A Density Limit for Randomly Packed Spheres

June 23, 2008

The problem of finding the most efficient way to pack identical spheres has a long mathematical history, going back to arrays studied by Johannes Kepler and random geometries explored by crystallographer John D. Bernal. Now, physicists have come up with a physical interpretation of why the most compact way to pack spheres (random close packing) results in a maximum density of about 64 percent.

Physicist Hernán Makse and students Chaoming Song and Ping Wang of the City College of New York base their model on the notion of a "jammed state," in which random close packing corresponds to the ground state of an ensemble of jammed matter. In this model, random packings of hard spheres in three dimensions cannot exceed a density limit of about 63.4 percent.

"Theoretically, the jammed state would be achieved by lowering the temperature of the spheres to absolute zero," Makse says. "In real life, however, it is attained by shaking the materials."

The researchers report their results in the article "A Phase Diagram for Jammed Matter," published in the May 29 Nature.

The issue of randomly packing hard spheres into a container has been a longstanding challenge for manufacturers that process granular materials. The new findings may aid in the formulation of a theory of powders that could enable manufacturers to develop new products more efficiently.

Source: City College of New York, June 2, 2008.