Isochronal Conditions—The Key To Maintain the Given Solubility Limit, of a Small Molecule within the Polymer Matrix, at Elevated Pressure

In this work, we proposed the method to maintain the desired level of drug’s solubility within the polymer matrix by adjusting conditions to uphold the same molecular dynamics of the system (e.g., temperature for set elevated pressure or vice versa). Namely, we observed, that recrystallization of the drug from the supersaturated drug–polymer system, initiated for the same structural relaxation time of the sample (τα-1) ceases when certain, different than the initial, molecular mobility of the systems is reached (τα-2)—regardless of a given combination of temperature and pressure conditions. Based on the presented results, one can conclude that the molecular dynamics seem to control the process of recrystallization of the excess amount of solute from the supersaturated solution (e.g., small molecules dissolved within the polymer). Therefore, it appears that the elevated pressure compensates the effect of solubility enhancement caused by the elevated temperature. Such information not only is of fundamental relevance in science but also, from a much broader perspective, could be potentially very useful considering extrusion-based manufacturing methods.


■ INTRODUCTION
The solubility of small molecules (SMs) within the polymer matrixes has been of great scientific interest in the past decades. 1−6 The special case of this phenomenon considering drugs as SMs dissolved within the polymers has been extensively explored because of its importance to the pharmaceutical industry. 5,7−16 A great number of the experiments, performed under isobaric (ambient) conditions, allowed to explore the subject of drug−polymer solubility. 3,5,10,11,15,17−19 As a result of those efforts, our knowledge about this process increased. Namely, among many factors that affect the solubility of SMs within the polymer matrix, the temperature is assumed to be the most important one, governing this phenomenon. 1,20−24 Furthermore, performed studies helped to develop and improve theoretical models that allow calculating the discussed solubility. Therefore, to this day, determination of the solubility of SMs within the polymer matrix can be predicted with the use of one of the following: (i) Flory−Huggins theory; 1,[20][21][22]25 (ii) Hansen's solubility parameter; 4,12,23 and (iii) perturbed-chain statistical associating fluid theory. 13,14,24 Nevertheless, it should be emphasized that when we compare the number of reports addressing this issue at ambient pressure conditions with those performed at elevated pressure, the significant disproportion will be found.
In a recent study, antiandrogen drugflutamide (FL)was dissolved within the copolymer matrixKollidon VA64 (PVP/VA)and its solubility was examined at various sets of elevated temperatures and pressures. 26 On the one hand, the generally accepted dependence between temperature and solubility limit [solubility (S) is proportional to temperature: S ∼ T] was observed regardless of applied pressure (under isobar conditions). On the other hand, the result of the increasing pressure (at constant temperature) was the reduction in the amount of FL that could be successfully dissolved within the polymer. Therefore, S ∼ T and at the same time, by following the cited report, solubility is inversely proportional to the applied pressure: S ∼ 1/p. This is crucial information considering extrusion-based manufacturing methods (e.g., hot melt extrusion) because of the fact that pressures generated within an extruder can reach very high values (up to 10,000 psi or 70 MPa), 27 especially, because it has been shown in our recent study that pressure in that range may cause the precipitation/crystallization of the original dissolved drug. By utilizing Broadband Dielectric Spectroscopy (BDS) to determine the solubility limit of the SMs (e.g., drugs) dissolved within the polymer matrixes, one can additionally monitor the . Temperature dependence of τ α in the supercooled liquid has been described by VFT equations (gray and red solid lines). Fits transferred horizontally are marked as brown and green solid lines. Left bottom and middle panels show relaxation maps of the FL + 13% PVP/VA mixture before and after the recrystallization under certain temperature and pressure conditions. (c) τ α (T) registered for the sample after isothermal crystallization at 0.1 MPA and at 343, 353, and 363 K (orange, brown, and dark green circles, respectively). (e) τ α (T) registered for the sample after