carbon nanotubes - latest seminar topics for engineering ...€¦ · carbon nanotubes materials....
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Allotropes of Carbon
Diamond, graphite, lonsdalerite, C60, C70, carbon, amorphous carbon, carbon nanotube
Carbon Nanotube (CNT)SWNT Single Wall is 1 atom thick
MWNT, Multi-walled is more than 1 atom thick
Typical diameter: 1 nm
Shown is zip-zag CNT
Note hemispherical cap
Chirality1. Pick an atom (A) on a blue
line and draw armchair vector to other blue line.
2. Find the atom on the other edge closest to the armchair intersection. Connect A & B w chiralvector R (red). Wrapping angle is angle between armchair and chiral vectors.
3. Cut tube parallel to axis, The edges correspond to the blue lines
4. a1 lines along zig-zag line. a2 is reflection of a1 about armchair vector.
5. na1 + ma2 = ROrgin: www.pa.msu.edu/cmp/csc/ntproperties/equilibriumstructure.html
DIAMETER CNT
2 23( )CCC ad m mn nπ π
= = + +
1 3tan2
nm n
− ⎡ ⎤Θ = ⎢ ⎥+⎣ ⎦
aCC = 0.142 nm C-C bond length
a = sqrt[3]aCC = 0.249 nm length unit vector
Importance of CNT Chirality
• Effects: conductance, density, lattice structure, and other properties.
• Metallic if n - m is divisible by three. Otherwise, semiconducting.
• CNT diameter: d = (n2 + m2 + nm)1/2 0.0783 nm
Bandgap CNTEgap=2 y0 acc / d
Where:y0 = C-C bonding energy [2.7 ev]
acc = nearest neighbor distance [0.142nm]
d = CNT diameter
CNT Bandgap - Crystalline
0.9( )( )gE eV
d nm=
0
0
2 1 ( 1) 2 cos(3 )
2.53 0.43 2 3
pCC CCa aEgd d
eV p n m i
γ β θ
γ β
⎡ ⎤= + −⎢ ⎥⎣ ⎦= = = − −
Simple formula
More accurate
Bandgap Amorphous CNT
2
23
1
32
(2 10 ),
(1600 )
CCC
C
aEg md
m mass of carbon g
average phonon energy cm
ω
ω
−
−
= < >
=
< > =
CNT Electron Transport• Ballistic
conductor• Resistivity
CNT robes 10-4 Ω-cm
• Max current density > 1013 amp/cm2
Source: Stefan Frank, Science 280, 1744 (1988)