Carbon Materials for Advanced Technologies Episode 3 doc

60 35 - 30 - 25 - h 25 20- h" 15 - 13.9 14.1 14.3 14.5 14.7 Lattice constant a (A) Fig. 13. Dependence of T, for various MsCfio and MS-~M&, compounds on the lattice constant a. Also included on the figure are data for superconducting samples under pressure [44]. 61 samples under pressure 1124, 125, 1261. Because of the close connection between the electronic density of states at the Fermi level N(EF) and the lattice constant a, plots of T, vs N(EF) similar to Fig. 13 have been made The reason why the T, is so much higher for M3C60 relative to other carbon- based materials appears to be closely related to the high density of states [c.f., Eq. (l)] that can be achieved at the Fermi level when the tl, LUMO molecular level is half filled with carriers. It is believed [127, 1281 that the dominant coupling mechanism for superconductivity is electron-phonon coupling and that the H,-derived high frequency phonons play a dominant role in the coupling. The observation of broad H,-derived Raman lines [89, 971 in M3 C~O is consistent with a strong electron-phonon coupling. The magnitude of the superconducting bandgap 2A has been studied by a variety of experimental techniques [122, 1291 leading to the conclusion that the superconducting bandgap for both K3Cso and Rb3C60 is close to the BCS value of 3.5 LT, [56, 64, 122, 1301. A good fit for the functional form of the temperature dependence of the bandgap to BCS theory was also obtained using the scanning tunneling microscopy technique [13 11. Measurements of the isotope effect also suggest that T, oc M-". Both small (a N 0.3 - 0.4) values [132, 1331 andlarge (a N 1.4)values [134, 1351 ofa have beenreported. Future work is needed to clarify the experimental picture of the isotope effect in the M3Cso compounds. Closely related to the high compressibility of C~O [35] and M3C60 (M = K, Rb) [125] is the large linear decrease in T, with pressure. These superconductors are strongly type II superconductors, with high values for the upper critical field H,z and a short superconducting coherence length Eo, with values of EO (2-3 nm) only slightly larger than a lattice constant for the fcc unit cell (-1.4 nm). A listing of values for the various parameters pertinent to the superconductivity of M3C60 (M = K, Rb) is given in Table 1. In this table: a0 is the lattice constant; T, is the superconducting transition temperature; 2A is the superconducting bandgap; P is the pressure; H,I, Hc2, and H, are, respectively, the lower critical field, upper critical field, and thermodynamic critical field; J, is the critical current density; (0 is the superconducting coherence length; XL is the London penetration depth; and L is the electron mean free path. [621. 3 Carbon Nanotnbes The field of carbon nanotube research was launched in 1991 by the initial experimental observation of carbon nanotubes by transmission electron mi- croscopy (TEM) [ 1511, and the subsequent report of conditions for the synthe- sis of large quantities of nanotubes [152,153]. Though early work was done on 62 Table 1. Experimental values for the macroscopic parameters of the superconducting phases of GC60 and RbsC60. Parameter K3C60 Rb&o a0 (A) 14.253" 14.436" 19.7' 5.2", 4.0", 3.6g, 3.6h -7.8' 13j 26j, 301, 29", 17.5' 0.38i 0.12j 2.6j, 3.11, 3.4", 4.5' 240j, 480°, 6OOp, 8OOq 92j 3.1'. 