Abstract
A model is proposed to calculate the melting points of nanoparticles based on the Lennard-Jones (L-J) potential function. The effects of the size, the shape, and the atomic volume and surface packing of the nanoparticles are considered in the model. The model, based on the L-J potential function for spherical nanoparticles, agrees with the experimental values of gold (Au) and lead (Pb) nanoparticles. The model, based on the L-J potential function, is consistent with Qi and Wang’s model that predicts the Gibbs-Thompson relation. Moreover, the model based on the non-integer L-J potential function can be used to predict the melting points of nanoparticles.
Highlights
Melting point is a thermal property that depends on the size of materials and was first observed in 1954 [1]
It is found that the calculated melting points of nanoparticles that do not consider the shape effect (Qi et al.’s model) are higher than spherical nanoparticles
As the size of a spherical nanoparticle reduces, the parameter sn becomes large, so the contribution of the surface atomic bonds is larger than the interior atomic bonds in the total energy of the nanoparticle, which makes its core less stable
Summary
Melting point is a thermal property that depends on the size of materials and was first observed in 1954 [1]. The first theoretical description of the size-dependent melting point of nanoparticles was in 1909 by the relation known as. D where Tm and Tmbulk are the melting points of the nanoparticle and bulk material, respectively, C is a constant that depends on the material of the nanoparticle, and D is the nanoparticle thickness (e.g., the diameter of spherical nanoparticles). The Gibbs-Thompson relation shows that the melting points of nanoparticles are linearly proportional to the reciprocal of the nanoparticle thickness. Many experimental works [11,13,14,15,16] have showed that the melting points of nanoparticles follow the Gibbs-Thompson relation
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