Acta Mechanica

, Volume 229, Issue 6, pp 2343–2378 | Cite as

Simulation of mechanical parameters of graphene using the DREIDING force field

  • S. N. Korobeynikov
  • V. V. Alyokhin
  • A. V. Babichev
Original Paper
  • 103 Downloads

Abstract

Molecular mechanics/molecular dynamics (MM/MD) methods are widely used in computer simulations of deformation (including buckling, vibration, and fracture) of low-dimensional carbon nanostructures (single-layer graphene sheets (SLGSs), single-walled nanotubes, fullerenes, etc). In MM/MD simulations, the interactions between carbon atoms in these nanostructures are modeled using force fields (e.g., AIREBO, DREIDING, MM3/MM4). The objective of the present study is to fit the DREIDING force field parameters (see Mayo et al. J Phys Chem 94:8897–8909, 1990) to most closely reproduce the mechanical parameters of graphene (Young’s modulus, Poisson’s ratio, bending rigidity modulus, and intrinsic strength) known from experimental studies and quantum mechanics simulations since the standard set of the DREIDING force field parameters (see Mayo et al. 1990) leads to unsatisfactory values of the mechanical parameters of graphene. The values of these parameters are fitted using primitive unit cells of graphene acted upon by forces that reproduce the homogeneous deformation of this material in tension/compression, bending, and fracture. (Different sets of primitive unit cells are used for different types of deformation, taking into account the anisotropic properties of graphene in states close to failure.) The MM method is used to determine the dependence of the mechanical moduli of graphene (Young’s modulus, Poisson’s ratio, and bending rigidity modulus) on the scale factor. Computer simulation has shown that for large linear dimensions of SLGSs, the mechanical parameters of these sheets are close to those of graphene. In addition, computer simulation has shown that accounting for in-layer van der Waals forces has a small effect on the value of the mechanical moduli of graphene.

Mathematics Subject Classification

74K20 74E15 

Abbreviations

MM

Molecular mechanics

MD

Molecular dynamics

SLGS

Single-layer graphene sheet

MLGS

Multilayer graphene sheet

GNR

Graphene nanoribbon

SWCNT

Single-walled carbon nanotube

QM

Quantum mechanics (first principles, ab initio)

CM

Continuum mechanics

DFT

Density functional theory

GGA

Generalized gradient approximation (approximation of DFT)

LDA

Local density approximation (approximation of DFT)

TB

Tight-binding

DFTB

Density functional tight-binding

vdW

van der Waals

REV

Representative elementary volume

ac-direction

Armchair direction

zz-direction

Zigzag direction

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Notes

Acknowledgements

The supports from the Russian Foundation for Basic Research (Grant No. 15-08-01635) and from Russian Federation Government (Grant No. P220-14.W03.31.0002) are gratefully acknowledged. The authors thank the anonymous reviewers whose comments and suggestions helped in revising the manuscript.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lavrentyev Institute of HydrodynamicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Sobolev Institute of Geology and MineralogyNovosibirskRussia

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