Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets

Roopam Khare, Steven L. Mielke, Jeffrey T. Paci, Sulin Zhang, Roberto Ballarini, George C. Schatz, Ted Belytschko

Research output: Contribution to journalArticle

240 Citations (Scopus)

Abstract

Coupled quantum mechanical/molecular mechanical (QM/MM) calculations were used to study the effects of large defects and cracks on the mechanical properties of carbon nanotubes and graphene sheets. The semi-empirical method PM3 was used to treat the QM subdomains and a Tersoff-Brenner potential was used for the molecular mechanics; some of the QM calculations were also done using density functional theory (DFT). Scaling of the Tersoff-Brenner potential so that the modulus and overall stress-strain behavior of the QM and MM models matched quite closely was essential for obtaining meaningful coupled calculations of the mechanical properties. The numerical results show that at the nanoscale, the weakening effects of holes, slits, and cracks vary only moderately with the shape of the defect, and instead depend primarily on the cross section of the defect perpendicular to the loading direction and the structure near the fracture initiation point. The fracture stresses for defective graphene sheets are in surprisingly good agreement with the Griffith formula for defects as small as 10 Å, which calls into question the notion of nanoscale flaw tolerance. The energy release rate at the point of crack extension in graphene was calculated by the J -integral method and exceeds twice the surface energy density by 10% for the QM(DFT)/MM results, which indicates a modest lattice trapping effect.

Original languageEnglish (US)
Article number075412
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume75
Issue number7
DOIs
StatePublished - Feb 9 2007

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Carbon Nanotubes
Graphite
Graphene
Carbon nanotubes
graphene
carbon nanotubes
Defects
defects
cracks
Cracks
Density functional theory
J integral
mechanical properties
density functional theory
Mechanical properties
Molecular mechanics
Energy release rate
Interfacial energy
surface energy
slits

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Khare, Roopam ; Mielke, Steven L. ; Paci, Jeffrey T. ; Zhang, Sulin ; Ballarini, Roberto ; Schatz, George C. ; Belytschko, Ted. / Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. In: Physical Review B - Condensed Matter and Materials Physics. 2007 ; Vol. 75, No. 7.
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Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. / Khare, Roopam; Mielke, Steven L.; Paci, Jeffrey T.; Zhang, Sulin; Ballarini, Roberto; Schatz, George C.; Belytschko, Ted.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 75, No. 7, 075412, 09.02.2007.

Research output: Contribution to journalArticle

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