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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Solubilities of Organic Semiconductors and Nonsteroidal Antiinflammatory Drugs in Pure and Mixed Organic Solvents: Measurement and Modeling with Hansen Solubility Parameter Yoshihiro Takebayashi,* Kiwamu Sue, Takeshi Furuya, and Satoshi Yoda Research Institute for Chemical Process Technology, National Institute of Advanced Industrial Science and Technology (AIST), Higashi 1-1-1, Tsukuba, Ibaraki 305-8565, Japan

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ABSTRACT: The solubilities of five organic semiconductors and four nonsteroidal anti-inflammatory drugs (NSAIDs) were measured by a static analytical method in a set of seven representative organic solvents at 298.15 K and 0.10 MPa to determine the Hansen solubility parameter (HSP) of the solutes by a quantitative correlation with the extended Hansen model. Solubilities of the organic semiconductors (N,N′-di-1-naphthyl-N,N′diphenylbenzidine (NPB), 4,4′-bis(9H-carbazol-9-yl)biphenyl (CBP), anthracene, tetracene, and perylene) exhibited similar solvent dependence to each other, increasing in the order of ethanol < acetonitrile < hexane < acetone < carbon tetrachloride < chlorobenzene ≈ chloroform due to the large dispersion parameter δD ≈ 21 and the small polarity and hydrogen bonding parameters (δP, δH) ≈ (5, 5) of the solutes. In contrast, the solubilities of NSAIDs (naproxen, diclofenac, indomethacin, and niflumic acid) were hexane < carbon tetrachloride < acetonitrile ≈ chlorobenzene < ethanol ≈ chloroform < acetone, indicating the smaller δD ≈ 19 and the larger (δP, δH) ≈ (10, 11). The HSP analysis enabled us to estimate the solubilities in other solvents and solvent mixtures; for example, the solubility maximum of indomethacin in the mixtures of ethanol with ethyl acetate, acetone, and acetonitrile was well described by the minimum Hansen distance. RS17 and -SAC18) as predictive ones. In the case of the correlative models, solubility measured in a small set of representative solvents covering a variety of molecular interaction (aliphatic/aromatic, nonpolar/polar, aprotic/protic, and haloganated) is correlated with the solvent parameters to determine the solute parameters. Once the solute parameters are identified, the thermodynamic models allow us to predict the solubilities in other solvents and solvent mixtures. Solubility data systematically collected are necessary not only for the correlation but also for the validation and improvement of the predictive models. In the present study, we apply the extended Hansen model to the solubility correlation and prediction, because the Hansen solubility parameter (HSP) can clearly explain the solvent dependence of the solubility in terms of the three types of molecular interactions: dispersion force, polarity, and hydrogen bonding.19 The HSP analysis seems to be rather primitive but has an advantage in the solvent screening, especially in finding the optimum solvent mixture, because the maximum solubility is directly related to the minimum Hansen distance. In our previous work, we measured the solubility of an organic semiconductor, N,N′-di-1-naphthyl-N,N′-diphenyl-

1. INTRODUCTION Since solubility of organic solid varies widely with the solvent, the choice of appropriate solvent plays an important role in obtaining high yield and selectivity of the relevant reactions, extractions, and crystallizations.1,2 For the solvent selection, solubility data measured in various solvents are indispensable. However, the experimental data are often limited for fine chemicals such as pharmaceuticals especially in mixed solvent systems.3,4 It is not practical, of course, to test all the solvent candidates including their mixtures of various combinations and compositions to find the optimal one. Thermodynamic modeling of the solubility is thus a powerful tool to greatly ease the solvent screening.5−10 In this article, we provide a set of experimental solubility data of organic semiconductors and pharmaceuticals systematically measured in seven representative solvents, and present a thermodynamic analysis of the solubility based on the extended Hansen model to explain the solvent dependence in terms of the solute−solvent interaction. For the solvent screening, various thermodynamic models have been applied to the solubility correlation and prediction:7 for example, the extended Hansen model,1,5,6 the perturbedchain statistical associating fluid theory (PC-SAFT),11,12 the nonrandom two-liquid segment activity coefficient (NRTLSAC),13,14 and the nonrandom hydrogen bonding (NRHB)15 as correlative models and the UNIFAC group contribution method16 and the conductor-like screening models (COSMO© XXXX American Chemical Society

