Printed shape-shifting materials mimic biological structures

For applications from electronics to tissue engineering, researchers have been striving to devise materials that distort into complex shapes in response to heat, light, or other stimuli. Sometimes the goal is to create a device that undergoes a reversible mechanical change; other times it’s merely to manufacture three-dimensional shapes that are difficult or impossible to make in any other way.

One promising approach involves embedding a liquid crystal in an elastic matrix. By driving the transition from the nematic phase—in which the liquid-crystal molecules are aligned—to the disordered phase, one can force the material to change shape. The shape change is governed by the director field—the initially spatially inhomogeneous orientation of the molecules—which can be difficult to precisely control. So far, researchers have successfully prepared the director fields to make arrays of cones and other simple geometries, and they’re working to expand the range of shapes they can create. (See the article by Carl Modes and Mark Warner, Physics Today, January 2016, page 32 .)

Now a team at Harvard University has come up with a new and potentially more flexible method using a 3D printer. ¹ Doctoral student Sydney Gladman and her adviser Jennifer Lewis formulated a hydrogel ink that swells anisotropically when immersed in water; when the ink is laid out in a spiral, crisscross, or other flat pattern, the hydrated structure buckles out of the plane. Meanwhile, their colleagues Elisabetta Matsumoto and L. Mahadevan developed a mathematical model to connect the printed patterns to the 3D structures they produce. Together, the researchers demonstrated the power of their technique by creating biologically inspired shapes such as the calla lily flower shown in figure 1.

Copying biology

The new work falls under the umbrella of the emerging field of 4D printing: creating 3D-printed structures that evolve in time. The term was coined in a 2013 TED talk by Skylar Tibbits, an architecture lecturer at MIT, who envisioned it as a method for creating self-assembling components for structural prototypes.

Around the same time, Lewis and Ralph Nuzzo (University of Illinois at Urbana-Champaign) were talking about a similar idea. But in contrast to Tibbits’s approach—which relies on shape-induced self-assembly of parts made from commercially available 3D-printer inks—Lewis and Nuzzo sought to create a palette of new materials that could mimic the shape-changing properties of plants: the blooming of flowers, opening and closing of pine cones, and curling of certain leaves and tendrils, all because of the arrangement of stiff cellulose fibrils in their cell walls.

The fibrils function much like the iron bars in reinforced concrete. They strongly resist stretching, and they lend their stiffness to the cell walls in which they’re embedded—but only along their length. In other directions, the walls remain pliable and less stiff. The orientation of the fibrils thus restricts the range of distortions the plant can undergo.

Reproducing that directional effect in a 3D-printer ink was a challenge. The ink needs to have not only the right material properties—anisotropic elasticity and swelling behavior—but also the right rheological properties to be compatible with the printer. Building on prior work from the Lewis lab, Gladman came up with a mixture of water, the hydrogel monomer N,N-dimethylacrylamide, cellulose fibrils, clay particles, and other ingredients. The clay gave the mix the right viscosity for printing, and curing the printed structure with UV light polymerized the hydrogel, transforming a viscous fluid into a soft elastic solid.

The alignment of the cellulose fibrils happens automatically. As shown in figure 2a, when the ink passes through the printer, shear forces in the nozzle orient the fibrils so they’re parallel to the extruded filament. As a result, the filament expands easily in the radial direction but not the longitudinal direction. When the hydrogel is immersed in water and swells, as shown in figure 2b, each filament expands 40% in diameter but only 10% in length.

Curvature by design

To create complex shapes by exploiting that anisotropy, the researchers arrange the filaments so that the swelling strains compete and can’t be accommodated in a planar structure. The material must therefore curl or buckle out of the plane. For example, in the crisscross pattern in figure 2c, each of the two layers of parallel filaments needs to swell in width but not in length. That requirement can’t be satisfied at the layers’ points of contact if each layer remains planar; as a result, the structure curves into a saddle shape, known mathematically as a region of negative Gaussian curvature. Likewise, a spiral pattern must swell in radius but not in circumference, so it forms a blunted conical cap—a region of positive Gaussian curvature.

Because the printer makes it easy to arrange the hydrogel filaments into nearly any conceivable planar pattern, it should be possible to create almost any 3D shape by combining elements of positive and negative curvature. But bioinspired forms like the calla lily target surface in figure 3a aren’t simple combinations of saddles and cones, but rather surfaces of continuously varying curvature.

That’s where Matsumoto and Mahadevan’s model comes in. They considered a two-layer printed structure in which each layer’s orientation and thickness can vary as a function of position. (The 3D printer that Gladman and Lewis used to make the experimental structures doesn’t allow the filament thickness to be changed, but adjusting the interfilament spacing tunes the layer’s effective thickness.) Then, using a generalization of the mechanical theory of bimetallic strips, they calculated the forces and torques on the surface as it swells, which determine its 3D equilibrium shape.

In mathematicians’ parlance, that’s known as the forward problem: Starting with the cause, one calculates the effect. More important for structure design is the so-called inverse problem: determining the cause, or printed pattern, that will yield a particular effect, or 3D shape. Inverse problems in mathematics are notoriously difficult, and this one is no exception: Among other reasons, there may be several completely different print paths—or none—that produce a given structure. Building on work by Eran Sharon and colleagues, ² Matsumoto and Mahadevan solved the inverse problem for the calla lily by capitalizing on the structure’s symmetry. They derived the print path in figure 3b, which was used to produce the structure in figure 1. “We’re currently looking at the general case,” says Mahadevan, “using mathematical and computational tools to reduce the number of possibilities in a systematic way.”

Material modularity

In most of the Harvard group’s experiments, the shape changes were effectively irreversible: Once the hydrogel absorbs water and swells, the only way to get the structure to revert to its initial planar form is to let it slowly dry out. But as Lewis points out, “The ink design is highly modular”: The N,N-dimethylacrylamide can be replaced by nearly any other hydrogel, some of which have very different behaviors. For example, Gladman and Lewis used an ink made from N-isopropylacrylamide, which swells in hot water and shrinks in cold water, to make floral shapes that “bloom” and reclose. Still other hydrogels swell in response to light, changes in pH, or other factors.

The cellulose fibrils, too, can be swapped out for other materials. Lewis envisions using carbon nanotubes, metal nanorods, or hydroxyapatite platelets. “The size and shape don’t really matter,” she says. “As long as they’re sufficiently anisotropic, they’ll undergo shear-induced alignment,” with rod-shaped objects oriented parallel to the extruded filament and plate-shaped ones parallel to the printed plane. Different materials can lend properties other than mechanical stiffness to the final structure: Nanotubes and nanorods conduct electricity, for example, and hydroxyapatite—the main mineral in bones and teeth—could form the basis for an artificial tissue.