Mechanical properties of graphene cantilever from atomic force microscopy and densityfunctional theory

Abstract

We have studied the mechanical properties of a few-layer graphene cantilever(FLGC) using atomic force microscopy (AFM). The mechanical propertiesof the suspended FLGC over an open hole have been derived from theAFM data. Force displacement curves using the Derjaguin–Müller–Toporov(DMT) and the massless cantilever beam models yield a Young modulus ofEc ∼ 37,Ea ∼ 0.7 TPa and a Hamakarconstant of ∼ 3 × 10 − 18 J. The threshold force to shear the FLGC was determined from a breaking forceand modeling. In addition, we studied a graphene nanoribbon (GNR), whichis a system similar to the FLGC; using density functional theory (DFT). Thein-plane Young’s modulus for the GNRs were calculated from the DFT outcomes ∼ 0.82 TPa and the results were compared with the experiment. We found that theYoung’s modulus and the threshold shearing force are dependent on the direction ofapplied force and the values are different for zigzag edge and armchair edge GNRs.