and measure the sound waves that are reflected back to the surface. That allows them to identify and map the layers of different types of rock thousands of feet underground.

Similarly, CAPS generates a pressure wave that passes through a chunk of semiconductor by blasting its surface with an ultrafast pulse of laser light. As this happens, the researchers bounce a second laser off the pressure wave and measure the strength of the reflection. As the pressure wave encounters defects and deformities in the material, its reflectivity changes and this alters the strength of the reflected laser light. By measuring these variations, the physicists can detect individual defects and measure the effect that they have on the material's electrical and optical properties.

The physicists tested their technique on a layer of gallium arsenide semiconductor that they had irradiated with high-energy neon atoms. They found that the structural damage caused by an embedded neon atom spread over a volume containing 1,000 atoms – considerably more extensive than that shown by other techniques.

"This is significant because today people are creating nanodevices that contain thousands of atoms," said Steigerwald. One of these devices is a solar collector made from quantum dots, tiny semiconductor beads that each contains a few thousand atoms. "Our results may explain recent studies that have found that these quantum-dot solar collectors are less efficient than predicted," he said.

"The fact is that we really don't understand how any atomic-scale defect affects the performance on an optoelectronic device," said Tolk. "Techniques like the one that we have developed will give us the detailed information we need to figure this out and so help people make nanodevices that work properly."

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Research Associate Professor Anthony B. Hmelo, Assistant Professor Kalman Varga and Stevenson Professor of Physics Leonard Feldman also contributed to the research.

The research was supported by Department of Energy grant FG02-99ER45781, Army Research Office grant W911NF-07-R-0003-02 and National Science Foundation grant ECCS0925422. In addition, portions of the work were performed at the Vanderbilt Institute of Nanoscale Science and Engineering, using facilities renovated with the NSF grant ARI-RW DMR-096331.

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Contact: David Salisbury david.salisbury@vanderbilt.edu 615-343-6803 Vanderbilt University