Multi Walled Carbon Nanotubes

Figure 5.13. Illustration of a nested nanotube in which one tube is inside the another.

The mechanism of nanotube growth is not understood. Since the metal catalyst is necessary for the growth of SWNTs, the mechanism must involve die role of (he Co or Ni atoms. One proposal referred to as the "scootter mechanism" suggests that atoms of the metal catalyst attach to the dangling bonds at the open end of the tubes, and that these atoms scoot around the rim of the tube, absorbing carbon atoms as they arrive. ■■*

Generally when nanotubes are synthesized the result is a mix of different kinds, some metallic and some semiconducting. A group at IBM has developed a method to separate the semiconducting from the metallic nanotubes. The separation was accomplished by depositing bundles of nanotubes, some of which are metallic and some semiconducting, on a silicon wafer. Metal electrodes were then deposited over the bundle. Using the silicon wafer as an electrode, a small bias voltage was applied that prevents the semiconducting tubes from conducting, effectively making them insulators. A high voltage is then applied across the metal electrodes, thereby sending a high current through die metallic tubes but not the insulating tubes. This causes the metallic tubes to vaporize, leaving behind only the semiconducting tubes.

5.4.2. Structure

There are a variety of structures of carbon nanotubes, and these various structures have different properties. Although carbon nanotubes are not actually made by rolling graphite sheets, it is possible to explain the different structures by consideration of the way graphite sheets might be rolled into tubes. A nanotube can be formed when a graphite sheet is rolled up about the axis T shown in Fig. 5.14. The Ch vector is called the circumferential vector, and it is at right angles to T. Three examples of nanotube structures constructed by rolling the graphite sheet about the T vector

Figure 5.14. Graphitic sheet showing the basis vectors a, and a^ of the two-dimensional unit cell, the axis vector 7"about which the sheet is roiled to generate the armchair structure nanotube sketched in Fig. 5.11 a, and the circumferential vector C„ at tight angles to T. Other orientations of T on the sheet generate the zigzag and chiral structures of Figs. 5.11b and 5.11c, respectively.

Figure 5.14. Graphitic sheet showing the basis vectors a, and a^ of the two-dimensional unit cell, the axis vector 7"about which the sheet is roiled to generate the armchair structure nanotube sketched in Fig. 5.11 a, and the circumferential vector C„ at tight angles to T. Other orientations of T on the sheet generate the zigzag and chiral structures of Figs. 5.11b and 5.11c, respectively.

having different orientations in the graphite sheet are shown in Fig. 5.11. When 7" is parallel to the C-C bonds of the carbon hexagons, die structure shown in Fig. 5.11a is obtained, and it is referred to as the "armchair" structure. The tubes sketched in Figs. 5.1 lb and 5.1 lc, referred to respectively as the zigzag and die chiral structures, are formed by rolling about a T vector having different orientations in die graphite plane, but not parallel to C—C bends. Looking down die tube of Ifae chiral structure, one would see a spiral ing row of carbon atoms. Generally nanotubes are closed at both ends, which involves the introduction of a pentagonal topological arrangement on each end of die cylinder. The tubes are essentially cylinders with each end attached to half of a large fullerenelike structure. In the case of SWNTs metal particles are found at the ends of the tubes, which is evidence for die catalytic role of the metal particles in their formation.

5.4.3. Electrical Properties

Carbon nanotubes have the most interesting property that they are metallic or semiconducting, depending on the diameter and chirality of the tube. Chirality refers to how the tubes are rolled with respect to the direction of the T vector in the graphite plane, as discussed above. Synthesis generally results in a mixture of tubes two-thirds of which are semiconducting and one-third metallic. The metallic tubes have the armchair structure shown in Fig. 5.1 la. Figure 5.15 is a plot of the energy gap of semiconducting chiral carbon nanotubes versus the reciprocal of the diameter, showing that as die diameter of the tube increases, the bandgap decreases. Scanning tunneling microscopy (STM), which is described in Chapter 3, has been used to

10fVD[1/A]

Figure 5.15. Plot of the magnitude of the energy band gap of a semiconducting, chiral carbon nanotube versus the reciprocal of the diameter of the tube (10 A= 1 nm). [Adapted from M. S. Dresseihaus et al., Molec. Mater. 4, 27 (1994).]

