Folds and buckles at the nanoscale: experimental and theoretical investigation of the bending properties of graphene membranes.

The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations.