3.3. nanotubesknordlun/nanotiede/nanosc3bnc.pdf · - they are nested inside each other with an...

3.3. Nanotubes

[Own knowledge, Dresselhaus, Dresselhaus and Avouris book, Poole-Owens, Enc. Nanoscience ch. 3]

3.3.1. History and structure

3.3.1.1. History

The history of carbon nanotubes is interesting in that they were found before they were really found.

- Standard reference: Iijima, Nature 354 (1991) 56.

- However, several people had actually observed them before, and one of them had actually described

it in some detail with clear figures in a regular publication: Oberline et al, J. Cryst. Mater. 32

(1976) 335.

- But in the 1970’s nobody much cared for nanoscale stuff, and the work passed with

little attention. The time was just not ripe

- When Iijima refound the tubes, nobody remembered Endos results

- Iijima also understood to make a lot of noise of his result

Introduction to Nanoscience, 2005 JJ J � I II × 1

Now Endo is also making noise, but too late for him...

3.3.1.2. Structure of single-walled tubes

- Nanotubes typically look something like this in a TEM image:

A single-walled nanotube (SWNT) is formed by taking a sheet of graphene of some finite width

w, and wrapping it up into a cylinder of fixed radius r and arbitrary length.

- The circumference of the tube will be≈ w+1.4 A, where the 1.4 A comes from the carbon-carbon

bond length.

- The wrapping up can be done in many ways.

- To describe the tube structure, a special notation has been introduced. Consider the following

figure:


- Basic idea: select a rectangle in sheet which joins four crystallographically equivalent positions in

the sheet. In this figure it is the rectangle OABB’.

- Because it is a rectangle, the vector OA is enough to uniquely determine the way in which the

sheet is wrapped up.


- The chiral index (n,m) of the tube is the given by which combination of the graphite unit vectors

(a1, a2) is needed to form the vector OA:

Ch = OA = na1 + ma2 (1)

The angle between the unit vectors is exactly 60◦.

- The length of a single bond is in the range

1.41A| {z }graphite

≤ aC−C ≤ 1.44A| {z }C60

(2)

and all bonds in the same tube may not be of exactly the same length This defines fully the length

of everything else in nanotubes.

- The unit cell size a of graphene is more than the nearest-neighbour distance! It is

a =√

3aC−C = 2.49 A (3)

- The particular Ch shown in the figure is (n, m) = (4, 2).

- The unit cell in the tube length direction is given by OB.


- Tells how far you have to move in the tube length direction to get back to a position

crystallographically equivalent with the original one.

In this way the following nanotube is generated:

- Because of symmetry, the non-equivalent indices are chosen such that

n ≥ m (4)

which of course is just an arbitrary choise.

- The chiral angle θ is defined as the angle between the direction a1 and the vector Ch.

- According to the wrapping up 3 types of nanotubes can be defined:

a) armchair tubes: n = m, θ = 30◦

b) zigzag tubes: m = 0, θ = 0◦

c) chiral tubes: all the others, 0◦ < θ < 30◦.


Types a) and b) are considered achiral.

Here is examples of the three types. a) armchair (5,5), b) zigzag (9,0), c) chiral (10,5):

The names “armchair” and “zigzag” are a bit silly, but can be understood if you look from the tube


with the length direction upwards. Then with considerable imagination you can see armchairs in

the tube. Here is a figure to help you out:

- zigzag simply comes from having in the same view a zigzag pattern of bonds across the tube, with

the pattern overall direction perpendicular to the tube length direction

- The smallest tubes ever manufactured are something like (3, m); smaller tubes than this are not

stable.

- Typical tubes are in the range (5, m) to maybe (20, m).


- The widest SW tube I have heard of is actually made in Finland [Esko Kauppinen, VTT/TKK]

with a diameter of some 7 nm. If this would be a zigzag tube this would correspond to about

(90, 0) !

See /group/elena/tule/elena pres.ppt

- The tube lengths are typically in the 100 nm to a few micron regime, but using surface growth

methods up to 4 cm long SW tubes have been made, and there appears to be no practical upper

limit.

4 cm for a 1-nm wide object is quite an aspect ratio!

3.3.1.3. Structure of multi-walled tubes

The tubes described above were single-walled (SW or SWNT). But it is actually easier to manufacture

multi-walled (MW or MWNT) nanotubes, and these were the ones Iijima originally found:


- Important special cases: double-walled tubes DWNT and triple-walled TWNT.

- Each part of the MW tubes are single-walled tubes, with same kind of structure and chirality as a

SW tube.

- They are nested inside each other with an interlayer separation of ∼ 3.4 A, i.e. just as in graphite


- Interlayer interaction is the same weak vdW-interaction as in graphite

- As the TEM images clearly show, the inside is empty and can be quite large.

- The chirality of one tube need not be correlated with that of others

- MW tubes can easily be tens or hundreds of microns long

3.3.1.4. Capped and uncapped nanotubes

- The nanotube ends, both SW and MW, may be either open or closed with fullerene-like gaps (see

figure above).

