CHEM01200604004 Shri Sanyasinaidu Boddu - Homi Bhabha ...

must be supersaturated either by directly dissolving the solute at higher temperature and then
cooling to low temperature or by adding the required amounts of reactants to the solution
during the reaction. Once the solution reaches a critical supersaturation of the particle
forming species, nucleation occurs. The overall free energy change ΔG for the nucleation
process is the sum of the free energy due to the formation of a new volume and the free
energy due to the new surface created (Fig.3) [13].
DG *
DG
r *
r
Fig.3. Schematic representation of variation of free-energy change as a function of nuclei
radius during nucleation and growth [13].
For spherical particles, free energy change involved in nucleation can be expressed by
equation 1 [13]
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Δ G =− r k T ln( S) + 4 r ……………………………… (1)
3 2
B
V π π γ
Where V is the molecular volume of precipitated species, r is the radius of the nuclei, k B is
the Boltzmann constant, S is the saturation ratio and γ is the surface free energy per unit
surface area. Saturation ratio S is defined as C/C 0 , where C and C 0 are solute concentration at
saturation and equilibrium respectively.
When saturation ratio S >1, ΔG has a positive maximum at a critical size, r*. This
maximum free energy corresponds to the minimum activation energy required for the
formation of nuclei with critical radius r*. Nuclei larger than the critical size will further
decrease their free energy by growth to form particles and nuclei smaller than critical size
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