Graphene-Based Bimorphs for Micron-Sized, Autonomous Origami Machines

Graphene-based bimorphs for micron-sized, autonomous origami machines

Marc Z. Miskina,b, Kyle J. Dorseyc, Baris Bircanc, Yimo Hanc, David A. Mullera,c, Paul L. McEuena,b,1 and Itai Cohena,b

aKavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY 14853; bLaboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853; and cSchool of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853

Contributed by Paul L. McEuen, November 12, 2017 (sent for review July 20, 2017; reviewed by John C. Crocker and A. John Hart) Origami-inspired fabrication presents an attractive platform for operate in temperature ranges upward of 140 K and chemical miniaturizing machines: thinner layers of folding material lead environments spanning at least 13 orders of magnitude in acid to smaller devices, provided that key functional aspects, such concentration. as conductivity, stiffness, and flexibility, are persevered. Here, Our material platform, atomically thin hard material, brings we show origami fabrication at its ultimate limit by using 2D opportunities to reduce origami structures by a factor of 10 with- atomic membranes as a folding material. As a prototype, we bond out sacrificing key functional properties. Specifically, our actu- graphene sheets to nanometer-thick layers of glass to make ultra- ators are capable of elastically deforming to micrometer-scale thin bimorph actuators that bend to micrometer radii of curva- folds, producing large force outputs, and electrically linking ele- ture in response to small strain differentials. These strains are two ments across folds. Looking forward, the capacity to create a orders of magnitude lower than the fracture threshold for the network of electrically interconnected actuators that produce device, thus maintaining conductivity across the structure. By pat- sufficient force to support embedded electronics presents oppor- terning 2-µm-thick rigid panels on top of bimorphs, we localize tunities to move away from static origami structures and toward bending to the unpatterned regions to produce folds. Although origami robotics at the micrometer scale. the graphene bimorphs are only nanometers thick, they can lift these panels, the weight equivalent of a 500-nm-thick silicon chip. Results Using panels and bimorphs, we can scale down existing origami As our prototype design, we engineer graphene and a 2-nm-thick patterns to produce a wide range of machines. These machines layer of silicon dioxide to function as a bending actuator (Fig. change shape in fractions of a second when crossing a tunable pH 1). Within the class of hard materials, graphene stands out as threshold, showing that they sense their environments, respond, an excellent choice, because it is extremely stiff and conductive and perform useful functions on time and length scales compa- but also, thin enough to bend to nanometer radii of curvature rable with microscale biological organisms. With the incorpora- without fracture (21, 22). Silicon dioxide has an elastic modu- tion of electronic, photonic, and chemical payloads, these basic lus comparable with graphene (80 and 1,000 GPa, respectively) elements will become a powerful platform for robotics at the and can be readily fabricated down to nanometer-thick layers. micrometer scale. In fact, designing a bimorph for maximum force output, subject to the constraint of elastic response, identifies graphene and a origami | graphene | bimorph | self-folding | atomic membranes hard, inorganic material, like silicon dioxide, as an optimal combination (SI Materials and Methods). Altogether, the stack’s total thickness of 2 nm (Fig. 1B) means that it can bend down to elf-folding sheets have opened the door to creating complex ∼100-nm radii of curvature before the glass fractures (23) and −4 S3D structures using planar fabrication techniques. Indeed, the device fails. Put differently, strains of only 10 are needed pioneering experiments have shown how to design self-folding in everything from polymers (1–6) to shape-memory alloys (7). Significance Current state of the art enables self-folding of structures with upward of 100 folds (3), algorithms to map arbitrary 3D structures into 2D fold patterns (8–10), and geometries approaching We build origami machines the size of cells by folding them 100-nm features (7, 11). Beyond static structures, recent work at out of atomically thin paper. At the heart of our approach is an the centimeter scale has enabled origami robots and mechanisms actuator technology made from graphene and a nanometer- with broad and useful functions, including locomotion (10) and thick layer of glass. We use these actuators to fold 2D pat- reprogrammable self-assembly (9). terns into targeted 3D structures. The resulting machines are Here, we extend the conceptual framework of origami fab- freely deployed in solutions, can change shape in fractions of rication (1–5, 7, 12–17) to the nanoscale: we work with atomi- a second, carry loads large enough to support embedded elec- cally thin sheets, defining the smallest possible size scale for self- tronics, and can be fabricated en masse. This work opens the folding actuation. door to a generation of small machines for sensing, robotics, Atomically thin sheets of inorganic, hard materials are ideal energy harvesting, and interacting with biological systems on for deployable small-scale origami machines, because they com- the cellular level. bine multiple functional properties into a single platform (18– Author contributions: M.Z.M., P.L.M., and I.C. designed research; M.Z.M., K.J.D., B.B., 20). Hard materials are the standard in semiconductor fabri- and I.C. performed research; Y.H. and D.A.M. contributed new reagents/analytic tools; cation, and thus, building our actuators around them offers M.Z.M., K.J.D., B.B., P.L.M., and I.C. analyzed data; and M.Z.M., P.L.M., and I.C. wrote the a straightforward route to process integration with other nan- paper. otechnologies. Hard materials offer a range of electronic, opti- Reviewers: J.C.C., University of Pennsylvania; and A.J.H., Massachusetts Institute of cal, and chemical functionalities that are well-characterized and Technology. tunable. Finally, hard materials possess extreme thermal, chem- The authors declare no conflict of interest. ical, and mechanical stability, assuring that the final devices will Published under the PNAS license. be robust to large temperature variations and caustic environ- 1To whom correspondence should be addressed. Email: [email protected]. ments, resist unintended stretching deformations, and bend with- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. out creep or stress relaxation. Indeed, the actuators shown here 1073/pnas.1712889115/-/DCSupplemental.

