DOI: 10.1039/D4CE00648H
(Paper)
CrystEngComm, 2024, Advance Article

Ruel Cedeno,
Romain Grossier,
Nadine Candoni and
Stéphane Veesler*

CNRS, Aix-Marseille Université, CINaM (Centre Interdisciplinaire de Nanosciences de Marseille), Campus de Luminy, Case 913, F-13288 Marseille Cedex 09, France. E-mail: stephane.veesler@cnrs.fr

Received
27th June 2024
, Accepted 21st August 2024

First published on 22nd August 2024

We developed a rapid polymorphic screening approach based on contracting sessile microdroplets, which offers several advantages: (1) achieves very high supersaturation to facilitate formation of metastable forms; (2) allows systematic labeling of samples; (3) gives access to the statistical distribution of polymorphic selectivity as a function of experimental conditions; (4) ensures the formation of crystal for each droplet, addressing the problem of uncrystallized droplets in traditional microfluidics. We studied the competitive nucleation of D-mannitol polymorphs and investigated the effect of droplet volume on polymorphic selectivity. We showed that our observed polymorph distributions at different volumes are qualitatively consistent with the predictions of classical nucleation theory except for very small volumes where thermodynamic confinement or surface effects could play a substantial role. Overall, our microfluidic approach can be a promising tool not only for routine screening of pharmaceutical polymorphs in the industrial context but also in the fundamental understanding of the mechanisms underlying the competitive nucleation of polymorphs.

In our previous work, we have developed a microfluidic platform that allows extraction of thermodynamic and kinetic parameters of nucleation in contracting sessile microdroplets.^{3,7} In this work, we further extend its application in the study of polymorphism. Using D-mannitol in water as a model system, we demonstrate how our platform enables rapid screening of polymorphic outcomes. Moreover, it also allows statistical investigation of the influence of volume and supersaturation ratio S (i.e. c_{sol}/c_{eq.} where c_{sol} is the solution concentration and c_{eq.} is the saturation concentration of the β polymorph) on polymorphic selectivity. We then rationalize our observed polymorphic distributions using classical nucleation theory, revealing interesting insights into the interplay of thermodynamics and kinetics in the stochastic nucleation of polymorphs.

Microdroplet generation and nucleation time detection are based on a previously reported experimental setup and protocol in ref. 7, consisting in deliquescence/recrystallization cycling.

However, unlike NaCl that dissolves upon exposure to humidity (RH > 75%), D-mannitol does not absorb enough moisture to undergo deliquescence, preventing the use of the RH cycling technique. We thus modified the procedure by generating initially undersaturated arrays of sessile microdroplets on PMMA coated glass immersed in a thin layer of polydimethylsiloxane (PDMS) oil (10 cSt) under ambient conditions (1 atm, 25 °C). This is done at RH close to 100% to minimize possible evaporation during microdroplet generation. Once the desired number of microdroplets is generated, the RH is lowered to 10%, causing the droplets to evaporate by diffusion of water in oil and eventually nucleate. Using a tailor-made evaporation model^{9} (details in section S1 in the ESI†), the supersaturation ratio of the microdroplets can be obtained as a function of time. The crystallized droplets are analysed in situ at the end of the experiment using a Kaiser RXN1 Raman microscope system. Measurements are made at room temperature using a 785 nm laser.

The resulting crystal from each microdroplet was then characterized using Raman spectroscopy. Three distinct spectra were obtained corresponding to the α, β, δ forms as shown in Fig. 1b. These spectra exhibit sufficiently resolved characteristic peaks for precise phase identification.

In contrast to conventional screening methods, our approach offers several advantages: (1) the relatively high supersaturation level achieved in microdroplets facilitates the formation of metastable polymorphs; (2) the linear arrangement of the immobilized crystals facilitates systematic labeling of each sample with respect to its position in the 2D array, allowing us to generate a cartography of the polymorph as shown in Fig. 1c. (3) The statistical distribution of polymorphic selectivity can be analyzed as a function of supersaturation ratio S as shown in Fig. 1d. We use image acquisition to track the droplets as they evaporate, so we know when nucleation occurred and at what concentration. We use Raman spectroscopy to characterize the nucleated phase. (4) The open geometry microfluidics ensures the formation of crystal for each droplet, unlike closed microfluidics (chips or tubing) where droplets can remain metastable for several days to weeks. (5) The method is relatively rapid, as the entire experiment from droplet generation to characterization took less than 4 hours in this work.

The polymorphic distribution for various volumes at saturation (0.2, 0.3, 0.7, 1.5, and 5 nL) is shown in Fig. 2a. Notice that the physical mixtures (α + β, α + δ, β + δ) occupy a non-negligible fraction across different volumes. The formation of polymorphic mixtures can be interpreted in three different ways:

Fig. 2 Distribution of polymorphs as a function of droplet volume in which mixtures are represented as (a) actual mixtures, (b) case 1, (c) case 2, and (d) case 3. N indicates the number of droplets. |

Case 1: independent nucleation: mixtures arise from the independent/concomitant nucleation event of each polymorph.

