Transcript Lecture 1 - 19 Feb 2008 - Scott Thompson

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What is a Carbon Nanotube?
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Start with Carbon
Graphite
C60
Single Wall Carbon Nanotubes
Multi Wall Carbon Nanotubes
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Start with Carbon
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Carbon contains six electrons
(1s)2, 2s, 2px,2py, 2pz
1s quantum number N=1 (2 electrons)
N=2 , four electrons
s orbital spherically symmetric about nucleous
p directed charge distribution
s and p form chemical bond
Y = s + lp
Solid carbon two main structures
–
–
–
–
Diamond sp3 109 degree bonds
Graphitic sheet sp2 120 degree bonds. Each bond in same plane
Graphite s, px, py
Sheets held together by weaker van der Waals Forces
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Sp3 and sp2 Bonds
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Discovery of C60
• Soccer ball-like molecule containing 60 carbon atoms
• Motivated by understanding light transmission through
interstellar dust
• Optical extinction: absorption and scattering of light from
interstellar dust
• C60 envisioned by theoretical chemist
• High powered pulsed laser simulate conditions of hot
carbon
• Prof. Richard Smalley (Rice) observed mass number 720
mass spectrometer (carbon mass #12)
• Smalley won Nobel prize
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C60
Ref: Intro to Nanotechnology
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Closed Network From Other Atoms
Ref: Intro to Nanotechnology
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Extension of C60, C70, C80
End closed
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Formation of an Armchair Nanotube
2D Graphene Sheet
armchair (n,n)
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Chiral vector is bent
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Unit Cell of 2D Graphene
(a) The unit cell and (b) Brillouin zone of two-dimensional graphite are shown
as the dotted rhombus and shaded hexagon, respectively. ai, and bi, (i = 1, 2) are
unit vectors and reciprocal lattice vectors, respectively. Energy dispersion relations
are obtained along the perimeter of the dotted triangle connecting the high
symmetry points, , K and M.
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“Roll” Carbon Nanotube from Graphite
L  Ch  Ch  Ch  a n 2  m 2  nm
DL

The unrolled honeycomb lattice of a nanotube, showing the unit vectors a1
and a2 for the graphene sheet. When we connect sites O and A, and B and B’,
a nanotube can be constructed. OA and OB define the chiral vector Ch and the
translational vector T of the nanotube, respectively. The rectangle OAB’B
defines the unit cell for the nanotube. The figure corresponds to Ch = (4, 2)
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Constructing Nanotubes from a Graphene Sheet
Chiral
angle
0,0
1,0
2,0
1,1
3,0
1,1
4,0
3,1
2,2
Zigzag
5,0
4,1
3,2
7,0
6,0
5,1
4,2
3,3
6,1
5,2
5,3
4,4
a2
a1
7,1
6,2
4,3
Ar
mc
8,0
ir
8,1
7,2
6,3
5,4
ha
9,0
9,1
8,2
7,3
6,4
5,5
10,0
10,1
9,2
8,3
7,4
6,5
12,0
11,1
10,2
9,3
8,4
7,5
6,6
11,0
10,3
8,5
7,6
11,3
9,6
8,7
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11,5
10,6
9,7
8,8
12,3
11,4
10,5
9,5
13,1
12,2
10,4
8,6
7,7
12,1
11,2
9,4
13,0
10,7
9,8
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3D Examples of 3 Types of Nanotubes
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Some More Properties of Nanotubes
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1-50nm in diameter
10 - 100 micrometer long
End capped with half fullerene molecule
Single and multi-wall nanotubes
Chirality refers to how the tubes are rolled
One-third metallic, two-thirds semiconducting
Energy gap: 1/(diameter of tube)
– Diameter of tube increases, bandgap decreases
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Metallic and Semiconducting CNT
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Examples of Band Structures
One-dimensional energy dispersion relations for (a) armchair (5, 5), (b)
zigzag (9, 0), and (c) zigzag (10, 0) carbon nanotubes.
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Bandgap of Semiconductor Tube
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Observed Nanotube Species
zigzag
1,0
2,0
4,0
2,1
5,0
3,1
7,0
5,1
3,2
6,1
4,2
arm
ch
air
10,0
8,1
6,2
4,3
8,0
5,3
9,1
9,1
11,0
11,1 12,1
12,1
11,1
9,2 10,2
10,2
9,2
7,2
7,3
5,4 6,4
6,4
5,4
8,3
8,3
1.0 nm diameter
13,3
13,3
17,1 1
15,2 16,2
14,3
16,3 1
14,4 15,4
12,5 13,5
13,5
12,5
10,6 11,6
11,6
10,6
8,7 9,7
9,7
8,7
16,0 17,0
14,1 15,1
15,1
11,4 12,4
12,4
11,4
9,5 10,5
10,5
9,5
7,6 8,6
8,6
7,6
14,0
12,2 13,2
13,2
12,2
10,3 11,3
11,3
10,3
8,4 9,4
9,4
8,4
6,5 7,5
7,5
6,5
13,0
15,5
13,6 14,6
11,7 12,7
9,8 10,8
10,8
9,8
10,9
10,9
12,8 13,8
11,9
11,10 12,10
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