Size- and temperature-dependent bending rigidity of graphene using modal analysis

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Abstract

The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices. The apparent bending rigidity of graphene membranes at macroscopic scale differs from theoretical predictions at micro-scale. This difference is believed to originate from thermally induced dynamic ripples in these atomically thin membranes. In this paper, we perform modal analysis to estimate the effective bending rigidity of graphene membranes from the frequency spectrum of their Brownian motion. Our method is based on fitting the resonance frequencies obtained from the Brownian motion in molecular dynamics simulations, to those obtained from a continuum mechanics model, with bending rigidity and pretension as the fit parameters. In this way, the effective bending rigidity of the membrane and its temperature and size dependence, are extracted, while including the effects of dynamic ripples and thermal fluctuations. The proposed method provides a framework for estimating the macroscopic mechanical properties in other 2D nanostructures at finite temperatures.

Original languageEnglish
Pages (from-to)334-341
JournalCarbon
Volume139
DOIs
Publication statusPublished - 2018

Keywords

  • Bending rigidity
  • Brownian motion
  • Characterization
  • Graphene
  • Molecular dynamics
  • Multi-modal approach

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