isothermal crystallization at 363 K and at 0.1, 20, and 50 MPa (dark green circles, diamonds, and pentagons, respectively). τ α (T) in the supercooled liquid has been described by VFT equations (red solid lines). Red dashed line is the horizontal transfer of the VFT fit of the nearest fully amorphous concentration. Right panels present experimentally determined concentrations dependencies of the T g of the FL-PVP/VA mixtures at 0.1 (d,f), 20 (f), and 50 MPa (f). Brown, and dark green points correspond to the concentrations obtained after the recrystallization under isothermal  353, and 363 K, respectively  conditions. Pentagons, diamonds, and circles correspond to the concentration at certain pressure  50, 20, and 0.1 MPa, respectively  conditions. Molecular Pharmaceutics pubs.acs.org/molecularpharmaceutics Article changes occurring in the molecular dynamics of the examined system during the whole process. 8,16,26,28,29 Furthermore, the value of the structural relaxation time (τ α ) of the measured system, which reflects its molecular mobility, 30−32 can be determined during dielectric measurements. As it was proven in the case of a viscous liquid, the effect of the increasing pressure on τ α is similar to the effect of the decreasing temperature. 33,34 Therefore, one can directly link it to temperature (as inversely proportional to) and pressure (as proportional to) in the following fashion: τ α ∼ 1/T and τ α ∼ p. 35−38 The central idea behind the present work is to provide an easy and simple way to determine the conditions needed to maintain a given level of the solubility under various pressures (temperature adjustment to prevailing pressure conditions). This is based on two parameters τ α and S. Given their inverse dependence on temperature and pressure: S ∼ T/p and τ α ∼ p/T, 33−38 their mutual relation can be considered. If that is the case, then solubility should be inversely proportional to the τ α of the system (S ∼ 1/τ α ) at the beginning of crystallization. This would mean that, regardless of the chosen temperature or pressure, while maintaining the isochronal conditions, one should always obtain the same limiting concentration. In order to facilitate the investigation, we decided to perform the necessary analysis on the system well-characterized under both ambient and elevated pressure conditionsFL-PVP/VA. 16,26 Furthermore, in order to determine the solubility limit of the system under compression as well as to determine its τ α , we utilized BDS.

■ EXPERIMENTAL SECTION
Materials. FL drug of molecular mass MW = 276.21 g mol −1 and purity ≥99% was purchased from Sigma-Aldrich and used without further purification. Poly vinylpyrrolidone vinylacetate  Kollidon VA64 (PVP/VA) of molecular mass MW = 45,000−47,000 g mol −1 was purchased from BASF SE (Ludwigshafen, Germany). The sample was received as a white powder and used without further purification.
The glass-transition temperature of the bulk polymer determined from the differential scanning calorimetry (DSC) measurements is 376 K (recorded on a second heating run, after cooling from 420 to 265 K with a cooling rate of 20 K/ min). From the dielectric relaxation studies, we get T g = 376 K (defined as a temperature at which τ α = 100 s, data not shown).
The glass-transition temperature of the drug determined from the DSC measurements is 274 K (recorded on a second heating run, after cooling from 410 to 253 K with a cooling rate of 20 K/min). From the dielectric relaxation studies, we get T g = 271 K (defined as a temperature at which τ α = 100 s). 16 Preparation of Binary Systems. To acquire homogeneous samples, we mixed the compound with the polymer at appropriate ratios in a mortar. Sample preparation for the BDS and high-pressure BDS measurements involved melting at T = 410 K, followed by vitrification on a previously chilled copper plate. All measurements were performed immediately after the preparation of the amorphous systems to avoid recrystallization.
Broadband Dielectric Spectroscopy. The dielectric measurements of FL-based ASDs were carried out using a Novo-Control GMBH Alpha dielectric spectrometer (Montabaur, Germany) in the frequency range from 10 −1 to 10 6 Hz at given temperatures with a heating rate ∼ 0.5 K/min. The temperature was controlled by a Quatro temperature controller with temperature stability better than 0.1 K. Dielectric studies of FL and its binary systems were performed immediately after its vitrification by fast cooling of the melt in a parallel-plate cell made of stainless steel (diameter 15 mm and a 0.1 mm gap with quartz spacers).
