ECE 802-604:
Nanoelectronics
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University
ayresv@msu.edu
Lecture 19, 31 Oct 13
Carbon Nanotubes and Graphene
Carbon nanotube/Graphene physical structure
Carbon bond hybridization is versatile : sp1, sp2, and sp3
sp2: origin of CNT/Graphene mechanical and electronic structures
CNT/Graphene electronic properties
R. Saito, G. Dresselhaus and M.S. Dresselhaus
Physical Properties of Carbon Nanotubes
Imperial College Press, London, 1998.
VM Ayres, ECE802-604, F13
Lecture 19, 31 Oct 13
Carbon Nanotubes and Graphene
Carbon nanotube/Graphene physical structure
SWCNT endcaps
Carbon bond hybridization is versatile : sp1, sp2, and sp3
sp2: origin of mechanical and electronic structures
Carbon nanotube/Graphene electronic ‘structure’
R. Saito, G. Dresselhaus and M.S. Dresselhaus
Physical Properties of Carbon Nanotubes
Imperial College Press, London, 1998.
VM Ayres, ECE802-604, F13
Lec 17: Introduction
Buckyball endcaps
Many different types of wrapping result
in a seamless cylinder.
But
The particular cylinder wrapping
dictates the electronic and mechanical
properties.
(10,10)
(9,0)
(7,4)
VM Ayres, ECE802-604, F13
Endcaps: ½ stable buckyball: C60
From Wikipedia:
C60 is very stable
truncated icosahedron
60 vertices with a carbon atom at each vertex and 32 faces
20 hexagons and 12 pentagons where no pentagons share a vertex
The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm)
http://www.sesres.com/Physica
lProperties.asp
C60 mean ball
diameter 6.83 Å
C60 ball outer
diameter 10.18 Å
C60 ball inner
diameter 3.48 Å
http://www.creativescience.org.uk/c60model.html
VM Ayres, ECE802-604, F13
Show same idea on a SWCNT:
Outer (Van Der Waals)
Mean structure dt
Inner (repulsion)
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Endcaps: ½ stable buckyball: C60
From Wikipedia:
C60 is very stable
truncated icosahedron
60 vertices with a carbon atom at each vertex and 32 faces
20 hexagons and 12 pentagons where no pentagons share a vertex
The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm)
http://www.sesres.com/Physica
lProperties.asp
Example: which
diameter should
you use as an
estimate for
matching a
SWCNT diameter?
C60 mean ball
diameter 6.83 Å
C60 ball outer
diameter 10.18 Å
C60 ball inner
diameter 3.48 Å
http://www.creativescience.org.uk/c60model.html
VM Ayres, ECE802-604, F13
Endcaps: ½ stable buckyball: C60
From Wikipedia:
C60 is very stable
truncated icosahedron
60 vertices with a carbon atom at each vertex and 32 faces
20 hexagons and 12 pentagons where no pentagons share a vertex
The van der Waals diameter of a C60 molecule is about 1.1 nanometers (nm)
http://www.sesres.com/Physica
lProperties.asp
C60 ball outer
diameter 10.18 Å
Example: which
diameter should
you use as an
estimate for
matching a
SWCNT diameter?
C60 ball inner
diameter 3.48 Å
Answer
C60 mean ball
diameter 6.83 Å
http://www.creativescience.org.uk/c60model.html
VM Ayres, ECE802-604, F13
Endcaps: ½ stable buckyball: C70
From Wikipedia:
C70 is also stable
70 vertices with a carbon atom at each vertex
25 hexagons and 12 pentagons
The mean ball diameter is ?
LBL: The structure of C70 molecule.
Red atoms indicate five hexagons
additional to the C60 molecule.
VM Ayres, ECE802-604, F13
C60
Guess:
C36
Guess:
C70
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Endcaps: ½ stable buckyball: C36
http://www.lbl.gov/tt/techs/lbnl1
366.html
The above image depicts the
D6h isomer of the C36
molecule
XZ Ke, et al, Physics Letters A 255 (1999) 294-300
Piskoti C., Yarger J., Zettl A., "A
New Carbon Solid", Letters to
Nature, v 393, 1997.
VM Ayres, ECE802-604, F13
Endcaps: ½ stable buckyball: C20
The smallest possible buckyball is the dodecahedral C20, a shape
consisting of 12 pentagonal faces and no hexagonal faces.
~4 angstroms
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Endcaps: ½ stable buckyball: C20  smallest SWCNT inside MWCNT
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Example Problems:
8. Based on dt ~ 0.4 nm, what ultrasmall SWCNT structures (n.m) are possible?
9. What types of CNT are they?
10. What physical issues would be involved in the self-assembly of these SWCNTs?
HW04: Find Ch, |Ch |, cosq, q, T, |T |, and N for the smallest SWCNT capped
with a C20.
VM Ayres, ECE802-604, F13
VM Ayres, ECE802-604, F13
VM Ayres, ECE802-604, F13
VM Ayres, ECE802-604, F13
Lecture 19, 31 Oct 13
Carbon Nanotubes and Graphene
Carbon nanotube/Graphene physical structure
Carbon bond hybridization is versatile : sp1, sp2, and sp3
sp2: origin of CNT/Graphene mechanical and electronic structures
CNT/Graphene electronic properties
R. Saito, G. Dresselhaus and M.S. Dresselhaus
Physical Properties of Carbon Nanotubes
Imperial College Press, London, 1998.
A. Beiser, Modern Physics, Chapter 13
E. Anderson, Quantum Mechanics, Chapter 7
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diamond
Benzene/graphene/CNTs/buckyballs
polyacetylene
acetylene
alkane
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~
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~
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These are simulations of e- |y|2 with 1s, 2s, and 2p marked:
Anderson, Quantum Mechanics
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The corresponding y are:
3D in
spherical
coordinates
Anderson, Quantum Mechanics
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So all of the directional character must come from 2p orbitals:
~
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Beiser, Modern Physics
Boundary surface diagrams
s-orbitals are all spherical: no
preferred direction
p-orbitals are highly directional
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A carbon hybrid orbital comes from combining a 2s and a 2p:
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sp1 (sp) hybridization:

sp1 hybridization
– Use orthonormality
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Problem without hybridization:
~
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sp1 hybridization:
ONE
~
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sp1 hybridization:
ONE
~
Warning: watch axes, these
directions have real meaning
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sp1 hybridization:
~
Warning: watch axes, these
directions have real meaning
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VM Ayres, ECE802-604, F13
sp1 hybridization:
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sp1 hybridization:
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sp1 hybridization:
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sp1 hybridization:
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sp1 hybridization:
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sp1 hybridization:
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sp1 hybridization:
Can get the 4th equation for 4 unknowns from the spherical character of the
|2s> components:
Therefore:
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sp1 hybridization:
~
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sp1 hybridization:
~
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sp1 hybridization:
~
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sp1 hybridization:
Therefore acetylene is:
~
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