Received: June 26, 2018 Accepted: September 14, 2018

A

DOI: 10.1021/acs.jced.8b00536 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Molecular structures of the solutes. Organic semiconductors: (a) NPB, (b) CBP, (c) anthracene, (d) tetracene, and (e) perylene. NSAIDs: (f) naproxen, (g) diclofenac, (h) indomethacin, and (i) niflumic acid.

Table 1. Specification of the Chemical Samples Used chemical name (abbreviation) Solutes (Organic Semiconductors) N,N′-di-1-naphthyl-N,N′-diphenylbenzidine (NPB) 4,4′-bis(9H-carbazol-9-yl)biphenyl (CBP) anthracene (ANT) tetracene (TET) perylene (PER) Solutes (NSAIDs) (S)-(+)-naproxen (NAP) diclofenac (DIC) indomethacin (IND) niflumic acid (NIF) Solvents acetone acetonitrile (CH3CN) carbon tetrachloride (CCl4) chlorobenzene (PhCl) chloroform (CHCl3) cyclohexane ethanol (EtOH) ethyl acetate (AcOEt) ethylene glycol n-heptane n-hexane methanol n-pentane 1-propanol 2-propanol toluene Solvatochromic indicators N,N-dimethyl-4-nitroaniline (NMe2) 4-nitroaniline (NH2) Reichardt’s dye (RD)

CASRN

molecular weight M/g mol−1

sourcea

purity

analysis methodb

123847-85-8 58328-31-7 120-12-7 92-24-0 198-55-0

588.75 484.60 178.23 228.29 252.32

TCI TCI Wako TCI TCI

≥0.980 ≥0.980 ≥0.995 ≥0.970 ≥0.980

HPLC HPLC GC HPLC GC

22204-53-1 15307-86-5 53-86-1 4394-00-7

230.26 296.15 357.79 282.22

Wako TCI Wako Wako

≥0.980 ≥0.980 ≥0.980 ≥0.980

titration GC titration HPLC

67-64-1 75-05-8 56-23-5 108-90-7 67-66-3 110-82-7 64-17-5 141-78-6 107-21-1 142-82-5 110-54-3 67-56-1 109-66-0 71-23-8 67-63-0 108-88-3

58.08 41.05 153.82 112.56 119.38 84.16 46.07 88.11 62.07 100.20 86.18 32.04 72.15 60.10 60.10 92.14

Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako Wako

≥0.995 ≥0.998 ≥0.995 ≥0.980 ≥0.980 ≥0.995 ≥0.995 ≥0.995 ≥0.995 ≥0.990 ≥0.960 ≥0.998 ≥0.980 ≥0.995 ≥0.997 ≥0.995

GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC GC

100-23-2 100-01-6 10081-39-7

166.18 138.13 551.68

TCI TCI Aldrich

≥0.980 ≥0.980 0.90

GC GC n.a.

a

Wako, FUJIFILM Wako Pure Chemical Corporation; TCI, Tokyo Chemical Industry Co., Ltd.; Aldrich, Sigma-Aldrich Corporation. The samples were used as purchased without purification. bHPLC, high-performance liquid chromatography; GC, gas chromatography; n.a., not available.

benzidine (NPB), in 23 organic solvents and quantitatively correlated it with the Hansen distance.20 Here we extend the solubility measurement and modeling to other organic semiconductors including an NPB analogue and three polycyclic aromatic hydrocarbons (PAHs) as well as to four nonsteroidal anti-inflammatory drugs (NSAIDs). HSP values of the solutes are determined by the correlation and are compared with each other to characterize the solvent dependence of the solubilities of these fine chemicals. The HSP values are further utilized for the solubility prediction in other solvents and solvent mixtures. We focus on the solvent

mixtures in which the solubility has a maximum as a function of the solvent composition. From the results, we discuss what is the necessary condition for the solubility maximum to appear and what is an essential factor in the thermodynamic modeling to describe the solubility maximum correctly.