- Which one they are will depend on how they were manufactured

- The closed ones are likely to be more stable, but may be less interesting from an application point

of view

- Whether they have open and close caps affect the electronic properties of the tube also far from

the opening.

3.3.2. Manufacturing nanotubes


There are several ways to manufacture carbon nanotubes, but the most commonly used ones share

some common charasteristics:

- The tube growth occurs at high temperature (1000 - 6000 ◦ C) in a hot carbon gas or plasma

- MW tubes can grow by themselves. To obtain SW tubes there needs to be a catalyst involved

which facilitates the growth. Typically the catalyst particles are small metal nanoparticles, e.g. Fe

or Co or Ni.

- Without the catalyst the SW nanotube end does not stay open during growth, but would close

spontaneously (i.e. the tube would never grow long but just be a fullerene).

- There of course has to be a carbon source involved. It can be graphite or some gas containing

carbon atoms.

Detailed example: aerosol growth techniques of Esko Kauppinen et al (VTT Processes):


- First a metal vapour is formed, this then condenses to metal nanoclusters (a variety of gas phase

condensation)

- Then it comes to contact with a carbon gas (CO2 or C2H5OH) where nanotubes grow out of the

metal particles.

- End result (collected at top or on side surfaces): SW or MW nanotubes capped with the metal

nanoparticles:

- These nanotubes have a fairly narrow size distribution:


- which is thanks to the fact that the nanoparticle size distribution is narrow and that the ratio of

the nanotube to the nanoparticle size is almost constant at 0.6:


- The current best understanding of the growth is that the hot metal nanoparticles obtain a

supersaturation of C at the surface and inside. From this supersaturated C the tube growth then

starts, and the tube grows outwards from the tube

- Issue is still under intense debate and study, though.

- Growth can be modelled with atomistic simulations, but the tube quality obtained is far from

perfect:


3.3.3. Nanotube mats, bundles, ropes and paper

- A collection of nanotubes grown on a surface such that they stick out of it and are roughly

perpendicular to each other is calles a nanotube mat. Sometimes also the term nanotube forestis used for this.


- A collection of nanotubes aligned parallell to each other, and bonded to each other with the van

der Waals interaction, is called a nanotube bundle

- A collection of nanotube bundles intertwined around each other is called a nanotube rope


- Note, however, that the terminology here is not quite stabilized yet; the terms rope and bundle

may be used for the same things in different sources

- Nanotube ropes can be manufactured in macroscopic thicknesses and lengths

- E.g. in [Zhu, Science 296 (2002) 884] a nanotube rope of similar length and width as

a human hair is reported, see fig. below.

- In Dalton, Nature 423 (2003) 703 CNT fibers of length 100 m is reported


Finally, since fibres can be manufactured from nanotubes, it is natural that one can also make paper

out of them (paper is a flat network of fibers).

- Known as nanotube paper or buckypaper.

- The paper is black

- Here is a figure of nanotube paper, taken on the lecturers office desk:

3.3.4. Strength of nanotubes


- One of the many interesting aspects of nanotubes is that they are very strong

- To be more precise:

- Youngs modulus is very high: 1.25 TPa for SWNT [Krishnan, PRB 58 (1998) 14013]. Compare

e.g. bulk Fe 211 GPa

- Tensile strength: theoretical value up to 300 Gpa, experimental 63 GPa. Compare e.g.

steels with 0.5 - 1.5 GPa. [http://www.isr.us/Downloads/niac pdf/chapter2.html; Science 287 (2000) 637 ]

Explain Youngs modulus, tensile strength

- But these values should be viewed with some caution. In practice most tubes have defects in

them, and these degrade the values from the above ones which are valid for high-quality tubes.

- For normal bulk materials a high Young’s modulus tends to indicate the material is also difficult

to bend. For carbon nanotubes this is not true, however, because of their narrow diamaters.

- Nanotubes are also special in that they can be bent a lot without them breaking, i.e. they are

resilient against bending.

- On extreme bendings the carbon hexagons in the tube change shape, in which case the tube may

get a permanent kink in them. But even then they do not break.


- The strength values are valid for single (SW or MW) tubes.

- But the major problem is again the van der Waals interaction between tubes: a single tube may

be very strong, but a collection of tubes, or tubes surrounded e.g. by a polymer, are usually much

weaker because the interaction between tubes is so weak!

- This is a very significant problem and it is not clear whether it can be fully solved.

- Possible solution: introduce defects with covalent bonds between shells of a MW tube, or between

a tube and a surrounding, to make it stronger:

- Defects can be introduced with electron or ion irradiation or possibly during growth or with

chemical methods.


[Figures courtesy of M. Sammalkorpi]


[Figure courtesy of A. Krasheninnikov]

3.3.5. Electronic properties

[Louies article in Dresselhaus book, p. 113. See also Scientific American 283 (Dec 2000) p. 62]

One of the most striking features of nanotubes is that they can be either semiconducting or metallic!


- Like graphite, electrons can move easily in the length direction of the tube, parallel to the graphene

sheets. But sometimes the tube nevertheless has a band gap, i.e. is a semiconductor.

