A New Protocol To Determine the Solubility of Drugs into Polymer

Article pubs.acs.org/molecularpharmaceutics

A New Protocol To Determine the Solubility of Drugs into Polymer Matrixes Aurélien Mahieu, Jean-François Willart,* Emeline Dudognon, Florence Danède, and Marc Descamps Université de Lille Nord de France, F-59000 Lille, USTL UMET (Unité Matériaux et Transformations), UMR CNRS 8207, F-59650 Villeneuve d’Ascq, France ABSTRACT: In this paper we present a new protocol to determine faster the solubility of drugs into polymer matrixes. The originality of the method lies in the fact that the equilibrium saturated states are reached by demixing of supersaturated amorphous solid solutions and not by dissolution of crystalline drug into the amorphous polymer matrix as for usual methods. The equilibrium saturated states are thus much faster to reach due to the extra molecular mobility resulting from the strong plasticizing effect associated with the supersaturation conditions. The method is validated using the indomethacin/polyvinylpyrrolidone mixture whose solubility diagram was previously determined by usual techniques. The supersaturated states have been directly obtained in the solid state by comilling, and the investigations have been performed by differential scanning calorimetry and powder X-ray diffraction. KEYWORDS: solubility diagram, supersaturation, drug, polymer, demixing, glass transition, calorimetry, Gordon−Taylor, Flory−Huggins

1. INTRODUCTION A high solubility in body fluids is a “sine qua non condition” for a drug to be therapeutically efficient. However, because of their increasing complexity, modern drugs are less and less soluble, which gives them a limited bioavailability.1,2 This makes the development of recently synthesized drugs through solid dosage forms increasingly difficult. The development of new formulation strategies able to overcome poor drug solubility thus appears to be a major challenge of the pharmaceutical research. It is known that the solubility is significantly improved when the drug is placed in a high energetic physical state. The amorphous state which has a higher free enthalpy than any crystalline polymorphs is thus generally considered to be the most soluble form.3−6 However, it is also the less stable physical form, and its recrystallization propensity cannot afford to guarantee the therapeutic characteristics of the material during storage.2,7−9 High solubility and long-term stability are thus intrinsically antagonist properties, which can hardly be accommodated.10 A possible strategy for stabilizing an amorphous drug against crystallization is to disperse it molecularly into a polymeric matrix in order to hinder drug reprecipitation and crystallization.6,11−15 This technique implies a good knowledge of the solubility of crystalline drugs in polymeric matrixes.15−19 This property is, in particular, important for selecting appropriate polymers for formulations since it defines the maximal drug loading without a risk of recrystallization. However, up to now, little is known about the solubility of drugs in polymers. This situation is mainly due to the fact that there is actually no © 2012 American Chemical Society

standardized rapid method for measuring the drug/polymer solubilities. The difficulty of such investigation arises from the high viscosity of polymers, which makes solubility equilibrium difficult to reach and the determination of solubility curves very time-consuming.16,17 In this paper we develop a new experimental protocol to determine more efficiently the solubility of drugs into polymeric matrixes. The idea is here to reach faster the equilibrium solubility by following the precipitation of the drug from a supersaturated homogeneous drug/polymer solid solution rather than by following the dissolution of the drug into the polymer matrix as it is usually done. The supersaturation of the drug into the polymer matrix is obtained here by the comilling technique,20−22 which is shown to form a homogeneous glass solution while forcing the solubility of the two compounds.23 This new protocol is tested and validated on the polyvinylpyrrolidone/indomethacin (PVP/indo) binary system which was previously investigated by Sun and coworkers using more conventional dissolution techniques.16,17 The structural and thermodynamic characteristics of the mixtures before and after precipitation are determined by powder X-ray diffraction (PXRD) and by differential scanning calorimetry (DSC). Received: Revised: Accepted: Published: 560

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Figure 1. Schematic time evolutions of the glass transition temperature of a drug/polymer mixture when reaching its equilibrium solubility upon annealing. The top curve corresponds to a dissolution process while the bottom curve corresponds to a demixing process.

