English
Menu

Nanomaterials

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?

  1. AAbout 802 K
  2. BAbout 1604 K
  3. CAbout 1070 K
Show answer and explanation

Answer: C. About 1070 K

β/d = 1.0/5.0 = 0.20, so Tm(d) = 1337 × (1 − 0.20) = 1337 × 0.80 ≈ 1070 K (about 796 °C), about 270 K below the melting point of bulk gold. About 802 K puts the radius, 2.5 nm, in place of d, giving 1 − 0.40, and about 1604 K reverses the sign to (1 + β/d), which would mean the melting point rises in nanoparticles. This expression is an approximation derived from the surface energy contribution being inversely proportional to size, and β = 1.0 nm is a value assumed for this problem. The actual β varies with the metal, the particle shape and the surrounding medium, and the approximation becomes rough as the size approaches about 2 nm, so it can deviate from measured melting points.

Report an error

Practice this topic Back to topic

More Nanomaterials questions

  1. 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?
  2. 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)?
  3. Which statement about the structure and properties of graphene is correct?
  4. 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.
  5. 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?