A single atomic layer of carbon atoms arranged in a honeycomb lattice by sp² bonds. Its band gap is essentially zero, its electron mobility is high, and its theoretical specific surface area counting both sides is about 2630 m²/g.
Japanese name: グラフェン
Graphene appears in 3 practice questions across 1 topic, including Nanomaterials.
Field: Nanomaterials
Graphene is a single atomic layer of carbon, one layer peeled from graphite. In 2004 Geim and Novoselov isolated single layers by peeling graphite with adhesive tape and measured their electrical properties, and the two received the Nobel Prize in Physics in 2010. The carbon atoms form a network of regular hexagons, with a C–C bond length of about 0.142 nm and a lattice constant a = √3 × 0.142 ≈ 0.246 nm. The area per atom is about 0.0262 nm², from which the areal density works out to about 0.76 mg/m² and the specific surface area counting both sides to about 2630 m²/g.
In graphene the conduction and valence bands meet at the K points with the apexes of two cones touching, and near them the electron energy is proportional to the wavenumber. Electrons behave like massless particles, and in clean samples the mobility far exceeds 10000 cm²/(V·s) even at room temperature. Mechanically, experiments pressing a tip into a suspended single layer give an estimated Young's modulus of about 1 TPa, among the stiffest of known materials. A single layer absorbs only about 2.3% of light, so it is also a candidate for transparent conductive films.
Graphite is many layers of graphene stacked, with an interlayer spacing of about 0.335 nm. As the number of layers increases, interlayer interactions change the band structure, and at about 10 layers the properties are said to be essentially those of graphite. Products sold as graphene therefore range from single layers to flakes of a few or tens of layers. Graphene oxide (GO), made by oxidizing and exfoliating graphite, has many oxygen-containing functional groups, is insulating and disperses easily in water; reduced graphene oxide (rGO), made by reducing it, still contains many defects and does not reach the conductivity of single-layer graphene.
High-quality single layers for research can be made by mechanical exfoliation with adhesive tape, but the areas are small and unsuited to mass production. For large-area films, a widely used method grows graphene by CVD, decomposing methane or similar gases on copper foil at high temperature, and transfers it to another substrate using a polymer support film. There is also a method that heats silicon carbide to high temperature to drive off silicon. Powdered multilayer flakes are made by chemical exfoliation of graphite or by sonication in liquids and are used as conductive additives in batteries, as additives to polymers and in heat-dissipating materials. When discussing properties, it is important to check how the material was made and how many layers it has.
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.
Being one atom thick, its thickness cannot be defined sharply, but the graphite interlayer spacing of about 0.335 nm is commonly taken as the thickness of one layer. When a single layer on a substrate is measured by atomic force microscopy, it often appears thicker than this because of adsorbates on the surface and the gap to the substrate.
Both are hexagonal networks of sp²-bonded carbon, but graphene is a flat two-dimensional sheet, while a carbon nanotube is that sheet rolled seamlessly into a one-dimensional cylinder. Nanotubes can be metallic or semiconducting depending on how they are rolled (the chiral indices), whereas flat graphene has a band gap of essentially zero.
Because in-plane carbon atoms are joined without gaps by strong sp² covalent bonds. Indentation of suspended single layers gives estimates of a Young's modulus of about 1 TPa and a breaking strength above 100 GPa. These are values for small defect-free regions, however; large-area films containing grain boundaries and defects, and composites with polymers, are far weaker.
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…Graphene is a single layer taken from graphite, in which carbon atoms form a honeycomb network of hexagons through strong sp²-hybridized covalent bonds.
Which statement about the structure and properties of graph…Carbon nanotube BET method Bottom-up synthesis Melting point depression of nanoparticles Quantum dot Specific surface area Zeta potential