Structure and Properties of CNT

  • Structures of carbon nanotubes

    Having diameters of about one nanometer, carbon nanotubes are synthesized when graphite sheets are rolled roundly and they show metallic characteristics or semiconductor characteristics with the rolling angles of graphite sheets.
    With wall numbers making up of carbon nanotubes, carbon nanotubes are classfied to single-walled nanotubes, multi-walled nanotubes and rope nanotubes. Figure 1 shows the structures of nanotubes.
    As it is shown in Figure 1, carbon nanotubes have two possible symmetric structures known as zigzag and armchair types. Actually, most carbon nanotubes have chiral structures where hexagons are aligned helically on tubular axis in stead of having those structures mentioned above.
    A simple way to classify each nanotube structure is a vector which connects tow points on the graphene lattice and it is designated with Ch. Rolled to meet the two points of the vector, the plane becomes a cylinder.
    Figure 2(a) shows graphene layer designated by Dresselhaus’ way. In the figure, the integer couple(n,m) expresses the possible structures of carbon nanotubes. Therefore, we can designate vector Ch with n and m as follows.
     
    Ch = na1 + ma2

    a1 and a2 are the unit vector of graphene layer and n ³m. In zigzag tubes m=0 and in armchair tubes, n=m values. The tubes different from the above conditions called “chiral”.
    The electrical properties of carbon nanotubes are metallic or semiconductor periodically as a function of diameter and chirality, and according to theoretical research a third of SWNT is metallic and the other is semiconductor whose band gap is inversely proportional to diameters of nanotubes. Generally when n-m=3q (where q is integer), (n,m) nanotubes have metallic properties as it is shown in Figure 2(b). All armchair structure nanotubes and about a third of zigzag structure nanotubes have metallic properties.
    While general metals have plane DOSes (density of state), each peak of the nanotube DOS has a lot of singularities in accordance with single quantum subband. These singularities are important to analysis the experimental data of STS (scanning tunneling spectroscopy) and resonant raman spectra.

  • Physics of Carbon nanotubes

    As we have dicussed, carbon nanotubes have the cylindrical structures which nanoscaled graphite sheets are rolled roundly, and they are macromolecules having unique physical properties with their sizes and shapes.
    Even if many researching groups have preceeded a lot of experiments to exam the physical properties of nanotubes on structures, we still have many problems to be resolved since carbon nanotubes have various physical properties on their diameters, lengths and chiralities.  
    In the next, we are going to describe electrical, thermal and mechanical properties, known to public recently, of carbon nanotubes.

  1. The electrical properties : In 1998, Frank measured conductivity of carbon nanotubes with SPM (Scanning Probing Microscopy) as dipping carbon nanotube into liquid mercury.
    As a result, he reported that carbon nanotubes show quantum mechanical behaviors and also have ballistic conductance. The conductivity of MWNT increased as much as 1 Go whenever nanotubes were added into liquid mercury. The value of 1 Go is 1/12.9 kW-1 . Sanvito et. al. measured conductivity of MWNt using scattering method and they reconfirmed Frank’s results.
    They also observed reduction of quantum mechanical conductive channel in the inside of MWNT and rearrangement of electron flow of each carbon nanotube by interwall reactions.
    Thess group found that the resistivity of rope shaped metallic SWNT is about 10-4 W-cm measured with four-point probe at 300 K and it is considered to be a higher value than that of high conductive carbon nano fiber. Frank et. al. and Avouris et. al. observed that the stable current densities are 107 A/cm2 and 1013 A/cm2 respectively.
  2. Thermal properties : The carbon nanotube’s thermal conductivity is dependent on a temperature and mean free path of phonons.
    In 1999, Hone et. al. reported that the conductivity of a carbon nanotube has a linear function of temperature : it has linear relationship at 7~25 K range, the gradient increases at 25~40 K range
    Where kz is thermal conductivity, C is the heat capacity, v is sound velocity. Hone et. al. introduced at room temperature, the conductivity of a single-walled nanotube rope is existing between 1,800 and 6,000 W/mK range.
    In 1999, Goddard group numerically calculated that the conductivity of (10,10) nanotube approaches to 2,980 W/mK as increasing applied current.
    In 2000, Tomanek group researched the correlation between thermal conductivity and temperature and it became a chance to reconfirm that at room temperature the thermal conductivity is very high value of 6,600 W/mK, which Hone et. al. suggested, and they theoretically verified that the value is caused by the very long mean free path of the phonon.
    However, Barber et. al. insisted that the correlation between thermal conductivity and temperature should have different characteristics rather than linearity. Namely, they reported it rises to the maximum value of 37,000 W/mK to 100K and it falls abruptly to 3,000 W/mK at 40 K.
  3. Mechanical properties : Recently, many research groups have studied the elastic behavior of SWNT in nanotube field. Mostly, SWNT is from 10 to 100 times stiffer than steel and it also shows a considerably strong endurance against physical shocks. When a force is given on a tip of a nanotube, the nanotube bends without any damage and when the force is removed, the nanotube goes back to its original state.
    However, to quantityfy this phenomena is known as a very difficult problem. The research teams of Princeton and Illinois in USA measured that the average Young’s modulus is 1.8 TPa in 1996. After they stood tubes randomly, the micro-photographs of tips were taken and the Young’s Modulus was calculated from the blur quantity at various temperatures. In 1997 Goddard showed various Young’s Moduluses of nanotubes: (10,10) armchair nanotube 640.30 GPa, (17,0) zizag nanotube 648.43 GPa and (12,6) chiral nanotube 673,93 GPa. These values were calculated from potentional’s two dimensional differential coefficient and it is shown that they considerably differ from the 1.8 TPa calculated above. In 1998, Treaty group reported the elastic modulus is 1.25 TPa and it is comparable to 1.28 TPa which was observed by Wong et. al. in MWNT in 1997.
    They made a tip of a nanotube, which doesn’t adhere on a supporting structure, deviated from the equilibrium state with an AFM and measured the modulus by recording the force applied on the tip. In 1999, Rubio et. al. showed the Young’s modulus of SWNT depends on its diameter and chirality through tight-binding calculation and also reported the moduluses are 1.22 TPa for the (10,0) and (6,6) tubes and 1.26 TPa for the (20,0) nanotube.
    In above results, we can know that for SWNT, the elastic modulus is strongly dependent on the diameter and structure. In the meanwhile, in 1999 Forro et. al. reported that for the MWNTs, their diameters don’t influence to modulus considerably, but mostly the modulus depends on their structural sides such as defects in nanotubes.
    They also reported the SWNT bundles, whose diameters are 15~20 nm, have the modulus of 100 GPa. They continue controversy about the Modulus and it is reported that this is caused by the reason why the researchers have analyzed the thickness of nanotubes by their own ways.
    Generally, if carbon molecules have a cylinder shaped perfect solid state, modulus would show smaller values than the values discussed in advance and we can imagine as decreasing the wall thickness of tubular carbon molecules, the modulus would increase.