264402 On Predicting Nuclei Shape Distribution
Modeling crystallization processes must account for the rate of nucleation as well as the shape distributions of nuclei. Most models that are based on the classical nucleation theory have limited considerations for non-uniform shapes and shape distributions of nuclei, anisotropic surface energies, and non-ideal solution behavior. We present a formalism to predict nuclei shape distribution accounting for the foregoing factors. The methodology includes formulation of Gibbs free energy function for all possible morphologies of a nucleus followed by multi-dimensional maximization to obtain critical shape and size of the nucleus at some supersaturation. Furthermore, the local fluctuations in the supersaturation due to Brownian motion of solute molecules can cause variations in the size and shape of nucleus. Such variations can be modeled using the Fokker-Planck equation provided their transition probabilities are known. The transition probabilities for supersaturation fluctuations are obtained from the framework of density fluctuations.1, 2 The corresponding Ito’s equation is solved following multidimensional optimization in morphology domains to obtain nuclei shape distribution of Potassium Acid Phthalate.
1. Smoluchowski, M., Drei vortrage uber diffusion, brownsche bewegung und koagulation von kolloidteilchen. Zeitschrift fur Physik 1916, 17, 557-585.
2. Chandrasekhar, S., Stochastic problems in physics and astronomy. Reviews of modern physics 1943, 15, (1), 1-89.