9 Carbon Nanotube: An Introduction

Dr. Anchal Srivastava

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Contents of this Unit

 

1.  Introduction

2.  Historical Overview

3. Conventional Allotropes of Carbon

3.1. Diamond and Graphite

3.2 C60: Buckminsterfullerene

4. Basics of Nanotubes

4.1 Structure of Carbon Nanotubes

4.2 Single-Wall Carbon Nanotubes

4.3 Multiwall Carbon Nanotubes

5. Comparison Between SWCNTs and MWCNTs

6. Summary

 

Learning Outcomes

  • After studying this module, you shall be able to learn
  • A history of carbon nanotube research
  • Some conventional allotropes of carbon like diamond, graphite and fullerene and their relations with nanotubes
  • Some basic definitions relevant to the structure and properties of carbon nanotubes. The difference between various kinds of nanotube structures.

 

1.      Introduction

 

Carbon nanotubes are remarkable objects that look set to revolutionize the technological landscape in the near future. Tomorrow’s society will be shaped by nanotube applications, just as silicon based technologies dominate society today. Space elevators tethered by the strongest of cables; hydrogen-powered vehicles; artificial muscles: these are just a few of the technological marvels that may be made possible by the emerging science of carbon nanotubes.

 

Of course, this prediction is still some way from becoming reality; we are still at the stage of evaluating possibilities and potential. Consider the recent example of fullerenes – molecules closely related to nanotubes. The anticipation surrounding these molecules, first reported in 1985, resulted in the bestowment of a Nobel Prize for their discovery in 1996. However, a decade later, few applications of fullerenes have reached the market, suggesting that similarly enthusiastic predictions about nanotubes should be approached with caution.

 

There is no denying, however, that the expectations surrounding carbon nanotubes are very high. One of the main reasons for this is the anticipated application of nanotubes to electronics. Many believe that current techniques for miniaturizing microchips are about to reach their lowest limits, and that nanotube-based technologies are the best hope for further miniaturization. Carbon nanotubes may therefore provide the building blocks for further technological progress, enhancing our standards of living. In this module, we describe the historical overview, carbon allotropes and then structures of carbon nanotubes.

 

2.      Historical Overview

 

Very small diameter (less than 10 nm) carbon filaments were prepared in the 1970’s and 1980’s through the synthesis of vapor grown carbon fibers by the decomposition of hydrocarbons at high temperatures in the presence of transition metal catalyst particles of <10nm diameter. However, no detailed systematic studies of such very thin filaments were reported in these early years, and it was not until the observation of carbon nanotubes in 1991 by Iijima of the NEC Laboratory in Tsukuba, Japan (see Fig. 1) using High-Resolution Transmission Electron Microscopy (HRTEM) that the carbon nanotube field was seriously launched. Independently, and at about the same time (1992), Russian workers also reported the discovery of carbon nanotubes and nanotube bundles, but generally having a much smaller length to diameter ratio.

 

A direct stimulus to the systematic study of carbon filaments of very small diameters came from the discovery of fullerenes by Kroto, Smalley, Curl, and coworkers at Rice University. A direct stimulus to the systematic study of carbon filaments of very small diameters came from the discovery of fullerenes by Kroto, Smalley, Curl, and coworkers at Rice University.

 

Figure 1. The observation by TEM of multi-wall coaxial nanotubes with various inner and outer diameters, di and do, and numbers of cylindrical shells N reported by Iijima in 1991: (a) N = 5, do=67˚A; (b) N = 2, do=55˚A; and (c) N = 7, di=23˚A, do=65˚A

 

In fact, Smalley and others speculated publically in these early years that a single wall carbon nanotube might be a limiting case of a fullerene molecule. The connection between carbon nanotubes and fullerenes was further promoted by the observation that the terminations of the carbon nanotubes were fullerene-like caps or hemispheres. It is curious that the smallest reported diameter for a carbon nanotube is the same as the diameter of the C60 molecule, which is the smallest fullerene to follow the isolated pentagon rule. This rule requires that no two pentagons be adjacent to one another, thereby lowering the strain energy of the fullerene cage. While there is not, as yet, a definite answer to a provocative question raised by Kubo and directed to Endo in 1977, regarding the minimum size of a carbon fiber, this question was important for identifying carbon fibers with very small diameters as carbon nanotubes, the one-dimensional limit of a fullerene molecule. A recent report of a carbon nanotube which a diameter of 0.4 nm C20 end cap may provide an answer to the question.

