Influence of Copolymer Composition on the Phase Behavior of Solid

Article pubs.acs.org/molecularpharmaceutics

Influence of Copolymer Composition on the Phase Behavior of Solid Dispersions Anke Prudic, Tobias Kleetz, Marcel Korf, Yuanhui Ji, and Gabriele Sadowski* Department of Biochemical and Chemical Engineering, Laboratory of Thermodynamics, TU Dortmund, Emil-Figge-Str. 70, D-44227 Dortmund, Germany ABSTRACT: The incorporation of poorly soluble active pharmaceutical ingredients (APIs) into excipients (e.g., polymers) to formulate an amorphous solid dispersion is a promising strategy to improve the oral bioavailability of the API. The application of copolymer excipients allows access to combinations of different monomers and thus to the design of excipients to improve solid-dispersion properties. In this work, the thermodynamic phase behavior of solid dispersions was investigated as a function of the API, type of monomer, and copolymer composition. The glass-transition temperatures and API solubilities in the solid dispersions of naproxen and indomethacin in polyvinylpyrrolidone, polyvinyl acetate, and copolymers with different weight fractions of vinylpyrrolidone and vinyl actetate were investigated. It is shown that the thermodynamic phase behavior of API/copolymer solid dispersions is a function of monomer type and copolymer composition. This effect was also predicted by using the perturbed-chain statistical associating fluid theory (PC-SAFT). The glass-transition temperature of the solid dispersions was calculated with the Gordon−Taylor equation. KEYWORDS: poorly soluble pharmaceutical, phase behavior, indomethacin, naproxen, copolymer, thermodynamic model, PC-SAFT

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INTRODUCTION Solid dispersions are formed to improve the oral bioavailability of active pharmaceutical ingredients (APIs), which have low solubility and/or slow dissolution rate in aqueous media.1,2 Therefore, the API, preferably in its amorphous state to increase solubility, is integrated into an excipient, typically a hydrophilic polymer. However, since solid dispersions are often thermodynamically metastable, the API tends to recrystallize, leading to the initial slow-dissolution behavior. To prevent recrystallization of the API or an amorphous phase separation of the solid dispersion, the phase behavior of API/polymer solid dispersions needs to be identified.3 One relevant quantity is the solubility of crystalline API in the polymer. It quantifies how much API can be loaded into the polymer to form a solid solution without supersaturation and the risk of recrystallization. The solubility is a function of different storage conditions, including temperature and relative humidity, and it also depends on the type of API, type of polymer, polymer molecular weight,4 and, in the case of copolymers, copolymer composition. Another important quantity is the glass-transition temperature, Tg, of the API/polymer solid dispersion. At temperatures below the glass-transition temperature, the molecular mobility is reduced, and a metastable amorphous state of the API can be stabilized for a time range up to years.5,6 To support long-term stability during storage, a high glasstransition temperature of the amorphous solid dispersion is preferred. Assuming that the glass-transition temperature of the © XXXX American Chemical Society

homogeneous solid dispersion lies between that of the pure polymer and the pure API, a polymer with a high glasstransition temperature would be preferred. The application of copolymers as excipients for solid dispersions allows adjustment of physicochemical properties by choosing the types of monomers as well as the copolymer composition. Examples of commercially available copolymer excipients are Soluplus,7 methacrylic acid-methyl methacrylate copolymers,8 and poly(lactic-co-glycolic acid) copolymers.9 Another successful example is the vinylpyrrolidone (VP)/ vinyl acetate (VAc) copolymer, PVPVA.10 Here, properties of the widely used hydrophilic polyvinylpyrrolidone (PVP) are combined with the hydrophobic monomers of polyvinyl acetate (PVAc). PVP itself has the advantage of a high glass-transition temperature, which increases the long-term stability of the solid dispersion. It is also highly soluble in water and improves the release rate of the API in the body.2 The major disadvantage of PVP, concerning long-term stability, is its high hygroscopy.11 Solid dispersions formulated with PVP can absorb large amounts of water from the surrounding atmosphere. The absorbed water reduces the glass-transition temperature of the solid dispersions and therewith acts as plasticizer.12 The absorbed water might even induce amorphous phase separation Received: June 12, 2014 Revised: September 15, 2014 Accepted: October 8, 2014

A

dx.doi.org/10.1021/mp500412d | Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Molecular Pharmaceutics

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weight of the copolymer), whereas PVPVA 64 contains 60% VP and 40% VAc monomers, respectively. The solid dispersions were prepared by spray drying and the phase behavior was measured by DSC to verify the results predicted using PCSAFT.

