Like cheerleaders forming a human pyramid, many particles might be able to assemble themselves into organized superstructures, a new study has found.

An object's shape can greatly affect how it responds to crowding, and some tiny material building blocks known as nanoparticles may be able to self-assemble into intricate patterns when forced to share space with neighbors. In the new study, researchers at the University of Michigan set out to perform a broad survey of how particle shape drives the formation of larger crystallike structures. The study, which appeared in the July 27 issue of Science, could help researchers predict the behavior of designer nanoparticles and build custom materials from relatively simple self-assembling building blocks. The long-term goal is to design new materials. "We want new stuff, better stuff," says study co-author Sharon Glotzer, a Michigan professor of chemical engineering, materials science and physics.

Rather than actually manufacturing countless tiny particles and monitoring their self-assembly from various starting conditions, the group used computer simulations to explore the properties of hypothetical particles of 145 different idealized polyhedral shapes. (A polyhedron is a solid formed by planar faces.)

When packed closely with identically shaped particles, the majority of those polyhedrons assembled into a crystal lattice or a crystallike arrangement, the simulations showed. What is more, a shape's propensity to self-assemble turned out to be strongly correlated with two simple quantities describing a particle's shape and its starting arrangement.

Glotzer and her colleagues had previously found that some shapes naturally self-assemble. But the new simulations showed that such behavior is the rule, not the exception. Some of the shapes assembled into regular crystals—lattices in which each particle has a fixed position and orientation—and some formed plastic crystals or liquid crystals. In a plastic crystal, each particle has a fixed position within the lattice but can rotate; a liquid crystal, on the other hand, contains particles with correlated orientations but fungible positions. Altogether, 101 of the 145 polyhedral types self-assembled into one of those ordered structures. "I would not have bet that the majority of those shapes would have organized into a crystal or a crystallike arrangement," Glotzer says. "How easy it would be for those particles to crystallize was a surprise."

Moreover, some of the shapes displayed an impressively coordinated assembly process. A pyramid shape with a square base, for instance, joined into "supercubes" of six pyramids apiece, which then formed a larger cubic lattice. "We found that many particles form incredibly complex structures," Glotzer says. "The system has to figure out as a whole that that is the best way to arrange things."

The researchers also found that the collective behavior of a certain particle type was far from random. In fact, two numbers all but foretell the outcome of the crystal-forming simulations. A number called the isoperimetric quotient, which roughly captures a particle's shape based solely on its volume and surface area, and a measure called coordination number, which describes how many close neighbors a particle has, predicted 94 percent of the time which of the crystalline forms a polyhedron would take. In broad terms, flat, squat polyhedrons—such as a horizontal slice of a hexagonal column—tended to form liquid crystals. Many-faceted particles, almost spherical in shape, favored the development of plastic crystals. And the domain of regular crystals contains many familiar shapes—cubes, triangular prisms, slant-sided rhombohedrons. The relation between shape and self-assembly could be used to tailor nanoparticles to exhibit a specific collective behavior.

Even the 44 polyhedrons that resisted self-assembly could provide fodder for future designer materials. "Some of them we ran and ran [the simulation] and we just couldn't get them to form anything," Glotzer says. "But for every one of these particles that won't crystallize, there's another particle that looks almost the same that crystallizes every time." If researchers could figure out precisely what makes one particle assemble into a crystal whereas a near-twin languishes in a disordered state, they might be able to design shape-shifter particles whose collective properties would transform with a slight structural tweak to the individual building blocks.

"This is sort of a holy grail of materials research, to just look at a building block and be able to say, 'Oh yes, I know all of the kinds of crystal structure that would be stable with this,'" Glotzer says. "This study allows us to take a first step in that direction."