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Multiscale Experimental Study and Modeling of l-Glutamic acid Crystallization: Emphasis on a Kinetic Explanation of the Ostwald Rule of Stages

This work presents an experimental and a numerical study to highlight a kinetic explanation to of the Ostwald rule of stages (ORS). To demonstrate this explanation, L-glutamic acid (LGlu) (a monotropic system with two polymorphs) were crystallized in three different scales: Liter scale in a 2L stirred crystallizer, milliliter scale in a 4ml stagnant cell and microliter scale in microfluidic channels. Cooling crystallization experiments were performed in water at different temperature and supersaturation conditions. The LGlu polymorphic system was found to follow the ORS at low temperature (between 5°C and 30°C). However, in similar operating conditions, the stable polymorph crystallized preferentially or exclusively in the stagnant cell and in microfluidics. To explain the ORS in the stirred crystallizer at low temperature, a model based on the kinetic equation was used. By taking into account the Gibbs Thomson effect (Solubility variation with size), the simulations in the nanoscopic scale showed the dissolution of the slow-growing stable phase nuclei in favor of the fast-growing metastable phase nuclei. Consequently, the numerical results showed that the Gibbs Thomson effect is a key factor in polymorph competition and that considering this effect, in certain kinetic and equilibrium conditions, could allow explaining and simulating the ORS.