No abstract

The measured induction times in droplet-based microfluidic systems are stochastic and are not described by the deterministic population balances or moment equations commonly used to model the crystallization of amino acids, proteins, and active pharmaceutical ingredients. A stochastic model in the form of a Master equation is formulated for crystal nucleation in droplet-based microfluidic systems for any form of nucleation rate expression under conditions of time-varying supersaturation. An analytical solution is provided to describe the (1) time evolution of the probability of crystal nucleation, (2) the average number of crystals that will form at time t for a large number of droplets, (3) the induction time distribution, and (4) the mean, most likely, and median induction times. These expressions are used to develop methods for determining the nucleation kinetics. Nucleation kinetics are determined from induction times measured for paracetamol and lysozyme at high supersaturation in an evaporation-based high-throughput crystallization platform, which give low prediction errors when the nucleation kinetics were used to predict induction times for other experimental conditions. The proposed stochastic model is relevant to homogeneous and heterogeneous crystal nucleation in a wide range of droplet-based and microfluidic crystallization platforms.

This study reports the selective growth of γ-glycine crystals via concentrating microdroplets of aqueous glycine solutions through slow evaporation of water using an evaporation-based crystallization platform. In prior studies, γ-glycine crystals could only be obtained from non-neutral pH solutions, by applying electromagnetic fields, or in the presence of impurities that suppress the formation of the kinetically favored R-glycine polymorph. Here in our work, pure γ-glycine crystals form below a certain rate of evaporation (i.e. below a certain rate of supersaturation). Below this rate the crystallizing solution stays close to equilibrium throughout the evaporating process, allowing the system to sample the lowest free energy state during the formation of nuclei. These results point to the interplay of kinetic and thermodynamic effects on selective crystallization of different polymorphs. Polymorphic analysis was performed by examining all samples as randomized polycrystalline particles. The resulting multiframe diffraction patterns were combined to generate a single powder X-ray diffraction (PXRD) spectrum of each sample. In comparison to traditional powder diffraction methods, the quantitative polymorphic analysis procedure reported here eliminates the need to mechanically grind crystalline material, thereby avoiding the potential for undesired polymorphic transformations prior to data collection.