 

It was the Iijima’s observation of the multiwall carbon nanotubes in Fig. 1 in 1991 that heralded the entry of many scientists into the field of carbon nanotubes, stimulated at first by the remarkable 1D dimensional quantum effects predicted for their electronic properties, and subsequently by the promise that the remarkable structure and properties of carbon nanotubes might give rise to some unique applications. Whereas the initial experimental Iijima observation was for Multi-Wall Nanotubes (MWNTs), it was less than two years before Single-Wall Carbon Nanotubes (SWNTs) were discovered experimentally by Iijima and his group at the NEC Laboratory and by Bethune and coworkers at the IBM Almaden laboratory. These findings were especially important because the single wall nanotubes are more fundamental, and had been the basis for a large body of theoretical studies and predictions that preceded the experimental observation of single wall carbon nanotubes. The most striking of these theoretical developments was the prediction that carbon nanotubes could be either semiconducting or metallic depending on their geometrical characteristics, namely their diameter and the orientation of their hexagons with respect to the nanotube axis (chiral angle). Though predicted in 1992, it was not until 1998 that these predictions regarding their remarkable electronic properties were corroborated experimentally. A major breakthrough occurred in 1996 when Smalley and coworkers at Rice University successfully synthesized bundles of aligned single wall carbon nanotubes, with a small diameter distribution, thereby making it possible to carry out many sensitive experiments relevant to 1D quantum physics, which could not previously be undertaken. Of course, actual carbon nanotubes have finite length, contain defects, and interact with other nanotubes or with the substrate and these factors often complicate their behavior.

 

A great deal of progress has been made in characterizing carbon nanotubes and in understanding their unique properties since their ‘discovery’ in 1991. This progress is highlighted in the module of this unit.

 

3. Conventional carbon allotropes and fullerene

 

Carbon is one of the most abundant elements in nature. It is essential to living organisms and it constitutes building blocks of a wide variety of compounds (e.g. the skeletons of complex molecules such as fats, steroids, hydrocarbons, oil, soot, solvents, etc.). Carbon possesses four electrons in its outer valence shell; the ground state configuration is: 2s2 2p2.

Figure 2. (a) Crystal structure of diamond is showing tetrahedral bonding among C atoms; (b) graphite crystal exhibiting overlapping honeycomb-like structures with interlayer separations of 3.35 Å; (c) C60, Buckminsterfullerene, third C allotrope discovered in 1985 by Kroto et al.

 

Figure 3. Structure of C60 predicted by Osawa in 1970.

 

3.1 Diamond and graphite

 

Diamond and graphite are considered as two natural crystalline forms of pure carbon. Their properties, morphology and characteristics are completely different, and can be explained in terms of the way carbon atoms are bonded to each other within the structure. In diamond, carbon atoms exhibit sp3 hybridization, in which four bonds are directed towards the corners of a regular tetrahedron. The resulting three-dimensional network (diamond) is extremely rigid (Fig. 2a). The bond length between sp3 carbon atoms in diamond is 1.56 Å.

 

For graphite, sp2 hybridization is present within three carbon bonds, evenly distributed in the x–y plane (120º), and a weak п bond in the z axis. The C–C sp2 bond length is 1.42 Å. A graphene sheet consists of sp2 hybridized carbon atoms forming a hexagonal (honeycomb) carbon lattice. The pz orbital is responsible for a weak bond, termed as van der Waals bond. The spacing between graphene layers is 3.35 Å (Fig. 2b). The van der Waals bonds are insufficient to prevent the honeycomb layers of graphite slipping over one another when an external force is applied. Additionally, the free electrons in the pz orbital move within this cloud and are no longer local to a single carbon atom (i.e. they are delocalized). This phenomenon lies behind the reason why graphite can conduct electricity. Diamond, on the contrary, behaves as an insulator because all electrons are localized in the bonds within the sp3 framework. However, when the latter is doped with other elements, it is possible to modify the electronic properties, thus transforming it into a wide-band gap semiconductor.