2. METHODS 2.1. Reagents. Molecular structures of the solutes−five organic semiconductors and four NSAIDs−are shown in Figure 1. Specifications of the chemical samples used are listed in Table 1. All the chemical samples were used as purchased B



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lit Table 2. Comparison of the Experimental and Literature Mole Fraction Solubilities, xexp 2 and x2 , Respectively, of Naproxen in 1-Propanol, 2-Propanol, and Ethyl Acetate and Indomethacin in Methanol and Ethyl Acetate at Temperature T = 298.15 K and Pressure p = 0.10 MPaa

solute

solvent

xexp 2

xlit 2

lit lit (xexp 2 − x 2 )/ x 2

lit

0.0122 0.0130 0.0118 0.0133 0.0234 0.0257 0.02633 0.0271 0.0275 0.00190 0.00228 0.0100 0.0112 0.0120

+0.056

Perlovich 200421 Daniels 200422 Yan 200923 Daniels 200422 Bustamante 199824 Rodriguez 201225 Aragon 201026 Yan 200923 Daniels 200422 Alhalaweh 201127 Hellsten 201128 Alhalaweh 201127 Hellsten 201128 Martinez 201129

naproxen

1-propanol

0.0133

naproxen

2-propanol

0.0126

naproxen

ethyl acetate

0.0244

indomethacin

methanol

0.00228

indomethacin

ethyl acetate

0.0111

+0.004 −0.062

+0.091 +0.003

Relative deviation from the averaged literature solubility x 2lit was calculated for validation. Standard uncertainties for temperature and pressure are u(T) = 0.2 K and u(p) = 5 kPa, respectively. Relative standard uncertainty for solubility is ur(x2) = 0.05. a

ij ρ − C2M 2 yzz x 2 = C2/jjjC2 + zzz j M1 k {

without purification. Water was purified to the specific resistance of 18 MΩ cm with a Millipore Direct-Q 3UV system. Tetrahydrofuran (Wako, purity ≥0.995, stabilizer-free) and phosphoric acid (Wako, 85 wt % aqueous solution) were used as received. 2.2. Solubility Measurements. Solubility was measured by a static analytical method and was determined from the UV−visible absorbance of the saturated solutions prepared in the following procedure. Solvent (3 cm3) and an excess amount of solute (50 to 500 mg) were loaded in a 6 cm3 screw-cap vial. The sample was sonicated in an ultrasonic cleaner (Iuchi US-2) for 20 min and then was equilibrated for 2 h in a mini cool block bath (AS ONE MyBL-10C) thermostated at 298.15 ± 0.2 K. Prolonged sonication and equilibration had a negligible effect on the solubility result. The undissolved solid was removed by filtration through a hydrophilic PTFE membrane filter (Millipore Millex LH, 0.45 μm pore size) to obtain the saturated solution. Molarity of solute in the saturated solution was measured with an HPLC system (Agilent LC1100). Without the chromatographic separation, absorption spectra of NSAIDs (20) are much larger than those of the organic solvents (14.9 to 19.0), while the (δP, δH) values are as small as those of CHCl3 and PhCl. This is why the organic semiconductors are highly soluble in the haloganated solvents with large δD values, whereas they are poorly soluble in solvents with small δD and large or zero (δP, δH) values, such as CH3CN, EtOH, and hexane. In contrast to the little difference in the HSP values, the coefficients a and b are very dependent on the solute species, as suggested by eqs 6 and 7. In Figure 4, the coefficients a and b are plotted against the solute molar volume v2 and the ideal solubility xideal 2 , respectively. The a values of NPB and CBP are twice as large as those of the polycyclic aromatic hydrocarbons (PAHs; anthracene, tetracene, and perylene), because of their large molar volumes v2. Between the NPB analogues, the exp(−b) value of CBP is larger than that of NPB in agreement with its larger ideal solubility xideal 2 , although at a quantitative level a deviation is found between exp(−b) and xideal 2 . In a similar way, the exp(−b) values of the PAHs are shown to increase in the order of tetracene < perylene < anthracene in proportion to their ideal solubility.

