The interplay of intra- and inter-layer interactions in bending rigidity of ultrathin 2D materials

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 (MoS2), 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 MoS2 significantly exceeds those of graphene or hBN of comparable layers, despite its much lower tensile modulus. Even on a per-thickness basis, MoS2 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 MoS2 is due to its large interlayer thickness and strong interlayer shear, which prevail over its weak in-plane bonding.