A model for the latent heat of melting in free standing metal nanoparticles

Abstract

Nanoparticles of many metals are known to exhibit scale dependent latent heats of melting. Analytical models for this phenomenon have so far failed to completely capture the observed phenomena. Here we present a thermodynamic analysis for the melting of metal nanoparticles in terms of their internal energy and a scale dependent surface tension proposed by Tolman. The resulting model predicts the scale dependence of the latent heat of melting and is confirmed using published data for tin and aluminum.

A slip-based model for the size-dependent effective thermal conductivity of nanowires

“…Due to the dependence of Kn = * (T * )/R * on temperature and the radius of the NW, Eqn. (16) can be reduced to simpler expressions in some limiting cases. For instance, at very low temperatures or for very small radii we have Kn 1.…”

“…For instance, at very low temperatures or for very small radii we have Kn 1. Using I 0 (ξ) = 1 + O(ξ 2 ) and I 1 (ξ) = ξ/2 + O(ξ 3 ) for ξ 1, as well as C(Kn) = 1 − Kn −1 + O(Kn −2 ) for Kn 1, we find that (16) can then be reduced to…”

“…2 (a). The ETC, given by (16), is plotted as a function of the Knudsen number in Fig. 2 (b) for two choices of the function C. The figures make it clear that there are three distinct regimes to consider, corresponding to diffusive (Kn 1), ballistic (Kn 1), and mixed (Kn = O(1)) modes of thermal energy transport.…”

“…It is widely known that many thermophysical material properties become size-dependent at the nanoscale [9][10][11][12][13][14][15][16]. Buffat and Borel [9] showed a dramatic decrease of the melting temperature of gold nanoparticles of almost 50% from the bulk value.…”

The Stefan problem with variable thermophysical properties and phase change temperature

“…In [43] it is shown that the formula of [33] underestimates the value of latent heat near the bulk value (where the data is most reliable). They also demonstrate that other formulations, such as those of [46,54], also provide a poor match with experimental data. They go on to propose an exponential fit to the data for tin nanoparticles which provides excellent agreement in the limit of large particles and only shows a noticeable discrepancy for R < 8 nm.…”