Topic 5: Carbon nanotubes

Question 1

• Describe the different ways in which carbon nanotubes can be folded

Answer 1

• Lattice vectors (a₁, a₂) affect how tube is rolled up and define roll up vector
• The two extremes of this are zigzag (n, 0) and armchair (n, n)
• Roll determines whether tube will behave as a metal or a semi-conductor electronically (function of chirality of tube)
• For semiconducting tubes, the diameter of the tube will change the band gap

Question 2

• What is a single wall carbon nanotube?

Answer 2

• A graphene (sp² carbons) sheet wrapped in to a tube of around 0.4 nm in diameter

Question 3

(?) How can a SWCNT possess variable electronic structure?

Answer 3

• The energy-k dispersion relation for graphene relates the momentum of electrons (p = ħk) and the wave vector of those electrons (k = 2π/ λ)
• Whole # of λ’s for electron wavefunctions confined to circumference of nanotube.
• Momentum states continuously move around section of circumference of tube.
• K vector will take any value along length of tube
• P_x propagation is quantised, resulting in slices of overall 2D plot, each defining all possible electron states in CB/VB
• Graphene is a flat sheet, therefore electrons can propagate in 2D
• Electron on axis rolls down PES to minima corresponding hole travels up VB to maxima
• Dirac point are where bands touch
• If passing through a Dirac point, corresponds to a metallic section of the nanotube, but most of the tube is semiconducting.

Question 4

• What is the relationship between chiral indices/roll up vector (n, m) of a SWCNT and its diameter?

Answer 4

• d = (a_C-C * √3 * (n² + m² + nm)^0.5)/π

Question 5

• What is the relationship between the band gap of a nanotube and its diameter?

Answer 5

• E_g = (2γ₀*a_C-C)/d

γ₀ = tight binding overlap energy

Question 6

• SWCNT has a … carrier mobility x… that of Si, which is … , meaning charges move along length of tube without being scattered

Answer 6

• SWCNT has a charge carrier mobility x10 that of Si, which is ballistic, meaning charges move along length of tube without being scattered

Question 7

• Outline two doping methods of semi-conducting nanotubes. WHat is an advantgae and disadvantage of this?

Answer 7

• n/p doping can be used to introduce defects
• intercalation of n/p dopant by heating vapour; n/p-type
• defect dangling bond created through σ-bond break, leave trapped π-e^- in wall; p-type
• an electron donor/acceptor can be covantly bound (e.g. COOH powerful electron acceptor; p-type
• doping increases conductvity however distrupt conjugtaion, reducing mobility

Question 8

• n/p type forms of doping reduce charge carrier … of SWCNT, what is another method of charge transfer doping that does not have this result?

Answer 8

• n/p type forms of doping reduce charge carrier mobility of SWCNT,
• Adsorb TCNQ on to SWCNT surface
• TCNQ significantly reduces the hole injection barrier as is a powerful electron acceptor with a very low LUMO, allowing spontaneous charge to transfer to occur

Question 9

• Unlocking full potential of SWCNT lies in synthesis of only one … type (… or … ) thereby forming a … … … structure.

Answer 9

• Unlocking full potential of SWCNT lies in synthesis of only one electronic type (semiconducting or metallic) thereby forming a continuous undisrupted pi structure.