A Population Balance Model for Chiral Resolution via Viedma Ripening

It has recently been observed that a mixture of two enantiomeric crystals subjected to attrition in a solution containing a racemizing agent undergoes symmetry breaking, with only one of the enantiomers eventually remaining in solid form. This process is believed to occur due to the interplay between racemization in solution, attrition, agglomeration and crystal growth and dissolution caused by the crystal size dependence of solubility. In this work, we present a mathematical model of this process based on population balances, incorporating all these elementary mechanisms. This model is able to explain the experimentally observed behavior. A sensitivity analysis on several parameters is carried out, leading to the conclusion that racemization, growth and dissolution, and agglomeration are necessary for deracemization to occur. While deracemization occurs also in the absence of attrition phenomena, these enhance it by reducing the time needed to achieve complete chiral purity.