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

Abstract

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).

Complete chiral resolution in a continuous flow crystallizer with recycle stream

“…Several groups have studied the behaviour of the process of temperature-cycling-induced deracemization, either experimentally or computationally via the use of population balance equations. While earlier experimental studies relied on simple first-order kinetics expressions to describe the progress and the time-evolution of the enantiomeric excess [8], later more detailed models using population balance equations have been developed [10][11][12][13]. In the context of this work, we were looking for a simple way to quantify the efficiency of the deracemization process depending on the process settings of individual trials and relate it to the number of cycles performed.…”

“…Existing literature addressing deracemization reveals no general agreement on the impact of various factors governing the shape of ee profiles during temperature cycling. While some results show an inflection point in the progress of ee with the number of temperature cycles [6,10,25,26], others show an exponential character throughout the evolution of the enantiomeric excess [8,9,21].…”

“…In contrast to Viedma ripening, where particle agglomeration and breakage are essential phenomena for driving the process, for temperature cycling the key factor is sizedependent solubility [6,10]: Following the Gibbs-Thomson equation the solubility of a certain particle is proportional (but not necessarily equal) to the bulk solubility of the substance (accessible via standard solubility measurements) [27]. The proportionality factor is a function of the particle size (as well as of the interfacial tension and the temperature).…”

Designing Isothermal Batch Deracemization Processes with Optimal Productivity: 1. Parametric Analysis Using a Population Balance Equation Model

“…Iggland and Mazzotti 22 for the isothermal case and Bodàk et al 28 for the polythermal case, the relevant population balance equations can be written as…”

On the Effect of Secondary Nucleation on Deracemization through Temperature Cycles

“…The observed increase in chiral enrichment in the solid phase has been ascribed to a difference in growth rate dispersion between the two enantiomeric crystal size distributions or to a crystal growth mechanism that involves (partial) incorporation of small chiral clusters into crystals of the same chirality . A recent publication that simulates TCID by using a population balance model claims that growth, dissolution, and racemization processes alone can explain deracemization without the need for breakage or agglomeration, as long as both temperature and size dependence of solubility (through the Gibbs–Thomson equation) are taken into account . Indeed, alternative mechanisms to conventional crystal growth following McCabe's Δ L law have been sought to explain deracemization, which, because it features equal growth/dissolution kinetics for the different chiral populations, would lead to no changes in enantiomeric enrichment during temperature cycling even in the presence of fast racemization .…”