xideal 2 1.80 3.97 1.02 3.78 2.57 2.05 3.83 7.11 3.88

× × × × × × × × ×

−5

10 10−4 10−2 10−4 10−3 10−2 10−3 10−3 10−3

a

Molar volume v2 calculated with the Fedors’ method.31 Melting temperature Tmp,2 and molar enthalpy of fusion Δfush2 measured in this work or reported in literature at pressure p = 0.10 MPa except for calculated from tetracene in a hermetic pan.32−35 Ideal solubility xideal 2 Tmp,2 and Δfush2 at temperature T = 298.15 K with eq 7. bThis work. Standard uncertainty for pressure is u(p) = 5 kPa. Standard uncertainty for melting temperature is u(Tmp,2) = 0.5 K. Relative standard uncertainty for enthalpy of fusion is ur(Δfush2) = 0.05. c Domalski 1996.32 dPaus 2015.33 eSurov 2009.34 fPerlovich 2007.35

in eq 7, the melting To calculate the ideal solubility xideal 2 temperature Tmp,2 and the molar enthalpy of fusion Δfush2 were measured for NPB, CBP, and tetracene with a differential scanning calorimetry (DSC) system (Shimadzu DSC-60) from 323.15 to 473.15 K at a heating rate of 10 K min−1 under a nitrogen atmosphere. For tetracene, a hermetic aluminum pan (Shimadzu 201-53090) was used to avoid sublimation of the sample. Melting quantities for the other solutes were taken from the literature.32−35 The values of Tmp,2 and Δfush2 and that of xideal calculated therefrom at 298.15 K are summarized 2 in Table 4. In addition to the DSC analysis, the powder X-ray diffraction (XRD) measurement was carried out to confirm that no transformation of the solid sample was induced by the solvent; for example, indomethacin is known to have several polymorphs including the most thermodynamically stable γform (or form I) and a metastable α-form (or form II) as well as to form a solvate with many organic solvents at high supersaturation.36,37 Excess solid sample in equilibrium with the saturated solution was dried under reduced pressure at room temperature to compare the XRD pattern and the DSC curve with those of the raw solid sample as purchased. The

Table 5. Experimental Mole Fraction Solubilities x2 of the Five Organic Semiconductors in the Seven Representative Organic Solvents at Temperature T = 298.15 K and Pressure p = 0.10 MPaa x2 solvent

NPB

CBP

anthracene

tetracene

perylene

EtOH CH3CN hexane acetone CCl4 PhCl CHCl3

0.000000559 0.00000156 0.00000315 0.0000211 0.000234 0.00131 0.00268

0.00000225 0.00000754 0.00000941 0.000153 0.000997 0.00491 0.00830

0.000428 0.000765 0.00120 0.00318 0.00481 0.00946 0.00995

0.00000691 0.00000797 0.0000150 0.0000327 0.0000461 0.000140 0.000132

0.0000242 0.0000468 0.0000553 0.000301 0.000444 0.00177 0.00134

a

Standard uncertainties for temperature and pressure are u(T) = 0.2 K and u(p) = 5 kPa, respectively. Relative standard uncertainty for solubility is ur(x2) = 0.05. E



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Figure 2. Correlation of the solubilities x2 of the organic semiconductors in the seven representative organic solvents at 298.15 K with eqs 4 and 5: exp (a) NPB, (b) CBP, (c) anthracene, (d) tetracene, and (e) perylene. The calculated solubilities xcalc 2 are plotted against the experimental ones x2 .