1.0' -1 .34b, -3.5' 30.0b 5.3d, 3.1", 3.6f, 3.0g,2.9Sh -9.7i 263, 19k 34j, 55', 16' 0.44i 1.9 2.0i, 2.0', 3.0" 168j, 370f, 46OP, 8004, 210k 843, 90k -3.8' 0.9' aRef. [27; 'Ref. [136]; cSTM measurements in Ref. [137]; %TM measurements in Ref. [131]; "NMR measurements in Ref. [138, 1391; fpSR measurements in Ref. [140]; Var-IR measurements in Ref. [141]; hFar-IR measurements in Ref. [142]; %Ref [125]; jRef. [143]; kReE [144]; 'Ref. [145]; "Ref. [146]; nRef. [147]; ORef. [148]; PRef. [138]; qRef. [129, 1491; 'Ref. [150]; sRef. [132]. coaxial carbon cylinders called multi-wall carbon nanotubes, the discovery of smaller diameter single-wall carbon nanotubes in 1993 [ 154, 1551, one atomic layer in thickness, greatly stimulated theoretical and experimental interest in the field. Other breakthroughs occurred with the discovery of methods to synthesize large quantities of single-wall nanotubes with a small distribution of diameters [156, 1571, thereby enabling experimental observation of the remarkable electronic, vibrational and mechanical properties of carbon nan- otubes. Various experiments carried out thus far (cg., high resolution TEM, STM, resistivity, and Raman scattering) are consistent with identifying single- wall carbon nanotubes as rolled up seamless cylinders of graphene sheets of sp2 bonded carbon atoms organized into a honeycomb structure as a flat graphene sheet. Because of their very small diameters (down to -0.7 nm) and relatively long lengths (up to N several pm), single-wall carbon nanotubes are prototype hollow cylindrical 1 D quantum wires. 3.1 Synthesis The earliest observations of carbon nanotubes with very small (nanometer) diameters [151, 158, 1591 are shown in Fig. 14. Here we see results of high resolution transmission electron microscopy (TEM) measurements, providing evidence for pm-long multi-layer carbon nanotubes, with cross-sections show- ing several concentric coaxial nanotubes and a hollow core. One nanotube has 63 Fig. 14. High resolution TEM observations of three multi-wall carbon nanotubes with N concentric carbon nanotubes with various outer diameters do (a) N = 5, do = 6.7 nm, (b) N = 2, do = 5.5 nm, and (c) N = 7, do = 6.5 nm. The inner diameter of (c) is d, = 2.3 nm. Each cylindrical shell is described by its own diameter and chiral angle [ 1511. only two coaxial carbon cylinders [Fig. 14(b)], and another has an inner diam- eter of only 2.3 nm [Fig. 14(c)] 11511. These carbon nanotubes were prepared by a carbon arc process (typical dc current of 50-100 A and voltage of 20- 25 V), where carbon nanotubes form as bundles of nanotubes on the negative electrode, while the positive electrode is consumed in the arc discharge in a helium atmosphere [160]. The apparatus is similar to that used to synthesize endohedral fullerenes, except that the metal added to the anode is viewed as a catalyst keeping the end of the growing nanotube from closing [156]. Typical lengths of the arc-grown multi-wall nanotubes are ~1 pm, giving rise to an aspect ratio (length to diameter ratio) of lo2 to lo3. Because of their small diameter, involving only a small number of carbon atoms, and because of their large aspect ratio, carbon nanotubes are classified as 1D carbon systems. Most of the theoretical work on carbon nanotubes has been on single-wall nanotubes and has emphasized their 1D properties. In the multi-wall carbon nanotubes, the measured interlayer distance is 0.34 nm [151], comparable to the interlayer separation of 0.344 nm in turbostratic carbons. Single-wall nanotubes were first discovered in an arc discharge chamber using a catalyst, such as Fe, Co and other transition metals, during the synthesis process [154,155]. The catalyst is packed into the hollow core of the electrodes and the nanotubes condense in a cob-web-like soot sticking to the chamber walls. Single-wall nanotubes, just like the multi-wall nanotubes and also conventional vapor grown carbon fibers [161], have hollow cores along the axis of the nanotube. The diameter distribution of single-wall carbon nanotubes is of great interest for both theoretical and experimental reasons, since theoretical studies indi- cate that the physical properties of carbon nanotubes are strongly dependent on the nanotube diameter. Early results for the diameter distribution of Fe-catalyzed single-wall nanotubes (Fig. 15) show a diameter range between 0.7 nm and 1.6 nm, with the largest peak in the distribution at 1.05 nm, and with a smaller peak at 0.85 nm [154]. The