or recrystallization of the API and further reduce the long-term stability of the solid dispersion. By combining VP-monomers with VAc-monomers in a copolymer, the hygroscopy is reduced and the stability during storage is enhanced.13 The API solubility in polymers can be measured via differential scanning calorimetry (DSC) using the dissolution end point method.14 The API solubility in the polymer, however, might be undetectable due to missing the dissolution event during DSC measurements. This is especially occurs in solid dispersions with a low weight fraction of API (wAPI). The glass-transition temperature of the homogeneous solid dispersions can be calculated by the Fox-equation15 or the Gordon−Taylor equation,16 which apply simple mixing rules to the glass-transition temperatures of the pure API and the pure polymer. In cases where the glass-transition temperature of a solid dispersion does not behave monotonically, it can be calculated using the Kwei equation,17 which uses an additional empirical fitting parameter q. The modeling of the API solubility in (co)polymers is more complicated. Since polymer and API differ in shape and size, solid dispersions cannot be regarded as ideal systems. To consider the nonideality of the system, the activity coefficient γLAPI of the API in the liquid API/polymer phase has to be determined. This quantity can be estimated by application of the Flory−Huggins theory18 or the perturbed-chain statistical associating fluid theory (PC-SAFT).19 In contrast to the Flory− Huggins theory, PC-SAFT allows explicit consideration of association (e.g., hydrogen bonding)20 and ionic21 and polar22 interactions between the compounds. Each component (APIs, solvents, or polymers) is characterized by model parameters that are physically meaningful and that do not depend on temperature, the concentration of the components, polymer molecular weight, or copolymer composition. This drastically improves the predictive power of the PC-SAFT model compared to Flory−Huggins theory, at the cost of simplicity. PC-SAFT was already successfully applied to model API solubilites in solvents and solvent mixtures23 and in polymers.4 Moreover, it was already used to predict the phase behavior of copolymer systems based on the knowledge of the respective homopolymer systems only.24,25 In this work, PC-SAFT is applied to model the thermodynamic phase behavior of API/copolymer solid dispersions as a function of monomer type and copolymer composition. Poorly soluble naproxen and indomethacin were chosen as model APIs. Their chemical structures are shown in Figure 1. The homopolymers PVP K25 and PVAc as well as the copolymers PVPVA 37 and PVPVA 64 were considered as excipients. The numbers 37 and 64 indicate the weight ratios of the monomers VP/VAc in the copolymer: copolymer PVPVA 37 consists of 30% VP and 70% VAc monomers (based on total

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MODELING Glass-Transition Temperature Predictions. In this work, the glass-transition temperature of a homogeneous amorphous solid dispersion was calculated using the Gordon−Taylor equation. Within this equation, the glass-transition temperatures of the pure API Tg,API and of the pure polymer Tg,polymer are weighted by the weight fractions wAPI and wpolymer, respectively16 Tg,SD =

wAPITg,API + KwpolymerTg,polymer wAPI + Kwpolymer

(1)

The parameter K is calculated by the densities of the amorphous API ρAPI and polymer ρpolymer and their glasstransition temperatures Tg,API and Tg,polymer.26 K≈

ρAPI Tg,API ρpolymer Tg,polymer

(2)

API Solubility Calculation. The prediction of API solubility in copolymers is based on the thermodynamic solid−liquid equilibrium (SLE) of the crystalline API (considered here as a solute) in an API/copolymer solid dispersion. At equilibrium, the chemical potential of the API in the solid phase equals that in the API/(co)polymer liquid phase. It is assumed that the solid phase is pure API, and the L API solubility xAPI (in mole fraction) can be calculated according to27 L xAPI =

1 L γAPI

SL ⎡ ΔhSL ⎛ T ⎞ ΔC p ,API exp⎢ − API ⎜1 − SL ⎟ − ⎢⎣ RT ⎝ R T API ⎠

⎛ ⎛ T SL ⎞ T SL ⎞⎤ ⎜⎜ln⎜ API ⎟ − API + 1⎟⎟⎥ T ⎝ ⎝ T ⎠ ⎠⎥⎦

(3)

T is the temperature of the system, and R is the universal ideal gas constant. The melting properties of the API, including the SL melting temperature TSL API, heat of fusion ΔhAPI, and the difference in the solid and liquid heat capacities of the API ΔCSL p,API, were determined experimentally by DSC measurements.28 All quantities except γLAPI in eq 3 are properties of the pure API and are therefore independent of the type of (co)polymer. To account for the influence of polymer on API solubility, the L activity coefficient γAPI of the API in the liquid API/ (co)polymer phase has to be estimated. The activity coefficient γLAPI of the API is a function of temperature and of the composition in API/(co)polymer solid dispersion and accounts for the differences in molecular shape and molecular interactions of the API and the (co)polymer. In the case of API/(co)polymer solid dispersions, the value of the API activity coefficient is typically very different from unity and needs to be considered for a quantitative description of experimental data. The determination of the activity coefficient γLAPI from PCSAFT was already described previously in more detail.4 Therefore, only a short introduction into PC-SAFT is given here.