Table 6. HSP Values of the Organic Semiconductors and the Coefficients a and b Determined by the Solubility Correlation with eqs 4 and 5. Root Mean Square Deviation (RMSD) and Range of Variation (ROV) in log x2 Were Calculated According to eqs 8 and 9, Respectively

NPB CBP anthracene tetracene perylene

δD2/MPa1/2

δP2/MPa1/2

δH2/MPa1/2

a/MPa−1

b

RMSD in logx2

ROV in logx2

RMSD ROV

21.7 21.5 20.2 20.5 21.0

3.5 4.9 5.3 4.3 5.8

4.9 5.4 5.3 5.9 5.6

0.0304 0.0319 0.0135 0.0133 0.0179

7.15 4.93 4.47 8.91 6.08

0.12 0.08 0.01 0.06 0.03

3.68 3.57 1.37 1.31 1.86

0.034 0.023 0.005 0.046 0.016

by the solvents. In contrast, the XRD patterns of the excess indomethacin in CHCl3 and CCl4 are attributed to neither αnor γ-indomethacin, suggesting a solvate formation. The DSC curve had a broad endothermic signal from 360 to 380 K overlapped with an exothermic peak at 376 K and the subsequent two endothermic peaks at 428 and 434 K. The signals are assigned to desolvation from the solvate, crystallization, and meltings of the α- and γ-forms of indomethacin, respectively.37 Because of the solvate formation, the solubility data of indomethacin in CHCl3 and CCl4 were excluded from the least-squares regression. No such solvate formation was observed for the other solutes. Solubilities of the four NSAIDs are listed in Table 7, and the correlation is shown in Figure 6. For all the NSAIDs, the solubility increased in the order of hexane < CCl4 < CH3CN ≈ PhCl < EtOH ≈ CHCl3 < acetone. The order is drastically different from that of the organic semiconductors. The HSP values and the coefficients a and b determined for the NSAIDs are summarized in Table 8. The δD values of the NSAIDs are very close to each other (19.5 ± 0.1), as shown in Figure 3a, except for a small δD of niflumic acid (17.2). As a result of the small δD, niflumic acid has relatively low solubilities in haloganated solvents with large δD values: PhCl < CH3CN and CHCl3 < EtOH in contrast to the other NSAIDs. The small δD is probably due to the CF3 group of niflumic acid, because fluorination of the alkyl group often reduces the dispersion parameter, for example, from n-C7H16 (δD = 15.3) to n-C7F16 (12.0) and from CH3COOCH2CH2

Figure 3. HSP values of the organic semiconductors (green rectangles) and the NSAIDs (blue circles) determined in this study in comparison with those of the representative organic solvents (red circles) plotted (a) along the δD axis and (b) on the δP-δH plane.

3.2. NSAIDs. Before explaining the solubility result, we discuss a solvate formation of indomethacin. Figure 5 shows the XRD pattern and the DSC curve of raw indomethacin and those of excess solids in equilibrium with the saturated solutions of various solvents. For all the samples but the excess solid in CHCl3 and CCl4, the XRD pattern was identical to that of the most stable γ-indomethacin in literature38 and no metastable α-polymorph39 was detected. The DSC curve of these samples exhibited a single endothermic peak. The onset temperature (433.0 ± 0.3 K) and enthalpy change (38.4 ± 1.5 kJ mol−1) agreed well with the melting temperature (433.25 K) and enthalpy of fusion Δfush2 (39.3 kJ mol−1) of γindomethacin,33 indicating that no transformation was induced F



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Table 7. Experimental Mole Fraction Solubilities x2 of the Four NSAIDs in the Seven Representative Organic Solvents at Temperature T = 298.15 K and Pressure p = 0.10 MPaa x2 solvent

naproxen

diclofenac

indomethacin

niflumic acid

hexane CCl4 CH3CN PhCl EtOH CHCl3 acetone

0.0000320 0.00172 0.00598 0.00636 0.0139 0.0255 0.0470

0.0000108 0.000591 0.00249 0.00258 0.00984 0.00610 0.0267

0.000000484 0.0000420b 0.00239 0.00230 0.00441 0.00876b 0.0234

0.00000535 0.0000706 0.00131 0.000297 0.0138 0.00166 0.0288

a

Standard uncertainties for temperature and pressure are u(T) = 0.2 K and u(p) = 5 kPa, respectively. Relative standard uncertainty for solubility is ur(x2) = 0.05. bSolvate formation was observed for the excess solid indomethacin in equilibrium with the saturated CCl4 and CHCl3 solutions.

