Almost all solid materials, from rubber and glass to granite and steel,
inevitably expand when heated. Only in very rare instances do certain
materials buck this thermodynamic trend and shrink with heat. For
instance, cold water will contract when heated between 0 and 4 degrees
Celsius, before expanding.
Engineers from MIT, the University of Southern California, and elsewhere
are now adding to this curious class of heat-shrinking materials. The
team, led by Nicholas X. Fang, an associate professor of mechanical
engineering at MIT, has manufactured tiny, star-shaped structures out of
interconnected beams, or trusses. The structures, each about the size of
a sugar cube, quickly shrink when heated to about 540 degrees Fahrenheit
Each structure’s trusses are made from typical materials that expand
with heat. Fang and his colleagues realized that these trusses, when
arranged in certain architectures, can pull the structure inward,
causing it to shrink like a Hoberman sphere — a collapsible toy ball
made from interconnecting lattices and joints.
The researchers consider the structures to be “metamaterials” —
composite materials whose configurations exhibit strange, often
counterintuitive properties that are not normally found in nature.
In some cases, these structures’ resistance to expanding when heated —
rather than their shrinking response per se — may be especially useful.
Such materials could find applications in computer chips, for example,
which can warp and deform when heated for 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
The researchers have published their results in the journal Physical
Review Letters. Fang’s co-authors include former MIT postdoc Qi Ge,
along with lead author Qiming Wang of the University of Southern
California, Jonathan Hopkins of the University of California at Los
Angeles, and Julie Jackson and Christopher Spadaccini of Lawrence
Livermore National Laboratory (LLNL).
In the mid-1990s, scientists proposed theoretical structures whose
arrangement should exhibit a property called “negative thermal
expansion,” or NTE. The key to the arrangement was to build
three-dimensional, lattice-like structures from two types of materials,
each with a different NTE coefficient, or rate of expansion upon
heating. When the whole structure is heated, one material should expand
faster and pull the other material inward, shrinking the entire
structure 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 has pioneered a 3-D printing technique called
microstereolithography, in which the researchers use light from a
projector to print very small structures in liquid resin, layer by
“We can now use the microstereolithography system to create a
thermomechanical metamaterial that may enable applications not possible
before,” said Spadaccini, who is the director of LLNL’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.
Taking inspiration from the general framework proposed previously by
theorists, 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-to-expand
copper-containing material, and a more elastic, fast-expanding polymer
substance. The internal beams were made from the elastic material, while
the outer trusses were composed of stiff copper.
“If we have proper placement of these beams and lattices, then even if
every individual component expands, because of the way they pull each
other, the overall lattice could actually shrink,” Fang says.
“The problem we’re treating is a thermal mismatch problem,” Wang says.
“These materials have different thermal expansion coefficients, so once
we increase the temperature, they interact with each other and pull
inward, so the overall structure’s volume decreases.”
“Room to experiment”
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. They
observed that as the structure was heated, it first maintained its
initial shape, then gradually bent inward, shrinking in size.
“It shrinks by about one part in a thousand, or about 0.6 percent,” Fang
says. While that may not seem significant, Fang adds that “the very fact
that it shrinks is impressive.” For most applications, Fang says
designers may simply prefer structures that do not expand when heated.
“Normal materials have positive thermal expansion, and this leads to
challenging problems in engineering when a device needs to maintain its
shape and work in a wide range of temperature,” says Xiaoming Mao, an
assistant professor of physics at the University of Michigan, who was
not involved in the study. “NTE materials are a great solution because
they can be combined with normal materials and cancel the stress coming
from thermal expansion. This leads to wide applications in space
technology, bridges, piping systems, et cetera.”
addition to their experiments, the researchers developed a computational
model to characterize the relationships between the interconnecting
beams, the spaces between the beams, and the direction and degree to
which they expand with heat. The researchers can control how much a
structure will shrink by tuning two main “knobs” in the model: the
dimensions of the individual beams, and their relative stiffness, which
is directly related to a material’s rate of heat expansion.
“We now have a tuning method for digitally placing individual components
of different stiffness and thermal expansion within a structure, and we
can force a particular beam or section to deflect or extend in a desired
fashion,” Fang says. “There is room to experiment with other materials,
such as carbon nanotubes, which are stronger and lighter. Now we can
have more fun in the lab exploring these different structures.”
This research was supported, in part, by the Defense Advanced Research