Atomic-Site-Specific Analysis on Out-of-Plane Elasticity of Convexly Curved Graphene and Its Relationship to s p 2 to s p 3 Re-Hybridizatio

Abstract

The geometry of two-dimensional crystalline membranes is of interest given its unique synergistic interplay with their mechanical, chemical, and electronic properties. For one-atom-thick graphene, these properties can be substantially modified by bending at the nanometer scale. So far variations of the electronic properties of graphene under compressing and stretching deformations have been exclusively investigated by local-probe techniques. Here we report that the interatomic attractive force introduced by atomic force microscopy triggers "single"-atom displacement and consequently enables us to determine out-of-plane elasticities of convexly curved graphene including its atomic-site-specific variation. We have quantitatively evaluated the relationship between the out-of-plane displacement and elasticity of convexly curved graphene by three-dimensional force field spectroscopy on a side-wall of a hollow tube with a well-defined curvature. The substantially small intrinsic modulus that complies with continuum mechanics has been found to increase significantly at atomically specific locations, where sp 2 to sp 3 re-hybridization would certainly take place.

A Review of Current Development of Graphene Mechanics

“…In widely used AFM-based nanoindentation, it is obvious that the carbon atoms in the center of the circular area are compressed by the indenter, but the characteristics of the mechanical response of these atoms are known less. In order to determine out-of-plane elastic properties of convexly curved graphene including its atomic-site-specific variation, Ashino et al [30] triggered the out-of-plane displacement of the "single" atom using atomic force microscope (AFM), and then solved out the relationship between the elasticity and out-of-plane displacement. The intrinsic modulus increases dramatically when the distance is over about 0.35 which is at atomic level.…”

“…(a) Schematic illustration of a 3D-FFS measurement; (b) Schematic illustration of a 3D-FFS measurement; (c) 2D force field map; (d) Interatomic force vs. vertical distance z. Reprinted (adapted) with permission from[30].…”