Figure 4. Relationship of the coefficients a and b in eq 5 with the solute properties: (a) 4RTa plotted against the solute molar volume v2. R is the gas constant and T = 298.15 K is the absolute temperature. The green and blue lines are the linear fits to the data for the organic semiconductors and the NSAIDs, respectively. (b) exp(−b) plotted calculated at 298.15 K on a log−log against the ideal solubility xideal 2 scale. The green solid line is the linear fit to the data for NPB and CBP, the green dashed line is that for anthracene, perylene, and tetracene, and the blue dashed line is that for naproxen, diclofenac, and niflumic acid.

Figure 6. Correlation of the solubilities x2 of the NSAIDs in the seven representative organic solvents at 298.15 K with eqs 4 and 5: (a) naproxen, (b) diclofenac, (c) indomethacin, and (d) niflumic acid. are plotted against the experimental The calculated solubilities xcalc 2 ones xexp 2 . For indomethacin, the solubility data in CHCl3 and CCl4 were not used for the regression because of the solvate formation in these solvents. Figure 5. (a) Powder XRD pattern and (b) DSC curve of raw indomethacin and those of excess solids in equilibrium with the saturated solutions of various organic solvents. Literature XRD patterns of the α-form39 and γ-form38 of indomethacin are shown as references.

exp(−b), probably due to the large ideal solubility xideal 2 . At a quantitative level, however, the coefficients a and b deviate from the theoretical values calculated from v2 and xideal with 2 eqs 6 and 7, respectively, although the reason has not been identified yet.

(16.0) to CF3COOCH2CH2 (13.9).19 On the other hand, the (δP, δH) values plotted in Figure 3b are found in the small area of (9.9 ± 0.5, 11.6 ± 0.8) for all the NSAIDs. The (δP, δH) values of the NSAIDs are larger than those of the organic semiconductors and are located between those of acetone and EtOH. In acetone + EtOH mixture, therefore, a higher solubility is expected for the NSAIDs than those in the individual pure solvents, as examined later in section 4.2. Among the NSAIDs, indomethacin has a large a value, as shown in Figure 4, in qualitative accordance with its large molar volume v2. Among the other three, naproxen has a large

4. SOLUBILITY PREDICTION 4.1. Solubility in Other Solvents. Now we estimate the solubilities of these solutes in other solvents using the HSP values and the coefficients a and b determined by the correlation. The calculated solubilities are compared with the experimental or literature ones to test the prediction. For NPB, we have the solubility data in 16 solvents other than the representative ones measured in our previous study.20 For anthracene, a number of literature solubility data are available G



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Table 8. HSP Values of the NSAIDs and the Coefficients a and b Determined by the Solubility Correlation with eqs 4 and 5. Root Mean Square Deviation (RMSD) and Range of Variation (ROV) in log x2 Were Calculated According to eqs 8 and 9

naproxen diclofenac indomethacina niflumic acid

δD2/MPa1/2

δP2/MPa1/2

δH2/MPa1/2

a/MPa−1

b

RMSD in log x2

ROV in log x2

RMSD ROV

19.5 19.5 19.3 17.2

9.6 9.7 10.3 9.4

11.0 11.6 10.8 12.4

0.0279 0.0273 0.0444 0.0323

1.58 2.49 1.48 3.24

0.20 0.24 0.10 0.24

3.17 3.39 4.68 3.73

0.064 0.070 0.022 0.063

a

For indomethacin, which formed solvate in CCl4 and CHCl3, the HSP values and the coefficients a and b were determined from the solubility data in the other five representative solvents, while the RMSD was calculated for all the seven representative solvents.

