The lowering of the melting point of nanoparticles below that of the bulk due to the surface energy contribution. The depression is roughly inversely proportional to particle size and becomes pronounced for particles a few nanometers across.
Japanese name: ナノ粒子の融点降下
Melting point depression of nanoparticles appears in 1 practice question across 1 topic, including Nanomaterials.
Field: Nanomaterials
When particles of metals or semiconductors are made as small as a few nanometers, they melt at temperatures well below the melting point of the bulk. For gold, electron diffraction and other methods have confirmed that particles a few nanometers in diameter melt several hundred K below the bulk melting point (1337 K). The melting point is usually treated as a constant characteristic of a substance, but for nanoparticles it becomes a quantity that depends on size. Wherever nanoparticles are heated in use, as in sintering, the degradation of catalysts or the temperature of joining, applying the bulk value can lead to wrong conclusions.
Whether the solid or the liquid is stable is decided by which has the lower free energy, and in a particle the energy of surfaces and interfaces is added on top. The ratio of surface to volume is inversely proportional to particle size, so the depression of the melting point is also roughly inversely proportional to size and can be written as Tm(d) = Tm∞(1 − β/d), where β is a length set by the substance and conditions. From this relation, a particle whose melting point falls by 5% at 10 nm in diameter would fall by about 10% at 5 nm and by about 2.5% at 20 nm. The depression grows rapidly as size decreases, so it is especially noticeable in the range of a few nanometers.
The mechanism differs from the freezing-point depression of solutions. Freezing-point depression occurs because a dissolved solute lowers the chemical potential of the liquid, and it is set by the solute concentration. Melting point depression in nanoparticles occurs in a pure substance through size alone. Nanoparticles also begin to melt at the surface first (surface melting), so melting often proceeds over a range rather than at a single temperature, and the heat of fusion becomes smaller as well. On the other hand, there are reports of superheating, in which particles embedded with coherent interfaces in a substance of higher melting point do not melt until above the bulk melting point.
Because a lower melting point means atoms move more easily, nanoparticles sinter at temperatures far below the bulk melting point. Techniques that print inks or pastes of silver or copper nanoparticles and heat them at relatively low temperatures to form wiring or joints exploit this. Another advantage is that the wiring or joints formed by sintering are no longer made of small particles, so in service they show heat resistance close to that of the bulk. Conversely, in metal nanoparticle catalysts, particles can move, merge and coarsen even at the operating temperature, reducing surface area and activity, so measures such as strengthening the bond to the support are taken.
Answer: A. More atoms sit at the surface, and the surface energy raises the free energy of the solid, so the liquid becomes stable at a lower temperature
Surface atoms have lost some of their bonds, so a surface energy term is added to the free energy of the particle. The smaller the particle, the larger the fraction of surface atoms and the more the free energy of the solid is pushed up, so the temperature at which the free energies of solid and liquid become equal, the melting point, falls (the Gibbs–Thomson effect). Considering the solid–liquid interfacial energy, the melting point depression is roughly inversely proportional to particle size. The quantum size effect concerns electron energy levels and is not the main cause of melting point depression in metals. Also, the heat of fusion actually tends to decrease in nanoparticles, so the reasoning that “a larger heat of fusion makes melting easier” runs backward.
Because the depression is roughly inversely proportional to size, it grows rapidly as particles get smaller. For particles of tens of nanometers the depression is slight, but it becomes large below about 10 nm, and at a few nanometers there are cases several hundred K below the bulk. The size at which it matters depends on the substance and the application.
Yes. The temperature at which liquid nanoparticles solidify is also lower than in the bulk, for the same reason. In addition, crystal nuclei form less easily inside small particles, so they often stay liquid while strongly supercooled below the melting point, and the difference between the melting and freezing temperatures tends to be large.
Once the particles sinter and join into larger bodies, the fraction of surface becomes small, so the melting point approaches the bulk value. A joint made at a low temperature can therefore be used even above the joining temperature. If sintering is incomplete and fine particles or voids remain, however, the microstructure can change in service.
Considering the solid–liquid interfacial energy, the melting point depression is roughly inversely proportional to particle size.
Nanoparticles of metals such as gold and tin melt at temper…Quantum size effect BET method Bottom-up synthesis Carbon nanotube Graphene Quantum dot Specific surface area Zeta potential