10fVD[1/A]

Figure 5.15. Plot of the magnitude of the energy band gap of a semiconducting, chiral carbon nanotube versus the reciprocal of the diameter of the tube (10 A= 1 nm). [Adapted from M. S. Dresseihaus et al., Molec. Mater. 4, 27 (1994).]

investigate the electronic structure of carbon nanotubes. In this measurement the position of the STM tip is fixed above the nanotube, and the voltage V between the tip and the sample is swept while the tunneling current / is monitored. The measured conductance G=I/V is a direct measure of the local electronic density of states. The density of states, discussed in more detail in Chapter 2, is a measure of how close together the energy levels are to each other. Figure 5.16 gives the STM data plotted as the differential conductance, which is (dI/dV)/(I/V), versus die applied voltage between the tip and carbon nanotube. The data show clearly the energy gap in materials at voltages where very little current is observed. The voltage width of this region measures the gap, which for the semiconducting material shown on the bottom of Fig. 5.16 is 0.7 eV

VOLTAGE (V)

Figure 5.16. Plot of differential conductance {dl/dV)(l/V) obtained from scanning tunneling microscope measurements of the tunneling current of metallic (top figure) and semiconducting (bottom figure) nanotubes. [With permission from C. Dekker, Phys. Today 22 (May 1999).]

VOLTAGE (V)

Figure 5.16. Plot of differential conductance {dl/dV)(l/V) obtained from scanning tunneling microscope measurements of the tunneling current of metallic (top figure) and semiconducting (bottom figure) nanotubes. [With permission from C. Dekker, Phys. Today 22 (May 1999).]

At higher energies sharp peaks are observed in the density of states, referred to as van Have singularities, and are characteristic of low-dimensional conducting materials. The peaks occur at the bottom and top of a number of subbands. As we have discussed earlier, electrons in the quantum theory can be viewed as waves. If the electron wavelength is not a multiple of the circumference of the tube, it will destructive^ interfere with itself, and therefore only electron wavelengths that are integer multiples of the circumference of the tubes are allowed. This severely limits the number of energy states available for conduction sound the cylinder. The dominant remaining conduction path is along die axis of die tubes, making carbon nanotubes function as one-dimensional quantum wires. A more detailed discussion of quantum wires is presented later, in Chapter 9. The electronic states of the tubes do not form a single wide electronic energy band, but instead split into one-dimensional subbands that are evident in the data in Fig. 5.16. As we will see later, these states can be modeled by a potential well having a depth equal to the length of the nanotube.

Electron transport has been measured on individual single-walled carbon nanotubes. The measurements at a millikelvin (T— 0.00IK) on a single metallic nanotube lying across two metal electrodes show steplike features in the current-voltage measurements, as seen in Fig. 5.17. The steps occur at voltages which depend on the voltage applied to a third electrode that is electrostatically coupled to the nanotube. This resembles a field effect transistor made from a carbon nanotube, which is discussed below and illustrated in Fig. 5.21. The step like features in the I- V curve are due to single-electron tunneling and resonant tunneling through single molecular orbitals. Single electron tunneling occurs when the capacitance of the nanotube is so small that adding a single electron requires an electrostatic charging

VOLTAGE (mV)

Figure 5.17. Plot of electron transport for two different gate voltages through a single metallic carbon nanotube showing steps in the t-V curves. [With permission from C. Dekker, Phys. Today 22 (May 1999).]