in IUPAC-NIST Data Series 58 and 98.40,41 The literature data agree well with our experimental results in the seven representative solvents, as shown in Figure 7 and Table S5.42−46 Thus, the literature data in other solvents (60 solubility data in 51 solvents)40,41 were used for the validation of the calculated solubilities.

focus on the binary solvent mixture that has a maximum solubility as a function of the solvent composition. Indomethacin was chosen as a test solute, because the solubility varies widely over 4.5 orders of magnitude and has a maximum in various pairs of solvent mixtures. From the result, we investigate (i) the solvent condition (combination and composition) required for the solubility maximum to appear and (ii) an essential factor in the thermodynamic modeling for a correct description of the solubility maximum. The solubilities of indomethacin in three mixed solvents (AcOEt + EtOH, acetone + EtOH, and CH3CN + EtOH) are shown in Table 11 and Figure 10 as functions of the mole fraction x′EtOH of EtOH on the solute-free basis. For the AcOEt + EtOH and acetone + EtOH mixtures, literature values are also plotted in the figure.28,29 In the two solvent mixtures, the solubility has a maximum at x′EtOH ≈ 0.35, in agreement with the literature data. Solubility at the maximum is 7 to 9 times as large as that in pure EtOH. We found a solubility maximum also in the CH3CN + EtOH mixture, where the maximum is located at x′EtOH ≈ 0.5. Solid and dashed lines in Figure 10 are the calculated solubilities in the mixed solvents assuming that HSP values of the mixed solvent δmix = (δD, mix, δP, mix, δH, mix) is given by a linear combination of those of the pure solvents weighted by the mole fraction x′ or volume fraction ϕ′ on the solute-free basis:

Figure 7. Comparison of the solubility x2 of anthracene in various solvents at 298.15 K measured in this work and those in literature (Cepeda1996,42 Roy1998,43 Roy1999,44 Taylor2003,45 and Draucker200746). The details are presented in Table S5.

Also for the NSAIDs, many solubility data are compiled in IUPAC-NIST Data Series 102, 4 as shown in Figure 8.21−29,35,47−54 Some of the literature data, however, are inconsistent with each other; for example, the solubility of naproxen in acetone is 0.0504 in one paper26 but 0.00281 in another one,23 and that of niflumic acid in 1-octanol is 0.0294 in one35 but 0.0000457 in another.52 The details are presented in Tables S6 to S9. These inconsistencies claim that a part of the literature data should be examined carefully before the use for thermodynamic analysis. We thus newly measured the solubilities of naproxen and indomethacin in nine additional solvents listed in Table 9 and compared them with the calculated values. Results of the solubility prediction for the four solutes (NPB, anthracene, naproxen, and indomethacin) are shown in Figure 9, and the RMSDs in log x2 are listed in Table 10. Good predictions were attained with the RMSDs in log x2 as small as 0.24 to 0.69, corresponding to 10.5 to 17.3% of the ROV in log x2. Most of the calculated solubilities are within the deviation of 1 order of magnitude, except for the four outliners: NPB in N-methylpyrrolidone, 2-methoxyethanol, and carbon disulfide and indomethacin in ethylene glycol. The result shows that the HSP analysis using the seven representative solvents can provide a solubility estimation sufficient for solvent screening. 4.2. Solubility Maximum in Mixed Solvents. Next we extend the solubility estimation to mixed solvents. Here we

δmix = x′solvent A ·δsolvent A + x′solvent B ·δsolvent B

(11)

