6. Carbon nanostructures: fullerenes and carbon nanotubes 1

C is unique in its versatility Diamond (sp3 Carbon): -hardest material -perfect insulator or semiconductor when doped Graphene (sp2 Carbon): -soft material -highly anisotropic Acetylene (sp1 Carbon): Fullerenes (C 60 ): Diameter = 0.71 nm SMALLEY 1985 Nanotubes: Metallic or Semiconducting Diameter: nm Length: < 50 µm IIJIMA

Carbon materials 19th century: 1st fibre by T. A. Edison(from bamboo filaments) 1950s introduction of carbon reinforced materials (composites) PAN (polyacrylonitrile) fibres C-whiskers vapor phase grown (CVD) 1985 discovery of fullerenesand conjecture of Smalley of the possible existence of 1d fullerenes discovery by Iijima with TEM breakthrough 3

Graphene 4

         Single perfect sheet of graphite (so called graphene) 5

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                           7

               8

           9

     “  ”   LCAO bandstructure of graphene 10

Reciprocal lattive of graphene and the -point 11

Fullerenes 12

◆ C 20+2n ⇒ 12 pentagonal rings n hexagonal rings Coordination number =3, ∼ sp 2 hybridization C 60 C 70 C 78 13

◆ - 12 pentagons and 20 hexagons - Icosahedral (I h ) point group symmetry (5-fold rotation axis) - σ and π bonds, two bond lengths 1.40 Å and 1.45 Å - Found first in astronomic spectra, then obtained in carbon-arc shoot (end of 80´s) C 60 14

C 60, buckminsterfullerene Solid C 60, FCC close packing 3 Å 10 Å 15

Solid C 60 Van der Waals bonds between molecules FCC lattice low T: oriented C 60 -molecules High T: rotation of C 60 -molecules molecular bonding 16

17 C 60 solids C 60 doped solid M 3 C 60, M=alcaline metal metal or type II superconductor, as the lattice parameter is changed fcc, semiconductor 0.5 eV C 60

MoleculeSolid HOMO εFεF semiconductor metal semiconductor LUMO band-gap 18

M 3 C 60 compounds are superconducting (Type II) - Relatively high Tc (45 K for pure (Tl 2 Rb)C 60 ), higher than other intermetallic as Nb 3 Ge - a↑ ⇒ g(ε F ) ↑ ⇒ Tc↑ (BCS) 19

Atoms encapsulated in C 60 20

Carbon nanotubes 21

Produced in DC-arc struck between two carbon electrodes (Iijima, NEC, Tsukuba 1991) Single-walled nanotube (usually concentric multi-walled nanotubes) 22

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The first experimental electron microscope images published, S. Iijima, Nature (1991), reporting the discovery of carbon nanotubes. First electron microscope image and diffraction pattern from single-walled carbon nanotubes [S. Iijima & T. Ichihashi Nature 363, 603 (1993).] The smallest CN 27

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Carbon nanotubes: types and description 30

Nanotube geometry 31

Nanotube = wrapped sheet of graphite Chiral vector A A’ 32

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Armchair nanotubes n=m, chiral angle 30°. Zigzag nanotubes, either nor m are zero, chiral angle is 0°. Chiral nanotubes chiral angles intermediate between 0° and 30° 35

Carbon nanotubes: band structure 36

1D bands of CN Bandstructure of a (10; 10) armchair carbon nanotube. The shaded region is the 1: Brillouin zone. Note, each band is doubly degenerate, except for the ones crossing E = 0 and the ones with maximal and minimal energy. There are in total 40 bands. 37

1D character 38

Metallic and semiconducting nanotubes Zig-zag-tube Arm-chair-tube metal semimetalsemiconductor e - -pockets graphite 1. BZ 39

40 1D model

a)Zig-zag tube - 1 BZ of graphite: elctron pockets at K ⇒ metallic - Tubes: periodicity around the axis → allowed -values on lines - If n=3p, p ∈ integer ⇒ line of allowed -points intersects K ⇒ metallic zig-zag -wire (3p,n) - If n=3p+1, 3p+2 ⇒ semiconductor b)Arm-chair tube - Line of allowed -points intersects K ⇒ metallic ⇒ transistors? 41

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Carbon nanotubes: properties and applications 43

Single-wall carbon nanotubes are also expected to be very strong and to resist fracture under extension, just as the carbon fibers commonly used in aerospace applications Unlike carbon fibres, however, single-wall nanotubes are remarkably flexible. Mechanical properties Ultimate material in strength 44

Ruoff et al. Science 287, 637 (2000) Mechanics, pulling... 45

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Viola Barwich & Ernst Meyer, Basel SFM tips 47

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Vibrating Carbon Nanotubes Ebbesen et al, Nature 381, 678 (1996) 49

Raman (radial breathing modes) 50

Nanoelectronics Electronic properties 51

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Nanotube transistors Gate (Si) SiO 2 Source (Au) Drain(Au) Nanotube FET at room temperature SET a 4 K 53

FET (unipolar) 54

D electronic properties: quantization of conductance de Heer’s experiment

Optical properties 56

Nanotube lights (different colors). Light emission when an electric field is applied 57

Nanotubes for better TV screens Aligned carbon nanotubes into different patterns New flat screens, longer lasting, more energy efficient, thinner and flexible. 58

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Fullereness (C 60 ) encapsulated in single wall CNs 60

References Science and Application of Nanotubes, edited by D. Tomanek and R. J. Enbody, (Kluwer Academic/Plenum Publishers, 1999) M. S. Dresselhaus, G. Dresselhaus and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes; Academic Press: New York, Carbon Nanotubes, edited by M.S. Dresselhaus, G. Dresselhaus and Ph. Avouris (Springer, Berlin Heidelberg, New York 2001) Physics Today, May 1999, p22 Physics World, Vol.13, Issue 6, June 2000 R. Saito, G. Dresselhaus and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998, 1999,