smallest reported diameter for a single-wall carbon nanotube is 0.7 nm [154], the same as the diameter of the C~O molecule (0.71 nm) [162]. Two recent breakthroughs in the synthesis of single-wall carbon nanotubes [156, 1571 have provided a great stimulus to the field by making significant amounts of available material for experimental studies. Single-wall carbon nanotubes prepared by the Rice University group by the laser vaporization method utilize a Co-Nilgraphite composite target operating in a furnace at 1200°C. High yields with >70%90%) conversion of graphite to single- wall nanotubes have been reported [156, 1631 in the condensing vapor of the heated flow tube when the Co-Ni catalystharbon ratio was 1.2 atom % Co-Ni alloy with equal amounts of Co and Ni added to the graphite (98.8 atom %I). Two sequenced laser pulses separated by a 50 ns delay were used to 65 0.7 OB 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Nanotube diameters (nm) Fig. 15. Histogram of the single-wall nanotube diameter distribution for Fe-catalyzed nanotubes [154]. A relatively small range of diameters are found, the smallest diameter corresponding to that for the hllerene (260. provide a more uniform vaporization of the target and to gain better control of the growth conditions. Flowing argon gas sweeps the entrained nanotubes from the high temperature zone to a water-cooled Cu collector downstream, just outside the furnace [156]. Subsequently, an efficient (>70%1 conversion) carbon arc method (using a Ni-Y catalyst) was found by a French group at Montpellier [157] for growing single-wall carbon nanotube arrays with a small distribution of nanotube diameters, very similar to those produced by the Rice group [156, 1631. Other groups worldwide are now also making single-wali carbon nanotube ropes using variants of the laser vaporization or carbon arc methods. The nanotube material produced by either the laser vaporization method or the carbon arc method appears in a scanning electron microscope (SEM) image as a mat of carbon “ropes” 10-20 nm in diameter and up to 100 pm or more in length. Under transmission electron microscope (TEM) examination, each carbon rope is found to consist primarily of a bundle of single-wall carbon nanotubes aligned along a common axis. X-ray diffraction (which views many ropes at once) and transmission electron microscopy (which views a single rope) show that the diameters of the single-wall nanotubes have a strongly peaked narrow distribution of diameters. For the synthesis conditions used by the Rice and Montpellier groups, the diameter distribution was strongly peaked at 1.38f0.02 nm, very close to the diameter of an ideal (1 0,10> nanotube. X-ray diffraction measurements [ 156, 1 571 showed that these single-wall nanotubes form a two-dimensional triangular lattice with a 66 lattice constant of 1.7 nm, and an inter-tube separation of 0.3 15 nm at closest approach within a rope, in good agreement with prior theoretical modeling results [164, 1651. Whereas multi-wall carbon nanotubes require no catalyst for their growth, either by the laser vaporization or carbon arc methods, catalyst species are necessary for the growth of the single-wall nanotubes [156], while two different catalyst species seem to be needed to efficiently synthesize arrays of single wall carbon nanotubes by either the laser vaporization or arc methods. The detailed mechanisms responsible for the growth of carbon nanotubes are not yet well understood. Variations in the most probable diameter and the width of the diameter distribution is sensitively controlled by the composition of the catalyst, the growth temperature and other growth conditions. 