2. EXPERIMENTAL SECTION Crystalline indomethacin (C19H16ClNO4; Mw = 357.79 g·mol−1 ; purity ≥99%) was purchased from Fluka and was used without further purification. Amorphous PVP K12 (Mw = 2000−3000 g·mol−1, 5% w/w moisture) was obtained from BASF and was used without purification. Milling and comilling were performed in a high energy planetary mill (pulverisette 7, Fritsch). We used a ZrO2 milling jar of 45 cm3 with seven balls (⌀ = 1 cm) of the same material. 1.1 g of material was placed in the planetary mill corresponding to a ball/sample weight ratio of 82.5:1. The rotation speed of the solar disk was set to 400 rpm. All the milling and comilling operations were performed during 8 h in a cold room at −8 °C and in a dry atmosphere (RH = 0%). We also took care to alternate milling periods (10 min) with pause periods (5 min) in order to limit the overheating of the sample. The powder X-ray diffraction (PXRD) experiments were performed with an XPERT PRO MPD diffractometer (λCuKα = 1.540 Å) equipped with an X'celerator detector. Samples were placed into Lindemann glass capillaries (⌀ = 0.7 mm). The differential scanning calorimetry (DSC) experiments were performed with the DSC Q1000 of TA Instruments. For all the experiments, the sample was placed in an open aluminum pan (container with no cover) and was flushed with highly pure nitrogen gas. Temperature and enthalpy readings were calibrated using pure indium at the same scan rates and with the same kind of pans used in the experiments.

whose time scale can exceed that of a typical DSC scan. In that case, the dissolution endotherm is artificially shifted toward the high temperatures, resulting in a systematic underestimation of the equilibrium solubility. This problem becomes crucial on approaching the glass transition temperature (Tg) of the mixture where the molecular mobilityessential to the mixing of the two chemical speciesdecreases the most rapidly. This method cannot thus be applied below Tg, where dissolution times are much larger than any reasonable experimental DSC time scale. Moreover, it must also be noted that the notion itself of equilibrium solubility in a nonequilibrium, glassy mixture raises many fundamental questions which are still to be addressed. To make easier the dissolution process of drugs into viscous polymers, Sun and co-workers16,17 have proposed to shortly cryomill the drug/polymer mixture prior to the DSC investigations to obtain a dispersion of small crystallites in the polymer matrix. The dispersion and the size reduction are both expected to speed up the dissolution mechanism by reducing the diffusive mixing necessary for dissolution. Besides this particular sample preparation Sun and co-workers have also developed two improved DSC protocols for measuring equilibrium solubilities. The first protocol17 consists of performing several DSC scans using different heating rates ranging from 10 °C/min to 0.1 °C/min so that Tend can be estimated at “zero scan rate” by extrapolation. While this method gives more accurate results, it is highly time-consuming since each equilibrium solubility point requires many DSC scans which use, for some of them, very slow heating rates. The second protocol16 was established to further increase the likelihood of achieving the equilibrium solubilities. Here a drug/polymer mixture of given concentration is annealed during a time considered long enough to reach the equilibrium solubility (typically 10 h) at a temperature Ta and then scanned with a high heating rate (typically 10 °C/min) to search for a residual dissolution endotherm. The absence of residual dissolution then indicates that, during the annealing at Ta, the dissolution process was completed and that the equilibrium dissolution temperature is located below Ta. The presence of a residual dissolution indicates, on the contrary, that, during the annealing at Ta, the dissolution process was not achieved and that the equilibrium dissolution temperature is located above Ta. However, in this latter case, longer annealing times must be performed to check that the incomplete dissolution is not merely due to the slowness of the dissolution process at Ta. By

3. METHOD 3.1. Usual Methods. Up to now, the determination of drug/polymer solubilities is generally obtained by the so-called “depressed melting points” method.15−18 In this method, a physical mixture of crystalline drug and amorphous polymer is heated until the solubility equilibrium is reached. In a typical heating DSC scan the progressive dissolution of the drug into the polymer matrix gives rise to an endothermic signal similar to that of a melting process. The temperature (Tend) at which this endothermic event comes to an end marks the completion of the dissolution process, and the initial drug concentration appears to be the equilibrium solubility at Tend. By varying the initial drug concentration it is thus theoretically possible to determine the solubility curve of drug/polymer systems. However, severe practical difficulties arise from the high viscosity of polymers, which results in slow dissolution kinetics 561

