Effect of Defects in the Mechanical
Properties of Carbon Nanotubes
PHY 472 / Lehigh University
Instructor: Prof. Slava V. Rotkin
By: Paul A. Belony, Jr.
Common Defects observed in CNT’s

Main types of defects

3 main groups
• Point defects
• Topological defects
• Hybridization defects

Subgroups









Vacancies (PD)
Metastable atoms
Pentagons (TD)
Heptagons (TD)
Stone–Wales (SW or 5–7–7–5)
(TD)
Fictionalization (HD) (sp3 bonds)
Discontinuities of walls
Distortion in the packing
configuration of CNT bundles
Etc…
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
Main Mechanical Properties
affected by Defects


Stiffness
Ultimate Strength
Ultimate Strain
Flexibility
Buckling and robustness under high pressure
•
CNT’s are among the most robust materials



•
•
High Elastic Modulus (order of 1 TPa)
High Strength (range up to 100’s of GPa)
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
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 Ǻ
 the Young modulus can be calculated as
the initial slope of the force–displacement
curve;
 The ultimate strength is calculated at the
maximum force point, σU = (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
εU = (ΔLU)/L, where L is the original tube
length.
SWNTs with more defects are likely to
break at smaller strains and have less
strength as well.
Force–displacement curves of nanotubes with
various average numbers of defects.
Types of stresses

virial stress
 atomic (BDT) stress
 Lutsko stress
 Yip stress
i, j  indices in Cartesian coordinate system
Ωtot
 total volume
Lα,β  fraction of the length of αβ bond inside the averaging volume
Α, β  atomic indices
۩ 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 crosssectional area S = πdh (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
Elastic modulus before defect
Bulk Stress (E=1.002
-Defect free (9,0) nanotube with
periodic boundary conditions
TPa)
Lutsko Stress (E= 0.997 TPa)
BDT Stress (E= 1.002 TPa)
60
Stress (GPa)
50
-Strains applied using conjugate
gradients energy minimization
40
- All stress and strain measures
yield a Young’s modulus value of
1.002TPa
30
20
10
0
0.01
0.02
0.03
0.04
Strain
0.05
0.06
0.07
5-7-7-5 Defect on CNTs
60

8 % Applied Strain
7 % Applied Strain
50
5 % Applied Strain
Stress (Gpa)
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
40
3 % Applied Strain
30
20
1 % Applied Strain
0 % Applied Strain
10
-20
-10
0
z - position
10
20
N. Chandra, S. Namilae and C. Shet
Contour plots of the longitudinal strain ε33 strain and stress σ33 near the defected region drawn at different applied strain levels.
a)
c)
e)
g)
Strain contours at an applied strain of 1%.
Strain contours at an applied strain of 3%.
Strain contours at an applied strain of 5%.
Strain contours at an applied strain of 8%.
b) Stress contours at an applied strain of 1%.
d) Stress contours at an applied strain of 3%.
f) Stress contours at an applied strain of 5%.
h) Stress contours at an applied strain of 8%.
60
(b)
(a)
50
Stress (GPa)
40
(c)
30
(9,0) CNT no defect
20
Type I defect
10
0
Type II defect
0
0.025
0.05
0.075
0.1
Strain
NT possess residual forces at zero strain (even when
defect free)
At about 1 TPa there’s a reduction of stiffness away from
the defect-free straight line
Measuring Mechanical Properties
L. Forro etal.

Use of Atomic Force
Microscopy (AFM)
• For individual CNTs
A)
3D representation of the adhesion of a SWNT to an alumina
ultra-filtration (tube is clamped allowing mechanical testing)
B)
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
Fracture process of a (6, 6) SWNT with three SW defects:
(a) crack initiation and propagation (A–I);
(b) (b) corresponding force time history.
Diameter dependence
The slope of the graphs seem to
be very close to each other for
different curvature of the NTs
50
40
Stress (GPa)
(9,0) at defect
30
(10,0) at defect
(11,0) at defect
(13,0) at defect
(15,0) at defect
20
(9,0) no defect
(10,0) no defect
(11,0) no defect
10
(13,0) no defect
(15,0) no defect
0
0
0.01
0.02
0.03
Strains
0.04
0.05
0.06
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
Charality Dependence
There’s a significant change
in the measured stiffness
when the charality varies
45
40
Stress (GPa)
35
30
25
20
(5,5) no defect
(5,5) at defect
(6,4) no defect
(6,4) at defect
(7,3) no defect
(7,3) at defect
(9,0) no defect
(9,0) at defect
15
10
5
0
0
0.01
0.02
0.03
Strain
0.04
0.05

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.
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 don’t affect the
decrease in stiffness significantly
 Changes in chirality have different
effect on stiffness
7-5-5-7
(10,10) NT under 10% strain
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.)
Heterojunction