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4. Single-Walled Carbon Nanotubes Sebastien Nanot, Nicholas A 105 Single-Walled4. Single-Walled Carbon Nanotubes Sebastien Nanot, Nicholas A. Thompson, Ji-Hee Kim, Xuan Wang, William D. Rice, Erik H. Hároz, Yogeeswaran Ganesan, Cary L. Pint, Junichiro Kono Single-walled carbon nanotubes (SWCNTs) are hol- walled nanotubes. Single-walled carbon nano- low, long cylinders with extremely large aspect tubes, the subject of this chapter, are especially ratios, made of one atomic sheet of carbon atoms interesting. They are ideal materials in which in a honeycomb lattice. They possess extraordinary to explore one-dimensional physics and strong Part A thermal, mechanical, and electrical properties and Coulomb correlations. In addition, their cylindri- are considered as one of the most promising nano- cal topology allows them to exhibit nonintuitive materials for applications and basic research. This quantum phenomena when placed in a paral- 4 chapter describes the structural, electronic, vibra- lel magnetic field, due to the Aharonov–Bohm tional, optical, transport, mechanical, and thermal effect. A number of research groups have found properties of these unusual one-dimensional (1-D) exotic many-body effects through a variety of nanomaterials. The crystallographic (Sect. 4.2.1), transport, optical, magnetic, and photoemission electronic (Sect. 4.2.2), vibrational (Sect. 4.2.3), experiments. optical (Sect. 4.4), transport (Sect. 4.5), thermal Their electronic properties are very sensitive to (Sect. 4.6.1), and mechanical (Sect. 4.6.2)proper- their microscopic atomic arrangements and sym- ties of these unusual 1-D nanomaterials will be metry, covering a wide spectrum of energy scales. outlined. In addition, we will provide an overview They can be either metallic or semiconducting with of the various methods developed for synthesizing varying band gaps, depending on their diam- SWCNTsinSect.4.3. eter and chirality. Semiconducting nanotubes are Even after more than two decades of exten- particularly promising for photonic device applica- sive basic studies since their discovery, carbon tions with their diameter-dependent, direct band nanotubes continue to surprise researchers with gaps, while metallic tubes are considered to be potential new applications and interesting discov- ideal candidates for a variety of electronic applica- eries of novel phenomena and properties. Because tions such as nanocircuit components and power of an enormous thrust towards finding practical transmission cables. applications, carbon nanotube research is ac- tively being pursued in diverse areas including 4.1 History ................................................ 106 energy storage, molecular electronics, nanome- chanical devices, composites, and chemical and 4.2 Crystallographic and Electronic Structure 106 bio-sensing. 4.2.1 Crystallographic Structure.............. 106 Structurally, carbon nanotubes are made up 4.2.2 Electronic Dispersion .................... 107 of sp2-bonded carbon atoms, like graphite, and 4.2.3 Phonon Dispersion ....................... 109 can be conceptually viewed as rolled-up sheets of 4.3 Synthesis ............................................. 111 single-layer graphite, or graphene. Their diam- 4.3.1 Substrate-Free Growth Techniques. 112 eter typically lies in the nanometer range while 4.3.2 Substrate-Bound Growth their length often exceeds microns, sometimes Technique ................................... 113 centimeters, thus making them 1-D nanostruc- 4.3.3 Growth Mechanisms ..................... 114 tures. Depending on the number of tubes that are arranged concentrically, carbon nanotubes are 4.4 Optical Properties ................................. 115 further classified into single-walled and multi- 4.4.1 Optical Absorption and Photoluminescence................ 116 !"#$%&'%(#)*+",-#!"#$%&'#()*%+,--.(-/(0*%-1*2'#$*34-#./0#12"122345367879:;7;2<5<76=:-# >#?@A(BCDA7$DAE%C#FDAE(B#GD(+DEHDAC#;218# 106 Part A NanoCarbons 4.4.2 Raman Spectroscopy..................... 118 4.6 Thermal and Mechanical Properties........ 128 4.4.3 Resonant Rayleigh Spectroscopy..... 119 4.6.1 Thermal Properties ....................... 128 4.4.4 Ultrafast Spectroscopy................... 120 4.6.2 Mechanical Properties................... 130 4.4.5 Excitonic Effects ........................... 121 4.7 Concluding Remarks ............................. 135 4.5 Transport Properties ............................. 123 References .................................................. 