On the Size Dependence of Molar and Specific Properties of Independent Nano-phases and Those in Contact with Other Phases

Nano-materials are materials with at least one nano-phase. A nano-phase is a phase with at least one of its dimensions below 100nm. It is shown here that nano-phases have at least 1% of their atoms along their surface layer. The ratio of surface atoms is proportional to the specific surface area of the phase, defined as the ratio of its surface area to its volume. Each specific/molar property has its bulk value and its surface value for the given phase, being always different, as the energetic states of the atoms in the bulk and in the surface layer of a phase are different. The average specific/molar property of a nano-phase is modeled here as a linear combination of the bulk and surface values of the same property, scaled with the ratio of the surface atoms. That makes the performance of all nano-phases proportional to their specific surface area. As the characteristic size of the nano-phase is inversely proportional to its specific surface area, all specific/molar properties of nano-phases are inversely proportional to the characteristic size of the phase. This is applied to the size dependence of the molar Gibbs energy of the nano-phase, which appears to be in agreement with the thermodynamics of Gibbs. This agreement proves the general validity of the present model on the size dependence of the specific/molar properties of independent nano-phases. It is shown that the properties of nano-phases are different for independent nano-phases (surrounded only by their equilibrium vapor phase) and for nano-phases in multi-phase situations, such as a liquid nano-droplet in the sessile drop configuration.