Universal relation for size dependent thermodynamic properties of metallic nanoparticles

The previous model on surface free energy has been extended to calculate size dependent thermodynamic properties (i.e., melting temperature, melting enthalpy, melting entropy, evaporation temperature, Curie temperature, Debye temperature and specific heat capacity) of nanoparticles. According to the quantitative calculation of size effects on the calculated thermodynamic properties, it is found that most thermodynamic properties of nanoparticles vary linearly with 1/D as a first approximation. In other words, the size dependent thermodynamic properties P(n) have the form of P(n) = P(b)(1 -K/D), in which P(b) is the corresponding bulk value and K is the material constant. This may be regarded as a scaling law for most of the size dependent thermodynamic properties for different materials. The present predictions are consistent literature values.