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3. Carbon nanostructures
[Poole-Owens 5, Wolf 6, own knowledge, Springer handbook ch. 3]
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3.1. Background: carbon bonding
To understand the basic C nanostructures we have to recall basics of C bonding, well known from
structure of matter and chemistry courses.
- C has 4 outer electrons, one s and three p electrons
- The energetically preferred arrangements of these electrons is to form so called sp-hybridized
electron wavefunctions, which can then form covalent chemical bonds with other atoms.
- sp hybridization: 2 bonds, bond angle 180o. Example: Acetylene C2H2
- sp2 hybridization: 3 bonds in plane, bond angle 120o. Example: Ethylene C2H4
- sp3 hybridization: 4 bonds in 3D, bond angle cos−1(−1/3) ≈ 109.47o. Example: Methane
CH4.
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- If you draw out the 4 bonds to equal length, then draw planes through the ends, you will get an
ideal tetrahedron pyramid shape.
The carbon bonds are very strong, typical energy/bond is of the order of 4 eV if they are to other
carbon atoms.
3.1.1. Bulk phases
- What happens if we form a solid out of these bonding types?
- sp: linear chain of C, possible but can not easily form a solid (would tend to suck in H from the
surrounding)
- sp2: since the bonds are all in same plane, it is natural to assume these all form a single 2D carbon
plane. With an angle of 120o between bonds this forms naturally a honeycomb (chickenwire/open
hexagon) network:
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- This is a called a graphene sheet.
- If you stack many of these on top of each other, you get graphite, which is the ground state
structure of carbon.
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The bonding structure of graphite is highly unusual, and key to understanding the remaining
properties of graphite. The sp2 bonds in the graphene planes are very strong, and carry almost all
of the cohesion of the material. The interatomic separation within the plane is about 1.4 Å.
The different graphene planes on the other hand are bonded only by a weak “van der Waals”
interaction which is only about 1/100 as strong as the in-plane covalent bonds. Moreover, the
separation between atoms in the planes is about 3.4 Å, i.e. more than twice that of the in-plane
atom separation.
This highly peculiar bonding configuration leads to numerous interesting properties of graphite, e.g:
- A single graphene sheet is very strong, but since the interplane interaction is weak, the sliding
friction is very low
- The sheets are electrically conductive in the in-plane direction: electrons can move easily in the
planar direction
- sp3:
The tetrahedral sp3 bonding arrangement can be arranged into a 3D solid in the diamond
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crystal structure, which looks like follows (both figures are the same structure, just from different
viewpoints):
- The cohesive energy of diamond is almost as large as that of graphite, for both the cohesive energy
per atom is about 7.4 eV/atom. This is among the highest of any element.
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Because the sp2 and sp3 solids have almost the same energy, it is possible to form amorphous
networks of these bonds which lead to amorphous carbon structures with almost the same cohesion
as the crystalline forms
Here is a sample structure (red atoms sp3 bonded, blue atoms sp2):
Introduction to Nanoscience, 2005
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- Approaches diamond if strength of H-free and has a high fraction of sp3 bonds.
3.1.2. Unusual bonding types
The ideal bonding types are by no means the only possible ones. From molecular structures it is
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well known that it is possible to form quite stable C bonding types which do no have exactly the
bonding angles described above.
- 5-fold member rings of C (e.g. in molecules with N)
- cubane: C8H8:
- carbon dodecahedron C20H20:
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3.2. Fullerenes
3.2.1. History and structure
[http://www.fkf.mpg.de/andersen/fullerene/intro.html and Poole-Owens]
Even though the ball-like C20H20 was already found in 1983, it still came as a big surprise when
Harold Kroto, James Heath, Sean O’Brien, Robert Curl, and Richard Smalley in 1985 (Nature 318,
162) found the C60 molecule, which consists of pure carbon and is almost perfectly spherical.
Soon after hearing it was discussed in the British House of Lords as follows. The answers of Lord
Reay are actually quite accurate, and do answer some of the basic questions on fullerenes.
Hearing in the House of Lords with the Parliamentary Under-Secretary of State, Department of Trade and Industry,
Lord Reay (Excerpt)
Baroness Seear: My Lords, forgive my ignorance, but can the noble Lord say whether this thing is animal, vegetable
or mineral?
Lord Reay: My Lords, I am glad the noble Baroness asked that question. I can say that Buckminsterfullerene is a
molecule composed of 60 carbon atoms known to chemists as C60. Those atoms form a closed cage made up of 12
pentagons and 20 hexagons that fit together like the surface of a football.
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Lord Renton: My Lords, is it the shape of a rugger football or a soccer football?
Lord Reay: My Lords, I believe it is the shape of a soccer football. Professor Kroto, whose group played a significant
part in the development of Buckminsterfullerenes, described it as bearing the same relationship to a football as a
football does to the earth. In other words, it is an extremely small molecule.
Lord Campbell of Alloway: My Lords, what does it do?
Lord Reay: My Lords, it is thought that it may have several possible uses; for batteries, as a lubricant or as a
semi-conductor. All that is speculation. It may turn out to have no uses at all.
Lord Russell: My Lords, can one say that it does nothing in particular and does it very well?
Lord Reay: That may well be the case.
Lord Callaghan of Cardiff: My Lords, where does the name come from?
Lord Reay: My Lords, it is named after the American engineer and architect, Buckminster Fuller, who developed the
geodesic dome, which bears a close resemblance to the structure of the molecule.
