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Ruizhi Li1 Mrityunjay Kothari1 Moon-Hyun Cha1 Kyung-Suk Kim1

1, Brown University, Providence, Rhode Island, United States

Single-layer graphene and few-layer graphene are known to exhibit characteristic dynamic ripples as well as static corrugations when suspended. Traditionally, shallow configurations of the ripples and the corrugations have been assumed to be in sinusoidal shape. In contrast, here, we report the discovery of a new, low-energy, subcritical mode shape that produces shallow-kink corrugation in graphene, particularly in multilayer graphene. Our DFT analysis shows that the configuration has a ~2 nm wide boundary layer of highly localized curvature that connects two regions of uniformly but oppositely sheared stacks of flat atomic sheets. The DFT and our flexoelectricity model analyses reveal that periodic kinks, named crinkles, are the lowest energy configuration of multilayer graphene under critical axial pressure. The results show that quantum flexoelectricity leads to emergence of the boundary layer in which curvature is focused primarily within a 0.86 nm fixed band width. Furthermore, the analyses predict high peak-polarization density, e.g. 0.03 -e/nm for 3o tilt angle. The polarization develops surface electric charge concentration in the fixed band width, along the crinkle ridges and valleys, on the top and bottom free surfaces of multilayer graphene. The surface electric charges are negative on the tops of ridges and positive on the bottoms of valleys. In our experiment, we compressed an assembly of multilayer graphene (~200 layers) attached to a PMMA or a silicon grating of grooves up to ~ 0.1% strain to observe the hinge-mode buckling with an atomic force microscope. The suspended portion of the graphene over the grooves pop out to make crinkle ridges on the PMMA grating, while they sink in to make crinkle valleys on the silicon grating. The ridges generate negative line charges to form N-type crinkles, and the valleys positive line charges to form P-type crinkles. We found that the parity of the crinkles can be controlled by choosing proper elastic moduli mismatch and the strength of adhesion between the graphene and the grating substrate. Our DFT analysis shows that typical adsorption potential bias of a neutral molecule, e.g. O2, on the line charges is ~30 meV, and much larger for charged molecules. Controlling the charge potential depth, the line charge acts as a molecular zipper which attracts and aligns bio-molecules, or nano-particles along the ridges or valleys. The graphene-crinkle molecular zipper is expected to be a powerful tool to study molecular adsorption, and self-organization of molecules and nanoparticles for various applications.

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