2.1 Introduction
Carbon nanotubes (CNTs) are fullerene-related structures which consist of graphene cylinders closed at either end with caps containing pentagonal rings. They were discovered in 1991 by the Japanese electron microscopist Sumio Iijima who was studying the material deposited on the cathode during the arc-evaporation synthesis of fullerenes [11]. He found that the central core of the cathodic deposit contained a variety of closed graphitic structures including nanoparticles and nanotubes, of a type which had never previously been observed. A short time later, Thomas Ebbesen and Pulickel Ajayan, from Iijima's lab, showed how nanotubes could be produced in bulk quantities by varying the arc-evaporation conditions. Subsequently, in 1993, Iijima's group at NEC and Donald Bethune's group at IBM's Almaden Research Center in California independently discovered single-wall nanotubes. Whereas the multiwall CNTs were tens of nanometres across, the typical diameter of a single-wall CNTs was just one or two nanometers. The past decade has seen an explosion of research into both types of nanotube.
2.2 Structures of CNTs
CNTs are extremely small, thin, hollow cylinders structure formed by rolling up
seamlessly a single layer of graphite whereas buckyballs are graphite sheets rolled into a ball as shown as Fig. 2-1 [12]. Nanotubes can be either multiwall tubes, having several concentric shells, or single-wall tubes, having one single shell. Scanning tunneling microscopy (STM) offers the potential to probe this prediction, as shown as Fig. 2-2 [13]. Depending on the growth process single-wall or multiwall CNTs can be selectively
produce by the carbon arc discharge method. CNTs come in a variety of diameters and lengths. Depending on the growth process, the length of the tubes can be from approximately 100 nanometers to several microns and the diameters vary from 1 to 20 nanometers, as shown as Fig. 2-3 [14]. CNTs are formed in the synthesis process. The CNTs physical properties range from 2-20 nm in diameter and 100 nm to several microns long with 5-20 graphitic layers, as shown as Fig. 2-4 [15].
A nanotube can be considered as a single sheet of graphite that has been rolled up into a tube, as shown as Fig. 2-5 [16]. The electronic properties of the resulting nanotube depend on the direction in which the sheet was rolled up, as shown as Fig. 2-6 [16]. A CNT of the chiral vector is defined on the hexagonal lattice as Ch = nâ1 + mâ2, where â1 and â2 are unit vectors, and n and m are integers. The chiral angle, q, is measured relative to the direction defined by â1. This diagram has been constructed for (n, m) = (4, 2), and the unit cell of this nanotube is bounded by OAB'B. To form the nanotube, imagine that this cell is rolled up so that O meets A and B meets B', and the
two ends are capped with half of a fullerene molecule. Different types of CNTs have different values of n and m. (b) Zigzag nanotubes correspond to (n, 0) or (0, m) and have a chiral angle of 0°, armchair nanotubes have (n, n) and a chiral angle of 30°, while chiral nanotubes have general (n, m) values and a chiral angle of between 0° and 30°, as shown as Fig. 2-7 [17]. According the theory, nanotubes can either be metallic or semiconducting. Some nanotubes are metals with high electrical conductivity, while others are semiconductors. Nanotubes also have remarkable mechanical properties [18]
that can be exploited to strengthen materials or to act as "tips" in scanning probe microscopes, as shown as Fig. 2-8 [19]. And since they are composed entirely of CNTs also have a low specific weight. MWNTs are close to hollow graphite fibers, except that they have a much higher degree of structural perfection. The interlayer spacing in MWNT (d(002) = 0.34 nm) is slightly larger than that in single crystal graphite (d(002) = 0.335 nm). This is attributed to a combination of tubule curvature and van der Waals force interactions between successive graphene layers. The single-walled nanotubes (SWNTs) and possess good uniformity in diameter about 1.2 nm. They are close to fullerenes in size and have a single-layer cylinder extending from end to end. Qin et al.
also reported that high-resolution transmission electron micrograph of an 18-shell CNT produced. The innermost shell has a diameter of 4 Å. The cylindrical structure of the
nanotube is shown by the reduced contrast towards the centre of the nanotube, where there are fewer atoms in the smaller tubes, as shown as Fig. 2-9 [20].
