CARBON NANOTUBES - 1.2. Carbon Nanotubes and Their Fundamental Parameters Nanotubes might be defected

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    MATRICULATION # 169026

    Date: July 2, 2010


    1. Carbon

    1.1 Bonding of Atoms in Carbon Materials

    1.2 Carbon Nanotubes and Their Fundamental Parameters

    1.2.1 Defect-Free Nanotube

    1.2.2 Defective Nanotubes

    2. Properties of Carbon Nanotubes

    2.1 Electronic Properties

    2.2 Optical and Optoelectronic Properties

    2.3 Mechanical and Electromechanical Properties

    2.4 Magnetic and Electromagnetic Properties

    2.5 Chemical and Electrochemical Properties

    2.5.1 Opening

    2.5.2 Wetting and Filling

    2.5.3 Adsorption and Charge Transfer

    2.5.4 Chemical Doping, Intercalation, and Modification

    2.6 Thermal and Thermoelectric Properties

    3. Progress of Single-walled carbon nanotube research

    4. References

  • 1. Carbon

    Carbon is the most versatile element in the periodic table, owing to the type, strength, and

    number of bonds it can form with many different elements. The diversity of bonds and their

    corresponding geometries enable the existence of structural isomers, geometric isomers, and

    enantiomers. These are found in large, complex, and diverse structures. The last few years have

    seen a large growth in the scientific interest in inorganic nanotubes and fullerene-like

    nanoparticles. Numerous studies have been published in this area.

    1.1. Bonding of Atoms in Carbon Materials

    To understand the structure and properties of carbon materials, the bonding structure and

    properties of carbon atoms are discussed first. A carbon atom has six electrons with two of them

    filling the 1s orbital. The remaining four electrons fill the sp 3 or sp

    2 as well as the sp hybrid

    orbital, responsible for bonding structures of diamond, graphite, nanotubes, or fullerenes, as

    shown in Figure 1.

    In diamond, the four valence electrons of each carbon occupy the sp3 hybrid orbital and

    create four equivalent σ covalent bonds to connect four other carbons in the four tetrahedral

    directions. This three-dimensional interlocking structure makes diamond the hardest known

    material. Diamond also has a high index of refraction, which makes large diamond single

    crystals gems. Diamond has unusually high thermal conductivity.

    In graphite, three outer-shell electrons of each carbon atom occupy the planar sp 2 hybrid

    orbital to form three in-plane σ bonds with an out-of-plane orbital (bond). This makes a planar

    hexagonal network. Van der Waals force holds sheets of hexagonal networks parallel with each

    other with a spacing of 0.34 nm. Graphite is stronger in-plane than diamond. In addition, an out-

    of-plane orbital or electron is distributed over a graphite plane and makes it more thermally

    and electrically conductive. The interaction of the loose electron with light causes graphite to

    appear black. The weak van der Waals interaction among graphite sheets makes graphite soft and

    hence ideal as a lubricant because the sheets are easy to glide relative to each other.

    A CNT can be viewed as a hollow cylinder formed by rolling graphite sheets. Bonding in

    nanotubes is essentially sp 2 . However, the circular curvature will cause quantum confinement

    and rehybridization in which three σ bonds are slightly out of plane; for compensation, the

    orbital is more delocalized outside the tube. This makes nanotubes mechanically stronger,

    electrically and thermally more conductive, and chemically and biologically more active than

  • graphite. In addition, they allow topological defects such as pentagons and heptagons to be

    incorporated into the hexagonal network. For convention, we call a nanotube defect free if it is of

    only hexagonal network and defective if it also contains topological defects such as pentagon and

    heptagon or other chemical and structural defects.

    Fullerenes are made of 20 hexagons and 12 pentagons. The bonding is also sp 2 , although

    once again mixed with sp 3 character because of high curvature. The special bonded structures in

    fullerene molecules have provided several surprises such as metal–insulator transition, unusual

    magnetic correlations, very rich electronic and optical band structures and properties, chemical

    functionalizations, and molecular packing. Because of these properties, fullerenes have been

    widely exploited for electronic, magnetic, optical, chemical, biological, and medical applications.