135 4.1 History This chapter summarizes some of the basic properties of graphene, i. e., a honey-comb lattice of sp2-bonded of carbon nanotubes (CNTs), one of the most ideal re- carbon atoms. The one-dimensionality of SWCNTsis Part A alizations of one-dimensional (1-D) systems available attractive, allowing researchers to explore exotic 1-D today. Since their discovery [4.1], much attention has physics in the quantum regime [4.6]andnewfunc- been given to their unique structure and properties that tionalities in optoelectronic devices [4.7, 8]. The strong 4.2 are promising for a wide range of applications and fun- 1-D confinement of electrons and phonons results in damental physical and chemical studies [4.2–5]. These unique anisotropic effects in various properties, e.g., hollow crystals of sp2-bonded carbon atoms have exhib- polarization-dependent Raman scattering [4.9]andop- ited a variety of extraordinary thermal, mechanical, and tical absorption [4.10–12], large magnetic susceptibility electrical properties and phenomena, fascinating scien- anisotropies [4.13–17], and anisotropic terahertz dy- tists and engineers in diverse disciplines. Even after namic conductivities [4.18–21]. more than two decades of extensive basic studies since One of the most striking properties of SWCNTs their discovery, they continue to surprise researchers is their chirality-dependent metallicity. Namely, de- through exciting discoveries of phenomena and prop- pending on their microscopic atomic arrangements and erties as well as novel potential applications, including symmetry, a SWCNT can be either metallic or semicon- energy storage, molecular electronics, nanomechanical ducting. A subtle structural difference leads to opening devices, composites, and chemical and bio-sensing. or closing of a band gap, which is also tunable by The diameters of carbon nanotubes are in the amagneticfieldappliedparalleltothetubeaxisviathe nanometer range while their lengths are typically mi- Aharonov–Bohm effect [4.10, 22–25]. Semiconducting crons and often millimeters, corresponding to aspect nanotubes are particularly promising for photonic de- ratios of millions, especially in single-walled carbon vice applications with their diameter-dependent, direct nanotubes (SWCNTs), the most prominent member of band gaps, while metallic tubes are considered to be the carbon nanotube family. A typical SWCNT has ideal candidates for a variety of electronic and electrical a diameter of 1nmandconsistsofjustoneatomic applications ranging from nano-circuit wires to power sheet, which can≈ be pictured as a rolled-up version transmission cables. 4.2 Crystallographic and Electronic Structure A SWCNT can be viewed as a graphene sheet rolled study we refer the reader to some of the many published into a cylinder which is terminated by two half-fullerene books [4.2, 5, 26–28]. caps. The diameter of these species typically ranges from 0.7to2.5nm,andtheiraspectratiocanbeashigh 4.2.1 Crystallographic Structure as 104 –105.Thisverystrongconfinementalongtheir circumference make them behave like 1-D materials. To give a formal description of the crystal structure The purpose of this section is to describe the crystal- of a SWCNT,itiseasiesttofirstconsideritspar- lographic and electronic structure of SWCNTs, which ent material, graphene. Graphene is a monolayer of will be used throughout the text. For a more detailed sp2-hybridized carbon atoms arranged in a honeycomb Single-Walled Carbon Nanotubes 4.2 Crystallographic and Electronic Structure 107 lattice. Its unit cell is defined by the primitive vectors a 1 a) and a2 (bottom right of Fig. 4.1,forareviewsee[4.29]). y Each SWCNT is then indicated by a chiral vector Ch, B' which specifies the two atoms of the graphene sheet which are identified upon formation of the tube (see the B x points O and A in Fig. 4.1). The chiral vector is defined with respect to the graphene primitive vectors as T θ Ch na1 ma2 (n, m) , (4.1) ≡ + ≡ R A where n and m are integers such that 0 m n.When ≤ ≤ a1 we express the chiral vector Ch in the form (n, m), we O Ch call it the chiral index.Thesetwotermsshouldbere- garded as synonymous. The angle θ formed between Ch a2 Part A and a1 is a quantity of great importance for determining the electronic properties of the SWCNT;itiscalledthe b) Zigzag chiral angle,andisdefinedthrough 4.2 Ch a1 2n m (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0) (9,0) (10,0) (11,0) cos θ · + . (4.2) = Ch a1 = 2√n2 m2 nm (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (7,1) (8,1) (9,1) (10,1) | || | + + The nanotube diameter can be computed from the chiral (2,2) (3,2) (4,2) (5,2) (6,2) (7,2) (8,2) (9,2) (10,2) vector by (3,3) (4,3) (5,3) (6,3) (7,3) (8,3) (9,3) (4,4) (5,4) (6,4) (7,4) (8,4) (9,4) aC C 2 2 dt Ch /π − 3(m mn n ) , (4.3) = | | = π + + y (5,5) (6,5) (7,5) (8,5) ! a1 where aC C 1.44 Å is the nearest neighbor distance (6,6) (7,6) (8,6) − ≈ between carbon atoms in graphene. a2 (7,7) x SWCNTscanbeclassifiedintothreemaintypes: Armchair 1. Armchair nanotubes for which n m (i. e. Ch (n, n)) = = 2. Zig-zag nanotubes for which m 0(i.e.Ch Fig. 4.1 (a) The unrolled hexagonal lattice of a nanotube. = = (n, 0)) When we connect sites O–A, and B–B',ananotubecan 3. Chiral nanotubes (n m 0) whose mirror images be constructed. OA and OB define the chiral vector Ch have a different structure&= and&= display different prop- and the translational vector T of the nanotube, respectively. erties, for example in circular dichroism. The rectangle OAB'Bdefinestheunitcellforthenanotube. The vector R denotes a symmetry vector. (b) The hexago- Armchair and zigzag nanotubes (having the high- nal lattice of all possible (n, m)speciesformedbyrolling est symmetry) (Fig. 4.1b) are named after the shape of the (0, 0) point onto (n, m).
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