A Simple Population Balance Model for Crystallization of L-Lactide in a Mixture of n-Hexane and Tetrahydrofuran

Abstract

In this contribution, crystallization was performed to assess the kinetics of nucleation and crystal growth of L-lactide. In most common solvents, this compound shows very high solubility even at low temperatures, which could be challenging for crystallization process design. In the first part of this paper, the anti-solvent effects of n-hexane on solutions of L-lactide in tetrahydrofuran (THF) were investigated through studying the influence of solvent compositions on the solubility. Thanks to these effects, the solubility of the interested compound can be adjusted to desired degrees of supersaturation by adding suitable amounts of the anti-solvent. In the second part, a solvent composition at a mass ratio of 45/55 (n-hexane/THF) was chosen, and an isothermal seeded crystallization process was implemented. The evolution of the particle sizes and changes in the solute concentration profile of this process were monitored. Based on the obtained data, a widely used model, i.e., the population balance equation (PBE), was then utilized to model the crystal size distribution (CSD). Reasonable assumptions were made to reduce the mathematical complexity of the PBE. In the simplified model, only crystal growth and secondary nucleation were considered for model formulation, with assumptions of the size-independent growth rate and negligible size of nuclei. The kinetic parameters were estimated by using the seed and final-time crystal density functions in combination with variations in the concentration of the mother liquor. Indeed, the numerical solution for the one-dimensional problem of the L-lactide crystallization based on the estimated parameters gained a relatively good agreement with the determined CSD. Furthermore, the obtained model also correlated well with the variations in the solute concentration of the mother liquor. In short, this simple approach can be used for predicting the productivity and CSD of the L-lactide crystallization.