Figure 1. Chemical structures of naproxen (a) and indomethacin (b). B



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PC-SAFT. Within PC-SAFT, the residual Helmholtz energy ares of a system is calculated as the sum of different contributions resulting from the repulsion (ahc), van der Waals attraction (adisp, where disp stands for dispersion), and hydrogen bonding (aassoc, where assoc stands for association) of molecules in a system as described in eq 4.19,20 a res = a hc + adisp + aassoc

component parameters can also be estimated by groupcontribution methods for polymers32,33 and for small molecules.34,35 In this work, the pure-component parameters of indomethacin and naproxen were estimated from fitting to solubility data in organic solvents.23 The pure-component parameters of the homopolymers were taken from the literature.36,37 Modeling the phase behavior of copolymer systems does not require any new parameters since the homopolymer parameters are also used for modeling the respective copolymers of any composition, as described in the Modeling API/Copolymer Solid Dispersions within PC-SAFT section. For modeling mixtures, PC-SAFT applies mixing rules for the segment diameter σ and dispersion-energy parameter u/kB of a mixture

(4)

To obtain the different contributions to the Helmholtz energy, each molecule (here, API, homopolymers, and copolymers) is described as a chain consisting of mseg i spherical segments of diameter σi. These chains are interacting with each other by van der Waals interactions characterized by the dispersion energy parameter ui/kB, where kB is the Boltzmann constant. If a system contains molecules that can form hydrogen bonds, then the contribution of association to the Helmholtz energy of the system is considered via aassoc.20 On the basis of the molecular structure, a molecule may have a certain number of association sites Niassoc. The range of the association sites is characterized by the association-volume parameter κAiBi, and the strength of the association interaction, by the association-energy parameter εAiBi/kB. In total, PC-SAFT requires five pure-component parameters for characterizing an associating molecule: segment number mseg i (not necessarily equal to the number of chemical groups or monomers), segment diameter σi, dispersion-energy parameter ui/kB, association-volume parameter κAiBi, and associationenergy parameter εAiBi/kB. The number of association sites is based on the chemical structure of the molecule. In the case of naproxen, the molecule contains two groups that can interact by hydrogen bonding (one ether group and one carboxylic acid group). For simplicity reasons, it was assumed that each group carries one electron acceptor and one electron donor, which results in a total of four association sites Niassoc for naproxen. Figure 2 shows how a naproxen molecule is schematically described within PC-SAFT.

σij =

1 (σi + σj) 2

uij =

(5)

uiuj (1 − kij)

(6)

The binary interaction parameter kij in eq 6 corrects for the deviation of the mixture energy parameter from the geometric mean of the two pure-component parameters. This parameter is fitted to experimental data of binary systems (here, API solubility in homopolymers). To improve the modeling results, in some cases kij is considered to be temperature-dependent according to eq 7, where kij,T and kij,b indicate the temperaturedependent and -independent parts of kij, respectively kij = kij ,TT + kij ,b

(7)

The cross-association interactions between two different associating components are accounted for by simply combining the rules of the pure-component association parameters. Therefore, no additional binary parameter has to be applied.38 ε A iBj =

1 A iBi (ε + ε AjBj) 2

A i Bj

A i Bi Aj Bj ⎜

κ

=

κ

κ

⎛ 2 σiiσjj ⎞3 ⎜ (σ + σ ) ⎟⎟ ⎝ ii jj ⎠

(8)

(9)

Modeling API/Copolymer Solid Dispersions within PC-SAFT. Within PC-SAFT, molecules like APIs or homopolymers were characterized as a chain with mseg i segments having the same segment diameter σi. For modeling of copolymers or short-chain-branched polymers, PC-SAFT allows for segments that differ in segment diameter (Figure 3) and in energy parameters.24,25 The copolymers in this work were assumed to consist of two different types of segments, VP and VAc, which have the diameters and also the corresponding dispersion-energy parameters, association-energy parameters, and association-

Figure 2. PC-SAFT schematically describes naproxen as a chain consisting of spherical segments (gray) carrying Niassoc association sites (black).

Concerning homopolymers, it was assumed that PVP and PVAc do not associate as pure substances but do cross associate in mixtures with the APIs in this study. Such a behavior is called induced association.29 Thus, PVP and PVAc were provided with one association site per monomer, which has no association energy. The latter ensures that an associating behavior is not predicted for each pure polymer or copolymer. By applying the mixing rules (eq 8) for the association energy in API/(co)polymer mixtures, this results in a cross-association energy that is half that of the pure API.29 Usually, the pure-component parameters are fitted to vapor pressures and liquid densities of the pure components. For many solvents, these data are already available in the literature.20,29,30 These data are, however, rarely available for APIs and polymers. Therefore, experimental data of binary systems are usually used for parameter estimation.23,31 If no experimental data for fitting are available, then PC-SAFT pure-

Figure 3. PC-SAFT scheme of the random copolymer consisting of two different types of segments, VP and VAc. In the case of copolymers, different segments belong to different monomer units; in the case of branched polymers, different segments correspond to chain segments and branching segments, respectively. C