For the high-pressure BDS measurements, we additionally employed a high-pressure Unipress U111 setup (Warszawa, Poland). Herein, the sample was measured in a similar, made of stainless steel, parallel-plate cell (diameter of 15 mm and a 0.1 mm gap with Teflon spacers). It was sealed and mounted by a Teflon tape to separate it from the silicon liquid. The temperature was adjusted with a precision of 0.1 K by the Julabo heating circulator (Seelbach, Germany).

■ RESULTS AND DISCUSSION
In order to test the validity of the proposed idea, we performed the series of dielectric measurements under various temperature and pressure conditions and additionally analyzed recently published data of FL-PVP/VA. 26 The initial part of this study will focus on the analysis of the already published data, especially on the temperature dependencies of the relaxation times of the FL-PVP/VA systems under various pressure conditions. The detailed analysis of obtaining such dependency is described along the experimental part later on. In recalled paper, we determined the solubility limit of FL within the polymer matrix under both ambient and elevated pressure conditions. Figure 1 shows the temperature dependence of the α-relaxation time [τ α (T)] registered for the FL + 13 wt % of PVP/VA sample both before (gray circles) and after isothermal crystallization at 0.1, 20, and 50 MPa and at 353 and 363 K (brown and green symbols, respectively). Temperature evolution of the structural relaxation time  in supercooled liquid region  usually shows non-Arrhenius-like behavior. Hence, in order to parameterize it, we used the Vogel−Fulcher−Tamman (VFT) equation that is defined as where τ ∞ , B, and T 0 are the fitting parameters. It has to be pointed out that in the case of some of the measurements, performed at elevated pressure (e.g., FL + 13 wt % of PVP/VA system after recrystallization at at 363 K and 20 MPa), the number of the experimentally determined τ α after recrystallization is not sufficient to parameterize it well with the VFT equation (see brown diamond in Figure 1a). However, because of the close proximity of different, well-parameterized concentrations: FL + 41 wt % of PVP/VA (VFT fit presented as dark gray solid line in Figure 1a,b), we decided to transfer horizontally its VFT fit to match determined τ α (T). Validation of the proposed approach can be seen in case of the recrystallization of the FL + 13 wt % of PVP/VA at 363 K and 20 MPa  Figure 1a  the horizontally transferred fit of the fully amorphous FL + 41 wt % of PVP/VA system registered at 20 MPa (green line) is in very good agreement with the VFT fit of the experimental points of the system registered after recrystallization at 363 K and 20 MPa (red solid line). Glass-transition temperature determined in both cases is equal to 318 K.

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pubs.acs.org/molecularpharmaceutics Article From the extrapolation of the VFT fit up to the temperatures of the isothermal crystallization, we were able to determine the initial τ α of the system (see Figure 1c,e). It has to be pointed out that its experimental determination would be impossible because of the sample's vast tendency toward recrystallization. 26 As can be seen, the relaxation time of the system becomes shorter as the temperature increases, which is a well-known phenomenon. However, focusing on the solubility limits determined in ref 26, one can observe that besides the fact that with increasing temperature (at constant pressure) the solubility of FL in the polymer matrix increases (which is consistent with data reported in the case of different pharmaceuticals 5,10,11,15,[17][18][19]42,43 ), the conditions that correspond to the longest relaxation time at the beginning of the recrystallization result in the lowest amount of the drug that can be successfully dissolved within the polymer (see Figure  1d). This would also not be a surprising phenomenon considering mutual dependence between the temperature and relaxation time observed in Figure 1c.
At this point, it should be mentioned that τ α does not depend solely on the temperature but can be affected by the pressure as well. 33,34 Therefore, we performed additional analysis on the recalled results obtained under elevated pressure conditions (see Figure 1e). As can be seen, the relaxation time is getting longer as the pressure elevates, which is an effect similar to the lowering of the temperature and has already been observed. 33,34 Accordingly, the highest amount of the FL, which can be effectively dissolved within the Kollidon VA64 matrix, is related to the conditions that correspond with the shortest relaxation time. Based on these examples, we propose the idea that the mentioned solubility is inversely proportional to the relaxation time of the system.