    (a) (b)


    Figure 1 Bonding structures of diamond (a), graphite (b), nanotubes (c), and fullerenes (c).

    1.2. Carbon Nanotubes and Their Fundamental Parameters

    Nanotubes might be defected or defect-free. Both types of nanotubes have been paid

    attention during the last two decades. In this section, the fundamental parameters for defected

    and defect-free carbon nanotubes are summarized and the basic relations governing these

    parameters are also given.

    1.2.1. Defect-Free Nanotubes

    There has been a tremendous amount of work studying defect-free nanotubes, including

    single or multiwalled nanotubes (SWNTs or MWNTs). A SWNT is a hollow cylinder of a

    graphite sheet whereas a MWNT is a group of coaxial SWNTs. SWNT was discovered in 1993,

    2 years after the discovery of MWNT. They are often seen as straight or elastic bending

    structures individually or in ropes by scanning electron microscopy (SEM), transmission electron

  • microscopy (TEM), atomic force microscopy (AFM), and scanning tunneling microscopy

    (STM). In addition, electron diffraction (EDR), x-ray diffraction (XRD), Raman, and other

    optical spectroscopy can also be used to study structural features of nanotubes.

    A SWNT can be visualized as a hollow cylinder, formed by rolling over a graphite sheet.

    It can be uniquely characterized by a vector C in terms of a set of two integers (n, m)

    corresponding to graphite lattice vectors a1 and a2 (Figure 2),

    C = na1+ ma2 (1.1)

    Thus, the SWNT is constructed by rolling up the sheet such that the two end-points of the

    vector C are superimposed. This tube is denoted as (n, m) tube with diameter given by


    where a = |a1| = |a2| is lattice constant of graphite. The tubes with m = n are commonly referred

    to as armchair tubes and m = 0 as zigzag tubes. Others are called chiral tubes in general with the

    chiral angle, θ defined as that between the vector C and the zigzag direction a1,


    θ ranges from 0 for zigzag (m = 0) and 30° for armchair (m=n) tubes. The lattice constant

    and intertube spacing are required to generate a SWNT, SWNT bundle, and MWNT. These two

    parameters vary with tube diameter or in radial direction. Most experimental measurements and

    theoretical calculations agree that, on average, the C–C bond length dcc = 0.142 nm or a = |a1| =

    |a2| = 0.246 nm and intertube spacing dtt = 0.34 nm. Thus, equations (1.1) to (1.3) can be used to

    model various tube structures and interpret experimental observations.

    Figure 2 Rolling of a graphite sheet along the chiral vector C = na1 + ma2 on the graphite to form a nanotube (n, m).

    By rolling graphite sheet in different directions, two typical nanotubes can be obtained: zigzag (n, 0), armchair (m,

    m) and chiral (n, m) where n>m>0 by definition.

  • Strain energy caused by forming a SWNT from a graphite sheet is proportional to 1/D per

    tube or 1/D 2 per atom. It is suggested that a SWNT should be at least 0.4 nm large to afford

    strain energy and at most about 3.0 nm large to maintain tubular structure and prevent collapsing.

    The smallest innermost tube in a MWNT was found to be as small as 0.4 nm whereas the

    outermost tube in a MWNT can be as large as hundreds of nm. But, typically, MWNT diameter

    is larger than 2 nm inside and smaller than 100 nm outside. A SWNT rope is formed usually

    through a self-organization process in which van der Waals force holds individual SWNTs

    together to form a triangle lattice with lattice constant of 0.34 nm.

    The significance of the tube chirality (n, m) is its direct relation with the electronic

    properties of a nanotube. STM can be used to measure tube geometry (d, θ)

    be used to derive (n, m).

    1.2.2. Defective Nanotubes

    Besides defect-free nanotubes, experimentally observed structures also include the

    capped, bent, branched (L, Y, and T), and helical MWNTs, and the bent, capped, and toroidal

    SWNTs. Figure 3 shows TEM images of some o