 

3.2 C60: Buckminsterfullerene

 

For several centuries, it was believed that the only allotropes of carbon were graphite and diamond. However, in 1985, a new form of carbon, C60: Buckminsterfullerene, was first produced and identified. The C60 molecule contains 60 carbon atoms arranged in a spherical way, as in a soccer ball (truncated icosahedron; Fig. 2c). In C60, sp2 hybridized carbon (as in graphite) is curved by the introduction of pentagonal rings. In fact, in order to close a graphene sheet completely, only 12 pentagons are needed according to Euler’s Law, which states V+F-E=2, where V is the number of vertices, F the number of faces and E the number of edges. For example, in C60, F=32 (12 pentagons and 20 hexagons), E=90 and V=60. The cage-like carbon molecules are generally known as fullerenes, and this definition also encompasses elongated fullerenes, now known as carbon nanotubes.

 

It is also important to note that in 1970, Osawa predicted the possibility of producing a stable icosahedral molecule with 60 carbon atoms (Fig. 3). However, the structure of the truncated icosahedron was already known by the Greeks and possibly earlier. This structure was also reported in the work of Leonardo da Vinci and Albrecht Dűrer.

 

4        Basics of Carbon Nanotube

 

4.1 Structure of Carbon Nanotubes

 

It is relatively easy to imagine a single-wall carbon nanotube (SWNT). Ideally, it is enough to consider a perfect graphene sheet (graphene is a polyaromatic monoatomic layer consisting of sp2-hybridized carbon atoms arranged in hexagons; genuine graphite consists of layers of this graphene) and to roll it into a cylinder (Fig. 4.1), making sure that the hexagonal rings placed in contact join coherently. Then the tips of the tube are sealed by two caps, each cap being a hemi-fullerene of the appropriate diameter (Fig. 4.2a–c).

 

4.2 Single-Wall Carbon Nanotubes

 

Geometrically, there is no restriction on the tube diameter. However, calculations have shown that collapsing the single wall tube into a flattened two-layer ribbon is energetically more favorable than maintaining the tubular morphology beyond a diameter value of ≈ 2.5nm. On the other hand, it is easy to grasp intuitively that the shorter the radius of curvature, the higher the stress and the energetic cost, although SWNTs with diameters as low as 0.4 nm have been synthesized successfully. A suitable energetic compromise is therefore reached for ≈ 1.4 nm, the most frequent diameter encountered regardless of the synthesis technique (at least for those based on solid carbon sources) when conditions ensuring high SWNT yields are used. There is no such restriction on the nanotube length, which only depends on the limitations of the preparation method and the specific conditions used for the synthesis (thermal gradients, residence time and so on). Experimental data are consistent with these statements, since SWNTs wider than 2.5 nm are only rarely reported in the literature, whatever the preparation method, while the length of the SWNTs can be in the micrometer or the millimeter range. These features make single-wall carbon nanotubes a unique example of single molecules with huge aspect ratios.

Fig. 4.1 Sketch of the way to make a single-wall carbon nanotube, starting from a graphene sheet.

 

Two important consequences derive from the SWNT structure as described above:

 

All  carbon  atoms  are  involved  in  hexagonal  aromatic  rings  only  and  are  therefore  in  equivalent positions,  except  at  each  nanotube  tip,  where  6×5  =  30  atoms  are  involved  in  pentagonal  rings (considering that adjacent pentagons are unlikely) – though not more, not less, as a consequence of Euler’s rule that also governs the fullerene structure. For ideal SWNTs, chemical reactivity will therefore be highly favored at the tube tips, at the locations of the pentagonal rings.

 

Although carbon atoms are involved in aromatic rings, the C=C bond angles are not planar. This means that the hybridization of carbon atoms is not pure sp2; it has some degree of the sp3 character, in a proportion that increases as the tube radius of curvature decreases. The effect is the same as for the C60 fullerene molecules, whose radius of curvature is 0.35 nm, and whose bonds therefore have 10% sp3. On the one hand, this is believed to make the SWNT surface a bit more reactive than regular, planar graphene, even though it still consists of aromatic ring faces. On the other hand, this somehow induces variable overlapping of energy bands, resulting in unique and versatile electronic behavior.

