Size- and shape-dependence of the thermodynamic properties of nanocrystals

The thermodynamic properties, especially the surface thermodynamic properties of nanocrystals (NCs) play important roles in the physicochemical changes involving NCs. However, it remains unclear about the influence regularities of size and shape on the thermodynamic properties of NCs. Thus by introducing interface variables into the Gibbs energy and combining Young-Laplace equation, relations between the thermodynamic properties (molar Gibbs energy, enthalpy, entropy, internal energy and heat capacity), respectively, and size of NCs with different shapes (sphere, cube, rodlike and sheet) were systematically derived. Theoretical estimations of the orders of the surface thermodynamic properties of NCs are in good agreements with available experimental values. Furthermore, the Tolman length and the surface tension were surprisingly obtained based on the calculated results of the surface thermodynamic properties of Al NCs. The influence regularities of size and shape on the thermodynamic properties of the reaction, the melting, the adsorption and the dissolution of NCs are reasonably explicated by the employment of the above thermodynamic relations.