VOLTAGE (mV)

Figure 5.17. Plot of electron transport for two different gate voltages through a single metallic carbon nanotube showing steps in the t-V curves. [With permission from C. Dekker, Phys. Today 22 (May 1999).]

energy greater than the thermal energy kBT. Election transport is blocked at low voltages, which is called Coulomb blockade, and this is discussed in more detail in Chapter 9 (Section 9.5). By gradually increasing the gate voltage, electrons can be added to die tube one by one. Electron transport in the tube occurs by means of electron tunneling through discrete electron states. The current at each step in Fig. 5.17 is caused by one additional molecular orbital. This means that the electrons in die nanotube are not strongly localized, but rather are spatially extended over a large distance along the tube. Generally in one-dimensional systems the presence of a defect will, cause a localization of the electrons. However, a defect in a nanotube will not cause localization because the effect will be averaged over the entire tube circumference because of die doughnut shape of the electron wavefunction.

In the metallic state the conductivity of the nanotubes is very high. It is estimated that they can carry a billion amperes per square centimeter. Copper wire fails at one million amperes per square centimeter because resistive heating melts the wire. One reason for the high conductivity of the carbon tubes is that they have very few defects to scatter electrons, and thus a very low resistance. High currents do not heat the tubes in the same way that they heat copper wires. Nanotubes also have a very high thermal conductivity, almost a factor of 2 more than that of diamond. This means that they are also very good conductors of heat.

Magnetoresistance is a phenomenon whereby the resistance of a material is changed by the application of a DC magnetic field. Carbon nanotubes display magnetoresistive effects at low temperature. Figure 5.18 shows a plot of the magnetic field dependence of the change in resistance AR of nanotubes at 2.3 and 0.35 K compared to their resistance R in zero magnetic field. This is a negative

MAGNETIC FIELD (Tesla)

Figure 5.18. Effect of a DC magnetic field on the resistance of nanotubes at the temperatures of 0.35 and 2.3 K. (Adapted from R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Nanotubes, Imperial College Press, 1998.)

MAGNETIC FIELD (Tesla)

Figure 5.18. Effect of a DC magnetic field on the resistance of nanotubes at the temperatures of 0.35 and 2.3 K. (Adapted from R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Nanotubes, Imperial College Press, 1998.)

magnetoresistance effect because the resistance decreases with increasing DC magnetic field, so its reciprocal, file conductance G=\/R, increases. This occurs because when a DC magnetic field is applied to the nanotubes, the conduction electrons acquire new energy levels associated with their spiraling motion about the field, ft turns out that for nanotubes these levels, called Landau levels, lie very close to the topmost filled energy levels (the Fermi level). Thus there are more available states for the electrons to increase their energy, and the material is more conducting.

5.4.4. Vibrational Properties

The atoms in a molecule or nanoparticle continually vibrate back and forth. Each molecule has a specific set of vibrational motions, called normal modes of vibration, which are determined by the symmetry of the molecule For example carbon dioxide CO2, which has the structure 0=C=0, is a tent molecule with three normal modes. One mode involves a bending of the molecule. Another, called the symmetric stretch, consists of an in-phase elongation of the two C=0 bonds. The asymmetric

E2j 17 cm-1

A,9165crrr1

Figure 5.19. Illustration of two normal modes of vibration of carbon nanotubes.

A,9165crrr1

Figure 5.19. Illustration of two normal modes of vibration of carbon nanotubes.

stretch consists of out-of-phase stretches of the C=0 bond length, where one bond length increases while die other decreases. Similarly carbon nanotubes also have normal modes of vibration. Figure 5.19 illustrates two of the normal modes of nanotubes. One mode, labeled Alg, involves an "in and out" oscillation of the diameter of the tube. Another mode, die E-ig mode, involves a squashing of the tube where it squeezes down in one direction and expands in the perpendicular direction essentially oscillating between a sphere and an ellipse. The frequencies of these two modes are Raman-active and depend on die radius of the tube. Figure 5.20 is a plot of the frequency of the A lg mode as a function of this radius. The dependence of this frequency on die radius is now routinely used to measure the radius of nanotubes.

5.4.5. Mechanical Properties

Carbon nanotubes sue very strong. If a weight IF is attached to the end of a thin wire nailed to the roof of a room, the wire will stretch. The stress S on the wire is defined as the load, or the weight per unit cross-sectional area A of the wire:

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