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APPLIED PHYSICAL SCIENCES the solution. For example, when the salt concentration is held at 1 M, the critical pH should shift from pH 9 to the equilibrium constant pK = 3.5. Indeed, when titrating bimorphs in 1 M sodium chloride by adding small volumes sodium hydroxide, the devices unfold at a new critical pH of 3 ± 1. The data in Fig. 2 enable us to rationally design 2D material patterns that self-fold into targeted 3D structures. Given a set of environmental conditions, we map the corresponding radius of curvature to a target fold angle by varying the length of bimorph between the rigid panels. Since every bimorph bends the same way, the angle between two panels at a fold is proportional to length of the bimorph between them divided by the bimorph radius of curvature. By varying the span between hinges, we can program specific fold angles. We present a range of structures designed by this approach to self-assemble at room temperature in acidic environments (Fig. 3). We can make polyhedra, including a 20-µm tetrahedron (Fig. 3A) and 50-µm cubes (Fig. 3F). We are able to build helices with programmable pitches (Fig. 3 B and C). We can also fold two faces on top of each other and clasp them shut with five interdigitated latches: three on one face and two on the other (Fig. 3D). Using mathematical constraints from rigid origami design, we can make structures where folds take on positive or nega- tive curvature. For instance, at a fourfold vertex, at most, three folds can be bent upward: the fourth must bend downward if the pads are sufficiently rigid (Fig. 3E, Right). We can program which bimorph bends downward by removing material along the width of one hinge (Fig. 3E, Left). In this case, the lowest energy state for the system as a whole is to bend this slender bimorph downward against its preferred folding direc- tion (14). We use this scheme to realize the Muira fold, a foundational fourfold vertex used heavily in origami structures, Fig. 3. Graphene–glass bimorphs can be used to fabricate numerous 3D robotics, and metamaterials at the macroscale (3, 10, 12) (Fig. structures at the micrometer scale. These include, but are not limited to, 3E, Center). tetrahedron (A), helices of controllable pitch (B and C), high-angle folds All of these structures are capable of fast and reversible fold- and clasps (D), basic origami motifs with bidirectional folding (E), and boxes ing through the pH actuation mode. We show what happens (F). In Left, we show the device flattened and still attached to the release when a concentrated drop of sodium hydroxide is dripped on layer. After they are etched, the bimorphs self-assemble to their targeted 3D top of a folded 20-µm tetrahedron in Fig. 4A. The tetrahedron geometries (Center). Images of the folded devices were obtained by focal plane stacking. All of the figures in Center are at the same scale. For com- springs open, returning to the flat state in approximately 100 ms. parison, we present paper models of the target geometry in Right. This high-speed motion is a unique feature of working with thin films: for bimorphs driven using either thermal effects or chemical diffusion, response times scale with the square of the layer but when the pH is raised above pH 9 by adding sodium hydrox- thickness. For a given material, moving from micrometer- to ide, it unrolls to a flat state. This process is fast (<1 s) and nanometer-thick films speeds up actuation 1 million-fold. When reversible: when the environment is rendered acidic again, the a drop of acid is added to neutralize the base, the box refolds bimorph curls back into a coil. By varying temperature and pH (Fig. 4B). The process can be repeated multiple times (Movies independently, we find that the strain state in the bimorph is a S1 and S2). linear combination of thermal stress and chemical stress: devices in basic solutions that start flat fold when heated. The two ions present in our experiment, sodium and hydronium, exchange with one another within the glass layer of the bimorph to produce the discrete transition in strain. The ratio of their concentrations in the glass is fixed by an equilibrium + [SiONa][H3O ] constant: pK = − log10 + . Thus, if enough sodium [SiOH3O][Na ] hydroxide is added to solution, the glass will eventually exchange the large hydronium ions for smaller sodium ions. Assuming that the bimorphs are swollen because of hydronium present in the glass, the strain in the bimorph will be given by (SI Materials and Methods) = m , 1 + 10−pK+pH−pNa Fig. 4. Devices made from graphene–glass bimorphs can fold and unfold where εm is the maximum strain that results when every dangling in fractions of a second in response to local pH changes. When the local pH bond associated with a hydronium molecule. We show that this surrounding a folded tetrahedron exceeds the critical unfolding threshold, equation best fits the data with pK = 3.5 in Fig. 2. the device springs open and into the flat state within 0.5 s (A). Changing This mechanism allows us to shift the pH transition point arbi- the surrounding environment to acidic can refold the tetrahedron within trarily by independently adjusting the sodium concentration of 4 s (B).

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APPLIED PHYSICAL SCIENCES ACKNOWLEDGMENTS. We thank Mark Bowick, William Dichtel, David Grant DMR-1435829, Air Force Ofﬁce of Scientiﬁc Research (AFSOR) multidis- Gracias, David Nelson, and Jiwoong Park for insightful discussions. We thank ciplinary research program of the university research initiative Grant FA2386- Peter Rose for preliminary experimental work. This work was supported by 13-1-4118, and the Kavli Institute at Cornell for Nanoscale Science, and it was Cornell Center for Materials Research Grant DMR-1719875, National Science performed at Cornell NanoScale Facility, a member of the National Nanotech- Foundation (NSF) Major Research Instrumentation Award DMR-1429155, NSF nology Infrastructure Network (NSF Grant ECCS-0335765).

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