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University chemists refute accepted particle packing theory

University scientists in the chemistry department have made a discovery that refutes a 40-year-old belief about how particles behave in a vessel.

Their discovery may offer new insights into the nature of non-crystalline materials and granular materials, according to chemistry professor Sal Torquato, who is a member of the team that made the breakthrough. "Knowing how particles pack in space is very important in understanding material microstructure," he said.


Torquato and two colleagues — chemical engineering professor Pablo Debenedetti and graduate student Tom Truskett — published their findings in the March 6 issue of Physical Review Letters.

An earlier theory, known as "random close packing," maintained that spheres pack in a way that always fills 64 percent of the space in the vessel.

"That idea is plain wrong," Torquato said. Depending on the protocol used, values can range from 58 percent to 74 percent of the vessel, according to Torquato.

The problem with random close packing, he said, was that "it wasn't well-defined mathematically. The concept itself was flawed."

The team has now advanced a theory it calls "maximally random jammed state," which makes the concept of random packing far more precise mathematically, Torquato said. In the maximally random jammed state, particles are so tightly packed that none of them can move, he explained.

"To me the most interesting part of the work is that it has forced us to ask the question how to quantify disorder," Debenedetti said. "We proposed — and seem to have found — a quantitative description on how disordered a system is. Basically we were able to come up with measures of disorder that vary between zero and one. It is a very powerful technique for looking at a system."


"Most materials and things we deal with are disorder. That we can explain how disordered they are and in what ways is a very intriguing notion," Debenedetti said.

Scientists have known that the maximum amount of space particles can fill, when perfectly ordered, is 74 percent of a vessel. At this value, particles form a face-centered cubic, which resembles a stack of oranges in a grocery store, Torquato explained.

Torquato's team, however, wanted to find the percentage of space a vessel filled when it was not perfectly ordered. They used computer simulation to prove that particles could be compressed to fill significantly more of a vessel than the 64 percent value originally believed to be universal.

"The old concept really was accepted. Some people suspected there was something wrong with it, but there were many who were completely comfortable with it," Torquato said.

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George McLendon, chair of the chemistry department, said his colleagues' findings are exciting and significant. "It's unusual to find that something that was thought to be well understood actually is not. It has some fundamental implications but potentially some very practical ones. [Torquato and Debenedetti] both are people who are very good teachers and very deep scholars."