I.e. it really has the shape of a traditional football, containing 5- and 6-membered C rings.
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This molecule is exceptionally stable and strong due to its high symmetry, and the fact that the C
bonds are still pretty close to the ideal sp2 bonding arrangement.
- Initially the names “bucky ball” and “buckminsterfullerene” were used a lot, but nowadays most
people use just “fullerene”.
- As in graphene, the bonding is primarily in strong covalent bonds
- Hence there is no H-termination of the C’s at the surface, which makes it differ significantly from
the previously known C20H20.
But C60 is by no means the only fullerene, in fact there is a whole spectrum of cage-like C molecules:
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- Not all of these are spherical, and the smallest ones may not even be closed.
3.2.2. Manufacturing fullerenes
The initial manufacturing of fullerenes was pretty much an accident. The authors were interested of
peculiar features of absorption in interstellar dust, and used high-power laser to produce hot vapors
of carbon to mimic the conditions in interstellar space. In the course of this research they found the
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fullerene (they actually failed to answer the question they first set out to study, but since they got
the Nobel prize for the fullerene this probably does not bother them too much).
- Later on people realized that fullerenes are regularly present in amounts of a few % in ordinary
carbon soot - no-one had just thought of looking for it there...
Nowadays fullerenes can be made in a multitude of ways, and also mass-produced very cheaply.
Here are the key points from a recipe on how to make them from Sussex university
[http://www.sussex.ac.uk/Users/kroto/workshop.html].
- Essentially a hot carbon vapor/plasma is formed where the clusters condense in a He atmosphere.
Akin to gas phase condensation of nanoparticles
Describe growth steps: C20 precursor, bowl-shaped...
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• Pump down the system and introduce Helium gas into the
chamber. Repeat (purge). Finally fill the bell-jar with about 100
Torr of Helium.
• Connect up the welding kit power supply. Turn the on / off
switch on the supply to the on position for 10 to 15 seconds.
Afterwards there should be plenty of black soot like material
produced inside the bell-jar.
• After a 5-10 min cool down period fill the bell-jar to atmospheric
pressure. Take the bell-jar off and scrape the glass surfaces clean,
collect all the material. Believe it or not, 10 % of the soot should
be made up of C60.
• Place as much of the collected soots as you can into a small
flask. Add 20-30 ml of toluene and stopper the flask. Shake
gently. [The colour changes]
• You have just extracted the fullerenes from the soot. The
coloured solution is due to a mixture of C60, C70 and larger
fullerene cage molecules.
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3.2.3. Strength of single fullerene
The elastic strength of a single fullerene is enormous due to the strength of the C-C bonds
- An experimental bulk modulus of 1 TPa has been reported for fullerenes [J Expt. and Theor.
Physics 87 (1998) p.741-6]
- This can be compered with the bulk modulus of diamond, 442 GPa.
- But strength of a single fullerence does not mean it is possible to manufacture a solid of them
with the same strength!
3.2.4. Fullerene solids
When fullerenes are allowed to condense, they do form a solid.
- Since they are spherical, they form a solid corresponding to close
packing of hard spheres: a face-centered cubic (FCC) lattice.
- Same structure as e.g. noble metals, but now spheres are
fullerenes instead of single atoms.
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- The bonding between the fullerenes is now, however, essentially the same weak van der Waals
bonding as that between sheets of graphene.
- Hence the fullerene crystal is actually quite weak. Its bulk modulus is only about 14 GPa [PRL
o
68 (1992) 2046] and melting/evaporation temperature some 300 C [?]. These are very low values
compared to those of graphite and diamond.
- But at the “melting” temperature the fullerenes themselves stay intact, it is only the crystal of
them which “melts”.
3.2.4.1. Superconducting C60 films
One of the interesting aspects of C60 crystals is that they can be made superconducting by inserting
alkali metals into them.
26% is free space
- Impurity atoms fit well into the empty space between the fullerenes. They are intercalated in
there.
- Prototypical example: K3C60
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Looks like BCC but note elongation, probably 4 FCC neighbours are left undrawn...
- The K atoms make the crystal electrically conducting
- K act as donors by giving electrons to the C60: K+ and C3−
60
- Moreover, the crystal becomes superconducting below about 18.4 K:
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- Other kinds of C60 doping has produced superconducting C materials with even
higher transition temperatures: Rubidium-thallium doped C60 has been observed to have
Tc = 45 K [Z. Iqbal et al., Science, 8 November 1991; E. Dagatto, Science 239, 2410 (2001)].
(- There was even a report of 117 K by Schön et al, which is now however discredited)
- This is a lot more than any traditional metal superconductor, and comparable to those of the
high-Tc superconducting oxides.
Mechanism a mystery: if you want the Nobel prize just solve it...
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3.2.5. Fullerene chemistry
- Despite its stability, it is possible to form molecules of fullerenes
- The discovery of C60 has stimulated a lot of activity in “Fullerene” chemistry.
- By 1997 about 9000 Fullerene compounds were known.
3.2.6. Endohedral fullerenes
[http://www.organik.uni-erlangen.de/hirsch/endo chem.html]
- Inside of fullerenes is empty
- Natural idea to insert atoms or molecules there
- Such a material is called an endohedral fullerene
- Enables interesting basic science studies of electronic structure of the enclosed molecules
- May have optoelectronic and medical applications
- Example: N endohedral to C60:
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