Carbon is the elemental equivalent of the perfect neighbor, friendly, and easygoing, as shown as Fig. 2-10 [21]. Under intense pressure, carbon atoms form co-valence bonds with four neighbor atoms, creating the pyramidal arrangement of diamond.
However, the activation energy of diamond is very high and carbon usually links up with just three neighbors, creating the hexagonal rings of graphite network.
The arrangement of graphite has a host of unpaired electrons, which essentially float above or below the plane of carbon rings. In this arrangement, the electrons have more freedom to move around the graphite surface, which makes the material a good electrical conductor. S. Paulson et al. reported that junction resistance between a CNT and a graphite substrate and show that details of momentum conservation also can change the contact resistance, as shown as Fig. 2-11 and Fig. 2-12 [22].
CNTs consist of concentric hexagon-rich cylinders, made up of sp2 hybridized carbon, as in graphite, and terminated by end-caps arising from the presence of 12 pentagons (six per end). It is possible to construct a cylinder by rolling up a hexagonal graphene sheet in different ways. Two of these are “non-helical” in the sense that the graphite lattices at the top and bottom of the tube are parallel. These arrangements are
named “armchair” and “zig-zag”. In the armchair structure, two C-C bonds on opposite sites of each hexagon are perpendicular to the tube axis, whereas in the zig-zag arrangement, these bonds are parallel to the tube axis. In all other conformation, the C-C bonds lie at an angle to the tube axis and a helical structure is obtained [15].
Theoretical calculations have predicted that all the armchair tubes are metallic whereas the zig-zag and helical tubes are either metallic or semiconducting. The electronic conduction process in nanotubes is unique since in the radial direction, the electrons are confined in the singular plane of the graphene sheet. The conduction occurs in the armchair (metallic) tubes through gapless modes as the valence and conduction bands cross each other at the Fermi energy, as shown as Fig. 2-13[23]. In most helical tubes, which contain large numbers of atoms in their unit cell, the one-dimensional band structure shows an opening of the gap at the Fermi energy, and this leads to semiconducting properties. This unique electronic behavior only occurs for small nanotubes. As the diameter of the tubes increases, the band gap (which varies inversely with the tube diameter) tends to zero, yielding a zero-gap semiconductor that is electronically equivalent to the planar graphene sheet. In a SWNT, the outer planar graphene-like tubes superimpose the electronic structure of the inner tubes. The band structure obtained from individual SWNT resembles that of graphite. Experiments have indicated that the pentagonal defects present at the tips can induce metallic character by
introducing sharp resonance in the local density of states, as shown as Fig. 2-14[24].
2.3 Characteristics of carbon nanotube
2.3.1 Mechanical properties
In a sheet of graphite each carbon atom is strongly bonded to three other atoms, which makes graphite very strong in certain directions. However, adjacent sheets are only weakly bound by van der Waals forces, so layers of graphite can be easily peeled apart - as happens when writing with a pencil. As we shall see, it is not so easy to peel a carbon layer from a multiwall CNTs. Carbon fiber is already used to strengthen a wide range of materials. A simple method was used to assemble single-walled CNTs into indefinitely long ribbons and fibers, as shown as Fig. 2-15[25]. The processing consists of dispersing the nanotubes in surfactant solutions, recondensing the nanotubes in the flow of a polymer solution to form a nanotube mesh, and then collating this mesh to a nanotube fiber, as shown as Fig. 2-16[25].
The special properties of CNTs mean that they could be the ultimate high-strength measured the Young's modulus of CNTs. The Young's modulus of a material is a measure of its elastic strength. Yu et al. reported that the tensile strengths of individual CNTs were measured with a nanostressing stage located within a scanning electron
microscope, as shown as Fig. 2-17[26]. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals, as shown as Fig. 2-18[26].
It is now known that the Young's modulus should approach a value of 1.25 terapascals. This is true both for multiwall and single-wall CNTs because the modulus is mainly determined by the carbon-carbon bonds within the individual layers.
The bending stiffness can also be measured by placing the nanotubes across probe and using an atomic force microscope to bend them in the middle. Wong et al. reported that atomic force microscopy was used to determine the mechanical properties of individual, structurally isolated silicon carbide (SiC) nanorods (NRs) and CNTs that were pinned at one end to molybdenum disulfide surfaces. The bending force was measured versus displacement along the unpinned lengths, as shown as Fig. 2-19 [27].