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volume parameters of the homopolymer segments PVP and PVAc, respectively. The segment diameter σi, dispersion energy ui/kB, association-energy εAiBi/kB, and association-volume parameter κAiBi of VP and VAc segments are assumed to be the same regardless of whether these segments are found in a homopolymer or a copolymer. The segment number mseg copol of the copolymer is simply obtained as the sum of segments of the number of VP seg (mseg copol,VP) and VAc (mcopol,VAc) segments in the copolymer according to seg seg seg mcopol = mcopol,VP + mcopol,VAc

(10)

The number of segments for each monomer type and seg mcopol,VAc are calculated in terms of the experimentally determined weight fractions wcopol,VP and wcopol,VAc of monomer units VP and VAc in the copolymer as well as of the molecular weight of copolymer Mcopol (Table 3) according to (11)

seg mcopol,VAc = (mseg /M )VAc wcopol,VAcMcopol

(12)

(mseg/M)VP and (mseg/M)VAc are the pure-component parameters (segment number divided by the molecular weight) of the homopolymers PVP and PVAc, respectively. From the number of segments per segment type in the copolymer, one directly obtains the segment fractions zcopol,VP and zcopol,VAc according to

zcopol,VP =

zcopol,VAc =

seg mcopol,VP seg mcopol

(13)

seg mcopol,VAc seg mcopol

(14)

The different arrangements of the segments within the copolymer backbone are accounted for by bond fractions BVP,VP. A bond fraction indicates the percentage of a particular bond type (e.g., VP−VP) among all bonds (VP−VP, VP−VAc, and VAc−VAc). For random copolymers (PVPVA 37 and PVPVA 64 considered in this work), these bond fractions can only be estimated.24 In the case of PVPVA 37, which contains more VAc monomers than VP monomers in the copolymer backbone (Zcopol,VP < Zcopol,VAc), the bond fractions were calculated according to24 seg seg B VP,VAc = 2[(zcopol,VPmcopol )/(mcopol − 1)]

(15)

B VP,VP = 0

(16)

B VAc,VAc = 1 − B VP,VP − B VP,VAc

(17)

In the case of PVPVA 64, there are more VP monomers than VAc in the copolymer and thus it is Zcopol,VP > Zcopol,VAc. In this case, the bond fractions were calculated as seg seg B VP,VAc = 2[(zcopol,VAcmcopol )/(mcopol − 1)]

(18)

B VAc,VAc = 0

(19)

B VP,VP = 1 − B VAc,VAc − B VP,VAc

(20)

MATERIALS AND METHODS

Materials. Indomethacin (purity >99%) was purchased from Sigma-Aldrich (Steinheim, Germany), and naproxen (purity >99%) was purchased from TCI (Zwijndrecht, Belgium). The polymer PVP K25 (Kollidon25, average Mw of 27 500 g/mol) and the random copolymers PVPVA 37 (Luviskol VA 37E) and PVPVA 64 (Luvitec VA 64 P, average Mw of 65 000 g/mol) were purchased from BASF (Ludwigshafen, Germany), and PVAc was purchased from VWR Chemicals BDH Prolabo (Darmstadt, Germany). PVPVA 37 was delivered in an ethanol solution and had to be isolated by spray drying. All other substances were used without any further purification. Methods. Solid-Dispersion Preparation. The solid dispersions were prepared using a mini spray dryer B-290 with an inert-loop from Büchi (Essen, Germany). For that purpose, (co)polymer and API were dissolved in an organic solvent with a total concentration for both (co)polymer and API of 3 g/200 mLsolvent. The solid dispersions with PVP and PVPVA 64 were dissolved in ethanol, and the ones with PVAc and PVPVA 37, in acetone. The inlet temperature was 80 or 65 °C for spray drying from solutions with ethanol or acetone, respectively. Nitrogen was used as the drying gas at 550 L/h. The feed rate of the solution was 8 mL/min. The prepared solid dispersions were stored in a vacuum oven at 25 °C for at least 24 h to remove the organic solvent and any water absorbed from the atmosphere. Homogeneity Analysis of API Distribution in Solid Dispersions. Five to ten samples (≈10 mg) of a freshly prepared solid dispersion were weighed with an accuracy of ±0.3 mg and dissolved afterward in a 50:50 (v/v) ethanol/ water solution. API concentrations in the samples were measured using a UV/vis spectrophotometer (Analytic Jena Specord210 Plus, Jena, Germany). Solid dispersions for which samples differed by less than 10% in API concentration were considered to have homogeneously dispersed API.39 Dissolution End Point Temperatures and Glass-Transition Temperatures of Solid Dispersions. Dissolution end point temperatures and glass-transition temperatures of each solid dispersion were determined using a modulated DSC apparatus Q2000 from TA Instruments (Eschborn, Germany) that was calibrated using indium. To maintain an inert atmosphere, the apparatus was purged with nitrogen at a flow rate of 40 mL/ min. A 10−15 mg sample of an API/(co)polymer solid dispersion of known API weight fraction (wAPI) was transferred into an aluminum pan. A lid was crimped on the pan to provide a hermetic seal. The mDSC method consisted of three steps. The first one was heating the sample from 298.15 to 433.15 K for naproxen and to 443.15 K for indomethacin at a heating rate of 2 K/min, a modulation period of 60 s, and an amplitude of 0.318 K. During this step, the remaining water was removed from the samples and moreover the samples were mixed upon melting. The dissolution end point temperature of the API was detected from an endothermic event, in which the API dissolved and diffused into the polymer. The offset of the dissolution peak was taken as the dissolution end point temperature. For the second step, the sample was quench-cooled with a cooling rate of 10 K/min, a modulation period of 60 s, and an amplitude of 1.592 K. To determine the glass-transition temperature of the solid dispersion, the sample was reheated again in a third step, choosing the same conditions as those for the first step.

