Spontaneous Folding of Suspended and Supported Graphene, and Other 2D Materials: Morphologies and Induced Pre-Tension

In the present study, we investigate the spontaneous folding of graphene and other 2D materials, considering the possibilities that they are suspended or supported, and dry or wet. By combining molecular dynamics simulations, a minimal analytical continuum model, and atomic force microscopy experiments, we assess the impact of interlayer adhesion on several folding conformations at various temperatures. We find that the folded structures induce tensile stress on graphene, and the magnitude of this stress depends on the morphology of the fold. The calculated stress values, in the range of 0.14–0.35 N/m, with experimentally reported pretension values in suspended graphene, suggest that folds may be a possible intrinsic source of pretension. The results of the simulations for graphene are reproduced by a one-parameter analytical continuum model of a 2D material, which naturally extends the predicted phenomenology of fold-induced pretension to other 2D materials. Our simulations also show the existence of folds in suspended graphene in a humid environment. We also performed experiments on supported and suspended regions of few-layer talc using atomic force microscopy and observed several folded structures with characteristics similar to those in the simulations. These results reveal that folding serves as an intrinsic and general mechanical mechanism for imparting residual tension in two-dimensional materials, with direct implications for nanomechanical measurements, strain engineering, and device stability.