Size-dependent cohesive energy, melting temperature, and Debye temperature of spherical metallic nanoparticles

It is necessary to theoretically evaluate the thermodynamic properties of metallic nanoparticles due to the lack of experimental data. Considering the surface effects and crystal structures, a simple theoretical model is developed to study the size dependence of thermodynamic properties of spherical metallic nanoparticles. Based on the model, we have considered Co and Cu nanoparticles for the study of size dependence of cohesive energy, Au and Cu nanoparticles for size dependence of melting temperature, and Cu, Co and Au nanoparticles for size dependence of Debye temperature, respectively. The results show that the size effects on melting temperature, cohesive energy and Debye temperature of the spherical metallic nanoparticles are predominant in the sizes ranging from about 3 nm to 20 nm. The present theoretical predictions are in agreement with available corresponding experimental and computer simulation results for the spherical metallic nanoparticles. The model could be used to determine the thermodynamic properties of other metallic nanoparticles to some extent.