mseg copol,VP

seg mcopol,VP = (mseg /M )VP wcopol,VPMcopol

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Figure 4. Phase behavior of naproxen (a) and indomethacin (b) in PVP (triangles) and PVAc (squares), respectively. Gray symbols represent the API solubilities in the polymers, and the black symbols represent the glass-transition temperatures of freshly prepared solid dispersions. The experimental data for the glass-transition temperatures of naproxen solid dispersions in PVAc that were not fully amorphous are marked as hollow squares. White triangles in panel b represent data from Sun et al.41

naproxen, the glass-transition temperature of the solid dispersion keeps constant and is close to that for a naproxen weight fraction wnaproxen of 0.1. This can be explained by the fact that it was obviously not possible to prepare fully amorphous solid dispersions of naproxen in PVAc for naproxen weight fractions higher than 0.4. The latter is also demonstrated by the DSC results of naproxen/PVAc solid dispersions shown in Figure 5. All curves

The measured dissolution end point temperatures and glasstransition temperatures were functions of the heating rate during the DSC measurements. It was found in our previous work that the obtained results decrease linearly with a reduction in heating rate.4 To determine this linear relationship for each API/(co)polymer solid dispersion, solid dispersions with an API weight fraction wAPI of 0.9 were measured at heating rates of 2, 5, and 10 K/min. The modulation period was kept constant (60 s), and the amplitudes were 0.318, 0.796, and 1.592, respectively. The dissolution end point temperature and glass-transition temperature of an API/(co)polymer solid dispersion with various concentrations were then obtained by extrapolating the heating rate to 0 K/min. At the obtained equilibrium temperature (dissolution end point temperature extrapolated to 0 K/min), the API solubility in the (co)polymer is equal to the API concentration in the sample.40

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RESULTS Phase Behavior of API/Homopolymer Solid Dispersions. Figure 4 shows the phase behavior of naproxen (a) and indomethacin (b) with PVP and PVAc, respectively. This includes the solubility of both APIs in the polymers as well as the glass-transition temperatures of each freshly prepared solid dispersion. The experimental data had an average uncertainty of less than ±1 K. Both naproxen and indomethacin have higher solubility in PVP than in PVAc. Moreover, the solubility of an API in PVP could be analyzed only at API weight fractions wAPI higher than 0.7 and 0.8 for naproxen and indomethacin, respectively. PVP obviously stabilizes the amorphous state of the API, and no dissolution event during DSC measurements could be detected for lower API weight fractions. These data are in a good accordance to the data measuered by Sun et al.41 (Figure 4b). In the case of PVAc, solubility data points could be measured at lower concentrations of each API. It seems that the performance of this polymer to stabilize the amorphous state of the API is not as good as that of PVP, especially in solid dispersions with naproxen. This might be due to the low glasstransition temperatures of solid dispersions with PVAc. For each of the four solid dispersions, the glass-transition temperature of the freshly prepared solid dispersions decreases essentially linearly with increasing content of naproxen or indomethacin. In the solid dispersions naproxen/PVAc, the glass-transition temperature curve follows this trend only to a naproxen weight fraction of 0.4. At higher concentrations of

Figure 5. DSC data (heat flow) of naproxen/PVAc solid dispersions with different naproxen weight fractions wNAP of 0.3, 0.4, 0.5, 0.7, and 0.9.

show an endothermic dissolution event of crystalline naproxen. However, only for solid dispersions with naproxen weight fractions below 0.5 does naproxen recrystallize (exothermic event) during the heating step in the DSC measurement. This means that in solid dispersions with naproxen contents higher than 0.4 naproxen was already in its crystalline state right after prepared by spray drying. This crystalline naproxen cannot act as a plasticizer, which would reduce the glass-transition temperature of a homogeneous solid dispersion. Both naproxen and indomethacin are more soluble in PVP, and the glass-transition temperatures of the solid dispersions with PVP are higher than that for PVAc solid dispersions. These factors both reduce the tendency of API recrystallization and stabilize the amorphous state of API over a longer time range. These results strongly suggest that, for the long-term stability of amorphous (water-free) solid dispersions, PVP seems to be a better excipient than PVAc. However, it should also be taken into consideration that PVP tends to absorb much more water from the atmosphere than does PVAc, which then induces recrystallization.42 E



