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-Hybridization

Anomalous Flexural Elasticities of Graphene Membranes Unveiled by Manipulating Topology

Mechanical behavior of atomically thin membranes is governed by bending rigidity and the Gaussian modulus. However, owing to methodological drawbacks, these two parameters have not been investigated sufficiently. We employed atomic force microscopy to demonstrate that the bending rigidity can be extracted from a quadratic relationship of adhesion energy with monolayer curvatures of rolled and unrolled graphene. The tip-induced topological defects revealed the Gaussian modulus; to the best of our knowledge, this is the first study on these parameters. Our study may hold great significance because existing investigations have been performed only on flat graphene. The configurational (strain) energy was evaluated via changes in the surface geometry, with subatomic resolution, by three-dimensional analyses of attractive interatomic forces. The mechanical parameters, evaluated at the hollow sites of the honeycomb lattice, were consistent with the isotropic elastic attributes. The remarkably large negative Gaussian modulus, observed when a single carbon atom was located at the center of the tip-induced bump, revealed attractive interactions between the topological defects and geometric potentials of the Gaussian curvature. Our approach will aid in developing two-dimensional materials and understanding cell biology.

A Review of Current Development of Graphene Mechanics

Graphene, a two-dimensional carbon in honeycomb crystal with single-atom thickness, possesses extraordinary properties and fascinating applications. Graphene mechanics is very important, as it relates to the integrity and various nanomechanical behaviors including flexing, moving, rotating, vibrating, and even twisting of graphene. The relationship between the strain and stress plays an essential role in graphene mechanics. Strain can dramatically influence the electronic and optical properties, and could be utilized to engineering those properties. Furthermore, graphene with specific kinds of defects exhibit mechanical enhancements and thus the electronic enhancements. In this short review, we focus on the current development of graphene mechanics, including tension and compression, fracture, shearing, bending, friction, and dynamics properties of graphene from both experiments and numerical simulations. We also touch graphene derivatives, including graphane, graphone, graphyne, fluorographene, and graphene oxide, which carve some fancy mechanical properties out from graphene. Our review summarizes the current achievements of graphene mechanics, and then shows the future prospects.