Fig. 4.2a–c Sketches of three different SWNT structures that are examples of (a) a zig-zag-type nanotube, (b) an armchair-type nanotube, (c) a helical nanotube.

 

As illustrated by Fig. 4.2, there are many ways to roll a graphene into a single-wall nanotube, with some of the resulting nanotubes possessing planes of symmetry both parallel and perpendicular to the nanotube axis (such as the SWNTs from Fig. 4.2a and 4.2b), while others do not (such as the SWNT from Fig. 4.2c). Similar to the terms used for molecules, the latter are commonly called “chiral” nanotubes, since they are unable to be superimposed on their own image in a mirror. “Helical” is however sometimes preferred (see below). The various ways to roll graphene into tubes are therefore mathematically defined by the vector of helicity Ch, and the angle of helicity θ, as follows (referring to Fig. 4.1):

 

OA= Ch = na1+ma2

With

 

 

Where n and m are the integers of the vector OA considering the unit vectors a1 and a2.

 

The vector of helicity Ch (= OA) is perpendicular to the tube axis, while the angle of helicity θ is taken with respect to the so-called zig-zag axis: the vector of helicity that results in nanotubes of the “zig-zag” type (see below). The diameter D of the corresponding nanotube is related to Ch by the relation:

The C−C bond length is actually elongated by the curvature imposed by the structure; the average bond length in the C60 fullerene molecule is a reasonable upper limit, while the bond length in flat graphene in genuine graphite is the lower limit (corresponding to an infinite radius of curvature). Since Ch, θ, and D are all expressed as a function of the integers n and m, they are sufficient to define any particular SWNT by denoting them (n,m). The values of n and m for a given SWNT can be simply obtained by counting the number of hexagons that separate the extremities of the Ch vector following the unit vector a1 first and then a2. In the example of Fig. 4.1, the SWNT that is obtained by rolling the graphene so that the two shaded aromatic cycles can be superimposed exactly is a (4, 2) chiral nanotube. Similarly, SWNTs from Fig. 4.2a to 4.2c are (9,0), (5,5), and (10,5) nanotubes respectively, thereby providing examples of zig-zag-type SWNT (with an angle of helicity = 0°), armchair-type SWNT (with an angle of helicity of 30°) and a chiral SWNT, respectively. This also illustrates why the term “chiral” is sometimes inappropriate and should preferably be replaced with “helical”. Armchair (n, n) nanotubes, although definitely achiral from the standpoint of symmetry, exhibit a nonzero “chiral angle”. “Zig-zag” and “armchair” qualifications for a chiral nanotube refer to the way that the carbon atoms are displayed at the edge of the nanotube cross-section (Fig. 4.2a and 4.2b).

Fig. 4.3 Image of two neighboring chiral SWNTs within a SWNT bundle as seen using high-resolution scanning tunneling microscopy (courtesy of Prof. Yazdani, University of Illinois at Urbana, USA).

 

Fig. 4.4a, b High-resolution transmission electron microscopy images of a SWNT rope. (a) Longitudinal view. An isolated single SWNT also appears at the top of the image. (b) Cross-sectional view.

 

Generally speaking, it is clear from Figs. 4.1 and 4.2a that having the vector of helicity perpendicular to any of the three overall C=C bond directions will provide zig-zag-type SWNTs, denoted (n, 0), while having the vector of helicity parallel to one of the three C=C bond directions will provide armchair type SWNTs, denoted (n, n). On the other hand, because of the six fold symmetry of the graphene sheet, the angle of helicity θ for the chiral (n,m) nanotubes is such that 0 < θ <30°. Figure 4.3 provides two examples of what chiral SWNTs look like, as seen via atomic force microscopy.