Throughout aforementioned steps we confirmed the following facts about the FL-PVP/VA systems: (i) τ α of this system is proportional to the pressure and inversely proportional to the temperature (τ α ∼ p/T); (ii) solubility of the FL within the PVP/VA matrix is proportional to the temperature and inversely proportional to the pressure (S ∼ T/p).
Considering proposed idea, one should obtain the same limiting concentration while maintaining the same molecular dynamics of the system, regardless of the chosen temperature or pressure. Therefore, in the following part of this study, we focus on the conducted measurements. We performed crystallization studies at which the sample was stored under isochronal conditions (at various sets of temperature and pressure conditions that were chosen with regard to the fully amorphous sample). We have chosen τ α = 0.13 μs, τ α = 0.52 μs, and τ α = 2.7 μs for our measurements because of the fact that the recrystallization under these conditions should progress relatively fast.
The representative dielectric loss spectra of the FL+ 10 wt % PVP/VA mixture which were obtained during heating, above sample's glass-transition temperature (T g ), are shown in Figure  2a. The presented spectra exhibit one well-resolved loss peak corresponding to the structuralαrelaxation. The intensity of this peak slightly decreases as it moves toward higher frequencies with the increasing temperature up to 307 K. Above this temperature (i.e., at 309 K), one can observe a substantial decrease of the dielectric strength (Δε), which corresponds to the considerable drop in the intensity of the structural relaxation peak. By acknowledging the fact that Δε is proportional to the number of units involved in structural relaxation, the discussed rapid drop would indicate the onset of the sample's recrystallization. 44,45 To obtain the values of τ α at various temperatures and consequently determine the temperature dependencies of the α-relaxation times for all examined systems, dielectric spectra collected above the sample's glass-transition temperature (T g ) were fitted using the HN function 46 where ε ∞ is high-frequency limit permittivity, ε 0 is the permittivity of vacuum, Δε is dielectric strength, ω is equal to 2πf, τ HN is the HN relaxation time, a and b are the parameters that represent symmetric and asymmetric broadening of relaxation peak, σ dc is the dc conductivity, and ε 0 is the dielectric permittivity of the vacuum (the example of the HN fitting is presented in Figure 2a as the shaded area). Using the Relaxation times obtained from the above described fitting procedure are presented in Figures 2b, 3a, 4a, and 5a. As can be seen, the FL + 10 wt % PVP/VA system begins to recrystallize at relatively low temperatures (under these conditions, the relaxation time of the sample is far from the desired value  see Figures 2b, 3a, 4a and 5a). Therefore, in order to determine the temperature that corresponds to the chosen τ α , we decided to use the VFT equation. From the extrapolation of the VFT fit up to the selected relaxation time (e.g., τ α = 0.13 μs), we were able to determine the temperature of the system (see the brown star in Figure 2b). As can be seen under ambient pressure conditions, the FL + 10 wt % PVP/VA sample needs to be heated up to the 347 K in order to have the relaxation time equal to τ α = 0.13 μs. This procedure was repeated for samples under each chosen pressure condition (i.e., 0.1, 20, and 50 MPa). Once it was done, we were able to perform isothermal crystallization studies under given conditions in order to determine the solubility limit of the drug within the polymer matrix. Figure 2c presents the representative example of performed recrystallization studies. The presented dielectric spectra show crystallization at 0.1 MPa and 347 K, t 0 indicates the first recorded spectrum at set temperature, and it does not correspond to the beginning of the crystallization because of the sample's tendency toward recrystallization. The light gray dotted spectrum is presented only as a visual aid and was not obtained during any measurement. When the recrystallization of the excess amount of the SM (FL) from the supersaturated system ceased, one well-resolved loss peakα′-processwas still visible (as in previously reported cases 8,16,26,28,29 ), see Figure 2c.
