On the size and shape dependence of the solubility of nano-particles in solutions.

The general equation is derived for the equilibrium of a small solid particle and a large solution, being consistent with the thermodynamics of Gibbs. This equation can be solved in a closed form for solubility if an ideal (or an infinitely diluted) solution is considered, if the interfacial energy is independent of the composition of the solution and if all physical parameters (other than the solubility itself) are taken size independent. The solubility of the particles is found to increase with increasing its specific surface area, i.e. if non-spherical particles are applied. This simplified solution further simplifies if the shape of the solid is supposed to be spherical. This latter equation, however, is found to be in contradiction with the Ostwald-Freundlich equation, widely used in chemistry, biology and materials science to describe the size dependence of solubility of a spherical crystal. The reason for its incorrectness is shown to be due to the incorrect application of the Laplace equation. It is found that the solubility increases with decreasing the size of the dissolving phase not due to the increased curvature of the phase (Kelvin and Freundlich), but rather due to the increased specific surface area of the phase (Gibss, Ostwald). Equations are also derived for the case, when the size effect of the interfacial energy is taken into account, and when the crystal is surrounded by several planes of different interfacial energies. The role of wettability is discussed on the size dependence of solubility.