Surface Energies from Solubility Changes

The variation of the free energy to form a spherical stable nucleus can be derived from its external surface and the surface energy of the solid particle. Using expression (III) and the Gibbs-Thomson equation, the change in the free energy of formation of the nucleus can expressed in terms of the solubility of the nucleus, its density and surface energy (VIII) (3). 

Here, r is the particle radius, y is the surface energy of particles, and Ag is the specific volume energy change. From this formula, it can be understood that the solubility of nuclei depends on particle size and they cannot exist stably in a solution when their size is less than the critical size, whereas they are stable when their size exceeds it. The particles of critical size are generally called critical nuclei. Nucleation rate (7)... 

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