Candy inspires scientific discovery

There is a right and a wrong way to pack things. This is a phenomenon that can be observed every time you pack the trunk of your car, chemistry professor Salvatore Torquato said.

And, believe it or not, this concept — called packing — has perplexed scientists for hundreds of years.

"People have been trying to determine the most efficient way to pack things in order to obtain the highest density," Torquato explained. In other words, they are trying to determine how to fit the most amount of stuff into a given space.

Over the past four centuries, many packing theories have been formulated. However, earlier this month, physics professor Paul Chaikin, Torquato and a few University students published a paper that challenges early theories and refutes ideas previously unquestioned. And they did it using M&Ms.

In the past, packing problems have been addressed using the simplest shape possible: spheres. "Think about cannonballs or oranges stacked in the supermarket," Torquato said. "Those are the structures we were studying."

Until recently, scientists assumed spheres could form the most densely randomly packed structures.

However, Torquato and Chaikin's new study has proven that spheres are not the ideal shape. Rather, oblate spheroids, the shape of M&Ms, pack more densely when randomly poured into a container and shaken.

The lesson learned here is that given the choice of a cup of gumballs, or the same sized cup of M&Ms, there will be more candy and less airspace in the container of M&Ms.

Torquato and Chaikin have both been interested in packing for a number of years, but it wasn't until four years ago that the pair joined forces.

Chaikin said he had previously used materials such as peas and couscous to observe the packing phenomenon, "but I figured, let's try something else," he said.

It seemed natural for Chaikin to choose M&Ms, which have made up his entire lunch for the past 20 years.

Additionally, M&Ms are cheap, nearly perfect oblate spheroids and are very uniformly made. "Look at them — they are all identical," Chaikin said, pouring a bag of M&Ms on the table.

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In the beginning of the research project, Chaikin had a student measure the density of a container of M&Ms. He assumed that because M&Ms are merely elongated — or squashed — spheres, the density would be similar to that of a container filled with spheres. Naturally, he was surprised when the results didn't reflect his hypothesis.

"I sat down to show the student why his data was wrong — and as soon as I saw the picture, I knew he was right, and I knew why," Chaikin said.

But Chaikin ran the experiment again to be sure, and he obtained the same results as his student had.

Next, in order to be sure that the M&Ms were not ordering themselves, and were in fact randomly oriented, the scientists took a field trip. "We filled up a container of M&Ms and took it over to the Princeton hospital and used the MRI to obtain an image of the M&Ms," Torquato said. Sure enough, the picture they saw showed hundreds of randomly oriented M&Ms very densely packed.

Randomly packed spheres generally produce a density of 64 percent, meaning 36 percent of the container is filled with air spaces. However, randomly packed M&Ms produced a 68 percent density.

The contact number, or the number of M&Ms each M&M touched, is closely correlated with the density, Chaikin said. He continued to explain that M&Ms with more contacts form denser packing. And on average, each M&M was touching 10 other M&Ms, though each gumball would only touch six other gumballs.

After discovering such surprisingly high densities in M&M's the scientists wondered if they could find an even more efficient packing shape. Aleksander Donev GS created a computer program that simulated different shapes and their packing densities.

Before long, Donev determined that an ellipsoid, which looks like a vertically stretched M&M, would have an even higher density than the M&Ms.

"Improvement in technology and knowledge of computers, as well as all the research that was done before, has led to this finding," Donev said.

Chaikin's lab began to produce Donev's ellipsoid models and is currently testing Donev's simulation in the lab. The only downside is that this research does not taste as good as M&Ms.

"A lot of the information was there, but nobody pulled it all together," Torquato said. "In the past, scientists believed spheres were a great description of systems found in nature. It has only been recently that we have discovered that the sphere is not a good model for everything, and it has changed the way that we have been looking at reality."

Chaikin and Torquato's research is applicable to practices such as making ceramics, which involves packing small grains into a solid form, or in understanding glass.

They have even stumbled across some biological applications of their research, in the shape of the eggs that fish carry in their mouths before they hatch. "If you want to fit the most eggs possible, they need to be the right shape," Torquato said.

"We seem to be the M&M experts now," Chaikin joked. "I bet we know more about M&Ms than the Mars Company does!"

For example, a five-liter flask can fit about 28,000 mini M&Ms. And, though it has not yet been documented, it has been scientifically proven that for every M&M placed in a beaker, five end up in the mouth, Chaikin quipped.

Although the Mars Company, which produces M&Ms, did not fund the research, they did send 125 pounds of pastel colored almond M&Ms when they heard about the project. The company has not contacted Torquato or Chaikin since the publication was released.

A number of years ago, as a prank, Chaikin's students painted the M&M logo on a 55-gallon barrel and snuck it into his office. Now, Chaikin spends about $300 each year to fill the barrel with peanut M&Ms for his colleagues and students. "It's my donation to the department," he joked. But why peanut M&Ms? "If it were plain M&Ms, I would eat them all!" he said.

Chaikin still continues to enjoy his daily lunch of M&Ms and coffee, a combination of which he seems to never tire. However, he is slightly disappointed with the new black and white candies. "Ever since they gave up color they have been sloppy," he said pouring out a container of M&Ms on the table.

"Look at that tiny one!" Donev said pointing out an imperfect candy.

"Yes, it really has all gone down hill," Torquato chimed in.