For centuries, practitioners of origami (‘ori’, fold; ‘kami’, paper) and kirigami (‘kiru’, cut) have fashioned sheets of paper into beautiful and complex three-dimensional structures. Both techniques are scalable, and scientists and engineers are adapting them to different two-dimensional starting materials to create structures from the macro- to the microscale1,2. Here we show that graphene3,4,5,6 is well suited for kirigami, allowing us to build robust microscale structures with tunable mechanical properties. The material parameter crucial for kirigami is the Föppl–von Kármán number7,8 γ: an indication of the ratio between in-plane stiffness and out-of-plane bending stiffness, with high numbers corresponding to membranes that more easily bend and crumple than they stretch and shear. To determine γ, we measure the bending stiffness of graphene monolayers that are 10–100 micrometres in size and obtain a value that is thousands of times higher than the predicted atomic-scale bending stiffness. Interferometric imaging attributes this finding to ripples in the membrane9,10,11,12,13 that stiffen the graphene sheets considerably, to the extent that γ is comparable to that of a standard piece of paper. We may therefore apply ideas from kirigami to graphene sheets to build mechanical metamaterials such as stretchable electrodes, springs, and hinges. These results establish graphene kirigami as a simple yet powerful and customizable approach for fashioning one-atom-thick graphene sheets into resilient and movable parts with microscale dimensions.
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We thank D. Nelson, M. Bowick, A. Kosmrlj, J. Alden, A. van der Zande, and R. Martin-Wells for discussions. We thank E. Minot for assistance with electrolyte gating. We thank R. Hovden for discussions on three-dimensional reconstruction theory and techniques, and R. Hovden, M. Hanwell, and U. Ayachit for developing and supporting the TomViz three-dimensional visualization software. We thank J. Wardini, P. Ong, A. Zaretski, and S. P. Wang for additional graphene samples, and F. Parish with Cornell’s College of Architecture, Art, and Planning for assistance with the paper models. We also acknowledge the Origami Resource Center (http://www.origami-resource-center.com/) for kirigami design ideas. This work was supported by the Cornell Center for Materials Research (National Science Foundation, NSF, grant DMR-1120296), the Office of Naval Research (N00014-13-1-0749), and the Kavli Institute at Cornell for Nanoscale Science. Devices were fabricated at the Cornell Nanoscale Science and Technology Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the NSF (ECCS-0335765). K.L.M. and P.Y.H. acknowledge support from the NSF Graduate Research Fellowship Program (DGE-1144153 and DGE-0707428). Tomography visualization software development was supported by a SBIR grant (DE-SC0011385).
Extended data figures
Once the graphene has been released from the surface, it can crumple dramatically, similar to a large sheet of paper. Surfactants in the solution allow the graphene to return to its original shape. Lifting a graphene device (2x speed). Driving the micromanipulator into an attached gold pad lets us fully release the device and lift it up off of the surface
Using a micromanipulator driven into one gold pad, we can repeatedly stretch and relax a kirigami spring. Soft graphene kirigami spring extends by ~240% (2x speed). A different kirigami pattern results in a softer spring that stretches dramatically. Z-scan used in 3D reconstruction (background subtracted). The left side of this spring is being held up by the probe tip, while the right side is still stuck to the substrate.
Infrared laser focused on a kirigami pyramid’s central pad and Kirigami pyramid actuation, laser filtered out of the video (1x speed).
The laser is fired from below the pyramid and pushes upwards on the pad, causing it to go out of focus. Twisting graphene with an iron pad and rotating magnetic field (2x speed). Surfactant in the solution allows the graphene to unfold again. A graphene hinge, actuated by a long graphene arm. Large field of view shows the mechanism. A graphene hinge after 1000 cycles (1x speed). This device survived through 10,000 cycles.