(527a) A Stochastic PBE-Model of Crystallisation Accounting for Nucleation, Growth, and Chemical Reaction

The stochastic nature of primary nucleation has been observed in several experimental studies, leading to the formation of various models to describe and interpret the data. Notwithstanding the progresses in understanding primary nucleation and the implications of its statistical nature, the current models cannot capture several of its features, particularly when multiple solid forms can develop in the system.

In this contribution, we have developed a Population Balance Equation model of crystallisation, which accounts for primary nucleation, secondary nucleation, and growth of the solid phase and a chemical reaction in the liquid phase. Each primary nucleation event occurs stochastically and, since growth and secondary nucleation are dependent on the primary events, the overall crystallisation process is itself stochastic.

The model structure is very flexible and allows to describe several types of systems. Here, we focus on three specific systems: first, the simplest scenario, where one single type of crystal can form; second, a system where an arbitrary number of polymorphs can form, each with its own set of kinetic and thermodynamic parameters; finally, a system with two enantiomers forming conglomerate crystals and coupled in the liquid phase by a racemisation reaction.

Using the model, we have studied the interplay of all phenomena acting in the system, their role in determining the detection times and the type of solid dominating, as well as the influence of the volume and the effect of scaling.