Like cheerleaders forming a human pyramid, particles, too, can assemble themselves into intricate patterns. In a new study, researchers at the University of Michigan found that an object's shape greatly affects how it responds to crowding and that, with a properly designed shape, tiny material building blocks known as nanoparticles could self-assemble into predictable larger structures simply by being forced to share space with neighbors. The study, which appeared in the July 27 Science, could help researchers design new materials.

The investigators ran computer simulations of 145 different particles having idealized polyhedral shapes. (A polyhedron is a solid formed by planar faces.) When packed closely with identically shaped particles, most of those polyhedrons assembled into a crystal lattice or a crystal-like arrangement. Study co-author Sharon Glotzer, a Michigan professor of chemical engineering, materials science and physics, and her colleagues had previously found that some particle shapes naturally self-assemble. Yet the new simulations showed that such behavior is the rule, not the exception.

Moreover, some of the shapes displayed an impressively coordinated assembly process. A pyramid shape with a square base joined into “supercubes” of six pyramids apiece, which then formed a larger cubic lattice. The researchers also found that the collective behavior of a given particle type is far from random. In fact, two numbers all but foretell the outcome. A number called the isoperimetric quotient, which roughly captures a particle's shape, and a measure called the coordination number, which describes how many neighbors a particle has, predicted 94 percent of the time which crystalline form a polyhedron would take. The relation between shape and self-assembly could be used to tailor nanoparticles to exhibit a specific collective behavior.

“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 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.”