 

The graphenes in graphite have π electrons which are accommodated by the stacking of graphenes, allowing van der Waals forces to develop. Similar reasons make fullerenes gather and order into fullerite crystals and SWNTs into SWNT ropes (Fig. 4.4a). Provided the SWNT diameter distribution is narrow, the SWNTs in ropes tend to spontaneously arrange into hexagonal arrays, which correspond to the highest compactness achievable (Fig. 4.4b). This feature brings new periodicities with respect to graphite or turbostratic polyaromatic carbon crystals. Turbostratic structure corresponds to graphenes that are stacked with random rotations or translations instead of being piled up following sequential ABAB positions, as in graphite structure. This implies that no lattice atom plane exists other than the graphene planes themselves (corresponding to the (001) atom plane family). These new periodicities give specific diffraction patterns that are quite different to those of other sp2-carbon-based crystals, although hk reflections, which account for the hexagonal symmetry of the graphene plane, are still present. On the other hand, 00l reflections, which account for the stacking sequence of graphenes in regular, “multilayered” polyaromatic crystals (which do not exist in SWNT ropes), are absent. This hexagonal packing of SWNTs within the ropes requires that SWNTs exhibit similar diameters, which is the usual case for SWNTs prepared by electric arc or laser vaporization processes. SWNTs prepared using these methods are actually about 1.35 nm wide (diameter of a (10, 10) tube, among others), for reasons that are still unclear but are related to the growth mechanisms specific to the conditions provided by these techniques.

 

4.3 Multiwall Carbon Nanotubes

 

Building multiwall carbon nanotubes is a little bit more complex, since it involves the various ways graphenes can be displayed and mutually arranged within filamentary morphology. A similar versatility can be expected to the usual textural versatility of polyaromatic solids. Likewise, their diffraction patterns are difficult to differentiate from those of anisotropic polyaromatic solids. The easiest MWNT to imagine is the concentric type (c-MWNT), in which SWNTs with regularly increasing diameters are coaxially arranged (according to a Russian-doll model) into a multiwall nanotube (Fig. 4.5). Such nanotubes are generally formed either by the electric arc technique (without the need for a catalyst), by catalyst-enhanced thermal cracking of mgaseous hydrocarbons, or by CO disproportionation. There can be any number of walls (or coaxial tubes), from two upwards. The inter-tube distance is approximately the same as the inter-graphene distance in turbostratic, polyaromatic solids, 0.34 nm (as opposed to 0.335 nm in genuine graphite), since the increasing radius of curvature imposed on the concentric graphenes prevents the carbon atoms from being arranged as in graphite, with each of the carbon atoms from a graphene facing either a ring center or a carbon atom from the neighboring graphene. However, two cases allow a nanotube to reach – totally or partially – the 3-D crystal periodicity of graphite. One is to consider a high number of concentric graphenes: concentric graphenes with a long radius of curvature. In this case, the shift in the relative positions of carbon atoms from superimposed graphenes is so small with respect to that in graphite that some commensurability is possible. This may result in MWNTs where both structures are associated; in other words they have turbostratic cores and graphitic outer parts. The other case occurs for c-MWNTs exhibiting faceted morphologies, originating either from the synthesis process or more likely from subsequent heat treatment at high temperature (such as 2500 ◦C) in inert atmosphere. Facets allow the graphenes to resume a flat arrangement of atoms (except at the junction between neighboring facets) which allows the specific stacking sequence of graphite to develop.

 

Fig. 4.5 High-resolution transmission electron microscopy image (longitudinal view) of a concentric multiwall carbon nanotube (c-MWNT) prepared using an electric arc. The insert shows a sketch of the Russian doll-like arrangement of graphenes.

 

Another frequent inner texture for multiwall carbon nanotubes is the so-called herringbone texture (h-MWNTs), in which the graphenes make an angle with respect to the nanotube axis (Fig. 4.6). The angle value varies upon the processing conditions (such as the catalyst morphology or the composition of the atmosphere), from 0 (in which case the texture becomes that of a c-MWNT) to 90◦ (in which case the filament is no longer a tube, see below), and the inner diameter varies so that the tubular arrangement can be lost, meaning that the latter are more accurately called nano-fibers rather than nanotubes. h-MWNTs are exclusively obtained by processes involving catalysts, generally catalyst-enhanced thermal cracking of hydrocarbons or CO disproportionation. One unresolved question is whether the herringbone texture, which actually describes the texture projection rather than the overall three-dimensional texture, originates from the scroll like spiral arrangement of a single graphene ribbon or from the stacking of independent truncated cone-like graphenes in what is also called a “cup-stack” texture.

