1. S. E. Thompson EEL 6935 1 What is a Carbon Nanotube? Start with Carbon Graphite C 60 Single Wall Carbon Nanotubes Multi Wall Carbon Nanotubes

2. S. E. Thompson EEL 6935 2 Start with Carbon Carbon contains six electrons (1s) 2, 2s, 2px,2py, 2pz 1s quantum number N=1 (2 electrons) N=2, four electrons s orbital spherically symmetric about nucleous p directed charge distribution s and p form chemical bond  = s + p Solid carbon two main structures –Diamond sp 3 109 degree bonds –Graphitic sheet sp 2 120 degree bonds. Each bond in same plane –Graphite s, px, py –Sheets held together by weaker van der Waals Forces

3. S. E. Thompson EEL 6935 Sp3 and sp2 Bonds 3

4. S. E. Thompson EEL 6935 4 Discovery of C 60 Soccer ball-like molecule containing 60 carbon atoms Motivated by understanding light transmission through interstellar dust Optical extinction: absorption and scattering of light from interstellar dust C60 envisioned by theoretical chemist High powered pulsed laser simulate conditions of hot carbon Prof. Richard Smalley (Rice) observed mass number 720 mass spectrometer (carbon mass #12) Smalley won Nobel prize

5. S. E. Thompson EEL 6935 5 C 60 Ref: Intro to Nanotechnology

6. S. E. Thompson EEL 6935 6 Closed Network From Other Atoms Ref: Intro to Nanotechnology

7. S. E. Thompson EEL 6935 7 Extension of C 60, C 70, C 80 End closed

8. S. E. Thompson EEL 6935 8 Formation of an Armchair Nanotube 2D Graphene Sheet Chiral vector is bent armchair (n,n)

9. S. E. Thompson EEL 6935 Unit Cell of 2D Graphene 9 (a) The unit cell and (b) Brillouin zone of two-dimensional graphite are shown as the dotted rhombus and shaded hexagon, respectively. a i, and b i, (i = 1, 2) are unit vectors and reciprocal lattice vectors, respectively. Energy dispersion relations are obtained along the perimeter of the dotted triangle connecting the high symmetry points, , K and M.

10. S. E. Thompson EEL 6935 10 “Roll” Carbon Nanotube from Graphite The unrolled honeycomb lattice of a nanotube, showing the unit vectors a 1 and a 2 for the graphene sheet. When we connect sites O and A, and B and B’, a nanotube can be constructed. OA and OB define the chiral vector C h and the translational vector T of the nanotube, respectively. The rectangle OAB’B defines the unit cell for the nanotube. The figure corresponds to C h = (4, 2)

11. S. E. Thompson EEL 6935 11 Constructing Nanotubes from a Graphene Sheet Roll-up vector a1a1 a2a2

12. S. E. Thompson EEL 6935 12 3D Examples of 3 Types of Nanotubes

13. S. E. Thompson EEL 6935 13 Some More Properties of Nanotubes 1-50nm in diameter 10 - 100 micrometer long End capped with half fullerene molecule Single and multi-wall nanotubes Chirality refers to how the tubes are rolled One-third metallic, two-thirds semiconducting Energy gap: 1/(diameter of tube) –Diameter of tube increases, bandgap decreases

14. S. E. Thompson EEL 6935 14 Metallic and Semiconducting CNT

15. S. E. Thompson EEL 6935 15 Examples of Band Structures One-dimensional energy dispersion relations for (a) armchair (5, 5), (b) zigzag (9, 0), and (c) zigzag (10, 0) carbon nanotubes.

16. S. E. Thompson EEL 6935 16 Bandgap of Semiconductor Tube

17. S. E. Thompson EEL 6935 17 Observed Nanotube Species