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  1. Continuum mechanics break down in bending stiffness calculations of mono- and few-layered two-dimensional (2D) van der Waals crystal sheets, because their layered atomistic structures are uniquely characterized by strong in-plane bonding coupled with weak interlayer interactions. Here, we elucidate how the bending rigidities of pristine mono- and few-layered molybdenum disulfide (MoS 2 ), graphene, and hexagonal boron nitride (hBN) are governed by their structural geometry and intra- and inter-layer bonding interactions. Atomic force microscopy experiments on the self-folded conformations of these 2D materials on flat substrates show that the bending rigidity of MoS 2 significantly exceeds those of graphene or hBN of comparable layers, despite its much lower tensile modulus. Even on a per-thickness basis, MoS 2 is found to possess similar bending stiffness to hBN and is much stiffer than graphene. Density functional theory calculations suggest that this high bending rigidity of MoS 2 is due to its large interlayer thickness and strong interlayer shear, which prevail over its weak in-plane bonding. 
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    Free, publicly-accessible full text available April 10, 2024
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