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(iii) In the third step, the equilibrium concentration of the drug remaining in the polymer matrix after the annealing is determined. This is done by determining the glass transition temperature of the demixed material upon a rescanning of the sample in the DSC after the annealing. The equilibrium dissolution concentration then derives directly from the Gordon−Taylor plot,26 which describes the glass transition temperature of the glass solution with respect to its concentration. By repeating steps ii and iii for different annealing temperatures it is thus possible to determine a large part of the solubility curve much more rapidly than with the actual methods. In the following, this new method is applied, as an example, to the polymer/drug mixture polyvinylpirrolydone (PVP)/ indomethacin.

repeating the annealing procedure at different temperatures it is thus possible to determine with an increasing accuracy the equilibrium dissolution temperature corresponding to the initial concentration. While providing accurate solubility curves, this protocol required a lot of DSC scans and a lot of long annealing stages which makes it even longer to implement than the first protocol. 3.2. New Method. In this paper we propose a new method for a faster determination of the equilibrium solubility curve of drug/polymer mixtures when the glass transition of the polymer is higher than the one of the drug in its glassy form. This method is based on the fact that the demixing kinetics of drugs from supersaturated polymers are expected to be much faster than the dissolution kinetics of drugs into undersaturated polymers. This difference arises directly from the molecular mobility in the polymer matrix, which is higher in the first case than in the second case. Indeed, in the course of a dissolution process, the plasticization effect of drug molecules leads to a progressive decrease of the glass transition temperature (Tg) of the polymer matrix as illustrated in the top part of Figure 1. This means that the molecular mobility in the polymer matrix, initially very low, slowly increases as the drug molecules invade the matrix to reach the equilibrium dissolution concentration. For a demixing process, we are faced with the opposite behavior. Since drug molecules leave the matrix, the plasticization effect vanishes progressively, which results in a progressive increase of the glass transition temperature of the solid solution, as illustrated in the bottom part of Figure 1. The initial molecular mobility in the supersaturated matrix, which is quite high, slowly decreases as the drug molecules escape from the matrix to reach the equilibrium dissolution concentration. A most important point emerging from Figure 1 is that the increasing Tg of a demixing system is always lower than the decreasing Tg of a dissolving system. This indicates that the demixing rate is always larger than the dissolution rate so that the time required to reach the equilibrium solubility at a given temperature is shorter in the first case. We have thus taken advantage of this behavior to design a new protocol to speed up the determination of equilibrium dissolution concentrations. The new protocol can be divided into three steps: (i) In the first step, a strongly supersaturated glass solution is formed by comilling a physical mixture of polymer and crystalline drug. The possibility to form homogeneous glass solutions directly in the solid state by comilling was already reported.20,21,24,25 We will show in section 4.1 that this technique also allows forcing the miscibility of the two compounds in order to reach supersaturated conditions. The comilling time used here is 8 h, and the composition of the drug/polymer physical mixture is [85:15]w/w, which most often corresponds to a situation of strong supersaturation at room temperature (RT). It must be noted that the formation of the glass solution requires that the comilling be performed at a temperature far enough below its expected glass transition temperature. (ii) The superaturated glass solution is then loaded in a DSC and annealed above its glass transition temperature to release the excess drug in the mixture and reach the equilibrium dissolution concentration at the annealing temperature. A two hour annealing time has been found to be sufficient to complete the demixing process in a wide range of annealing temperatures.

4. RESULTS 4.1. Formation of Supersaturated Glass Solutions by Comilling. Figure 2 shows the X-ray diffraction patterns of

Figure 2. Powder X-ray diffraction patterns recorded at room temperature: (a) unmilled crystalline indomethacin, (b) milled (8 h) indomethacin, (c) unmilled PVP K12, (d) milled (8 h) PVP K12, and (e) comilled (8 h) physical mixture of indomethacin−PVP [85:15]w/w.

