Bending energy of 2D materials: Graphene, MoS₂ and imogolite

The bending process of 2D materials, subject to an external force, is investigated, and applied to graphene, molybdenum disulphide (MoS2), and imogolite. For graphene we obtained 3.43 eV Å2 per atom for the bending modulus, which is in good agreement with the literature. We found that MoS2 is-11 times harder to bend than graphene, and has a bandgap variation of ∼1 eV as a function of curvature. Finally, we also used this strategy to study aluminosilicate nanotubes (imogolite) which, in contrast to graphene and MoS2, present an energy minimum for a finite curvature radius. Roof tile shaped imogolite precursors turn out to be stable, and thus are expected to be created during imogolite synthesis, as predicted to occur by self-assembly theory.