Modeling of Dissolution and Re-Crystallization of Paracetamol in Ethanol

Dissolution and crystallization are important phenomena occurring in a variety of reactions and separations. Several factors like reactor configuration & operating parameters, temperature history, solute-solvent properties etc. influence these phenomena significantly. Hence, the modeling of dissolution and re-crystallization is very challenging. In the present study we wish to develop a modelling framework to quantitatively capture dissolution and crystallization. Experimentation was done using a paracetamol-ethanol system.

In our previous work^[1], we carried out experiments where a saturated paracetamol-ethanol solution was cooled at a fixed cooling rate until after crystallization and then reheated at the same rate until after complete dissolution. The experiments we carried out in a Mettler OptiMAX reactor setup. The Mettler FBRM probe was used for monitoring the evolution of particle count and particle chord length distribution with time. These experiments were carried out for different heating/cooling rates (0.3, 0.5, 0.7 & 1 K/min). When the particle counts were plotted versus reactor temperature for different heating/cooling rates, a peculiar hysteresis was observed (shown in figure). As the heating/cooling rate is reduced, the hysteresis loop ‘twists' as the particle count starts falling even after crystallization. This peculiarity was hypothized to occur because of Ostwald's ripening. Ostwald's ripening means the growth of larger particles at the expense of smaller particles. The particle count falls as many small particles would be consumed for the growth of a few large particles. Also, Ostwald's ripening is reported to occur at near equilibrium conditions. When the heating/cooling rate is slow, the solution is more ‘near-equilibrium', which would promote the incidence of Ostwald ripening and would explain why the peculiarity is pronounced at lower rates. The hypothesis regarding the occurrence of Ostwald's ripening is supported by experimental evidence as the chord length distribution is seen to reflect the growth in larger particles although very slightly.

The molecular phenomena occurring in such systems are typically crystal growth, primary/secondary nucleation, Ostwald's ripening, aggregation, breakage and dissolution. All of these phenomena occur simultaneously in the system and also compete with each other depending on the thermodynamic state of the system. It is clear that the peculiar ‘twisting' of the hysteresis loop arises because of the interplay between these phenomena. In the present study, we have attempted to quantitatively capture the hysteresis as also the ‘twisting' of the hysteresis loop. A population balance equation was used as the basic canvas for this modelling framework. The population balance approach is already widely used to model dissolution^[2]. The model proposed by Kubota^[3] was used to determine the occurrence of first nucleation events as well as for obtaining the (initial) primary nucleation rate. Similarly, the various other phenomena are appropriately addressed by suitably modifying or adding certain elements to the basic population balance equation. The developed model was then used to qualitatively predict the ‘twisting' effect of the hysteresis loop. Then, after appropriately calibrating the model, model predictions of the hysteresis loop were compared to experimental predictions. We hope that focusing our effort to quantitatively capture the observed peculiarity will help in developing a robust modelling framework for crystallization systems as well as serve for its rigorous validation.

Comparison between the hysteresis observed during the dissolution and

Re-crystallization of Paracetamol in Ethanol at different heating/cooling rates

References:

[1] A. V. Pandit and V. V. Ranade, “Hysteresis during Dissolution and Re-Crystallization”, Poster presentation at European Congress of Chemical Engineering (ECCE9), 2013.

[2] D. Ramakrishna, “Population Balances: Theory and Applications to Particulate Systems in Engineering”, Academic Press, 2000.

[3] N. Kubota, “A new interpretation of metastable zone widths measured for un-seeded solutions”, Journal of Crystal Growth, Volume 310, Issue 3, 2008, 629–634.