Solvent-Mediated Polymorphic Transformations in Molten Polymers: The Account of Acetaminophen

Abstract

Solvent-mediated polymorphic transformations (SMPTs) employing nonconventional solvents (polymer melts) is an underexplored research topic that limits the application of polymer-based formulation processes. Acetaminophen (ACM), a widely studied active pharmaceutical ingredient (API), is known to present SMPTs spontaneously (<30 s) in conventional solvents such as ethanol. In situ Raman spectroscopy was employed to monitor the induction time for the SMPT of ACM II to I in polyethylene glycol (PEG) melts of different molecular weights ($M_{\text{w}}$, 4000, 10 000, 20 000, 35 000 g/mol). The results presented here demonstrate that the induction time for the SMPT of ACM II to I in PEG melts is driven by its diffusivity through the polymer melts. Compared to conventional solvents (i.e., ethanol) the mass transfer (diffusion coefficient, $D$) in melts is significantly hindered $(D_{\text{ethanol }}=4.84\times {10}^{-9}{\text{m}}^2\text{/s}>D_{\text{PEGs}}=5.32\times {10}^{-11}-8.36\times {10}^{-14}{\text{m}}^2\text{/s)}$. Ultimately, the study proves that the induction time for the SMPT can be tuned by understanding the dispersant’s physicochemical properties (i.e., $\eta$) and, thus, the diffusion coefficient $D$ of the solute in the dispersant. This allows one to kinetically access and stabilize metastable forms or delay their transformations under given process conditions.

Graphical Abstract

INTRODUCTION

Polymorphism affects physicochemical properties of active pharmaceutical ingredients (APIs), such as solubility and bioavailability.^1,2 Therefore, it is vital to control polymorphic phase transformations during processes leading to solid dose drug formulations.^1,2 To date, most of the research on the discovery, understanding, and control of polymorphism including phase transformation focuses on solution crystallization^3–9 employing conventional solvents, defined as having molecular weights $\text{(}{M}_{\text{w}}\text{)}<150\text{g/mol}$, boiling points $\text{(}{T}_{\text{Bp}}\text{)}<200\text{°C}$, and viscosities $(\eta )<5\text{mPa·s}$.¹⁰ In these efforts, often solvent-mediated polymorphic transformations (SMPTs) are encountered.^{3–6,11–23} In general, SMPTs in solution crystallization occur through three fundamental steps: dissolution of the metastable form, followed by nucleation and growth of the stable form.^4,18 Yet, SMPTs in nonconventional solvents (i.e., polymer melts) need to be addressed to broaden the application of polymer-based formulations including crystalline solid dispersions (CSDs).

Moreover, the growing interest in polymer-based formulation strategies (i.e., hot melt extrusion, HME, and 3D printing, 3DP)^24–27 justifies the need to investigate SMPT using nonconventional solvents. Polymer-based formulation strategies are employed to prepare amorphous and CSDs. While CSDs have been effective in enhancing the API solubility,^{24,25,28–32} their implementation has been limited due to a lack of understanding of polymorphic phase transformations.³³ To the best of our knowledge, only a few accounts exist regarding polymorphism in polymer melts.^33–35 These studies mainly focused on the control of polymorphic phase transformations of the model compound, flufenamic acid (FFA III to I), in polymer-based formulation processes where the polymer $M_{\text{w}}$ and the phase transition temperature $\text{(}{T}_{\text{p}}\text{)}$ had an impact on the induction time for the polymorphic phase transformation.^33,35 However, the effect of the solvent’s (i.e., polymer melt) $\eta$ and its correlation to the solute’s diffusivity (i.e., molecular mobility) with the induction time for the SMPT were not assessed. To study this impact, the SMPT of a monotropic system will be assessed in nonconventional solvents, specifically polyethylene glycol (PEG) melts. Acetaminophen (ACM), an antipyretic drug, which possesses nine polymorphic forms,³⁶ was employed as a model API. Only ACM I and II are known to be stable at ambient conditions.^36,37 The SMPT of ACM II to I has been documented in conventional solvents,^20–22 specifically, ethanol, where the induction time occurred in ∼30 s at 25 °C.²⁰ However, the effect of nonconventional solvents in the SMPT of this system has not been investigated.

