Barriers to motion and rotation of graphene layers based on measurements of shear mode frequencies

Abstract

Both van der Waals corrected density functional theory and classical calculations show that the potential relief of interaction energy between layers of graphite and few-layer graphene can be described by a simple expression containing only the first Fourier components. Thus a set of physical quantities and phenomena associated with in-plane relative vibration, translational motion and rotation of graphene layers are interrelated and are determined by a single parameter characterizing the roughness of the potential energy relief. This relationship is used to estimate the barriers to relative motion and rotation of graphene layers based on experimental measurements of shear mode frequencies.

AA stacking, tribological and electronic properties of double-layer graphene with krypton spacer

“…On the basis of experimentally measured shear mode frequencies for few-layer graphene and graphite, the barrier to relative motion of graphene layers and the magnitude of corrugation of the potential energy relief for bilayer graphene were estimated to be 1.7 meV and 15 meV per carbon atom of one of the graphene layers, respectively. 68 The optPBEvdW and vdW-DF2 methods underestimate these quantities by 40% and 50%, respectively, whereas the DFT-D2 method overestimates these quantities by only 25% (Table I). Thus, it can be expected that the DFT-D2 method is more accurate in the prediction of tribological properties of krypton-separated double-layer graphene.…”

“…For double-layer graphene with the commensurate krypton spacer A, the formula parameterized on the basis of the DFT-D2 calculations gives the frequency f = 10.5 cm −1 , which is three times smaller than for the graphene bilayer. 57,68,69,72 This can be explained by the one-order difference in the magnitudes of corrugation of the potential energy reliefs for kryptonseparated double-layer graphene and graphene bilayer. 57,68,69 For the material consisting of alternating graphene layers and commensurate krypron spacers A, the formula (4) parameterized on the basis of the DFT-D2 calculations gives the shear mode frequency f = 14.8 cm −1 , three times smaller than for graphite.…”

“…From this equation, the magnitude of corrugation of the potential energy relief and the barrier to relative motion of the graphene and krypton layers can be found as E max ≈ 4.5U 1 = 1.62 meV and E gr-Kr ≈ 4U 1 = 1.44 meV per carbon atom, respectively. It should be also noted that the first Fourier components were previously shown to be sufficient for the description of the potential reliefs of interlayer interaction energy in bilayer graphene 54,55,57,68,69 and interwall interaction energy in carbon nanotubes. 51,70,71 As shown previously for argon spacers, 37 the contribution of graphene-graphene interaction to corrugations of the potential energy relief in double-layer graphene does not exceed 0.003 meV per carbon atom of one of the layers.…”

“…This formula looks just the same as for graphene bilayer. 57,68 However, here U 1 characterizes the krypton-graphene interaction instead of the graphene-graphene interaction. For double-layer graphene with the commensurate krypton spacer A, the formula parameterized on the basis of the DFT-D2 calculations gives the frequency f = 10.5 cm −1 , which is three times smaller than for the graphene bilayer.…”

“…57,68,69 For the material consisting of alternating graphene layers and commensurate krypron spacers A, the formula (4) parameterized on the basis of the DFT-D2 calculations gives the shear mode frequency f = 14.8 cm −1 , three times smaller than for graphite. 68 The shear modulus of this material can be estimated as…”