Next, in order to exclude the possibility of correlating this additional process to either segmental or secondary relaxation originating from residual amorphous polymer, remaining after the recrystallization of the whole amount of the drug from the mixture, we followed the procedure proposed in ref 16. In order to obtain relaxation times in a wide temperature range needed to determine the glass-transition temperature related to the α′-process [T g = T(τ α′ = 100 s)], we cooled down the sample  when no further changes in molecular dynamic of the system were observed (no changes for approx. 15 h, see Figure 2c), during/after crystallization  and then measured it again during heating. As can be observed in Figure  2a (brown lines), during this measurement, the dielectric spectra of the examined sample have been registered up to the temperature of the performed isothermal crystallization (e.g., 347 K). Dielectric spectra obtained throughout this procedure, just as the spectra of the fully amorphous sample, were then fitted using the HN fitting function (see Figure 2a).
Determination of the origin of this additional process was possible, once the temperature dependence of the α′-relaxation times [τ α′ (T)] of the partially recrystallized sample was obtained. Because of the nonlinear behavior of τ α′ (T) and the fact that it follows the VFT equation (see brown circles in Figure 2b), one can easily conclude that the α′-process is the primary relaxation process of different than initial concen-

Molecular Pharmaceutics
pubs.acs.org/molecularpharmaceutics Article tration of the drug in the FL-PVP/VA system. We determined its T g value by extrapolation of its VFT fit to 100 s. Thus, the saturated FL-PVP/VA system established under 347 K and 0.1 MPa conditions is characterized by a glass-transition temperature equal to 314 K (see Figure 2b). Next, by following this procedure in the case of the studies performed at elevated pressure, we determined the T g of the saturated systems. Similarly, as in the case of the measurements, analyzed at the beginning of this work, the number of the experimentally determined τ α after recrystallization at elevated pressure is not sufficient to parameterize it well with the VFT equation. This can be explained by the increased dc conductivity contribution during BDS measurements at elevated pressure. Therefore, we decided to transfer horizontally the VFT fit of the FL + 41 wt % PVP/VA system to match determined τ α (T) (red dashed line in Figure 3a, 4a and 5a). Figure 3a presents the τ α (T)s registered for the fully amorphous FL + 10 wt % of PVP/VA (at 0.1, 20, and 50 MPa) samples as well as these samples after crystallization under isochronal conditions (τ α = 0.13 μs): (i) 363 K and 50 MPa; (ii) 353 K and 20 MPa; (iii) 347 K and 0.1 MPa (blue pentagons, turquoise diamonds, and dark green circles, respectively). Dielectric spectra obtained when the recrystallization process ceased exhibit one extraordinary feature, and despite different temperature and pressure conditions, they all had been characterized by the same relaxation time  determined based on the HN fit  τ α = 1.27 ms (see Figure  3b). It is interesting that the recrystallization carried out under the conditions that correspond to τ α-1 ceases at certain  different than initial  τ α-2 . By applying the procedure discussed in this work, we determined the T g s of the saturated systems. By comparing the obtained values to the previously reported T g to concentrations dependencies of the FL-PVP/ VA mixtures at 0.1, 16 20, and 50 MPa 26 we were able to identify the concentration of the tested system. As can be seen in Figure 3c, the concentrations obtained by the recrystallization under conditions that correspond with τ α = 0.13 μs are equal to 57, 58, and 59 wt % at 50, 20, and 0.1 MPa, respectively. It has to be pointed out that small differences between determined concentrations might be due to the, for example, extrapolation of the VFT fits and/or small number of the experimental data after the recrystallization of the sample (because of the increased dc conductivity contribution during BDS measurements at elevated pressure).
To confirm the validity of our assumption that τ α is the key to maintain the desired solubility limit of a SM within the polymer matrix at elevated pressure, we conduct additional measurements for different initial τ α . Namely, we performed recrystallization measurements under isochronal conditions (τ α = 0.52 and 2. Analogously as in previously chosen τ α when the recrystallization ceased, dielectric spectra collected under various sets of temperature and pressure conditions have been characterized by the exact same relaxation time: τ α = 13 ms (see Figure 4b) and τ α = 0.3 s (see Figure 5b). Moreover, as can be seen in Figures 4c and 5c, concentrations obtained by the recrystallization of the excess amount of the drug under isochronal conditions are equal to 56, 57, and 58 wt % at 50, 20, and 0.1 MPa, respectively, while starting at τ α = 0.52 μs and 54, 55, and 56 wt % at 50, 20, and 0.1 MPa, respectively, while starting at (τ α = 2.7 μs). Once again small deviations between determined concentrations are present; the explanation of which has already been given. However, one can observe that there is a constant difference between the solubility limit obtained while starting from τ α = 2.7 μs, 0.52 μs or 0.13 μs. It has to be pointed out that in all presented cases of chosen τ α (as a starting point for the recrystallization) systems reach a defined solubility, based on their initial relaxation time.
