A Population Balance Model for Temperature Cycling-Enhanced Deracemization

© 2018 American Chemical Society. It has been recently observed that a suspension of conglomerate crystals of both chiralities in contact with a solution where racemization takes place can undergo symmetry breaking due to periodic fluctuations in temperature. The interplay between the mechanisms behind this process is still a matter of debate, although there is consensus that growth/dissolution of crystals and racemization in the solution phase play a crucial role. In this work, we present a population balance model (PBM), based on temperature-size dependent solubility, which simulates a system of enantiomeric crystals of both chiralities subjected to Ostwald ripening under periodic temperature fluctuations, in the presence of a liquid-phase racemization reaction. Our simulations reveal that for a racemic system with small initial size asymmetries between the enantiomers complete deracemization is achieved due to temperature fluctuations, whereas isothermal Ostwald ripening only leads to partial enantiomeric enrichment. This implies that size-temperature dependence of solubility is an essential mechanism in temperature cycling-enhanced deracemization. Although enantiopurity is achieved with only growth, dissolution and temperature cycling, other mechanisms, such as breakage, could also be included. While our model qualitatively reproduces many of the experimental observations in temperature cycling-enhanced deracemization, the autocatalytic nature of the process is not captured and, similarly to Viedma ripening, some sort of chiral feedback mechanism (e.g., agglomeration or secondary nucleation) seems to be required to fully describe the process dynamics. The results presented here offer further insight into temperature cycling-enhanced deracemization and help pinpoint the influence of the various mechanisms in the process.