Case 2: Ostwald's rule of stages: the less stable polymorph nucleates first then gradually transforms to a more stable polymorph.

Case 3: surface nucleation: the more stable polymorph nucleates first, which then facilitates the nucleation of the less stable ones on its surface.

It should be noted that the method used to measure induction time makes it possible to observe simultaneously hundreds of droplets at the cost of a loss of resolution,^{11} which makes it impossible to distinguish between the 3 cases described above.

The resulting distribution based on case 1, case 2, and case 3 representations is plotted in Fig. 2b, c, and d respectively, considering only the first polymorph that appeared according to case 2 or 3 respectively.

Among these three mixture interpretations, we believe case 3 is highly unlikely because as the stable form nucleates and grows, it quickly depletes the supersaturation level in the droplet which consequently dissolves the precursors/pre-critical clusters of the more soluble metastable forms. Therefore, in the following discussion, we will concentrate on cases 1 and 2, for which it is impossible to give a definitive answer.

Recall that the order of stability for D-mannitol polymorphs is δ < α < β. During droplet contraction, the experimental conditions inside each droplet move on the phase diagram from undersaturated to supersaturated. They first cross the solubility curve of form β, before crossing the solubility curve of form α and then δ. The same trend is expected for the metastable limit of the three forms. Therefore, we would expect that the stable β form will dominate at larger volumes. This is due to the lower surface area to volume ratio of larger droplets, which implies that their supersaturation ratio S increases more slowly (Fig. S2b in the ESI†), allowing more time in the stable β-form nucleation area. Meanwhile the least stable δ form will dominate at smaller volumes due to the higher surface area to volume ratio of smaller droplets, and so their supersaturation ratio S increases more rapidly (Fig. S2b in the ESI†). Hence, metastable products are favoured according to Ostwald's rule of stages, as previously observed by the Myerson group in a confined environment for sulfathiazole and glycine^{12,13} and by Buanz et al. for crystallization in printed droplets of D-mannitol.^{14} As shown in Fig. 2b and c, the trend in % δ-form qualitatively agrees with our hypothesis, i.e., it tends to increase as the volume decreases (except at 0.2 nL). Surprisingly, the % β-form does not increase with volume, and the least stable δ-form dominates across all studied volumes. Interestingly, the medium stable α-polymorph follows the expected trend of the stable polymorph.

(1) |

For simplicity, given that the mass transfer properties (i.e. diffusivity, viscosity, etc.) in the liquid phase are identical regardless of the solid form, we can suppose that parameter A (related to the mass transfer rate towards the nucleus) is similar for all polymorphs. This assumption is similar to that of Sato^{15} and Deij et al.^{16} Consequently, the relative nucleation rate ln(J/A) is only a function of γ_{eff}. In principle, γ_{eff} can be measured from the probability distributions of nucleation time for each polymorph. Unfortunately, given the dominance of the δ-form, the number of data points for other polymorphs is not sufficient to extract reliable statistical distribution. For this reason, we decided to apply the empirical correlation of Mersmann^{17} which correlates the interfacial energy (between crystal and solution) γ_{SL} with the solubility, written as

(2) |

Fig. 3 (a) Relative nucleation rate and (b) relative selectivity as a function of the supersaturation ratio computed based on classical nucleation theory and Mersmann correlation. The green area in the graph corresponds to the estimated supersaturation at nucleation in the different experiments presented in Fig. 2. |

To interpret the results in Fig. 3, remember that nucleation time is inversely proportional to the droplet volume (t_{n} = 1/JV). Under continuous evaporation, smaller droplets can therefore achieve higher supersaturation within the nucleation zone. Thus, Fig. 3b suggests that larger droplets would favor the α-form while the smaller ones would favor the δ-form. Reassuringly, this behavior is coherent with what we observe in Fig. 2b and c, showing the predominance of polymorphs α and δ, except that of the 0.2 nL dataset. While one could speculate several possible explanations, such a change in trend at very low volumes could be likely due to confinement effects^{10} which lower the effective supersaturation and consequently promote the α-form. Moreover, diminishing droplet volume provides a higher surface to volume ratio, potentially affecting nucleation mechanisms and rates.

Indeed, our microfluidic platform and modeling approach reveal interesting insights into the impact of volume on the stochastic nucleation of mannitol polymorphs. Moreover, our approach can be extended to study other polymorphic materials of interest.

Thanks to this platform, we studied the competitive nucleation of D-mannitol polymorphs and investigated the effect of droplet volume on polymorphic selectivity. We showed that our observed polymorph distributions at different volumes are qualitatively consistent with the predictions of the classical nucleation theory except for very small volumes where thermodynamic confinement or surface effects could play a substantial role.

Overall, our microfluidic approach can be a promising tool not only for routine screening of pharmaceutical polymorphs in the industrial context but also in the fundamental understanding of the mechanisms underlying the competitive nucleation of polymorphs.

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ce00648h |

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