A carbon material formed by rolling graphene into a tube about 1 nm to several tens of nanometers in diameter. Depending on the rolling direction (the chiral indices) it can be metallic or semiconducting, and its strength along the axis is extremely high.
Japanese name: カーボンナノチューブ
Carbon nanotube appears in 3 practice questions across 1 topic, including Nanomaterials.
Field: Nanomaterials
A carbon nanotube (CNT) has the structure of graphene, carbon atoms arranged in hexagons by sp² bonds, rolled seamlessly into a cylinder. There are single-walled CNTs with just one layer and multiwalled CNTs with many concentric layers; the interlayer spacing of multiwalled CNTs is about 0.34 nm, close to that of graphite. The rolling direction is given by the pair of integers (n, m) of the chiral vector Ch = na₁ + ma₂, which becomes the circumference; n = m is called armchair, m = 0 zigzag, and the rest chiral. The diameter can be calculated as d = a√(n² + nm + m²)/π (a = 0.246 nm), and most single-walled CNTs are about 1–2 nm.
The electronic states of a single-walled CNT are determined by which of graphene's band states survive, namely only the wave vectors allowed as standing waves around the circumference. When a line of allowed wave vectors passes through the K point, where graphene's conduction and valence bands touch, that is, when n − m is a multiple of 3, the tube is metallic; otherwise it is semiconducting. All armchair tubes are metallic. The band gap of semiconducting CNTs is roughly inversely proportional to the diameter, a few tenths of an eV to about 1 eV at a diameter of about 1 nm. Ordinary synthesis produces a mixture of metallic and semiconducting tubes, so separation or selective growth is a challenge for applications such as transistors.
Along their axis, CNTs are joined only by strong sp² bonds, so they have a very high Young's modulus of about 1 TPa and tensile strengths of several tens of GPa, with a low density of about 1.3–2 g/cm³. Their axial thermal conductivity is also high. Exploiting these properties, they are used as small additions to resins and rubbers to raise conductivity and strength, as conductive additives in lithium-ion battery electrodes, in transparent conductive films and as interconnect materials. To bring out the outstanding properties of a single CNT in large materials such as bundles, yarns and composites, however, dispersion, alignment and load transfer between CNTs must be engineered.
Answer: A. The (6, 6) armchair tube
A single-walled carbon nanotube is a cylinder made by rolling a graphene sheet so that the chiral vector Ch = na₁ + ma₂ becomes the circumference. Whether it is metallic or semiconducting depends on whether wave vectors passing through the K point, where the graphene bands touch, are allowed around the circumference, and the condition is that n − m is a multiple of 3. (6, 6) has n − m = 0, so it is metallic, and all armchair tubes, with n = m, are metallic. (10, 0) has n − m = 10 and (7, 5) has n − m = 2; neither is a multiple of 3, so both are semiconducting. Zigzag tubes (m = 0) are metallic only when n is a multiple of 3. For randomly chosen chiral indices, about one third are metallic and two thirds semiconducting.
Answer: B. About 1.36 nm
n² + nm + m² = 100 + 100 + 100 = 300, so √300 ≈ 17.32. The length of the chiral vector (the circumference) is 0.246 × 17.32 ≈ 4.26 nm, and dividing by π gives a diameter d ≈ 1.36 nm. About 4.26 nm forgets to divide by π and takes the circumference as the diameter. About 0.78 nm uses the C–C bond length of 0.142 nm instead of the lattice constant a = 0.246 nm, confusing the relation a = √3 × 0.142 nm. (10, 10) is an armchair tube and so is metallic. Most single-walled carbon nanotubes have diameters of about 1–2 nm.
Besides arc discharge and laser ablation, mass production mainly uses chemical vapor deposition (CVD), in which hydrocarbons are decomposed and CNTs grow from fine catalyst particles of iron, cobalt and the like. The CNT diameter can be controlled to some extent by the size of the catalyst particles.
n − m is a multiple of 3 about one third of the time, so about one third are metallic and about two thirds semiconducting.
Multiwalled CNTs contain a mixture of metallic and semiconducting layers, and the band gaps of the wide outer layers are small, so overall they usually show metallic conduction.
A single-walled carbon nanotube is a cylinder made by rolling a graphene sheet so that the chiral vector Ch = na₁ + ma₂ becomes the circumference.
The electronic properties of a single-walled carbon nanotub…Most single-walled carbon nanotubes have diameters of about 1–2 nm.
The diameter of a single-walled carbon nanotube is given by…The sol-gel method, condensation from the vapor phase and CVD growth of carbon nanotubes are also bottom-up methods.
Methods for making nanomaterials are divided into top-down …Graphene Bottom-up synthesis BET method Melting point depression of nanoparticles Quantum dot Specific surface area Zeta potential