The CNTs were about two times as stiff as the SiC NRs. Continued bending of the SiC NRs ultimately led to fracture, whereas the MWNTs exhibited an interesting elastic buckling process. The strengths of the SiC NRs were substantially greater than those found previously for larger SiC structures, and they approach theoretical values.
Because of buckling, the ultimate strengths of the stiffer MWNTs were less than those
of the SiC NRs, although the MWNTs represent a uniquely tough, energy-absorbing material, as shown as Fig. 2-20 [27]. The Young’s modulus, strength, and toughness of nanostructures are important to proposed applications ranging from nanocomposites to probe microscopy.
Occasionally a nanotube spanned one of the pores and the microscope was used to measure how the deflection, which is inversely proportional to the Young's modulus, varied with the applied force. Tombler et al. show that the effects of mechanical deformation on the electrical properties of CNTs are of interest given the practical potential of nanotubes in electromechanical devices. He reports an experimental and theoretical elucidation of the electromechanical characteristics of individual SWNTs under local-probe manipulation. Use AFM tips to detect suspended SWNTs reversibly, without changing the contact resistance; in situ electrical measurements reveal that the conductance of an SWNT sample can be reduced by two orders of magnitude when deformed by an AFM tip. The tight-binding simulations indicate that this effect is owing to the formation of local sp3 bonds caused by the mechanical pushing action of the tip, as shown as Fig. 2-21 and Fig. 2-22 [28]. One recent experiment used the tip of an AFM to manipulate CNTs, revealing that changes in the sample resistance were small unless the nanotubes fractured or the metallic-tube contacts were perturbed. But it remains
nanotubes.
CNTs are different: first they will bend over to surprisingly large angles, before they start to ripple and buckle, and then finally develop kinks as well. The amazing thing about CNTs is that these deformations are elastic - they all disappear completely when the load is removed.
2.3.2 Electronic properties
CNTs are giant molecular wires in which electrons can propagate freely, just as they do in an ordinary metal. This contrasts strongly with conventional "conducting" in which the electrons are localized. These molecules are actually insulators and only become conductors if they are heavily doped, as shown as Fig. 2-23 [29]. CNTs can be doped either by electron donors or electron acceptors. After reaction with host materials, the dopants are intercalated in the intershell spaces of the CNTs, and in the case of single-walled nanotubes either in between the individual tubes or inside the tubes, as shown as Fig. 2-24 [29]. The reaction of intercalation can be carried out in the vapour or liquid phase, and electrochemically.
Graphite, on the other hand, can conduct electricity because one of the four valence electrons associated with each carbon atom is delocalized and can therefore be shared by all the carbon atoms. However, it turns out that a single sheet of graphite (also known as graphene) is an electronic hybrid. Although not an insulator, it is not a semiconductor or a metal either. Graphene is a "semimetal" or a "zero-gap"
semiconductor. This peculiarity means that the electronic states of graphene are very sensitive to additional boundary conditions, such as those imposed by rolling the graphene into a tube. A CNT can be thought of as being formed by folding a piece of graphene to give a seamless cylinder. The description of this process in terms of the chirality vector and the naming of nanotubes are given in Fig. 2-25(a) [30]. The interesting electrical properties of CNTs are due in a large part to the peculiar electronic structure of the graphene. Its band-structure (E vs. k relation) and the hexagonal shape of its first Brillouin zone are shown in Fig. 2-25(b) [30].
It can be shown that a stationary electron wave can only develop if the circumference of the nanotube is a multiple of the electron wavelength. This boundary condition means that a nanotube is either a true metal or a semiconductor - a fact that has been confirmed in experiments with single-wall nanotubes.
The high stability of metallic CNTs is maintained as long as the electron (hole)
energy is not high enough to excite optical phonons. When these vibrational modes become excited the resulting energy dissipation eventually leads to the breakdown of the CNT structure. Since in defect-free CNTs transport is ballistic, high-energy carriers can be formed by hot carrier injection at the contacts. Thus, the stability of a CNT depends on the nature of the contacts. Another factor that influences the stability of a CNT is the gaseous environment it is in. Experiments have shown that the threshold power that is needed to induce breakdown in a CNT is drastically lower in air than it is in vacuum. Particularly interesting is the breakdown behavior of MWCNTs. Fig. 2-26 [30] shows the variation with time of the current flowing through a MWCNT under a
bias leading to breakdown. A very regular current staircase is clearly seen.