This study intends to understand the effect of PEG at $M_{\text{w}}$ of 4000, 10 000, 20 000, and 35 000 g/mol as nonconventional solvents on the induction time for the SMPT of ACM II to I. In situ Raman spectroscopy was employed to monitor the effect of the process temperature $(T)$ and intrinsic properties of the polymer (i.e., $M_{\text{w}}$ and $\eta$) on the induction time for the SMPT of this system in a melt suspension. The correlation of the $T$ and the solvent $\eta$ will allow to determine the diffusion coefficient $(D)$ of the solute in the solvent systems employed. The calculated $D$ values will enable to quantify the solutes molecular mobility and compare the effect of conventional and nonconventional solvents on the induction time for the SMPT. This study contributes to the understanding of crystallization from melt, including but not limited to polymorph discovery,³⁶ and highlights the potential of nonconventional solvents (i.e., polymer melts) to control SMPT in melt crystallization processes as those employed in polymer-based formulation strategies.

MATERIALS AND METHODS

Materials.

Acetaminophen form I (ACM I, ≥98%) and polyethylene glycol (PEG, ≤100%) with an average $M_{\text{w}}$ of 4000 and 35 000 g/mol were purchased from Sigma-Aldrich (St. Louis, MO). PEG (≤100%) with an average $M_{\text{w}}$ of 10 000 and 20 000 g/mol was acquired from Alfa Aesar (Ward Hill, MA). All chemicals were used “as received” without further purification.

Physical Mixture Preparation.

ACM II Preparation.

Adapted from Di Martino et al.,³⁸ 20 mL scintillation vials filled with approximately 300 mg of ACM I were placed with constant magnetic agitation for 4 min inside a heating block on top of a hot plate previously heated to 180 °C. After 4 min, the vials containing the molten ACM were placed at 70 °C in a VWR Digital block heater for 15 min. The recrystallized ACM II material was stored in the same closed scintillation vials at ambient conditions and powder X-ray diffraction (PXRD) measurements were conducted before further use to confirm that neat ACM II has been generated (within the detection limits of the PXRD).

Physical Mixtures.

Physical mixtures were prepared as reported in the literature.^33,34 Briefly, 1–90 wt % ACM I or ACM II with PEG was gently ground using a mortar and pestle for 5 min at ambient conditions in the absence of solvents. Afterward, the physical mixtures were analyzed by PXRD to confirm that the energy input through grinding had no adverse effect on the polymorphic form prior to the phase diagram elucidation by differential scanning calorimetry (DSC) and SMPT induction time experiments.

Characterization.

Powder X-ray Diffraction (PXRD) Analysis.

PXRD data were collected at 300 K in a Rigaku XtalLAB SuperNova microfocus X-ray diffractometer, with a Cu Kα radiation (λ = 1.5417 Å, 50 kV and 1 mA) source equipped with a HyPix3000 X-ray detector in transmission mode. Powders were affixed in MiTeGen microloops with a small amount of parafilm oil. The diffractograms were collected over an angular 2θ range of 6–60° (step size of 0.01°) using the fast phi experiment (120 s exposure). Data was analyzed in CrysAlisPro software v 1.171.3920a.

Differential Scanning Calorimetry (DSC) Measurements.

DSC analysis was performed in a TA Q2000 instrument equipped with a single-stage refrigeration system (RCS40) and calibrated with a standard (indium). Samples (∼4.000 mg) were weight in using a XP26 (Mettler Toledo) microbalance (±0.002 mg) and placed in hermetically sealed aluminum pans. To generate the ACM I–PEG (±000, 20 000, and 35 000) phase diagrams, the physical mixtures were equilibrated at 25 °C for 10 min followed by heating to 200 °C at a 5 °C/min rate under N₂ atmosphere (50 mL/min). A faster heating rate was employed to the physical mixtures containing PEG 10 000 allowing the endothermic event of the polymorphic phase transformation from ACM II to I to be recorded. Moreover, to compare the phase diagram of ACM I–PEG 10 000 with the one elucidated for ACM II–PEG 10 000, the same heating profiles were applied. To generate the phase diagram of ACM (I–II)–PEG 10 000, the physical mixtures were equilibrated at 25 °C for 10 min followed by a heating to 200 °C at a rate of 30 °C/min under N₂ atmosphere (50 mL/min). The eutectic temperature and melting points of the liquidus curve were determined as peak temperatures in duplicate measurements using the TA Universal Analysis software v 4.5A.