3.2 Structure of Carbon Nanotubes The structure of carbon nanotubes has been explored by high resolution TEM and STM characterization studies, yielding direct confirmation that the nanotubes are cylinders derived from the honeycomb lattice (graphene sheet). Strong evidence that the nanotubes are cylinders and are not scrolls comes from the observation that the same numbers of walls appear on the left and right hand sides of thousands of TEN images of nanotubes, such as shown in Fig. 14. In pioneering work, Bacon in 1960 [166] synthesized graphite whiskers which he described as scrolls, using essentially the same condtions as for the synthesis of carbon nanotubes, except for the use of helium pressures higher by an order of magnitude to synthesize the scrolls. It is believed that the cross-sectional morphology of multi-wall nanotubes and carbon whisker scrolls is different. A single-wall carbon nanotube is conveniently characterized in terms of its diameter dt, its chiral angle 8 and its 1D (onsdimensional) unit cell, as shown in Fig. 16(a). Measurements of the nanotube diameter dt and chiral angle 8 are conveniently made by using STM (scanning tunneling microscopy) and TEM (transmission electron microscopy) techniques. Measurements of the chiral angle 8 have been made using high resolution TEM [154, 167, and 8 is normally defined by taking 8 = Oo and 6' = 30°, for zigzag and armchair nanotubes, respectively. While the ability to measure the diameter dt and the chiral angle 8 of individual single-wall nanotubes has been demonstrated, it remains a major challenge to determine dt and 0 for specific nanotubes that are used for an actual physical property measurements, such as resistivity, Raman scattering, infrared spectra, etc. The circ_umference of any carbon nanotube is expressed in terms of the chiral vector ch = nfi1 + mfia which connects two crystallographically equivalent sites on a 2D graphene sheet [see Fig. 16(a)] [162]. The construction in 67 -+ Fig. 16. (a) The chiral vector OA or & = niL1 + miL2 is defined on the honeycomb lattice of carbon atoms by unit vectors iL1 and iL2 of a graphene layer and the chiral angle 0 with respect to the zigzag axis (0 = 0"). Also shown are the lattice vector OB= T of the 1D nanotube unit cell, the rotation angle $ a2d the translation 7'. The lattice vector of the 1D nanotube T is determined by ch. Therefore the integers (n, m) uniquely specify the symmetry of the basis vectors of a nanotube. The basic symmetry operation for the carbon nanotube is R 5 ($I?). The diagram is constructed for (n, m) = (4,2). (b) Possible chiral vectors ch specified by the pairs of integers (n, m) for general carbon nanotubes, including zigzag, armchair, and chiral nanotubes. According to theoretical calculations, the encircled dots denote metallic nanotubes, while the small dots are for semiconducting nanotubes [162]. -+ 68 Fig. 17. Schematic models for a single-wall carbon nanotubes with the nanotube axis normal to: (a) the B = 30” direction (an “armchair” (n, n) nanotube), (b) the 0 = 0’ direction (a “zigzag” (n, 0) nanotube), and (c) a general direction, such as OB (see Figure 16), with 0 < 0 < 30” (a “chiral” (n, m) nanotube). The actual nanotubes shown here correspond to (n, rn) values of: (a) (5,5), (b) (9,0), and (c) (10,5) [168]. Fig. 16(a) shows the chiral angle 8 between the vector C?h and the “zigzag” direction (0 = 0), and shows the unit vectors iL1 and 62 of the hexagonal honeycomb lattice [Figs. 16(a) and 171. An ensemble I of chiral vectors specified by pairs of integers (n, m) denoting the vector ch = n6l + m& is given in Fig. 16(b) [169]. The cylinder connecting the two hemispherical caps of the carbon nanotube is formed by superimposing the two ends of the vector C?h and the cylinder joint is made along the two lines OB and AB’ in Fig. 16(a). The lines OB and AB’ are both perpendicular to the vector eh at each end of 6h [162]. The intersection of OB with the first lattice point determines the fundamental 1D translation vector T’ and thus defines the length of the unit cell of the 1D lattice [Fig. 16(a)]. The chiral nanotube, thus generated has no distortion of bond angles other than