Elastic properties and mechanical tension of graphene

Abstract

Room temperature simulations of graphene have been performed as a function of the mechanical tension of the layer. Finite-size effects are accurately reproduced by an acoustic dispersion law for the out-of-plane vibrations that, in the long-wave limit, behaves as $\rho {\omega }^2=\sigma k^2+\kappa k^4$. The fluctuation tension $\sigma$ is finite ($\sim 0.1$ N/m) even when the external mechanical tension vanishes. Transverse vibrations imply a duplicity in the definition of the elastic constants of the layer, as observables related to the real area of the surface may differ from those related to the in-plane projected area. This duplicity explains the variability of experimental data on the Young modulus of graphene based on electron spectroscopy, interferometric profilometery, and indentation experiments.

6 pages, 4 figures

References in corpus (5)

• Symmetry constraints on phonon dispersion in graphene
• Quantum effects in graphene monolayers: Path-integral simulations
• Anharmonic effects in the optical and acoustic bending modes of graphene
• Path-integral molecular dynamics simulation of 3C-SiC
• Compressibility of solid helium

Cited by in corpus (11)

• Hidden area and mechanical nonlinearities in freestanding graphene
• Thermal properties of graphene from path-integral simulations
• Thermodynamic properties of graphene bilayers
• Bending mode and thermal expansion of graphene
• Anharmonicity of the acoustic modes of graphene
• Phonon dispersion in two-dimensional solids from atomic probability distributions
• Nuclear quantum effects in graphane
• Nuclear quantum effects in graphene bilayers
• Quantum effects in structural and elastic properties of graphite: Path-integral simulations
• Isotopic effects in structural properties of graphene
• Perturbative renormalization and thermodynamics of quantum crystalline membranes