Thermogravimetric Analysis (TGA).

Thermographs were recorded in a TGA Q500 instrument (TA Instruments Inc.) calibrated with calcium oxalate monohydrate. Samples (2–5 mg) were equilibrated at 25 °C for 10 min prior to heating to 300 °C under N₂ atmosphere (60 mL/min) at a 5 °C/min rate. Data was analyzed with TA Universal Analysis software v 4.5A.

In Situ Raman Spectroscopy.

ACM II polymorphic phase transformation caused by elevated temperatures applied by a temperature controlled hot-stage (Linkam Scientific Instruments Ltd., LTS 420) was monitored in situ using a RXN2Multichannel Raman Analyzer (Kaiser Optical Systems, Inc.) equipped with a 785 nm laser diode and a PhAT probe (6 mm spot size) coupled with the hot stage in a 180° backscattering geometry.³⁹ The Raman spectra of the samples was recorded through the quartz glass window of the hot stage in the range of 150–1890 cm⁻¹ with optimized parameters. Experiments employing a dynamic temperature profile, 25–200 °C at 30 °C/min, were performed with 3 s exposure time, 1 accumulation, and 5 s sampling interval for 7 min. Experiments that employed an isothermal temperature profile to measure the induction time of the SMPT from ACM II to I in molten PEGs were performed with 28 s exposure time, 1 accumulation, and 30s sampling interval. The applied temperature profile begins at 25 °C followed by a heating to the desired temperature (65, 70, 75, or 80 °C) at a rate of 20 °C/min for 30 min to finally cool the sample down to 25 °C at the same rate (20 °C/min). The induction time for the SMPT of ACM II to I in water at 25 °C was measured by placing ∼25 mg of ACM II onto an aluminum foil surface shaped cup within a customized black box to avoid interferences from cosmic rays. After pipetting ∼2 mL of distilled water Raman spectra were recorded using 13 s exposure time, 1 accumulation, and 15 s sampling interval. The data was analyzed with an automatic Cosmic ray filter and intensity correction. The Raman signals reported for ACM I and II (1245 and 1234 cm⁻¹, respectively)⁴⁰ were monitored employing the iC Raman software (v 4.1.917).

Viscosity Determination.

The viscosity of the PEGs and ethanol were determined to calculate the diffusion coefficient of ACM in these solvents. Diffusion coefficient values for solutes in solvents are often elusive in the literature; if available, these are found at low concentrations or infinite dilution.⁴¹ Therefore, the viscosity of ACM in PEG or ethanol solutions were not employed, instead, the viscosity of neat PEGs was determined and employed. The viscosity of neat ethanol at 25 °C was obtained from the CRC Handbook of Chemistry and Physics.⁴²

Viscosity of Neat PEGs.

An Anton Paar Rheometer (MCR 302) equipped with a temperature-controlled hood accessory (H-PDT 200) and a 25 mm parallel-plate (PP25/TG) was used to determine the viscosities of the molten PEGs employed in this study. Briefly, the shear rate-dependent viscosity was measured at 65 °C by applying a shear rate from 1 to 200 s⁻¹ within 300 s to determine the shear rate to be employed for the viscosity measurements where the PEGs behave as Newtonian liquids (Figure S12 in the Supporting Information).^43–45 The temperature-dependent viscosity was obtained by placing the PEGs on the Peltier plate, which was set to 65 °C and the gap between the parallel-plate and the Peltier plate was reduced to a measuring gap size of 0.4 mm. Prior to the viscosity measurement the samples were conditioned at 65 °C for 2.5 min (PEG 4 000), 5 min (PEG 10 000), 7.5 min (PEG 20 000), and 10 min (PEG 35 000) before a linear temperature profile from 65 to 80 °C at 2.5 °C/min and a constant shear rate of 10 s⁻¹ was applied.⁴³

Diffusion Coefficient Calculation.

