Graphene kirigami

The ratio of in-plane stiffness to out-of-plane bending stiffness of graphene is shown to be similar to that of a piece of paper, which allows ideas from kirigami (a variation of origami that allows cutting) to be applied to micrometre-scale graphene sheets to build mechanically stretchable yet robust electrodes, springs and hinges. Graphene structures make the cut The paper arts of origami and kirigami (which allows cutting as well as folding) are scalable, and increasingly used by scientists and engineers to create structures from the macro- to the microscale. Melina Blees and colleagues now show that graphene is well suited for kirigami: its relative stiffness against in-plane stretching as opposed to out-of-plane bending is similar to that of a piece of paper, owing to the presence of ripples that stiffen the graphene sheets and dramatically increase their bending stiffness over the predicted atomic-scale value. Ideas from kirigami can thus be applied quite readily to micrometre-sized graphene sheets, and used to build mechanically stretchable yet robust electrodes, springs and hinges that could find use in atomically thin membrane devices for sensing, manipulation, and possibly even robotics applications. 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 microscale 1 , 2 . Here we show that graphene 3 , 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 number 7 , 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 membrane 9 , 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