New 3-D printed ‘metamaterial’ defying the laws of physics

Anyone who’s ever had grammar school science knows that heat makes things expand. Rubber, glass, granite or steel, heat it up and it grows in volume. Right?

There are in nature a few very rare cases of materials that buck this thermodynamic rule and actually shrink when heated. Not many. Cold water, when heated from 0 to 4 degrees Celsius, will actually contract before expanding.

Thanks to decades-old theories and 3-D printer technology, a team of engineers at MIT and USC is adding to this odd-ball group of heat-shrinking materials.

Led by Nicholas X. Fang, an associate professor of mechanical engineering at MIT who got his master’s in physics at Nanjing University, the team has manufactured tiny, starshaped structures out of interconnected beams and trusses, each about the size of a sugar cube, that quickly shrink when heated to about 540 degrees Fahrenheit.

Each truss is made from materials that expand with heat, but Fang and his colleagues realized that these trusses, if arranged in particular architectural configuration, could actually pull the overall structure in on itself, causing it to shrink like a Hoberman sphere — those collapsible toy balls made of geodesic domelike lattices and joints.

Dubbing the structure a “metamaterial” — a composite that exhibits strange, counterintuitive properties not normally found in nature — the scientists say that just by not expanding when heated it could be especially useful for computer chips, which can warp and deform when heated over long periods of time.

“Printed circuit boards can heat up when there’s a CPU running, and this sudden heating could affect their performance,” Fang says. “So you really have to take great care in accounting for this thermal stress or shock.”

The results of their experiments, funded in part by the Pentagon, were published in the recent edition of the journal Physical Review Letters.

The theory of negative thermal expansion, or NTE, goes back to the 1990s when scientists theorized about building three-dimensional, lattice-like structures from two types of materials, each with different expansion rates. When heated, one material should expand faster, pulling the other inward and shrinking the whole as a result.

“These theoretical papers were talking about how these types of structures could really break the conventional limit of thermal expansion,” Fang says. “But at the time, they were limited by how things were made. That’s where we saw this as a very good opportunity for microfabrication to demonstrate this concept.”

Fang’s lab pioneered a 3-D printing technique called microstereolithography, which uses light from a projector to print very small structures in liquid resin, layer by layer.

“We can now use the microstereolithography system to create a thermomechanical metamaterial that may enable applications not possible before,” said team member Christopher Spadaccini, who is director of the Lawrence Livermore National Laboratory’s center for engineered materials and manufacturing. “It has thermomechanical properties not achievable in conventional bulk materials.”

“We can take the same idea as an inkjet printer, and print and solidify different ingredients, all on the same template,” Fang says.

Fang and his colleagues printed small, three-dimensional, star-shaped structures made from interconnecting beams. They fabricated each beam from one of two ingredients: a stiff, slow-expanding copper material for the outside, and a more elastic, faster-expanding polymer for the inside.

“If we have proper placement of these beams and lattices,” Fang said, “once we increase the temperature, they interact with each other and pull inward, so the overall structure’s volume decreases.”

The researchers put their composite structures to the test by placing them within a small glass chamber and slowly increasing the chamber’s temperature, from room temperature to about 540 degrees Fahrenheit. At first it maintained its shape, then gradually shrunk.

Not by much — about 0.6 percent to be precise, but that is still significant. “The very fact that it shrinks is impressive,” Fang said, for most applications, something that doesn’t expand under heat would be enough.

“There is room to experiment with other materials,” Fang said. “Now we can have more fun in the lab exploring these different structures.”