The diffusion coefficient ($D$, m²/s) was calculated to quantify the role of the solvent on the diffusivity of the solute (ACM) and its effect on the induction time for the SMPT of ACM II using the Stokes–Einstein equation⁴⁶ (eq 1)

$$D=\frac{kT}{6\pi \eta r}$$ (1)

where $k$ is the Boltzmann constant (J/K), $T$ is the temperature in $\text{K}$, $\eta$ is the viscosity of the neat solvent (PEGs) obtained by viscosity measurements (Pa·s), and $r$ is the hydrodynamic radius assuming a spherical solute (m, ACM: 4.2 × 10⁻¹¹ m).^47,48 The $D$ of ACM in ethanol was also calculated in this study as it has not been previously reported.²⁰

For an accurate application of the Stokes–Einstein equation, the size of the diffusing particle (ACM) should be considerably larger than that of the dispersant (PEG melt).^47,49 The hydrodynamic radius reported in literature for ACM (4.2 × 10⁻¹¹ m)⁴⁸ is smaller than the hydrodynamic radius for PEGs (>3.4 × 10⁻¹⁰ m),⁵⁰ which might lead to an underestimation of the diffusion coefficient. Additionally, the Stokes–Einstein equation assumes that the molecule (ACM) is infinitely diluted and therefore neglects API-polymer interactions.⁴⁹ This assumption is in agreement with the scientific literature, which up to date reports no strong interactions for the ACM-PEG system.^51,52 Only weak hydrogen bonding interactions have been observed by FT-IR.⁵² Nevertheless, while there might be an underestimation of the D values due to the previously discussed assumptions, the D values obtained in this study can be observed as a good estimation of the diffusivity effect on the SMPT of ACM as a model compound.

RESULTS AND DISCUSSION

ACM II and Physical Mixture Characterization.

In this study, ACM II was crystallized from melt modifying a previously reported method³⁸ to reduce the decomposition of ACM. In the new method, the processing time at 180 °C was decreased to ≤4 min, which resulted in ∼34% less decomposition than the original method³⁸ as evidenced by TGA data (Figure S4 in the Supporting Information). PXRD analysis confirmed the phase purity of ACM II (Figure S2 in the Supporting Information).

Physical mixtures of the commercially available polymorph, ACM I, with PEGs (4000, 10 000, 20 000, or 35 000) were prepared and characterized by PXRD, DSC, and TGA (Figures S1, S3, and S5 in the Supporting Information). Additionally, physical mixtures containing the metastable ACM II and PEG 10 000 were prepared and characterized by PXRD. The PXRD served to confirm that the exerted energy input of grinding with a mortar and pestle to produce the physical mixtures did not cause a polymorphic phase transformation to the more stable polymorph, ACM I (Figure S2 in the Supporting Information).² Thereafter, the thermodynamic characterization of the ACM II–PEG 10 000 physical mixtures was performed by DSC. The phase diagrams and thermal stability data attained by these methods aided in defining the thermodynamic design spaces for these systems, as further detailed below.

ACM–PEG Phase Diagram Determination.

To overcome the polymorphic phase transformation of ACM II to I during the DSC measurements at a heating rate of 5 °C/min, ACM I–PEG 10 000 and ACM II–PEG 10 000 were analyzed at a faster heating rate (30 °C/min).^38,53 Despite increasing the heating rate, a small endothermic event was observed for the ACM II – PEG 10 000 system (Figure 1) indicating a possible polymorphic phase transformation. According to Burger and Ramberger,⁵⁴ ACM is one of the few exceptions where, in a monotropic system, an endothermic event reveals a phase transformation from the metastable (ACM II) to the more stable form (ACM I). To confirm the polymorphic phase transformation observed in the DSC thermograms a hot stage was coupled with in situ Raman spectroscopy (Figure 1).³⁹

Figure 1.