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Figure 6. Phase behavior of naproxen (a) and indomethacin (b) in PVPVA 64 (circles) and PVPVA 37 (stars), respectively. Gray symbols represent the API solubilities in the copolymers, and the black symbols represent the glass-transition temperatures of the freshly prepared solid dispersions. The experimental data for the glass-transition temperatures of solid dispersions that were not fully amorphous are marked as hollow symbols. White circles in panel b are solubility data of indomethacin in PVPVA 64 from the literature.41

Figure 7. Glass-transition temperatures of solid dispersions with naproxen (a) and indomethacin (b) in PVP (triangles), PVPVA 64 (circles), PVPVA 37 (stars), and PVAc (squares). The lines show the calculated results using the Gordon−Taylor equation using properties from Tables 1 and 3. The experimental data for the glass-transition temperatures of solid dispersions that were not fully amorphous are marked as hollow symbols. The gray symbol in panel a represents the estimated glass-transition temperature of pure naproxen.

Table 1. PC-SAFT Pure-Component Parameters, Melting Properties, Densities, and Glass-Transition Temperatures of Naproxen, Indomethacin, PVAc, and PVP

naproxen indomethacin PVAc PVP

M

mseg/M

σ

u/kB

εAB/kB

(g/mol)

(mol/g)

(Å)

(K)

(K)

230.26 357.788 90 000 25 700

0.0352a 0.0399e 0.0506h 0.0407j

2.939a 3.535e 3.397h 2.710j

229.450a 262.791e 204.650h 205.599j

934.2a 886.4e 0 0

κAB 0.02a 0.02e 0.02 0.02j

Nassoc 2/2a 3/3e 1047 90j

TSL

ΔhSL

ΔCSL p

ρ

Tg

(K)

(kJ/mol)

(J/(mol·K))

(g/(cm3))

(K)

429.47b 433.25b

31.5b 39.3b

87.44b 116.95b

1.25c 1.32f 1.18i 1.25f

265.15d 317.6g 316.83g 441.51g

a

Fitted to API solubility data in ethyl acetate, acetone, ethanol, methanol and 2-propanol between 278.15 and 320.15 K from literature.43 bPaus et al.28 cPaudel et al., 2010.44 dEstimated in this work. ePrudic et al., 2014.4 fHancock et al., 1995.45 gMeasured in this work. hTumakaka et al., 2002.37 i Jelinska et al., 2010.46 jPrudic et al.36

Phase Behavior of API/Copolymer Solid Dispersions. Figure 6 shows the phase behavior of naproxen (a) and indomethacin (b) in the copolymers PVPVA 37 and PVPVA 64. The copolymer PVPVA 37 consists of 30% weight fraction VP-monomers and 70% VA-monomers, whereas PVPVA64 consists of 60% weight fraction VP-monomers and 40% VAmonomers. The monomer ratio of VP/VAc in the copolymer influences the API solubility. Due to the better solubility in PVP (Figure 4), it can be observed that the APIs are more soluble in PVPVA 64 than in PVPVA 37 (Figure 6). Although the copolymer composition has a relatively small effect on the API solubility, it can substantially influence the glass-transition temperature of the solid dispersion. For the same API, the glass-transition temperature is higher for the solid dispersions with PVPVA 64 compared to that with PVPVA 37, and it decreases with an increasing amount of API. In the case of naproxen, this trend is

followed only for weight fractions below 0.6 and 0.7 in PVPVA 37 and PVPVA 64, respectively.

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DISCUSSION

Glass-Transition Temperature Predictions. The glasstransition temperature for each of the investigated solid dispersions was calculated using the Gordon−Taylor equation. The densities as well as the glass-transition temperatures of the pure APIs and homopolymers are listed in Table 1, and those of the copolymers are summarized in Table 3. It becomes obvious that the Gordon−Taylor equation is suitable for estimating the glass-transition temperature of homogeneous amorphous solid dispersions. The calculated results are in a good accordance with the experimental data, especially in the case of solid dispersions with indomethacin.

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Figure 8. Solubility of naproxen (a) and indomethacin (b) in PVP (triangles) and PVAc (squares), respectively. The curves show the modeling results for the API solubility estimated using PC-SAFT. White triangles represent the solubility data of indomethacin in PVP from the literature.41

to those in the respective homopolymers. Thus, the parameters from Table 1 were also used for predicting the API solubility in the copolymer systems. Three binary interaction parameters kij were used to predict API/copolymer systems (Figure 9): two kij

As shown in Figure 7, the glass-transition temperature decreases with increasing amounts of naproxen and indomethacin, whereas the slope of these curves is a function of the polymer type in the order PVP > PVPVA 64 > PVPVA 37 > PVAc. For naproxen solid dispersions with PVPVA 37 as well as PVAc, respectively, the glass-transition temperatures remained constant at higher weight fractions of naproxen. They neither follow a linear trend nor can they be described by the Gordon−Taylor equation. Modeling of API Solubility in API/Homopolymer Solid Dispersions. To calculate the solubility of naproxen and indomethacin in the homopolymers PVAc and PVP using eq 3, the API activity coefficients were determined by PC-SAFT. The PC-SAFT pure-component parameters required for the modeling as well as the properties of the pure APIs, such as SL the melting temperature TSL API, heat of fusion ΔhAPI, and the difference of solid and liquid heat capacities of the API ΔCSL p,API, are summarized in Table 1. Figure 8 shows the calculated solubility lines of naproxen (a) and indomethacin (b) in PVP and PVAc in comparison with the experimental data shown in Figure 4. The binary interaction parameters kij between APIs (naproxen and indomethacin) and homopolymers (PVP and PVAc) were estimated from the experimental solubility data from Figure 8; they are listed in Table 2.