PVP and indomethacin before and after an 8 h milling process. In the case of PVP (respectively c and d patterns), both X-ray diffraction patterns are identical and free of Bragg peaks. This indicates that PVP is in an amorphous state which is structurally not modified upon milling. In the case of indomethacin the situation is different. The X-ray diffraction pattern recorded before milling (a) shows clearly the Bragg peaks characteristic of the stable crystalline form γ27 while that recorded after milling (b) is free of Bragg peaks. This difference suggests that indomethacin has been amorphized during the milling process. Figure 2 also shows the X-ray diffraction pattern (e) of a mixture PVP:indomethacin [15:85]w/w which has been comilled for 8 h at −8 °C. The absence of Bragg peaks indicates that the overall material has been amorphized upon comilling. In order to determine whether the comilling produced a simple mixture of amorphous PVP and amorphous indomethacin or a real amorphous molecular alloy in which the two chemical species are mixed at the molecular level, DSC experiments were performed. Figure 3 shows the DSC heating scans (5 °C/min) of PVP and indomethacin before and after an 8 h milling process. In the case of PVP (respectively run 4 and run 5) the two DSC scans show a broad endotherm ranging from RT to 75 °C and a 562

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min at 40 °C was necessary to release the residual water caught by the PVP and to avoid the water loss endotherm around 50 °C that would have hidden the Cp jump (as seen in runs 4 and 5). This glass transition is located between those of pure PVP and pure indomethacin, and no sign of glass transition corresponding to pure PVP or pure indomethacin can be detected around 107 and 45 °C. Such a single glass transition thus indicates that the mixture amorphized by comilling is characterized by a single relaxation process, which strongly suggests21,25,30 that the comilling has produced a homogeneous glass solution where the two chemical species are mixed at the molecular level. Between 100 and 160 °C, run 3 also shows two consecutive events which are respectively exothermic and endothermic with almost equal enthalpies. The exotherm seen between 100 and 130 °C corresponds to the recrystallization of indomethacin from the amorphous molecular alloy. Since indomethacin is molecularly dispersed in the polymer matrix, its recrystallization is necessarily preceded by (or accompanied by) a demixing of the two chemical species, which indicates that the amorphous molecular alloy formed by comilling at −8 °C is highly supersaturated with indomethacin. The endotherm seen between 130 and 160 °C is much broader than the melting peak of pure indomethacin (run 1), and it occurs in a noticeably lower temperature range. In particular, the starting point is depressed by more than 30 °C while the end point is also depressed by a few degrees. Such an endothermic signal is characteristic of a dissolution process, and it reflects the increasing solubility of a solute into a solvent for increasing temperature.31 This signal then abruptly stops when there remains no more drug to dissolve. The broad endotherm seen at high temperature in run 3 thus corresponds to the redissolution, into the polymer matrix, of the indomethacin which has previously recrystallized at lower temperature. Figure 3 thus indicates that comilling can be used to rapidly form homogeneous glass solutions of PVP and indomethacin which are strongly supersaturated with indomethacin. Moreover, these supersaturated mixtures appear to demix rapidly above 100 °C to reach their equilibrium saturated state. This behavior is expected to provide an easy way to explore the solubility curve in this temperature domain. 4.2. Gordon−Taylor Plot of PVP:Indomethacin Glass Solutions. By comilling physical mixtures of PVP/indomethacin for different compositions it was possible to obtain homogeneous glass solutions in the whole range of concentrations. The glass transition temperatures of these glass solutions are reported in Table 1 and plotted in Figure 4b. They appear to be totally compatible with those determined by Sun and colleagues in the case of quenched liquid mixtures,16 which reveals the equivalence of the two coamorphization

Figure 3. DSC scans recorded upon heating at 5 °C/min: run 1, unmilled crystalline indomethacin; run 2, milled (8 h) indomethacin; run 3, comilled (8 h) physical mixture of indomethacin−PVP [85:15]w/w; run 4, milled (8 h) PVP K12; run 5, unmilled PVP K12. Arrows mark the glass transition temperature positions.