In situ Raman spectroscopy during a heating profile employed in a hot stage to emulate the DSC measurements at a heating rate of 30 °C/min: black solid line (DSC thermogram of 80 wt % ACM II–20 wt % PEG 10 000) as well as blue squares and red triangles (in situ Raman characteristic peaks at 1234 and 1329 cm⁻¹ for ACM I and II, respectively).⁴⁰

Figure 1 shows the relative intensity of characteristic Raman shifts of ACM I (1234 cm⁻¹, blue squares) and ACM II (1329 cm⁻¹, red triangles) as a function of temperature, overlaid with the 80 wt % ACM II–20 wt % PEG 10 000 DSC thermogram.⁴⁰ It can be observed that the intensity of the Raman signal for ACM II (red triangles) decreases once the melting at the eutectic temperature occurs (first endotherm, Figure 1A). On the other hand, the Raman signal of ACM I (blue squares) increases starting at ∼70 °C reaching a maximum intensity at ∼100 °C (second endotherm, Figure 1B). The latter confirms that the second endotherm corresponds to the phase transformation of ACM II to I, which is completed at ∼100 °C. Lastly, the third endothermic event (Figure 1A) corresponds to the melting of ACM I (172 °C). These results agree with previous reports^38,53 where the phase transformation of ACM II to I was presented in the absence of a polymer with a heating rate of ≤10 °C/min. The slightly increased melting point reported in this work is most likely caused by the faster heating rate, known to shift the melting point to higher temperatures.⁵⁵ Collectively, these results allow the identification of the thermodynamic design space of ACM II–PEG 10 000, defined as the two-phase region where ACM II is in the crystalline state and the polymer (PEG) is molten (green area, Figure 2).³⁵ Moreover, the phase diagrams for ACM I–PEGs (4000, 10 000, 20 000, and 35 000) were generated to understand the thermodynamic design spaces of the systems (Figure S5 in the Supporting Information). It was observed that the thermodynamic design space of ACM I–PEG systems did not change significantly as a function of the PEG $M_{\text{w}}$ and, therefore, only the phase diagram of the more elusive ACM II with PEG 10 000 was elucidated.

Figure 2.

Phase diagram of ACM I (blue) and II (red) in PEG 10000. Green area accounts for the thermodynamic design space in which PEG is molten and ACM II is in the crystalline state. The trend lines correspond to the best possible data fit utilizing mathematical expressions with the best possible fit. Origin (OriginLab Corporation, v. 9.7.0.188) was utilized to solve the nonlinear curve-fitting problems employing the Levenberg–Marquardt algorithm. If the error bars are not observed, they are obstructed by the data points.

Figure 2 shows the combined phase diagrams for ACM I (blue) and ACM II (red) with PEG 10 000, respectively. The thermodynamic design space (green area) is located above the eutectic temperature (∼59 °C, lower red line) and below the average transformation temperature of ACM II to I (∼100 °C, upper red line). Within the derived thermodynamic design spaces one can determine the induction time for the SMPT of ACM II to I in PEGs (4000, 10 000, 20 000, and 35 000).

Solvent-Mediated Polymorphic Phase Transformation of ACM II.

To obtain the induction time for the SMPT of ACM II in PEG (4000, 10 000, 20 000, and 35 000), a hot stage coupled with an in situ Raman was employed. This technique allowed us to continuously monitor the onset of the polymorphic phase transformation at temperatures inside the thermodynamic design spaces (65, 70, 75, and 80 °C). Each physical mixture (80 wt % ACM II–20 wt % PEG) was exposed to the desired temperature for 30 min, and the change in Raman shifts from ACM II (1245 cm⁻¹) to I (1234 cm⁻¹)⁴⁰ was closely monitored. Here, the induction time for the SMPT was determined as the time elapsed at the selected temperature when the characteristic Raman shift of ACM I (1234 cm⁻¹) was first observed.^33,56 Figure 3 shows a representative Raman spectra for an 80 wt % ACM II and 20 wt % PEG 20 000 physical mixture heated to 65 °C for 30 min.

Figure 3.

In situ Raman spectra as a function of time (30 min) to monitor the induction time for the SMPT of an 80 wt % ACM II–20 wt % PEG 20 000 heated at 65 °C. The Raman shift for ACM II and I were monitored at 1245 and 1234 cm⁻¹, respectively. Bottom (surface plot from virtual matrix) and top (top view on surface plot from virtual matrix).

