(789g) 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.