Phenomenological predictions of cohesive energy and structural transition of nanoparticles

In this paper, it is shown that a liquid-drop model (LDM) can predict the size-dependent cohesive energy (SDCE) of large nanoparticles and clusters (particles with few atoms) quantitatively. The cohesive energy decreases linearly with the inverse of the particle size both for large nanoparticles and clusters though the slopes are different. This indicates that there are three different regions (I-III) of SDCE in the complete size range. Regions I and II represent the SDCE of large nanoparticles and clusters, respectively, while region II represents the intermediate region where the cohesive energy is almost size-independent. Different regions of SDCE correspond to different structures of nanoparticles, and structural transition associated with the particle size can easily be predicted from the SDCE. Analyzing the cohesive energy data on the basis of LDM, it is shown that the surface tension decreases with decreasing size for very small nanoparticles. The Tolman equation can account for the variation of surface tension by predicting the size dependency of the Tolman length.