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Abstract
A new mathematical model that relies on the classical nucleation theory is proposed to predict the nucleation rate, nucleation rate kinetic constant and the Gibbs free energy of nucleation from the MSZW measured as a function of solubility temperatures. The model allows to calculate the nucleation rate at different cooling rates. The model seems to be universal as it well predicts the experimental data of 16 different combination of APIs and solvents that involves 10 APIs. According to the proposed model, the nucleation rate was found to be in the range of 1020 to 1024 molecules/m3s and the Gibbs free energy of nucleation was found to be in the range of 8 – 62 kJ/mol. The proposed model is also used to obtain the induction time based on MSZW obtained at different cooling rate. The proposed model is further exploited to obtain the thermodynamic parameters that includes the surface free energy, size of the critical nucleus and the number of unit cells that constitute the critical nucleus.
