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

Abstract

This work presents an experimental and a numerical study to highlight a kinetic explanation of the Ostwald rule of stages (ORS). To demonstrate this explanation, L-glutamic acid (LGlu) (a monotropic system with two polymorphs) was crystallized in three different scales: liter scale in a 2 L stirred crystallizer, milliliter scale in a 4 mL stagnant cell, and microliter scale in microfluidic channels. Cooling crystallization experiments were performed in water at different temperatures and supersaturation conditions. The LGlu polymorphic system was found to follow the ORS at low temperature (between 5 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 at 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.

l-Glutamic acid crystals of pure α form and uniform size distribution from continuous non-seeded reaction crystallization in slug flow

“…3) were collected after proper residence time (minutes) in slug flow. If those nuclei were not in pure α-form, then one likely reason for the pure product is the relatively faster growth kinetics of the α-form than the β-form, 51 so only α-nuclei gets to grow to a stable or evident size (above the critical nuclei size in classical nucleation theory 50 ), while β-nuclei dissolves before reaches critical nuclei size. 50…”

Ostwald Rule of Stages─Myth or Reality?

“…Some authors have sought to explain Ostwald’s Rule of Stages − while others have sought to challenge or limit its scope. , Despite the empirical status of Ostwald’s Rule of Stages (ORS) it has been invoked for many different types of materials and fieldsinorganics, ,, metals, metal–organic frameworks, organic molecules, biological molecules, , drugs, polymers, supramolecules, , and 2D systems …”

“…Some authors have sought to explain Ostwald's Rule of Stages 16−18 while others have sought to challenge or limit its scope. 19,20 Despite the empirical status of Ostwald's Rule of Stages (ORS) it has been invoked for many different types of materials and fields�inorganics, 12,21,22 metals, 23 metal− organic frameworks, 24 organic molecules, 25 biological molecules, 18,26 drugs, 27 polymers, 28 supramolecules, 29,30 and 2D systems. 31 While Ostwald's statement is framed in thermodynamic terms its observational basis means that the statement should be looked at as one of conjecture.…”

Nucleation Work on Curved Substrates

“…In a supersaturated solution, ∆µ decreases as a consequence of the formation of crystals; thus, nucleation work and nucleation kinetics change over time [8].…”