# Elastic properties and mechanical tension of graphene

## TL;DR

This study uses simulations to explore how graphene's elastic properties and mechanical tension are affected by out-of-plane vibrations, revealing a finite fluctuation tension and explaining experimental variability in elastic constants.

## Contribution

It introduces an acoustic dispersion law for out-of-plane vibrations and clarifies the impact of transverse vibrations on elastic constant measurements.

## Key findings

- Finite fluctuation tension exists even without external tension.
- Out-of-plane vibrations cause a discrepancy in elastic constant definitions.
- Variability in experimental Young modulus data is explained by vibrational effects.

## 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.