Common candies yield physics discovery

by Steven Schultz
For most people, a regular lunch of M&M's and coffee would lead to no good. For Princeton physicist Paul Chaikin and collaborators, it spurred fundamental insights into an age-old problem in mathematics and physics

Chaikin and Princeton chemist Salvatore Torquato used the candies to investigate the physical and mathematical principles that come into play when particles are poured randomly into a vessel. While seemingly simple, the question of how particles pack together has been a persistent scientific problem for hundreds of years and has implications for fields such as the design of high-density ceramic materials for use in aerospace or other applications.

The researchers discovered that oblate spheroids, the shape of M&M's chocolate candies, pack surprisingly more densely than regular spheres when poured randomly and shaken. Extending the work with further experiments and sophisticated computer simulations, they found that a related shape, the ellipsoid, packs at random even more densely than the tightest possible, perfectly ordered arrangement of spheres. Previously, scientists did not know that randomly assembled particles could pack so densely.

"It is a startling and wonderful result," said Sidney Nagel, a physicist at the University of Chicago. "One doesn't normally stop to think about this. If you did, you might have guessed what would happen, but you'd have guessed wrongly."

The researchers published their results in the Feb. 13 issue of Science magazine.

A surprising element of the results is that the small change from sphere to spheroid -- one is just a squashed or stretched version of the other -- produced a major change in the random packing density. When poured randomly, spheres occupy about 64 percent of the space in the container. M&M's, by contrast, achieve a density of about 68 percent. In non-random packings -- those that are laid out in regular repeating patterns -- changing from sphere to spheroid has no significant effect on the packing density.

"We just stretched a sphere and suddenly things changed dramatically," said Torquato. "I think that is remarkable."

The full story is available in a news release.