(358d) Molecules As Building Blocks in a Novel Population Balance Model for Flash Nano-Precipitation: Investigation of the Different Good Solvents Effect on Nanoparticle Formation

  Polymeric
nanoparticles (NP) production is becoming more and more popular in the recent
years due to the wide range of applications and research efforts are being
focused on the understanding of the phenomena involved in one of the most
common preparation techniques: Flash Nano-Precipitation (FNP). More
specifically, the effect of fluid dynamics on NP formation and its role in
controlling the final NP size is of paramount importance (Lince, at al., 2008).
The standard modeling approach used so far considered three different steps
separately in the population balance equations with the characteristic NP
length as internal coordinate. In this way, nucleation, molecular growth and
aggregation are treated separately in the model. An alternative approach that
we here propose and validate is to overcome the concepts of nucleation, molecular
growth and aggregation, proposing a novel purely-aggregative population balance
model (PBM) by using as internal coordinate the number of molecules (building
blocks) within each NP, coupled with computational fluid dynamics (CFD).

  Molecules
are treated as objects aggregating between themselves (self-assembly), once the
local solubility limit is reached and overcome (supersaturation ratio greater
than one). This is justified by the fact that particle formation is a
supersaturation-driven process. The test case shown here is the NP formation
via solvent displacement (acetone and water in the role of good solvent and
anti-solvent respectively), with a polymer (poly-e-caprolactone,
PCL) as solute, in a confined impinging jets mixer (CIJM, Fig. 1). The rate
with which PCL molecules aggregate is expressed by the aggregation kernel, expressed
in terms of number of molecules which form a particle (say n), referred
to as aggregation number, and considered here as the internal coordinate of the
PBM. When a cluster of n molecules collides with a cluster of n’
molecules, then a cluster of n+n’ molecules (or molecular building
blocks, as shown in Fig. 2) is formed, assuming the freely jointed chain
hypothesis (Flory, 1953). The aggregation kernel considers both the aggregation
due to Brownian movements and turbulent fluctuations and, for the first time,
it is built upon molecular dynamics (MD) (Di Pasquale, et al, 2014);
furthermore, the PBM and CFD are coupled together in a solely tool, thanks to a
suitable user define function (UDF) implemented in Ansys Fluent 15.

  The
effect of different good solvents (acetonitrile and THF) is also investigated via
the PBM-CFD code, in order to achieve a better insight into both the physical-chemical
and transport phenomena (e.g. the role of the aggregation kernel) that lead to
different experimental mean NP size (Ferri, et al, 2017). The model results are
satisfactory and promising in terms of validation against experiments, showing
a good agreement with them (Fig. 3), and in terms of identification of the key
parameters able to control the mean NP size when different good solvents are
employed in FNP processes.  

 
Future work is recommended to understand what kind of phenomena plays a key
role at low solute concentration, and at the same time, also the investigation
and validation of this purely-aggregative multiscale model on different
geometries (e.g. multi inlet vortex mixers).

Figure 1.
Sketch of the nanoparticle formation process in a CIJM. On the left side of the
mixer there is the acetone and PCL inlet (solvent, red); on the other side, the
water (antisolvent, blue). The multiscale approach is represented: the molecular
level (molecular dynamics scale), the mesoscale (represented by the PBM), and
the macroscale (CFD).

Figure 2. Two nanoparticles, formed by n
and n’ solute molecules (building blocks) respectively, collide
leading to n+n’ molecules nanoparticle.

Figure 3.
Model predictions (empty symbols) against experimental data (measured by
Dynamic Light Scattering, black triangles). From top to bottom and left to
right the initial PCL concentration corresponds to 0.5, 2.5, 5.0, 10.0, 15.0,
and 25.0 mg/mL.

References

Di Pasquale, N., Marchisio, D.L., Barresi,
A.A., Carbone, P., 2014. Solvent
structuring and its effect on the polymer structure and processability: the
case of water-acetone poly-e-caprolactone mixtures. J. Phys. Chem. B, 118, pp. 13258–13267.

Ferri, A. , Kumari, N. , Peila, R., Barresi, A. A., 2017. Production of menthol‐loaded nanoparticles by
solvent displacement. Can. J. Chem. Eng., 95, 1690-1706.

Flory, P., 1953. Principles of Polymer Chemistry. Cornell Univ. Press.

Lavino, A. D., Di Pasquale, N., Carbone, P.,
Marchisio, D. L., 2017. A novel
multiscale model for the simulation of polymer flash nano-precipitation. Chem.
Eng. Sci., 171, pp. 485-494.

Lince, F., Marchisio, D. L., Barresi, A. A., 2008.
Strategies to control the particle size distribution of
poly-ε-caprolactone nanoparticles for pharmaceutical applications, J.
Colloid Interface Sci., 322, pp. 505–515.