sluggish Cp jump ranging from 85 to 120 °C. The endotherm corresponds to the release of some free water included in this very hygroscopic compound. The Cp jump is characteristic of a glass transition whose midpoint (Tg = 107 °C ± 1 °C) is not modified by the milling process. The value of the Cp jump is ΔCp(PVP) = 0.42 J/g/°C. In the case of indomethacin the DSC scan recorded before milling (run 1) only shows a melting peak. The temperature (Tm = 160 °C ± 1 °C) and the enthalpy (ΔHm = 108 J/g ± 2 J/g) of melting are close to those expected for the γ form of indomethacin28 previously identified by PXRD (Figure 2). After milling, the DSC scan (run 2) is totally different. It shows a clear Cp jump at 45 °C ± 1 °C (ΔCp = 0.43 J/g/°C) characteristic of a glass transition, a strong recrystallization ranging from 80 to 100 °C and a melting peak at 160 °C. The Cp jump and the recrystallization prove that a large part of the sample has been amorphized upon milling. Moreover, the similarity of the melting temperatures of the milled material (run 2) with that of the nonmilled material (run 1) indicates that the recrystallization of the amorphized fraction occurs toward the initial crystalline form. This point was also confirmed by the X-ray diffraction pattern of the recrystallized sample, which appears clearly to be that of the stable γ form (data not shown). The fraction of the material amorphized upon milling can be obtained from the ratio of the enthalpy of crystallization (ΔHcryst = 82 ± 2 J/g) with that of the enthalpy of melting at the crystallization temperature (ΔHm(Tcr)), which is given by29 ΔHm(Tcr) = ΔHm(Tm) − (Tm − Tcr)ΔCp = 82 ± 2 J/g (1)

Table 1. Glass Transition Temperatures of PVP/ Indomethacin Mixtures Determined by DSC upon Heating at 5 °C/min

where ΔHm(Tm) = 108 J/g is the melting enthalpy at the melting point Tm = 160 °C, Tcr = 97 °C is the temperature corresponding to the half-crystallization, and ΔCp = 0.43 J/g/ °C is the Cp difference between amorphous and crystalline phases between Tcr and Tm (assuming it is constant). This ratio is close to 1, which indicates that the material has been totally amorphized upon milling. The DSC heating curve of the PVP:indomethacin [15:85]w/w mixture comilled during 8 h is also reported in Figure 3 (run 3). It reveals a Cp jump (ΔCp = 0.28 J/g/°C) characteristic of a glass transition at Tg = 49 °C ± 1 °C. It should be noted that, prior to the DSC run, a short annealing of the sample during 15 563

Xindo

Tg (°C) ± 1 °C

1.00 0.85 0.70 0.50 0.35 0.20 0.00

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importance of interactions between the two chemical species involved in the mixture is generally estimated by comparing the previous value of K with that corresponding to the ideal case of a regular solution.26,32 In this latter case K is readily obtained from eq 3: K=

routes. The composition dependence of the glass transition temperature has been fitted (Figure 4b, solid line) by the usual Gordon−Taylor law:26 X indoTg(indo) + K (1 − X indo)Tg(PVP) X indo + K (1 − X indo)

ΔCp(indo)

= 0.98 (3)

where ΔCp(PVP) = 0.42 J/g/°C and ΔCp(indo) = 0.43 J/g/°C are the amplitude of the Cp jump at Tg respectively determined for pure PVP and pure indomethacin. The good agreement between the values of K determined from eq 3 and by fitting eq 2 could make us believe that the interactions between the two chemical species are very weak. In fact, the interactions between PVP and indomethacin have already been studied in detail by Taylor and Zografi.33 These authors have clearly identified a strong hydrogen bonding between the carbonyl group of PVP and the hydroxyl group of indomethacin. They have also shown that pure amorphous indomethacin is mainly composed of carboxylic acid dimers involving two hydrogen bonds. The formation of the hydrogen bonds between PVP and indomethacin in the mixture thus requires the disruption of an equivalent number of hydrogen bonds involved in the indomethacin dimers. This could explain the apparent weakness of interactions suggested by the Gordon−Taylor plot and suggests that the two kinds of hydrogen bonds are equivalent in terms of energy. 4.3. Determination of the Solubility Curve of PVP:Indomethacin Mixtures. It has been shown in section 4.1 that supersaturated glass solutions of PVP/indomethacin obtained by comilling release rapidly their excess indomethacin fraction when heated above 100 °C. We have taken advantage of this behavior to obtain equilibrium saturated states of PVP/ indomethacin mixtures at different temperatures above 100 °C in order to establish the solubility curve in this temperature range. As an example, Figure 4 presents the two steps of the experimental protocol which has been used to first reach the equilibrium saturated state at 120 °C and then determine the indomethacin fraction corresponding to this state. In the first step, a supersaturated glass solution PVP/indo (Xindo = 0.85) obtained by comilling is heated (5 °C/min) in the DSC up to the temperature at which the equilibrium solubility has to be determined (120 °C in this example). The corresponding DSC scan (run 1, Figure 4a) shows a glass transition at 49 °C ± 1 °C followed by a recrystallization which starts at 100 °C and which is not yet completed at 120 °C. The sample is then annealed at 120 °C for two hours to complete the recrystallization of the remaining excess indomethacin in order to reach the equilibrium saturated state at this annealing temperature. This evolution can be clearly followed by monitoring the corresponding exothermic heat flow during the isothermal treatment so that the completion of the recrystallization process can be easily detected. At 120 °C, it appears that the completion of the recrystallization and, thus, the equilibrium saturated state are reached within one hour of annealing. In the second step, the equilibrium saturated state obtained upon annealing at 120 °C is rescanned at 5 °C/min in the DSC. The rescan (run 2, Figure 4a) still clearly shows a Cp jump characteristic of a glass transition. However, this jump occurs at higher temperature than that observed in the first scan, and its amplitude is slightly smaller. The smaller amplitude is due to