One would expect to find more complex behavior for CNTs because of interactions between adjacent layers, and this is the subject of ongoing research. Moreover, by combining different nanotubes, and supplementing them with gate electrodes, there is the potential to make a wide variety of electronic devices, ranging from quantum wires to field effect transistors.
On the fundamental side, a perfect metallic nanotube should be a ballistic conductor. In other words, every electron injected into the nanotube at one end should come out the other end. Although a ballistic conductor does have some resistance, this
resistance is independent of its length, which means that Ohm's law does not apply.
Indeed, only a superconductor (which has no electrical resistance whatsoever) is a better conductor. Any wave that hits two semireflective barriers, one after the other, will produce an interference pattern. This pattern consists of regular oscillations in the intensity of the transmitted wave across the double barrier, as a function of wavelength.
Liang et al. report such oscillations in the transmission of electrons through a metallic SWNT hundreds of nanometres long that is held between two electrodes, as shown as Fig. 2-27 [31]. This experiment demonstrates the quantum-mechanical wave nature of
electrons. It also shows that the propagation of electrons in the nanotube is ballistic-largely free from scattering-over distances of thousands of atoms. A few years ago, we predicted theoretically the possibility of ballistic propagation of electrons over such distances in metallic SWNTs. The creation by Liang et al. of a device that relies on this effect for its operation confirms this and other results that indicate ballistic transport through metallic CNTs, and is a stunning achievement.
2-3-3. Quantized conductance
This method for making electrical contact with nanotubes is very different to techniques that rely on sub-micron fabrication technology. Quantized conductance will
only be observed if ideal contacts are made to the nanotube, and these can be very difficult to achieve. (In an ideal contact none of the electrons entering or leaving the nanotube will be backscattered by the contact.) Early experiments with microfabricated contacts found strong evidence that electrons were scattered. The transport therefore appeared to be diffusive rather than ballistic. Limiting the length of a CNT leads to a
“particle-in-a-box” quantization of the energy levels. Such discrete energy levels have been observed in transport experiments on individual nanotubes and ropes. The electron wave functions corresponding to these discrete states can in principle be imaged by scanning tunneling microscopy (STM). The well-known STM work on quantum corrals demonstrated that wave patterns could be directly imaged in the local density of states of a 2D metal surface, as shown as Fig. 2-28 [32]. The wave functions of several adjacent energy levels can be displayed simultaneously by plotting the differential conductance dI/dV as a function of the voltage and the position x along the tube (Fig.
3A). Wave patterns can be observed for four different energy levels appearing at bias voltages of 0.11, 0.04, 0.00, and –0.05 V (15), as shown as Fig. 2-29 [32]. At each level, a horizontal row of about seven maxima is resolved in dI/dV as a function of position x along the tube (see Fig. 2-28 for the 1D spatial profile of the wave functions belonging to these states).
2.3.4 Thermal properties
Many phenomena in nature occur as the result of some kind of imbalance. For instance, heat is transported when there is a temperature gradient between two boundaries of a material. Despite their ubiquity in everyday life, many aspects of such phenomena are still the subject of debate among theoretical physicists. One central issue is the role of spatial constraints, caused by the dimensionality of a system: the response of a system to external forces is intimately related to statistical fluctuations within it, and these, in turn, depend strongly on whether the system is one-, two or three-dimensional. Because of the variety and complexity of specific interactions, simplified microscopic models are an invaluable tool for the study of transport mechanisms in reduced dimensions, as shown as Fig. 2-30 [33]. The old problem of heat conduction on the thermal conductivity should increase with the system size. In other words, the larger the system, the more efficiently heat is transported (assuming that the density of the material and the temperature gradient are fixed)-in physical terms, the mean free path of the ‘heat carriers’increases with the length of the sample.
A system of fewer than three dimensions-confirming that space dimensionality is crucial in anomalous transport properties. More specifically, the thermal conductivity diverges as the length of a one-dimensional system increases, following a power law
with exponent 1/3; for a two-dimensional system, the divergence is much weaker and
with exponent 1/3; for a two-dimensional system, the divergence is much weaker and