Hauptseminar: Kohlenstoffbasierte
Materialien WS 13/14
Carbon Nanotubes
Simon Seyfferle
25 February 2014
1 Motivation
Since their discovery carbon nanotubes have gathered a lot of fame, not only in
scientific circles but also beyond that in popular science. The promise of carbon
nanotubes is to apply them in a widespread area ranging from for example
nano-electronics to reinforcements of macroscopic objects by utilizing their
unique and fascinating properties. The actual realization of carbon nanotube
incorporating products has however lagged behind the ambitious expectation
and plans. In order to understand what makes these nanotubes so special and
what one can really expect from them one should take a closer look at their
synthesis, structure and properties.
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2 Introduction
2.1 General Remarks
A carbon nanotube (CNT) is probably best described by imagining a sheet of
graphene being rolled up. If the honeycomb lattice of the graphene is seamlessly joined along a cutting line a cylindrical object is being formed (see Fig.
1). The diameters of carbon range from 1 to 50 nm and the length can reach
Figure 1: a) Joining the two opposite sides of a graphene sheet seamlessly forms a
carbon nanotube. b) There are two types of carbon nanotubes: singlewalled carbon nanotubes (SWNT) and multi-walled carbon nanotubes
(MWNT).
a few millimeters. A general classification of the CNTs can be established
by dividing them in Single-Walled Carbon Nanotubes (SWNT) and SingleWalled Carbon Nanotubes (SWNT). As the names already suggest a SWNT
is made of just one rolled up sheet of grapheneee, while a MWNT is made
of several grapheneee sheet wrapped around each other and interacting via
van-der-Waals-forces.
2.2 Historical Notes
The discovery of CNTs is largely credited to the japanese scientist Sumio Iijima
who discovered tube-like nanostructures on graphite electrodes after an arcdischarge in 1991. This was rather a discovery by chance since Iijima actually
wanted to investigate fullerenes. His original discovery included only MWNTs.
Two years later then he discovered SWNTs as well.
3 Synthesis
There are three reliable methods to produce CNTs that shall be quickly introduced.
3.1 Arc-Discharge
This method incorporates the evaporation of carbon in an inert gas (such as
Helium). The CNTs grow on carbon electrodes. A voltage is applied to the
carbon electrodes and if the current is large enough a plasma is ignited and
an arc-discharge occurs. CNTs can then be found attache to the electrodes.
The growth conditions can be controlled via the gas pressure and the current.
There are still residual graphitic particles left among the CNTs, subsequently
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purification processes are necessary. In order to grow SWNTs a catalyst in
form of a transition metal (commonly iron or nickel) inserted into the carbon electrodes is necessary. SWNTs do never grow without a catalyst (which
accounts for all the methods of synthesis).
3.2 Laser Ablation
This method uses intense laser pulses shot at a carbon target in a tube furnace
at about 1200◦ C. A gas flow through the tube carries the synthesized CNTs
away. The laser ablation method produces CNTs mostly in bundles and ropes,
so here purification processes are necessary, too. The problems with laser
ablation and arc discharge are that the CNTs are produced in bundels which
makes it difficult to investigate and manipulate single CNTs.
3.3 Chemical Vapor Deposition (CVD)
CVD allows to grow CNTs in a more controlled way as wells as it is producing
singled nanotubes. The approach of CVD is to grow nanotubes at nanoparticles
anchored on a substrate. The substrate is put into a tube furnace and heated
under gas flow to 700◦ C to 1100◦ C. CNTs grow when a hydrocarbon gas (such
as methane) is flowed through the tube. The hydrocarbon molecules dissociate
catalyzed by the transtion metal in the nanoparticles and subsequently the
carbon atoms saturate and attache to the nanoparticles and form nanotubes.
CVD displays the crucial advantages of high quality CNTs, great lengths and
allows also to grow CNTs from defined positions on the substrate.
4 Structure
Just like grapheneee CNTs are made of hexagonal carbon atom rings arranged
in a lattice with a two-atomic basis. Each atom has three nearest neighbours
and the interatomic distance is 1,421Å. The unit cell of the lattice is spanned
by two vectors ~a1 and ~a2 (see Fig. 2). If the graphene sheet is rolled up one
Figure 2: a) Structure of a graphene sheet. See text for explanations. b) There are
three different types of nanotubes depending on their chirality: armchair,
zigzag and chiral.
obtaines three different kinds of chiralities for the nanotubes. This chirality
can be described by a circumferential vector
Ch = n~a1 + m~a2
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with integers n and m. With these two integers the chirality can be easily
expressed. If both integers have the same value (n, n) a so-called armchairnanotube is formed. If the second integer is zero (n, 0) a zigzag structure is
build. And if both integers have different values the nanotubes have random
chirality (see Fig. 2). Special importance have the diameter and the chirality
because they define the properties of the CNT. The diameter is given by
d=
|Ch |
π
and the chiral angle θ (seen in Fig. 2) is given by
n + m/2
θ = arccos √
n2 + nm + m2
If θ = 0◦ a zigzag-nanotube is formed. In case of θ = 30◦ a armchair-nanotube
is present.
