Generalized non-integer Lennard-Jones potential function vs. generalized Morse potential function for calculating cohesive energy and melting point of nanoparticles

Abstract

A generalized non-integer Lennard-Jones (L-J) potential function with an additional parameter m is proposed to calculate the cohesive energy and melting point of nanoparticles. The model based on the new generalized non-integer L-J potential function has been successful in predicting experimental values. The calculated cohesive energies show an excellent agreement with the experimental values of the cohesive energies of molybdenum (Mo) and tungsten (W) nanoparticles (Kim et al., 2002). Moreover, the calculated melting points based on the generalized non-integer L-J potential function agree with the experimental values for large gold (Au) nanoparticles including n≥1000 atoms (Buffat and Borel, 1976) and small silica-encapsulated gold (Au) nanoparticles including n≤1500 atoms (Dick et al., 2002). The stability of nanoparticles is due to two conditions: the increase of the range of the attractive force and the high gradient attractive interaction in the potential function when rij≈r0.