Comparing the solubility limit values obtained during the recrystallization at constant pressure, constant temperature, and constant relaxation time, one can notice some significant

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pubs.acs.org/molecularpharmaceutics Article differences (see Figure 6). Namely, maintaining the constant pressure (either for 0.1 MPa or 50 MPa), while altering the temperature, we obtained the generally accepted dependence between temperature and solubility limits  the higher the temperature, the larger amount of the SMs (in our case FL) can be successfully dissolved within the polymer matrix 5,10,11,15,17−24 (e.g., 59 wt % of FL at 343 K and 64 wt % of FL at 363 K for 0.1 MPa). On the other hand, recrystallization conducted at a constant temperature (either 343 or 363 Korange and green stars, respectively, in Figure  6), while applying different pressures, results in the following: with increasing pressure, the solubility of the FL within the polymer matrix is decreasing (e.g., 64 wt % of FL at 0.1 MPa and 57 wt % of FL at 50 MPa for 363 K)  effect similar to decreasing temperature at constant pressure. However, measurements carried out at the same relaxation time (either for τ α = 2.7 μs or τ α = 0.13 μs), regardless of chosen set of temperature and pressure conditions, results in the same concentrationthe same solubility limit (e.g., approx. 55 wt % of FL for τ α = 2.7 μs and 58 wt % of FL for τ α = 0.13 μs), which confirms the initial assumption that the solubility of the SMs (e.g., FL) within the polymer matrix is inversely proportional to the τ α of their system (S ∼ 1/τ α ).
It should be pointed out that our understanding of the role of the isochronal conditions in the solubility limit studies is still limited and thus the role of many factors (e.g., drug−polymer interactions) is yet to be understood. The mentioned interactions have been known to affect both the thermodynamics and kinetics of the precipitation. 47−49 Although in recent study Prasad et al. showed (on the example of indomethacin drug) that despite the fact that both used polymers (Eudragit E100 and PVP K90) interfere with the kinetics of precipitation via drug−polymer interactions no significant change in solubility was observed with any of the added polymers, 50 one has to acknowledge that drug−polymer interactions might either inhibit or induce precipitation (crystal growth or nucleation) in a manner that is difficult to predict, which in turn could affect the extent and duration of supersaturation. 51,52 Furthermore, the complexity of this issue increases when one considers the additional factor  elevated pressure. The densification of the molecular packing of the system is a direct result of the applied high pressure and can lead to the improvement of drug−polymer interactions 53 or vice versa the weakening of hydrogen bonding between drug and polymer. 54 Nevertheless, we strongly believe that this approach along with the dielectric measurement might become an irreplaceable tool in predicting the limiting polymer concentration for the extrusion-based manufacturing purposes. Even though one might conclude, based on the presented results, that there is a potential risk, that a change in the solubility limit caused by the elevated pressure might lead to recrystallization of the excess amount of the drug during the extrusion process, the presented idea has not yet been tested during production conditions. Therefore, we strongly encourage further exploration of this kind of behavior.

■ CONCLUSIONS
To summarize, the presented experimental results confirm that regardless of the chosen temperature or pressure, while sustaining the same initial relaxation time, one would maintain a desired level of solubility. Furthermore, it seems that the elevated pressure compensates the effect of solubility enhance-ment caused by the elevated temperature. Such information is not only of fundamental relevance in science but also, from a much broader perspective, could be potentially very useful considering extrusion-based manufacturing methods. However, it is but a first step toward the validation of the proposed idea: mutual dependence between the solubility of all SMs within the polymers and τ α of their systems.