5 Properties
5.1 Thermal Properties
CNTs display one of the highest measured thermal conductivity of any known
material. SWNTs have a room temperature thermal conductivity of 3500 Wm−1 K−1
while the value for copper in comparison is only 385 Wm−1 K−1 . Generally
phonons and electrons contribute to the thermal conductivity. To determine
κ
the dominating contributor one applies the Wiedemann-Franz-law σT
≈ L0 =
−8 2
2
2, 45 · 10 V /K which gives the ratio of electrical and thermal conductivity
of a sample. Experiments yielded values of L = 2−7·10−6 V2 /K2 . That means
that the thermal conductivity of SWNTs is dominated by phonons since the
value of L is higher than L0 . Measurements of the thermal conductivity κ show
an increase of κ with growing temperature. However at higher temperatures a
decrease of κ is found. In this temperature range Umklapp-scattering sets in
which hinders the thermal conductivity effectively.
5.2 Mechanical Properties
The most striking mechanical property is that CNTs are the strongest known
fibres to date. Their Youngs modulus is predicted to be 1 TPa (the value for
steel is only 200 GPa). An interesting phenomenon can be observed if CNTs
are bent. If a CNT is grown over a trench in a silicon substrate and pushed
downwards with an AFM tip a decrease of the conductance is measured (see
Fig. 3). If the tip retracts the full original conductance is restored indicating
a full reversibility of the bending. Pushing the tip onto the CNT results in
a deformation of the bonds in the area where the force is applied. sp2 -bonds
change into sp3 -bonds which decreases the local π-electron density and thus
the electrical conductance.
5.3 Electronic Properties
Depending on the geometric structure of the nanotubes they display different
eletronic properties. Generally CNTs are either metallic or semiconducting.
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Figure 3: a) Measurement setup: An Afm tip pushes a CNT grow over a trench
downward while the conductance is monitored. b) Measurement of conductance versus time. Each push of the AFM tip decreases the conductance.
Armchair nanotubes are found to be always metallic while zigzag and chiral
nanotubes show semiconducting behavior with a tiny energy gap if n − m = 3j
(j an integer) or a large gap in all other cases. The bandstructure of the nanotubes is based on the bandstructure of graphene. The cylindrical geometry of
the CNTs however imposes additional boundary conditions on the wave vector perpendicular to the tubes axis. This is a consequence of the confinement
of the two-dimensional graphene bandstructure into one-dimension by rolling
it up. This is called the zone-folding approximation. While ~kk is continuous
along the tubes axis, ~k⊥ is quantized. The valence band and the conduction
band touch at the so-called K-point at the corners of the Brillouin zone. In
the vicinity of the K-point the bandstructure can be linearly approximated by
two cones. If the allowed states of ~k⊥ cross the K-point a metallic nanotube is
formed and no bandgap is present (see Fig. 4 a)). If the allowed states of ~k⊥ do
not cross the K-point a bandgap opens up and the nanotube is semiconducting
(see Fig. 4 b)).
Figure 4: a) Formation of a metallic nanotube. ~k⊥ crosses the K-point. b) Formation
of a semiconducting nanotube. ~k⊥ does not cross the K-point.
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6 Applications
Carbon nanotubes surely display a variety of impressive properties but how can
one make use of them? Applications in fields such as electron field emission,
sensors, probing tips, lithium and hydrogen storage and mechanical reinforcements to name only a few are imaginable. Applications that have already been
realized are for example a flat panel display which is operated by electron field
emission. At a sufficient electric field electrons near the Fermi level are able
to escape into the vaccuum forming a current. In such a flat panel display
carbon nanotube due to their high electrical conductance function as excellent
emitters. Another application that has already been realized is using CNTs as
nanoprobes like an AFM tip. Nanotubes can be attached to an AFM tip and
serve as valuable tools in high resolution imaging of nanoscale surfaces.
Future plans of scientist include for example the building of complete computer circuits based on nanotubes and applying CNTs in cancer therapy by
injecting nanotubes around cancerous cells and heating them up by irradiating microwaves. This would destroy the cancer cell without damaging healthy
tissue.
7 Discussion & Outlook
Carbon nanotubes clearly promise possibilities for applications in never before
seen ways. The predictions however made around the hype after their discovery
have lead to too high expectations which could not be fulfilled in time and the
result is disappointment and disillusionment. But there is usually a time lag
of many years or decades between the discovery of a concept and real products
on the market.
Some remaining challenges of carbon nanotube research lie in understanding
the growth mechanism and develope means to manipulate single CNTs and
produce them in quantities suffiecient for industrial use.
8 Literature
• S. Iijima. Helical microtubules of graphitic carbon. Nature, 354, p. 5658, (1991).
• M. S. Dresselhaus, G. Dresselhaus, P. Avouris. Carbon Nanotubes Synthesis, Structure, Properties, and Applications. Springer, Topics in applied physics, Volume 80.
• K. Goss. Interactions between parallel carbon nanotube quantum dots.
Ph.D. thesis, Forschungszentrum Jülich, (2011).
• J. Hone, M. Whitney, C. Piskoti, A. Zettl. Thermal conductivity of
single-walled carbon nanotubes. PHYSICAL REVIEW B, 59, 2514, (1999).
• M. S. Dresselhaus, G. Dresselhaus, J. C. Charlier, E. Hernandez. Electronic, thermal and mechanical properties of carbon nanotubes. The
Royal Society, 362, 2065, (2004).
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