Numerical Evaluation of the Surface Energy of Polyhedral Nanoparticles

Nanoparticles have been used widely in various fields, and their size and shape greatly affect the functional properties. Therefore, controlling the morphology of the particles is important, and evaluation of the surface energy is indispensable for that purpose. In this study, the surface energy of nanoparticles was evaluated by numerical simulation and formulated in a polynomial equation. First, molecular dynamics simulations were carried out for variously shaped polyhedral nanoparticles. A cube and an octahedron were introduced as reference shapes, and truncated hexahedrons and truncated octahedrons were created by cutting out their vertices. The surface energy was plotted for various polyhedrons. The lowest energy was observed in an octahedron because of the stability of the (111) plane, and the highest energy was observed in a cube because of the relatively higher energy of the (100) plane. Then, the surface energy was formulated in a polynomial equation, in which the parameters obtained by the molecular-dynamics simulations were introduced. As a result, stability of the octahedron and relative instability of the cube were fairly captured by the proposed polynomial equation, while a slight underestimation was inevitable. Finally, the parameters were revised to continuous numbers to extend the application range. Consequently, an application for various materials, such as a cube having equivalent stability to an octahedron, was demonstrated by imposing rather exaggerated parameters.