Figure 4. (a) DSC heating scans (5 °C/min) of a supersaturated indomethacin−PVP [85:15]w/w glass solution obtained by comilling. Run 1 corresponds to the first heating scan. Run 2 corresponds to a rescan of the material after a 2 h annealing at 120 °C. (b) Evolutions of the glass transition temperature (blue ●) and the equilibrium solubility concentration (red ●) of the PVP−indomethacin mixtures at different temperatures. The data previously obtained by Sun and coworkers16 are also reported (green ◆). The evolution of the glass transition temperature is fitted with a Gordon−Taylor law and the evolution of solubility with a Flory−Huggins model. The straight dashed lines illustrate how the solubility curve and the Gordon− Taylor plot of panel b are directly constructed from the DSC scan shown in panel a. Tcrossing indicates the temperature at which the solubility curve crosses the Gordon−Taylor plot.

Tg(X indo) =

ΔCp(PVP)

(2)

In this expression, Tg(Indo) and Tg(PVP) are respectively the glass transition temperature of pure indomethacin and pure PVP, Xindo is the indomethacin fraction in the mixture, and K is a fitting parameter characterizing the curvature of the evolution. The best fit is obtained for K close to 1 (K = 0.99) as expected from the apparent linear variation of Tg with Xindo. The 564

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solubility curve crosses the Gordon−Taylor plot. If the annealing is performed below this temperature, the Tg of the demixing system will unavoidably approach Ta leading to a dramatic slowing down of the molecular mobility and thus of the demixing process which preventsin practicethe reaching of the equilibrium saturated state. It must be noted that, for indomethacin/PVP mixtures, the possibility to get a complete demixing process in less than two hours stops about 50 °C above Tcrossing. However, for some other drug/polymer systems (to be published), complete and rapid demixing can be achieved as low as 20 °C above Tcrossing. These different demixing kinetics just above Tcrossing are not yet clearly understood, but they are likely to result from the molecular mobility of the polymer chains themselves, i.e., from the molecular weight and the architecture of the polymer. The method presented in this paper thus appears to be

the previous recrystallization of indomethacin, which has reduced the total amount of amorphous dispersion. The higher glass transition temperature reflects the smaller indomethacin concentration in the remaining amorphous dispersion, which weakens the plasticization effect. This Tg is characteristic of the equilibrium saturated concentration reached at the annealing temperature. This concentration can thus be readily derived from the Gordon−Taylor plot Tg(Xindo) determined in the previous section and shown in Figure 4b. The solubility curve has been determined between 160 °C (melting point of indomethacin) and 120 °C using the above method (see Table 2). The results are shown in Figure 4b Table 2. Equilibrium Saturated Concentration (Xindo) of Indomethacin in PVP Obtained for Different Annealing Temperatures (Ta) Ta (°C)