- Depends directly on chirality:

- (n, n) (armchair) tubes are metals

- (n, m) tubes with n−m divisible by 3 are very-small band gap semiconductors

- All other are large-band gap semiconductors

- The reason to this is not quite trivial, but here is a short summary (if you have not taken a course

on solid state physics, you probably can not follow this, so then never mind):


Electronic states in graphene

States in reciprocal space in a

nanotube; left is metallic (allowed

k lines hit K points)

- A single graphene sheet is an insulator with a bandgap of zero at the K point in the Brillouin zone

- In a rolled-up graphene sheet (a nanotube) onlycertain k points of all the possible graphene pointsare allowed because there are periodic boundariesin the circumferential direction (analogous to thequantization of possible wavefunction in a 1D periodicarray of atoms)

- If the allowed k states hit the K point, the tubebecomes metallic; otherwise it is semiconducting (ina tight-binding model).

- This would give the rule that all tubes with (n−m)divisible by 3 would be metals, but curvature effectsmodify things from the tight-binding picture such thatthey actually are very small band gap semiconductors.

Comment on separating metallic and semiconducting nanotubes

- Although the above features are well understood, the actual nature of electron transport in

nanotubes is still under intense debate and study. For some time it was believed that the electrons

in a nanotube behave as a so called Luttinger liquid, but the more recent knowledge is interpreted

to indicate that they are very good ballistic conductors.


Luttinger liquid: ground state of correlated electrons in 1D. Wet dream of electron theorists... ballistic conductor: uncorrelated

electrons moving with no backscattering, best normal conductor possible. Two eigenmodes.

- Since ballistic conductance is very efficient, the current carrying capacity of tubes is enormous. It

is believed to be 1000 MA/cm2, to be compared with the value for copper of 1 MA/cm2!

3.3.5.1. Nanotube devices

[If you known Finnish see Hakonen, Kauppinen, Nordlund, Prosessorilehti, Marraskuu 2004 s. 32-34].

- Because of both fundamantal interest (e.g. the Luttinger liquid question) and the huge current

carrying capacity, there is strong interest in manufacturing nanotube devices.

- Nanotube transistors have been manufactured for some time.

- Figure of single-electron transistor manufactured at low-temperature laboratory at the Helsinki

University of Technology:


- The transistors have been shown to work, and have very promising properties.

- There is lots of speculation like that they might even become the active component in conventional

Si electronics

- But the big issue is how the nanotube devices can be manufactured reliably on a mass-production

scale. So far they usually have been made manually one at a time, which of course is completely

out of the question for mass produced chips which may have literally billions of transistors each.


- No clearly working solution has yet been demonstrated, but there are some promising developments:

- Growing nanotubes from one electrode to the next using electric-field directed growth

- Nanotube memories using several nanotubes at each memory component already exist (see e.g.

Scientific American 292 (2005) 64).

3.3.6. Nanotube chemistry

- Open-ended nanotubes have several unsaturated “dangling” C bonds at the end.

- Hence it is easy to get them to react with other atoms.

- But even though graphene sheets are considered chemically inert, chemists have already learnt

how to attach things also to the side walls of nanotubes.

- As for fullerenes, rich field of nanotube chemistry exists

3.3.7. Endohedral nanotubes

- As for fullerenes, it is interesting to insert things into carbon nanotubes


- This is easier than for fullerenes since the nanotube ends can be open, allowing for a straightforward

path for ions to enter the tubes

- Hydrogen storage in nanotubes was for a long time considered extremely promising in view of the

forthcoming “hydrogen economy”. But now most people who worked on that are rather pessimistic

about this, achieving this is much harder than initially thought.

Explain hydrogen economy

Need to both get H in and out at the same temperatures as fuel cells operate. Also repeatability of research results problematic

- A really funny kind of endohedral nanotubes: carbon peapods i.e. nanotubes with fullerenes in

them:


3.4. Carbon onions

[Florian Banharts work, e.g. http://www.staff.uni-mainz.de/banhart/c-nanostructures/onions.htm]

- There are still many more kinds of pure carbon nanostructures than the ones mentioned here. One

funny variety is carbon onions, which is concentric shells of carbon spheres inside each other.


- If you think carbon onion sounds silly, think about the equivalents in your native tongue: FIN:Hiilisipuli, SWE: Kollok, GER: Kohlenstoffzwiebeln.

[F. Banhart, ”Diamantbildung in Kohlenstoffzwiebeln”, Physikalische Blatter 53, 33-35 (1997)]

Just don’t enter your grocery store and ask for them...


3.5. Nanodiamonds

- It is also possible to manufacture nanosize diamonds

- There are at least two distint ways of making them

- They form during heavy ion irradiation, and thus also in naturally occuring minerals with radioactive

heavy isotopes in them [Dalton, Science 271 (1996) 1260].

- Another is related to the carbon onions: long-term electron irradiation creates vacancies from the

shells, which then migrate outwards. Thus the concentric C shells shrink, creating a large pressure

in the innermost shells which allow for diamond nucleation


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