Size Dependent Interface Energy of Nanomaterials

The reduction of size of the low dimensional materials leads to a dramatic increase of surface-to-volume ratio. The properties of a solid are essentially controlled by related surface/interface energies. Although such changes are believed to dominate behaviors of nanoscale structures, little experience or intuition for the expected phenomena, especially the size dependent properties and their practical implications, are modeled. In this contribution, the classic thermodynamics as a powerful traditional theoretical tool is used to model different bulk interface energies and the corresponding size dependences where emphasis on the size dependence of interface energy is given, which is induced by size dependence of coherent energy of atoms within nanocrystals. It is found that solid-vapor interface energy, liquid-vapor interface energy, solid-liquid interface energy, and solid-solid interface energy of nanoparticles and thin films fall as their diameters or thickness decrease to several nanometers while the solid-vapor interface energy ratio between different facets is size-independent and is equal to the corresponding bulk ratio. The predictions of the established analytic models without any free parameter, such as size and temperature dependences of these four kinds of interface energies, are in agreement with the experimental or other theoretical results of different kinds of low dimensional materials with different chemical bond natures.