Fig. 4.6a, b Some of the earliest high-resolution transmission electron microscopy images of a herringbone (and bamboo) multiwall nanotube (bh-MWNT, longitudinal view) prepared by CO disproportionation on Fe-Co catalyst. (a) As-grown. The nanotube surface is made of free graphene edges. (b) After 2900 ◦C heat treatment. Both the herringbone and the bamboo textures have become obvious. Graphene edges from the surface have buckled with their neighbors (arrow), closing off access to the inter graphene space.

 

Fig. 4.7a,b Transmission electron microscopy images from bamboo multiwall nanotubes (longitudinal views). (a) Low magnification of a bamboo-herringbone multiwall nanotube (bh-MWNT) showing the nearly periodic nature of the texture, which occurs very frequently. (b) High-resolution image of a bamboo-concentric multiwall nanotube (bc-MWNT)

 

Another common feature is the occurrence, to some degree, of a limited amount of graphenes oriented perpendicular to the nanotube axis, thus forming a “bamboo” texture. This is not a texture that can exist on its own; it affect either the c MWNT (bc-MWNT) or the h-MWNT (bh-MWNT) textures (Figs. 4.6 and 4.7). The question is whether such filaments, although hollow, should still be called nanotubes, since the inner cavity is no longer open all the way along the filament as it is for a genuine tube. These are therefore sometimes referred as “nanofibers” in the literature too.

Fig. 4.8 Sketch explaining the various parameters obtained from high-resolution (lattice fringe mode) transmission electron microscopy, used to quantify nanotexture: L1 is the average length of perfect (distortion-free) graphenes of coherent areas; N is the number of piled-up graphenes in coherent (distortion-free) areas; L2 is the average length of continuous though distorted graphenes within graphene stacks; β is the average distortion angle. L1 and N are related to the La and Lc values obtained from X-ray diffraction.

 

One nano-filament that definitely cannot be called a nanotube is built from graphenes oriented perpendicular to the filament axis and stacked as piled-up plates. Although these nano-filaments actually correspond to h-MWNTs with a graphene/MWNT axis angle of 90◦, an inner cavity is no longer possible, and such filaments are therefore often referred to as “platelet nano-fibers”. Unlike SWNTs, whose aspect ratios are so high that it is almost impossible to find the tube tips, the aspect ratios for MWNTs (and carbon nanofibers) are generally lower and often allow one to image tube ends by transmission electron microscopy. Aside from c-MWNTs derived from electric arc (see Fig. 4.5), which grow in a catalyst-free process, nanotube tips are frequently found to be associated with the catalyst crystals from which they were formed.

 

5 Comparison between SWNTs and MWNTs Table 1.

 

 

6 SUMMARY

 

Carbon nanotubes are in the structural family of fullerene. They are molecules composed entirely of carbon atoms. The carbon atoms are usually arranged in a hexagonal pattern, bonded together with extremely strong covalent bonds.

 

A carbon nanotube can be visualized as a finite number of carbon graphite shells arranged around a hollow center axis with a constant spacing of around 0.34 nm, a tubular diameter normally ranging from 2-25 nm, and with lengths up to several microns.

 

This number of graphite shells is the basis for the major division in carbon nanotubes: single walled nanotubes (SWNT) and multi walled nanotubes (MWNT). The concept of either single walled or multiwalled carbon nanotubes is important because the properties change significantly with respect to each other.

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Learn More:

  1. A. Ozin and A. C. Arsenault, Nanochemistry, RSC Publishing, Cambridge, 2006, Chapter5. G. Cao, Nanostructures and Nanomaterials, Imperial College Press, London, 2006, Chapter 6.
  2. Harris, Carbon Nanotube Science, Cambridge University Press, New York, 2009, Chapters 2, 4, 5 & 9.

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