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.

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What is a Carbon Nanotube?What is a Carbon Nanotube?

• Start with Carbon• Graphite• C60

• Single Wall Carbon Nanotubes• Multi Wall Carbon Nanotubes

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Start with CarbonStart 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 sp3 109 degree bonds– Graphitic sheet sp2 120 degree bonds. Each bond in same plane– Graphite s, px, py– Sheets held together by weaker van der Waals Forces

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Sp3 and sp2 BondsSp3 and sp2 Bonds3

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Discovery of CDiscovery of C6060

• 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

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CC6060

Ref: Intro to Nanotechnology

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Closed Network From Other AtomsClosed Network From Other Atoms

Ref: Intro to Nanotechnology

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Extension of CExtension of C6060, C, C7070, C, C8080

End closed

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Formation of an Armchair NanotubeFormation of an Armchair Nanotube

2D Graphene Sheet Chiral vector is bent

armchair (n,n)

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Unit Cell of 2D GrapheneUnit Cell of 2D Graphene9

(a) The unit cell and (b) Brillouin zone of two-dimensional graphite are shownas the dotted rhombus and shaded hexagon, respectively. ai, and bi, (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.

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““Roll” Carbon Nanotube from GraphiteRoll” Carbon Nanotube from Graphite

The unrolled honeycomb lattice of a nanotube, showing the unit vectors a1 and a2 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 Ch and the translational vector T of the nanotube, respectively. The rectangle OAB’B defines the unit cell for the nanotube. The figure corresponds to Ch = (4, 2)

nmmnaCCCL hhh 22

LD

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Constructing Nanotubes from a Graphene Sheet

Roll-up vector

a1a2

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3D Examples of 3 Types of Nanotubes 3D Examples of 3 Types of Nanotubes

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Some More Properties of NanotubesSome 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

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Metallic and Semiconducting CNTMetallic and Semiconducting CNT

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Examples of Band StructuresExamples of Band Structures

One-dimensional energy dispersion relations for (a) armchair (5, 5), (b) zigzag (9, 0), and (c) zigzag (10, 0) carbon nanotubes.

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Bandgap of Semiconductor TubeBandgap of Semiconductor Tube

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Observed Nanotube Species