Figure 9. PC-SAFT scheme of a solid dispersion with naproxen and a copolymer, which consists of segments VP and VAc. Three interaction parameters, kAPI,VP, kAPI,VAc, and kVP,VAc, are used to correct the dispersion energy parameter between different segments according to eq 6.

to correct the dispersion-energy parameter between API and monomer segments VP and monomer segments VAc, respectively, and a third kij for correcting the interaction energy between the two different segments VP and VAc. API solubilities in the copolymers were then predicted on the basis of the following two assumptions: (1) The binary interaction parameter kVP,VAc between VP and VAc segments is zero. (2) The binary interaction parameters kAPI,VP and kAPI,VAc between APIs and VP and VAc segments, respectively, are equal to those between API and the respective homopolymer segments (Table 2). Using these two assumptions, no additional parameters had to be fitted to copolymer data, and the API solubility in the copolymers could be fully predicted with PC-SAFT. The molecular weights and segment fractions of the copolymers used for the PC-SAFT modeling as well as copolymer densities and glass-transition temperatures required for the Gordon− Taylor equation are listed in Table 3. Figure 10 shows the predicted solubilities of naproxen (a) and indomethacin (b) in the two copolymers PVPVA 37 and PVPVA 64, respectively, in comparison to the API solubilities in the homopolymers PVP and PVAc.

Table 2. Binary Interaction Parameters kij between APIs (Indomethacin and Naproxen) and the Homopolymers (PVP and PVAc) as Used in This Work API

polymer

kij,T

kij,b

indomethacin

PVP PVAc PVP PVAc

−0.000633 0 0.000128 0

0.0922 −0.0118 −0.1297 −0.0111

naproxen

In the case of PVP solid dispersions, the binary interaction parameter kij was considered to be temperature-dependent, whereas this temperature dependency could be neglected for PVAc solid dispersions. As shown in Figure 8, the calculated results with PC-SAFT are in a good accordance with the experimental data for all four systems. The so-determined binary interaction parameters kij between homopolymers and APIs were further used to predict the API solubility in the copolymers in the next section. Prediction of API Solubility in API/Copolymer Solid Dispersions. The pure-component parameters of the VP and VAc segments in the copolymers were assumed to be identical G



Article

Table 3. Molecular Weights, Weight Fractions of VP Monomers in Copolymer, Segment Fractions, Densities, and GlassTransition Temperatures of Copolymers PVPVA 37 and PVPVA 64

PVPVA 37 PVPVA 64 a

Mcopol

wcopol,VP

(g/mol)

(g/g)

65 000b 65 000

0.3 0.6

zcopol,VP 0.352 0.655

ρ

Tg

(g/cm3)

(K)

1.19a 1.19c

338.6b 383.9b

zcopol,VAc 0.648 0.345

Assumed to be equal to the molecular weight and density of PVPVA 64. bMeasured in this work. cSix et al., 2004.47

Figure 10. Solubilities of naproxen (a) and indomethacin (b) in the copolymers PVPVA 64 (circles) and PVPVA 37 (stars), respectively. The curves show the modeling results of the API solubility in (co)polymers by PC-SAFT. White symbols are additional solubility data of indomethacin in PVPVA 64 (circles) and PVP (triangles) from the literature.41

The solubility of naproxen and indomethacin in PVPVA copolymers obviously is a function of monomer weight ratio VP/VAc. The higher the amount of VP monomers in the copolymer, the more soluble is each API. This trend is also confirmed by the predictions with PC-SAFT, which are in excellent agreement with the experimental data. For a better evaluation of the prediction performance, the maximum relative deviation (MRD) and the average relative deviation (ARD) between the experimental and predicted results were calculated according to eqs 21 and 22. MRD = 100 max

1 nexp

PC-SAFT Indomethacin PVAc PVPVA 37 PVPVA 64 PVP Naproxen PVAc PVPVA 37 PVPVA 64 PVP

wcalc, i − wexp, i

i = 1, nexp

ARD = 100

Table 4. MRD and ARD of Solubility Predictions with PCSAFT as Well as Predictions of API Concentration in the Homogenous Solid Dispersion at a Given Glass-Transition Temperature Using the Gordon−Taylor Equation

nexp

∑ i=1

wexp, i

(21)

wcalc, i − wexp, i wexp, i

Gordon−Taylor

MRD (%)

ARD (%)

MRD (%)

