Elastic coupling between layers in two-dimensional materials

Abstract

Two-dimensional materials, such as graphene and MoS2, are films of a few atomic layers in thickness with strong in-plane bonds and weak interactions between the layers. The in-plane elasticity has been widely studied in bending experiments where a suspended film is deformed substantially; however, little is known about the films' elastic modulus perpendicular to the planes, as the measurement of the out-of-plane elasticity of supported 2D films requires indentation depths smaller than the films' interlayer distance. Here, we report on sub-ångström-resolution indentation measurements of the perpendicular-to-the-plane elasticity of 2D materials. Our indentation data, combined with semi-analytical models and density functional theory, are then used to study the perpendicular elasticity of few-layer-thick graphene and graphene oxide films. We find that the perpendicular Young's modulus of graphene oxide films reaches a maximum when one complete water layer is intercalated between the graphitic planes. This non-destructive methodology can map interlayer coupling and intercalation in 2D films.

Å-Indentation for non-destructive elastic moduli measurements of supported ultra-hard ultra-thin films and nanostructures

“…Notably, while the Hertz model is valid in the case of non-adhesive contact, the Johnson-Kendall-Roberts (JKR) and the Derjaguin-Muller-Toporov (DMT) are popular models for predicting the contact behavior in the presence of adhesive forces [19,[40][41][42]. In particular, the JKR model is often adopted in the case of contact with compliant solids, whereby the radius R is large and the adhesion forces are also large.…”

“…MoNI/ÅI has recently found applications in the characterization of the mechanical properties of the transverse mechanical stiffness of supported 2D materials, and in particular supported epitaxial graphene [19,35]. The enhanced resolution of MoNI/ÅI has enabled for the first time the direct measurement of the inter-layer stiffness of few layer thick graphene and graphene oxide supported films [19] and has led to the discovery of the room-temperature diamondization of epitaxial bi-layer graphene on silicon carbide [35,36]. These measurements have been possible only due to the extremely high spatial resolution of MoNI/ÅI.…”

Measuring Interlayer Shear Stress in Bilayer Graphene

“…From a classic view of multilayer systems, one of the most critical issues that determine its overall performance, durability, and even fabrication process lies in the interfacial load transfer [9]. For the atomically thin layers, the interfacial effects could be even more critical because fundamentally thermal, electronic, optical, and tribological properties could all be affected by the interlayer deformation (especially under shear mode) of multilayer structures [10][11][12], whereas corresponding mechanical parameters are far from well characterized.…”

Stacking order dependent mechanical properties of graphene/MoS2 bilayer and trilayer heterostructures

“…This methodology can also be used to study interlayer elastic coupling, thereby improving our understanding of the effect of dopants/intercalants between layers, which are important for modulating the electronic properties of layered 2D materials. 8,9,52 R …”