The induction time for this physical mixture shown in Figure 3 was determined to be 7 min. At this time, the characteristic peak of ACM I initially appear at 1234 cm⁻¹, and its intensity continuously increases until the transformation is completed at the end of the residence time (30 min). Figure 4 shows the induction time for the SMPT determined for the ACM II–PEGs (4000, 10 000, 20 000, and 35 000) systems as a function of process temperature $(T)$. These results demonstrate that the induction time for the SMPT decreases with increased $T$ and lower polymer $M_{\text{w}}$. The vital role of PEG on the induction time for the ACM II to I transformation is reiterated, by a control experiment, where neat ACM II was exposed to the highest $T$ employed in this study (80 °C) for 60 min and no polymorphic phase transformation was observed (Figure S10 in the Supporting Information).

Figure 4.

Induction time for the SMPT of ACM II to I as a function of the T for 80 wt % ACM II in 20 wt % PEG 4000 (black circles), PEG 10 000 (orange triangles), PEG 20 000 (blue squares), and PEG 35 000 (red diamonds). The trend lines composed of four data points for each system correspond to the best possible data fits utilizing mathematical expressions with the best possible fit (Table S1 in the Supporting Information). Origin (OriginLab Corporation, v. 9.7.0.188) was utilized to solve the nonlinear curve-fitting problems employing the Levenberg–Marquardt algorithm. The data points at 80 °C for PEG 4000, 10 000, and 20 000 are overlapping each other. If error bars are not observed, they are obstructed by the data points.

The results presented in Figure 4 are consistent with a previous study where the impact of the $T$ and $M_{\text{w}}$ of PEG was reported on the induction time for the SMPT of an enantiotropic system (FFA I and III).³³ However, the effect of the polymer’s viscosity $(\eta )$ on the induction time was not addressed. This evaluation would allow us to relate the change in induction time to an intrinsic property (i.e., $\eta$), which is $T$ dependent instead of a $T$ independent intrinsic property (i.e., $M_{\text{w}}$) of the dispersion media. To this end, the dynamic $\eta$ of the neat PEGs (4000, 10 000, 20 000, and 35 000) was measured in a rheometer while heated at the temperatures (65, 70, 75, and 80 °C) employed in the SMPT induction time experiments. The $\eta$ of the PEGs decreases with increasing $T$ and decreasing polymer $M_{\text{w}}$ (Figure S13 in the Supporting Information). Figure 5 depicts the induction time for the SMPT of ACM II to I as a function of the $T$ and the $\eta$ for PEGs of different $M_{\text{w}}$.

Figure 5.

Induction time for the SMPT of ACM II to I as a function of the temperature $(T)$ and viscosity $(\eta )$ of PEG 4000 (black circles), PEG 10 000 (orange triangles), PEG 20 000 (blue squares), and PEG 35 000 (red diamonds). The data points projected on the $XY$ plane show the effect of $T$ on the PEG $\eta$, and the data points on the $YZ$ plane illustrate the effect of the PEG $\eta$ on the induction time for the SMPT of ACM II to I.

In general, it is observed (Figure 5) that, by lowering the $T$, the $\eta$ of the PEGs slightly increases ($XY$ projection plane) which yields a slower induction time for the SMPT. Specifically, for the 80 wt % ACM II–20 wt % PEG 35 000, decreasing the $T$ from 80 to 65 °C increased the PEG $\eta$ by 19 Pa·s (30%), which resulted in an increase in the induction time for the SMPT of ∼19 min (361%). The increase in the induction time for the SMPT could be due to a reduced diffusivity of the solute (ACM) in the polymer melt as a consequence of the higher $\eta ({\eta }_{\text{<ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.ncbi.nlm.nih.gov/protein/PEG35000" ext-link-type="uri">PEG35000</ext-link> }}>{\eta }_{\text{<ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.ncbi.nlm.nih.gov/protein/PEG20000" ext-link-type="uri">PEG20000</ext-link>}}>{\eta }_{\text{<ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://www.ncbi.nlm.nih.gov/protein/PEG10000" ext-link-type="uri">PEG10000</ext-link> }}>{\eta }_{\text{PEG4000}})$.⁵⁷ To prove this point, the $D$ for the systems under study (ACM II–PEGs) were calculated using eq 1. The resulting $D$ values (Table S2 in the Supporting Information) indicate that the higher the $\eta$ of the PEGs, the lower the diffusivity of ACM in the polymer melts.