ARD (%)

1.159 0.778 3.775 0.769

0.499 0.321 1.226 0.440

0.428 1.024 0.476 1.613

0.1965 0.589 0.298 0.868

0.327 1.426 0.395 0.069

0.081 0.602 0.180 0.041

0.168 2.127 2.414 1.379

0.123 1.626 1.238 0.781

(22)

wcalc,i and wexp,i are the calculated and experimental data for the API solubility in the (co)polymers and the API concentration in the homogeneous solid dispersion at a given glass-transition temperature, respectively, and nexp is the number of data points included for the evaluation of a system. The results are listed in Table 4. As shown in Table 4, the solubility of indomethacin and naproxen could be modeled in PVP and PVAc with an MRD below 1.2% and fully predicted in PVPVA 64 and PVPVA 37 with an MRD below 4%. This demonstrates that PC-SAFT is a capable tool for modeling the solubility of APIs in homopolymers and even for predicting it in copolymers with high accuracy. The glass-transition temperatures of the investigated solid dispersions could be successfully described with the Gordon−Taylor equation with an MRD below 2.5%, whereas for solid dispersions with naproxen and PVAc and PVPVA 37, only the glass-transition temperatures following the linear trend were considered. It can thus be concluded that the combination of PC-SAFT and the Gordon−Taylor equation allows reliable determination

of the phase behavior of API/(co)polymer solid dispersions. Using the PC-SAFT calculations shown in Figures 8 and 10, it is also possible to estimate the API solubility in (co)polymers at room temperature. Table 5 summarizes the calculated solubilities of naproxen and indomethacin in PVAc, PVPVA 37, PVPVA 64, and PVP at room temperature. These calculated data cannot be verified experimentally since measurements cannot be performed under these conditions. The application of a thermodynamic model like PC-SAFT, however, helps to estimate the API solubility in (co)polymers at room temperature. For a long-term stable amorphous solid solution, the API concentration should always be lower than the API solubility in the (co)polymer. As can be seen in Table 5, the API solubilities in copolymers increase with increasing VP content in the copolymers and is highest in PVP. On the basis of the PC-SAFT predictions, solid dispersions of up to 36 wt % naproxen in PVP, 34 wt % indomethacin in PVPVA 64, and 43 wt % indomethacin in PVP can be prepared with little to no risk of recrystallization. One has to keep in mind that this solubility prediction considers only the binary API/(co)H


Molecular Pharmaceutics Table 5. Calculated Solubilities of Naproxen and Indomethacin in PVAc, PVPVA 37, PVPVA 64, and PVP, respectively, at Room Temperature (298.15 K) API

polymer

indomethacin

PVAc PVPVA PVPVA PVP PVAc PVPVA PVPVA PVP

37 64

37 64

wAPI 0.01 0.07 0.19 0.36 0.01 0.21 0.34 0.43

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REFERENCES

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polymer system. During storage at non-negligible humidity, the API solubility in (co)polymers is also influenced by absorbed water, which can lead systems to a much lower solubility, particularly in PVP.36 This will be considered in a subsequent article.

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CONCLUSIONS The focus of this work was to investigate the influence of monomer type and copolymer composition on the phase behavior of solid dispersions of naproxen and indomethacin. For this purpose, the homopolymers PVP and PVAc as well as the copolymers PVPVA 64 and PVPVA 37 were selected as model excipients. It was shown that the glass-transition temperature of these solid dispersions can be calculated with high accuracy using the Gordon−Taylor equation. Solubility data of the API in a polymer were described using the thermodynamic model PCSAFT. Fitting the binary interaction parameter between API and polymer to solubility data at high temperatures even allows for extrapolation toward lower temperatures (e.g., room temperature). On the basis of the knowledge of the API solubility in the respective homopolymers, PC-SAFT is even able to successfully predict the API solubility in copolymers. Without fitting any parameters to the copolymer systems, PC-SAFT could almost quantitatively predict the API solubility in copolymers as a function of temperature and copolymer composition. The PC-SAFT approach drastically reduces the experimental effort compared to that from application of the Flory−Huggins theory, which requires fitting a binary interaction parameter χ between an API and a (co)polymer as a function of temperature, (co)polymer concentration, and copolymer composition and thus does not allow for extrapolations. The prediction of API solubility in copolymers using PCSAFT is a new approach that could significantly reduce the cost of designing copolymers as excipients for APIs to ensure the formation of a long-term stable amorphous solid dispersion.

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ACKNOWLEDGMENTS

The authors acknowledge the financial support from the CLIBGraduate Cluster Industrial Biotechnology (A.P.) and from the Alexander von Humboldt Foundation (Y.J.). They would also like to thank the reviewers for helpful advice.

(g/g) naproxen

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AUTHOR INFORMATION

Corresponding Author

*Tel: +49-231-755-2635; Fax: +49-231-755-2572; E-mail: g. [email protected]. Notes

The authors declare no competing financial interest. I



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Influence of Copolymer Composition on the Phase Behavior of Solid

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