distortions caused by the cylindrical curvature of the nanotube. Differences in the chiral angle B and in the nanotube diameter dt give rise to differences in the properties of the various graphene nanotubes. In the (n, m) notation for (?h = n&1 + miL2, the vectors (n, 0) or (0, m) denote zigzag nanotubes and the vectors (n, n) denote armchair nanotubes. All other vectors (n, rn) correspond to chiral nanotubes [169]. In terms of the integers (n, m), the nanotube diameter dt is given by + dt = &ac-c(m2 + mn + n2)1’2/x (2) 69 and the chiral angle 8 is given by e = tan-l(J?;n/(2m + n)). (3) The number of hexagons, N, per unit cell of a chiral nanotube is specified by the integers (n, m) and is given by 2(m2 + n2 + nm) dR N= (4) where dR is the greatest common divisor of (2n + m, 2m + n) and is given by (5) d 3d if n - m is not a multiple of 3d if n - m is a multiple of 3d, dR= { where d is the greatest common divisor of (n, m). The addition of a hexagon to the structure corresponds to the addition of two carbon atoms. As an example, application of Eq. (4) to the (5,5) and (9,O) nanotubes yields values of 10 and 18, respectively, for N. Since the 1D nanotube unit cell in real space is much larger than the 2D graphene unit cell, the 1D Brillouin zone is therefore much smaller than the one corresponding to a single 2-atom graphene unit cell. The application of Brillouin zone-folding techniques has been commonly used to obtain approximate electron and phonon dispersion relations for carbon nanotubes with specific symmetry (n, m), as discussed in 53.3. Because of the special atomic arrangement of the carbon atoms in a carbon nanotube, substitutional impurities are inhibited by the small size of the carbon atoms. Furthermore, the screw axis dislocation, the most common defect found in bulk graphite, is inhibited by the monolayer structure of the Cs0 nanotube. For these reasons, we expect relatively few substitutional or structural impurities in single-wall carbon nanotubes. Multi-wall carbon nanotubes frequently show “bamboo-like’’ defects associated with the termi- nation of inner shells, and pentagon-heptagon (5 - 7) defects are also found frequently [7]. 3.3 Electronic Structure Structurally, carbon nanotubes of small diameter are examples of a one- dimensional periodic structure along the nanotube axis. In single wall carbon nanotubes, confinement of the structure in the radial direction is provided by the monolayer thickness of the nanotube in the radial direction. Circumferen- tially, the periodic boundary condition applies to the enlarged unit cell that is formed in real space. The application of this periodic boundary condition to the graphene electronic states leads to the prediction of a remarkable electronic structure for carbon nanotubes of small diameter. We first present [...]... (1992) 30 R Taylor and D R M Walton, Nature (London) 36 3,685 (19 93) 31 G A Olah, I Bucsi, R Aniszfeld, and G K Surya Prakash, Carbon 30 , 12 031 21l(1992) ! 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(London) 38 6 ,37 7 (1996) 219 K Suenaga, C Colliex, N Demoncy, A Loiseau, H Pascard, and E Willaime, Science 278 (1997) 95 CHAPTER 3 Active Carbon Fibers TIMOTHY J MAYS Department of Materials Science and Engineering University o Bath f Bath BA2 7AK United Kingdom 1 Introduction It is usually the physical, especially mechanical, properties of carbon fibers that promote their use in advanced technologies For . 92j 3. 1'. 1.0' -1 .34 b, -3. 5' 30 .0b 5.3d, 3. 1", 3. 6f, 3. 0g,2.9Sh -9.7i 2 63, 19k 34 j, 55', 16' 0.44i 1.9 2.0i, 2.0', 3. 0" 168j, 37 0f,. Parameter K3C60 Rb&o a0 (A) 14.2 53& quot; 14. 436 " 19.7' 5.2", 4.0", 3. 6g, 3. 6h -7.8' 13j 26j, 30 1, 29", 17.5' 0 .38 i 0.12j 2.6j, 3. 11, 3. 4",. conclusion that the superconducting bandgap for both K3Cso and Rb3C60 is close to the BCS value of 3. 5 LT, [56, 64, 122, 130 1. A good fit for the functional form of the temperature dependence