Xindo

160 150 140 130 120

1.00 0.79 0.74 0.72 0.67

(i) very efficient between the melting point of the drug and Tcrossing + 20/50 °C (ii) usable between Tcrossing + 20/50 °C and Tcrossing while requiring increasing annealing times in some cases (iii) unusable below Tcrossing since crystallization is generally recognized not to occur below Tg

together with those obtained by Sun and co-workers16 using a conventional method. The two data sets are fairly identical, which validates the new method presented in this paper. In the frame of the Flory−Huggins model these data are expected to obey the following relationship: ΔHm ⎛ 1 ⎛ 1⎞ 1⎞ − ⎟ = ln(v1) + ⎜1 − ⎟v2 + χ (v2)2 ⎜ ⎝ R ⎝ Tm T⎠ λ⎠

5. CONCLUSION The usual methods used to determine drug/polymer solubility curves generally come up against the difficulty to mix the two chemical species at the molecular level in order to reach the equilibrium saturated states. This difficulty mainly arises from the high viscosity of polymers which makes very slow the thermal diffusion of drug molecules into the polymer matrix leading to incredibly long equilibration times.16,17 In this paper, we have presented and validated a new method to determine more rapidly the solubility curve of some polymer/drug mixtures. The idea is to reach faster the equilibrium saturated states by demixing of supersaturated solutions rather than by the usual dissolution of drugs into polymer matrixes. The fact that the demixing process is systematically much more rapid than the dissolution process lies in the fact that it benefits from an enhanced plasticizing effect of the drug molecules, which increases the overall mobility of the material and thus the rate at which equilibrium is reached. The supersaturated glass solutions have been obtained here directly in the solid state by comilling the drug and the polymer far below the glass transition of the resulting solution. This sub-Tg condition is required to produce and maintain such a nonequilibrium material. Up to now, solubility curves of polymer/drug mixture are generally obtained by “trial and error” methods or extrapolation methods which both require a great number of experiments involving long annealing stages.16−18 Conversely, in the present method one experiment gives directly access to one point of the solubility curve so that it appears to be more direct and thus much more rapid to implement than the usual methods. As a result, the time required to determine a solubility curve with the method presented in this paper is expected to be divided by ten in comparison with other methods. However, while faster, the present method does not give access to a more extended part of the solubility curve. As for usual methods the equilibrium saturated states become rapidly unreachable in a reasonable amount of time when they approach the glass transition line in the state diagram.

(4)

where T is the temperature at which the solubility of the drug is measured, ν1 and ν2 are respectively the volumic fraction of the drug and of the polymer, λ = 0.93 is the molar volume ratio of the polymer and the drug and χ is the fitting parameter describing the drug−polymer interactions. The volumic fractions νi directly derived from the density of the drug (ρ1 = 1.37) and of the polymer (ρ2 = 1.25) according to eq 5: νi =

x ρi x ρ1

+

1−x ρ2

(5)

Figure 4b shows the best fit of eq 4 to the two data sets (full line for the new method, dashed line for conventional method). It appears that, in each case, the Flory−Huggins model fits the data reasonably well and leads to very close fitting parameters: χ = −8.6 ± 0.7 (for the present method) and χ = −8.2 ± 0.6 (for the data of ref 16). The solubility curves derived from the new protocol are thus in complete agreement with those previously reported and obtained by a totally different method. Below 120 °C, the determination of the solubility curve becomes increasingly more difficult since the time required to reach the equilibrium saturation rapidly exceeds any reasonable laboratory time scale. The rapidity of the demixing process is highly sensitive to the molecular mobility and thus to the relative position of the Tg of the demixing mixture with respect to the annealing temperature (Ta). It clearly appears that the demixing process can only be achieved in a reasonable amount of time if the increasing Tg of the demixing system remains below Ta. The lowest temperature at which the method can be applied is thus given by the temperature (Tcrossing) at which the 565

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AUTHOR INFORMATION

Corresponding Author

*Université de Lille Nord de France, F-59000 Lille, USTL UMET (Unité Matériaux et Transformations), UMR CNRS 8207, F-59650 Villeneuve d’Ascq, France. E-mail: jean-francois. [email protected]. Tel: 33 (0)3 20 43 68 34. Fax: 33 (0)3 20 43 68 57. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the interreg IV “2 mers seas zeeën” cross-border cooperation programme 2007-2013.

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REFERENCES

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dx.doi.org/10.1021/mp3002254 | Mol. Pharmaceutics 2013, 10, 560−566