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

Abstract

The bending process of 2D materials, subject to an external force, is investigated, and applied to graphene, molybdenum disulphide (MoS2), and imogolite.

Recent Advances in Strain-Induced Piezoelectric and Piezoresistive Effect-Engineered 2D Semiconductors for Adaptive Electronics and Optoelectronics

“…Strain engineering in 2D materials: from basic theories to applications [81,200,[222][223][224] front set of four equations corresponds to the direct piezoelectric effect, and the latter set corresponds to the converse piezoelectric effect. There are 21 non-centrosymmetric crystal classes in a total of 32 crystal classes, and 20 exhibit direct piezoelectricity.…”

Micromechanical exfoliation of graphene on the atomistic scale

“…4b). Graphene exhibits very little friction between adjacent layers 33 and an extremely low bending energy 34 which make it unique amongst laminar materials. Friction and bending are so easily overcome that when the force is applied in the normal direction the sheets are able to bend and slide in a peeling motion.…”

Active Site Engineering on Two-Dimensional-Layered Transition Metal Dichalcogenides for Electrochemical Energy Applications: A Mini-Review

“…As shown in Figure 1, the inner, bulk-like bands (the red lines) are qualitatively similar for R = 8.12 Å and R→∞, but the band gap is~0.8 eV smaller, indicating that it is possible to control the bandgap of a MoS 2 nanosheet by bending it [35]. [35]. The different color shows the location of the eigenvalues: The inner subbands (i.e., bulk-like) and the edge subbands are red and blue, respectively; the hybridization of bulk and edge states are between red and blue.…”

“…In 2018, Gonz'alez et al investigated the bending process of 2D-layered materials, which is related to external forces [35], and studied the bending of a MoS 2 band in order to increase the complexity of the material, in this case, using the bending force on the central Mo layer while permitting the S atoms to move freely. As shown in Figure 1, the inner, bulk-like bands (the red lines) are qualitatively similar for R = 8.12 Å and R→∞, but the band gap is~0.8 eV smaller, indicating that it is possible to control the bandgap of a MoS 2 nanosheet by bending it [35]. [35].…”