Effect of Defects in the Mechanical Properties of Carbon Nanotubes

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Effect of Defects in the Mechanical Properties of
Carbon Nanotubes
PHY 472 / Lehigh University Instructor Prof.
Slava V. Rotkin By Paul A. Belony, Jr.
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Common Defects observed in CNTs

• Main types of defects
• 3 main groups
• Point defects
• Topological defects
• Hybridization defects
• Subgroups
• Vacancies (PD)
• Metastable atoms
• Pentagons (TD)
• Heptagons (TD)
• StoneWales (SW or 5775) (TD)
• Fictionalization (HD) (sp3 bonds)
• Discontinuities of walls
• Distortion in the packing configuration of CNT
  bundles
• Etc

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Stone-Wales (5-7-7-5) Defects

• Stone-Wales defect is
• Composed of Two Pentagon-Heptagon pairs
• Formed by rotating a sp2 bond by 900
• In other words, formed when bond rotation in a
  graphitic network transforms four hexagons into
  two pentagons and two heptagons, which is
  accompanied by elongation of the tube structure
  along the axis connecting the pentagons, and
  shrinking along the perpendicular direction

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Main Mechanical Properties affected by Defects

• Stiffness
• Ultimate Strength
• Ultimate Strain
• Flexibility
• Buckling and robustness under high pressure
• CNTs are among the most robust materials
• High Elastic Modulus (order of 1 TPa)
• High Strength (range up to 100s of GPa)

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Main effects on Stiffness
Changes in stiffness observed. Stiffness
decrease with topological defects and increase
with fictionalization Defect generation and
growth observed during plastic deformation and
fracture of nanotubes
Deepak Srivastava etal.
Qiang Lu and Baidurya Battacharya
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• Force-Displacement curves are used in order to
  show the response of the SWNTs under loading
• Reduced units
• 1 time ru 0.03526 ps
• 1 force ru 1.602 nN
• 1 displacement ru 1 ?

SWNTs with more defects are likely to break at
smaller strains and have less strength as
well. Forcedisplacement curves of nanotubes
with various average numbers of defects.

• the Young modulus can be calculated as the
  initial slope of the forcedisplacement curve
• The ultimate strength is calculated at the
  maximum force point, sU (Fmax)/A, where F is
  the maximum axial force, A is the cross section
  area
• the ultimate strain, which corresponds to the
  ultimate strength, is calculated as
• eU (?LU)/L, where L is the original tube
  length.

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Types of stresses

• virial stress
• atomic (BDT) stress
• Lutsko stress
• Yip stress

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• The applied force is computed by summing the
  interatomic forces for the atoms along the end of
  the nanotube where the displacement is
  prescribed.
• The stress is calculated from the
  cross-sectional area S pdh (h is the chosen
  interlayer separation of graphite)

Belytschko et al. Force-Deflection curve for a
model of zigzag NT (Normalized to Stress vs.
Strain)
Crack formation in a 40, 40 armchair NT with SW
defect (evolution from left to right 12.5 12.8
ps)
Evolution of cracks in the NT Bond-breaking
spreads sideways after the initially weakened
bond failed
The crack grows in the direction of maximum shear
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Elastic modulus before defect

• Defect free (9,0) nanotube with periodic boundary
  conditions
• Strains applied using conjugate gradients energy
  minimization
• - All stress and strain measures yield a Youngs
  modulus value of 1.002TPa

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5-7-7-5 Defect on CNTs

• The graph shows the graph for Lutsko stress
  profile for (9,0) zigzag NT with (5-7-7-5) defect
• The defected region facilitates Stress
  amplification
• When applied strains increase, this amplification
  reduces
• A different situation is observed for (n,n)
  armchair NT there is a decrease in stress at the
  defect region

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N. Chandra, S. Namilae and C. Shet

• Contour plots of the longitudinal strain e33
  strain and stress s33 near the defected region
  drawn at different applied strain levels.
• Strain contours at an applied strain of 1. b)
  Stress contours at an applied strain of 1.
• c) Strain contours at an applied strain of 3. d)
  Stress contours at an applied strain of 3.
• e) Strain contours at an applied strain of 5.
  f) Stress contours at an applied strain of 5.
• g) Strain contours at an applied strain of 8. h)
  Stress contours at an applied strain of 8.

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NT possess residual forces at zero strain (even
when defect free) At about 1 TPa theres a
reduction of stiffness away from the defect-free
straight line
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Measuring Mechanical Properties
L. Forro etal.

• Use of Atomic Force Microscopy (AFM)
• For individual CNTs

1. 3D representation of the adhesion of a SWNT to an
   alumina ultra-filtration (tube is clamped
   allowing mechanical testing)
2. How AFM works in schematic way (a load F is
   applied to the suspending portion of the NT with
   length L. So the max deflection d is
   topologically measured

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• Fracture process of a (6, 6) SWNT with three SW
  defects
• crack initiation and propagation (AI)
• (b) corresponding force time history.

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Diameter dependence
The slope of the graphs seem to be very close to
each other for different curvature of the
NTs So, stiffness values of various tubes of
same SW defect but different diameters do not
change significantly Stiffness in the range of
0.61TPa to 0.63TPa for different (n,0)
tubes Curvature is not significantly affected by
Mechanical properties of SW defect
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Charality Dependence
Theres a significant change in the measured
stiffness when the charality varies
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• Defects can occur in the form of atomic
  vacancies.
• High levels of such defects can lower the tensile
  strength by up to 85.
• Due to the almost one-dimensional structure of
  CNTs, the tensile strength of the tube is
  dependent on the weakest segment of it in a
  similar manner to a chain, where a defect in a
  single link will greatly diminish the strength of
  the entire chain.

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Summary

• Mechanical behavior of defects such as 5-7-7-5
  defect is examined
• A considerable decrease in stiffness at 5-7-7-5
  defect location in different nanotubes is
  observed
• Changes in diameter dont affect the decrease in
  stiffness significantly
• Changes in chirality have different effect on
  stiffness

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7-5-5-7
STM images and corresponding atomic positions for
a C2 dimer absorbed into different nanotubes (a)
and (b) show a (10,10) tube (c) and (d) a (17,0)
tube. All under a 10 strain (tip at 10.5 eV.)
(10,10) NT under 10 strain
Heterojunction