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Nanomaterials

Check the relation between specific surface area and particle size, melting point depression of nanoparticles, the structure and properties of carbon nanotubes and graphene, quantum dots, synthesis methods for nanoparticles, agglomeration and dispersion, and BET specific surface area with multiple-choice questions, including calculations with explanations.

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Nanomaterials: key points

As particles get smaller, the specific surface area increases in inverse proportion to size and, for spheres, can be estimated as S = 6/(ρd). As the fraction of surface atoms grows, surface energy starts to affect the properties of the whole material, and the melting point of metal nanoparticles falls below that of the bulk. In semiconductor quantum dots, confinement widens the effective band gap, so the emission color can be tuned by size. For carbon, graphene and the carbon nanotube, graphene rolled into a tube, are the representative examples.

Nanoparticles are made by top-down methods, which crush or carve larger materials, or by bottom-up methods, which assemble atoms and molecules through nucleation and growth. The key to uniform sizes is concentrating nucleation in a short time. The resulting particles agglomerate easily, so dispersion is maintained with surface charge or dispersants. Specific surface area is measured by the BET method, and comparing it with the TEM primary particle size and the size in liquid reveals the degree of agglomeration.

All Nanomaterials questions (12)
  1. Spherical TiO₂ nanoparticles 20 nm in diameter (density 4.0 g/cm³) are all the same size and fully dispersed. Which value is closest to the surface area per gram of powder (the specific surface area)?
  2. Nanoparticles of metals such as gold and tin melt at temperatures below the bulk melting point when their size falls to a few nanometers. Which is the main cause of this melting point depression?
  3. Suppose the melting point of spherical metal nanoparticles can be approximated in terms of the diameter d as Tm(d) = Tm∞(1 − β/d). With the bulk melting point of gold Tm∞ = 1337 K and β taken as a hypothetical model value of 1.0 nm, which value is closest to the melting point of gold nanoparticles 5.0 nm in diameter?
  4. The electronic properties of a single-walled carbon nanotube are determined by the chiral indices (n, m), which describe how the graphene sheet is rolled: it is metallic if n − m is a multiple of 3 and semiconducting otherwise. Which of the following is metallic?
  5. The diameter of a single-walled carbon nanotube is given by d = a√(n² + nm + m²)/π, using the graphene lattice constant a = 0.246 nm. Which value is closest to the diameter of a nanotube with chiral indices (10, 10)?
  6. Which statement about the structure and properties of graphene is correct?
  7. For CdSe quantum dots (bulk band gap 1.74 eV), assume a simple model in which the confinement energy increase is inversely proportional to the square of the radius R, and that it is 0.30 eV for R = 3.0 nm. Which value is closest to the effective band gap of a quantum dot with R = 2.0 nm? Neglect the Coulomb interaction between electron and hole.
  8. Methods for making nanomaterials are divided into top-down methods, which break larger materials into smaller pieces, and bottom-up methods, which assemble atoms and molecules. Which is a bottom-up method?
  9. Why does the hot-injection method (rapidly injecting precursors into a hot solvent) readily give nanoparticles of uniform size (monodisperse)?
  10. Which is an appropriate way to keep oxide nanoparticles dispersed in water from agglomerating and settling?
  11. Which correctly describes the principle of the BET method for measuring the specific surface area of a powder?
  12. For an alumina nanopowder, the primary particle diameter observed by TEM was about 30 nm, and the particle size obtained from the BET specific surface area assuming spheres was also about 30 nm. However, the mean particle size measured by dynamic light scattering after dispersing it in water was about 400 nm. Which interpretation of these results is most appropriate?

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