Population-Based Mathematical Model of Solid-State Deracemization via Temperature Cycles

Recently, temperature cycles have been shown to lead to total deracemization of conglomerate forming compounds, in the presence of a racemizing agent. Even though several experimental studies have been performed, a clear explanation of the phenomena involved in this process and a detailed model have not been reported yet. This contribution aims at filling this gap, by presenting a mathematical model of temperature cycle induced deracemization. The model, based on population balance equations, describes the interplay of several phenomena (size-dependent solubility, crystal growth and dissolution, agglomeration, and racemization), explicitly accounting for the dependence of their thermodynamic and kinetic parameters not only on the particle size, but also on temperature. After discussing how to numerically solve the model, we present several simulations investigating the effect of the main chemicophysical parameters and of the operating conditions. Our results not only illustrate the effect of each parameter on the process and the relative importance of the different phenomena, but also compare well qualitatively with the experimental results recently reported on the deracemization of N-(2-methylbenzylidene)-phenylglycine-amide in the presence of 1,8-diazabicyclo(5.4.0)undec-7-ene (DBU).