Figure 6 shows that lower $D$ values yield slower induction time for the SMPT of ACM II to I. In this regard, while the system containing PEG 35 000 generally follows this behavior, it shows a major increase in the induction time for the SMPT (gray area in Figure 6). Here, it is presumed that the $\eta$ of PEG 35 000 is influenced by the solid–liquid equilibrium, since the melting point of this polymer (63.7 °C) might be too close to the $T$ employed (65 °C) accounting for the increased induction time. In general, the lower diffusivity of ACM in the polymer melt, delays the nucleation of ACM I due to a slower mass transfer⁵⁸ of the solute causing an increase in the induction time for the SMPT. Moreover, it is shown that the induction times for the SMPT of ACM II to I reported by Kachrimanis et al.²⁰ in ethanol and by this study in water are much faster at a considerably lower temperature (25 °C) than those observed here for the PEGs. The faster induction time obtained in ethanol and water can be attributed to the much higher calculated $D$ (4.84 × 10⁻⁹ and 5.85 × 10⁻⁹ m²/s, respectively)^20,42 at infinite dilution in the two conventional solvents when compared to those obtained for the infinite dilution in the nonconventional solvents employed here (i.e., 5.32 × 10⁻¹¹−8.36 × 10⁻¹⁴ m²/s). Moreover, despite a considerably higher solubility of ACM in ethanol (209.91 g/kg)⁵⁹ compared to water (14.90 g/kg),⁵⁹ the induction times for the SMPT of ACM II to ACM I are 0.5 min²⁰ and 0.6 ± 0.3 min, respectively. These results suggest that the nucleation in a SMPT process is driven by the mass transfer of the solute,^12,61,62 which can be quantified by its $D$ in the solvent. This might be explained by the stagnant (static) conditions of the solution/melt^41,60 employed during the SMPT experiments. Moreover, this study reveals the feasibility of the molten polymers to delay the onset of the SMPT by decreasing the diffusivity of the solute in the polymer melt. These results might be relevant in the context of the growing number of novel high-energy polymorphic forms or concomitant polymorphs discovered from melt crystallization (single³⁶ or multicomponent melt^34,63,64). Specifically, according to Ostwald’s rule, if several polymorphs of the same compound can crystallize from the same liquid (i.e., supercooled melts), the least stable polymorph should appear first. However, as demonstrated here, the diffusivity in supercooled melts is at least 2 orders of magnitude slower than that in conventional solvents. Thus, the mass transfer needed for the SMPT in melt crystallization is significantly hindered compared to conventional solvents. Ultimately, the study has proven that the induction time for the SMPT can be tuned by understanding the dispersant’s physical properties (i.e., $\eta$) and, thus, the diffusion coefficient of the solute in the dispersant. This allows the reaction to kinetically access and stabilize metastable forms or delay their transformations under given process conditions.

Figure 6.

Induction time for the SMPT of ACM II to I as a function of the diffusion coefficient ($D$, m²/s) for ACM II at infinite dilution in ethanol (magenta cross),^20,42 water (green diagonal cross), PEG 4000 (black circles), PEG 10 000 (orange triangles), PEG 20 000 (blue squares), and PEG 35 000 (red diamonds). The induction time for the two highest $D$ values of PEG 4000 are overlapping. The shaded gray area shows a schematic representation of the general trend observed for the induction time as a function of the D values in PEGs. If error bars are not observed, they are obstructed by the data points.

CONCLUSIONS

The work presented here demonstrates that the induction time for the SMPT from a metastable to a more stable polymorph is driven by the solute diffusivity through the dispersant medium. The induction time for the SMPT of ACM II to I in nonconventional solvents (molten polymers) was significantly delayed compared to those previously reported in a conventional solvent (ethanol). Thus, nonconventional solvents such as molten polymers allow a wider range of opportunities for polymorph discovery and control due to the tunable nature of their $M_{\text{w}}$, which correlates to their $\eta$ and, hence, their diffusivity. Ultimately, this study increases our understanding of melt crystallization processes, including but not limited to those employed for polymorph discovery,³⁶ and highlights the potential of nonconventional solvents to control SMPT in polymer-based formulation strategies (HME, 3DP).