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Lecture 5 ?????????????
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2D-view (???)
???? CC-C
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?-???????
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?-electron
Isotropic conduction
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?????isotropic conduction ????
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3D-view
?-bond
?-wave function
?-bond (sp2)
?-Wave function (electron cloud)
???
????????????, ?????????????
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e-
120?
e-
?-??????3D?????
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???
?-?????, ???????????????, ??????
???
???????, ??????hopping(??tunneling)????
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?? ??? (??3D view)
??????
???
z
????????, ??????? ?????????????, x, y, z
x
y
??????????????
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?????(wave function)?z???????1Å??,
?????? ?z??????. ??x, y???????
z
x
1Å
y
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y
x
E
?????
spiral conduction
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???????
2D isotropic conduction (???????)
3D along x (circumference) and y (tube axial)
axes conduction without external electric
field
3D spiral conduction occurs when external
electric field is applied
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STM images
Standing wave pattern
Wave function image
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1st Brillourin zone
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6 k-points
CB
3D-view
VB
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CB joins with VB at k-points
CB
k-point
EF
VB
Above means that if any sub-bands cross at
k-points would be metallic nature otherwise tube
is a semiconducting property.
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One atom one energy level (sub-band) with
unpaired electron
anti-bonding
Two atoms two energy levels with one bonding and
one anti-bonding
bonding
Three atoms three energy levels with one bonding,
one anti-bonding and one unpaired electron
Each sub-band has own velocity and wave vector If
any of these vectors cross at k-points or
intercept EF the nanotube would be a metallic
nature.
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Metallic nature
Wave vector
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Band-gap
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where a1 and a2 are unit vectors, and n and m are
integers. A nanotube constructed in this way is
called an (n,m) nanotube
Chiral vector Ch na1 ma2
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d (3)1/2?aC-C(m2 mn n2)1/2/?)
Where aC-C 1.42 Å the nearest neighbor
carbon-carbon distance
? tan-1(3)1/2n/(2mn)
Example for zigzag tube when ? 0? with (n,0)
(9,0), d 7.05 Å for armchair
tube, (n,n) (5,5), d 6.83 Å
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(n,m) notation
(n,0) zigzag tubes (n,n) armchair tubes (n,m)
chiral tubes
m
zigzag edge
n
(1,0)
(2,0)
(3,0)
(4,0)
(0,0)
30?
(1,1)
(2,1)
(3,1)
(4,1)
(2,2)
(3,2)
(3,3)
armchair
Semiconducting
metallic
2n m 3q (q integer)
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?????????????????(tube diameter) ???? (chirality)
???????????
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Determination by tube Chirality
? 15?
? 25?
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???????????nanotubes?armchair edge ??metallic
nature (no band gap)
??????? ???k-points? ???????? ???????
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???zigzag nanotube???????metallic
tube,?????semiconductor
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Bent Nanotube- Nano-Schottky barrier
1/3M, 2/3S
M
zigzag
armchair
???S-M(???), ????????, ?????????M??S ????
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zigzag
armchair
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Localized state (local Schottky device)
??????
?????????????
STM TIP
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Science by C.M. Leiber et al
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?????????????---??????, ???????, ??????????????
(?? ??????????? ???????????
Innermost layer
??
Outermost layer
e-
e-
e-
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???????????????, ????????? ???????.
Removal of carbon layers by Electrical breakdown
S
M
Science,292, 706, 2001
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S
M
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Contribution to total conductance from individual
layers
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Carbon nanotubes can carry electrical current up
to 109 A/cm2
So how to remove carbon layers in a vacuum via
electrical breakdown?
Current induced defect formation
Self-heating
Removal of carbon layer on the order of ms
Defect extension
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Summaries
1. Alternative electronic property of MWNTs,
M-S-M-S
2. Removal of each layer reduces current of 19 ?A.
3. A MWNT conducts electrical current only at
outer-layer where they contact with
electrodes. Nevertheless, when MWNTs are
modulated at higher bias voltage the
inner-layers also contribute to nanotube
conductance via inter-layer barriers
(thermally activated conduction).
4. Inner layers only contribute limitedly to
nanotube conductance, because they have to
overcome interlayer barriers of 0.34 nm spacing.
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??????????
1. J. Vac.Sci.Tech. B, 13, 327, 1995, by Rivera
et al (STM)
2. Syn.Metals. 70, 1393, 1995, by Langer et al
(STM lithographic tech)
3. Nature, 382, 54, 1996, by Ebbesen et al (four
terminal lithographic tech)
4. Science, 272, 523, 1996, by Dai et al (four
terminal lithographic tech)
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Two terminal method
Four terminal method
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Summaries of nanotube resistivity measurements
1. Averaged resistivity of nanotube tube is 10-4
10-5 ?m.(arc made)
2. Resistivity of metallic nanotubes is 10-6 ?m.
(arc made)
3. Resistivity of defective carbon nanotubes is
10-2 10-3 ?m. (pyrolysis made)
4. Band gap of semiconducting nanotubes is 0.1
2 eV, and is thermally activated type
(negative temp coefficient of resistivity), also
is gate voltage dependent conductance.
5. Metallic nanotubes are gate voltage
independent and positive temp coefficient of
resistivity.
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Negative temp coefficient of resistivity
R
Positive temp coefficient of resistivity
Temp (k)
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VG dependent
VG dependent
dI/dV(G)
VG independent
VG
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Resistivity of CNT films
By Baumgartner et al, PRB, 55, 6704, 1997
?
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?ll
?
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e-hopping
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Resistivity of CNT-polymer composites
polymer
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electrodes

• Low content of CNT in polymer
• a. Primary capacitive phase
• b. High resistance
• c. No conduction paths
• between electrodes

3. High CNT load a. Low capacitance b.
Low resistance c. Conduction path formation
2. CNT load increases a. capacitance
decreases b. Resistance decrease c.
conduction paths begins to establish
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Adv.Mater, 10, 1091, 1998
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Adv.Mater, 11, 937, 1999
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Technical challenges for CNTs in polymer
1. Dispersion of CNTs in polymers
2. Interfacial binding between CNTs and polymers
CNT enriched regions
CNT deficit regions
Uneven distribution of CNTs
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Dispersion of CNTs in polymers
1. Lengthy mechanical blending, (ultra-sonicate,
magnetic stirring)
2. Surfactant assistant (lowering interfacial
strength, so CNTs move easily in polymer
solution)
surfactant
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CNT deficit regions
CNT enriched region
Chem.Mater, 12, 1049, 2000
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Interfacial binding between CNTs and polymers
Carbon, 40, 1605, 2002
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Negative reinforcement
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• Untreated CNTs polymer
• A. Weak bonding between nanotube defects
  and polymer functional groups

CH3-CH2-CH2-OH
B. Van der waals interaction (polymer chain
wrapping around CNT)
CPL, 342, 265, 2001
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APL, 73, 3842, 1998
APL,74, 3317, 1999
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??
Polymer coating
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Adv.Mater, 10, 1091, 1998
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APL, 76, 2868, 2000
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APL, 79, 4225, 2001
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2. Treated CNTs polymers
a. Functionalized CNTs (on tube surfaces)
PVA, PVC
-OH
???
CO
???
Polymers containing amino-acid
CH3
O
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b. Surfactants
polymer
???
???
CNT