δmix = ϕ′solvent A ·δsolvent A + ϕ′solvent B ·δsolvent B

(12)

or

The solubility maximum is successfully described for all the three solvent mixtures, although a slight overestimation is observed for the maximum solubility in CH3CN + EtOH for both the x′- and ϕ′- weighted calculations. A possible reason for the overestimation is a deviation from the linear combination of HSP assumed in eq 11 or 12, as discussed later in detail. Let us interpret the solubility maximum in terms of the Hildebrand and Hansen solubility parameters. First we determine the Hildebrand solubility parameter δ of indomethacin from the solvent dependence of the solubility. In Figure 11, the solubility of indomethacin in various pure solvents listed in Tables 7 and 9 is plotted against the Hildebrand δ1 of the solvent. The solubility shows a marked increase with increasing δ1 up to 20, whereas it tends to decrease at δ1 larger than 23. The δ1 dependence of the solubility suggests that the δ value of indomethacin is 21.5 ± 1.5. This is consistent with the solubility maximum observed in the AcOEt + EtOH and acetone + EtOH mixtures, because the mixing of AcOEt (δ = 18.2) or acetone (19.9) with EtOH (26.5) at xEtOH ′ = 0.35 H



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Figure 8. Comparison of the solubilities x2 of the NSAIDs in various solvents at 298.15 K measured in this work and those in the literature: (a) naproxen (Bustamante1998,24 Perlovich2004,21 Daniels2004,22 Martinez’s group,25,26,47,48 and Yan200923), (b) diclofenac (Barra200049 and Perlovich200750), (c) indomethacin (Alhalaweh2011,27 Hellsten2011,28 Martinez2011,29 and Cantillo201351), and (d) niflumic acid (Bustamante1998,52 Bustamante2002,53 Perlovich2007,35 and Domanska201154). The details are presented in Tables S6 to S9.

Table 9. Experimental Mole Fraction Solubilities x2 of Naproxen and Indomethacin in the Nine Additional Organic Solvents at Temperature T = 298.15 K and Pressure p = 0.10 MPaa x2 solvent

naproxen

indomethacin

pentane heptane cyclohexane ethylene glycol toluene methanol 1-propanol 2-propanol ethyl acetate

0.0000222 0.0000388 0.0000750 0.00284 0.00347 0.0122 0.0133 0.0126 0.0244

0.000000331 0.000000613 0.0000187 0.000509 0.000908 0.00228 0.00433 0.00465 0.0111

Figure 9. Prediction of the solubilities x2 of NPB, anthracene, naproxen, and indomethacin in various organic solvents other than the seven representative ones at 298.15 K. The calculated solubilities are plotted against the experimental solubility xexp of NPB xcalc 2 2 measured in our previous work,20 that of anthracene in literature,40,41 and those of naproxen and indomethacin measured in this work. The dashed lines denote deviations of 1 order of magnitude.

a

Standard uncertainties for temperature and pressure are u(T) = 0.2 K and u(p) = 5 kPa, respectively. Relative standard uncertainty for solubility is ur(x2) = 0.05.

Table 10. Root Mean Square Deviation (RMSD) and Range of Variation (ROV) in log x2 of the Solubility Prediction for NPB, Anthracene, Naproxen, and Indomethacin Shown in Figure 9

provides the δ value (21.1 or 22.2, respectively) close to that of indomethacin, as pointed out in literature.28,29 The Hildebrand δ, however, cannot explain the solubility maximum in the CH3CN (δ = 24.4) + EtOH (26.5) mixture, because both the pure solvents have δ values larger than that of indomethacin. Vectorization from δ to HSP enables us to explain all the solubility maxima including the AcOEt + EtOH mixture. Figure 12 illustrates the geometry of the HSP of indomethacin and those of pure solvents. The blue, green, and red solid lines connecting the pure solvents denote the solvent mixtures of EtOH with AcOEt, acetone, and CH3CN, respectively. On the

NPB anthracene naproxen indomethacin

I

RMSD in log x2

ROV in log x2

RMSD ROV

0.69 0.24 0.40 0.60

3.99 2.32 3.04 4.53

0.174 0.105 0.132 0.132



Article

Table 11. Experimental Mole Fraction Solubilities x2 of Indomethacin in Solvent Mixtures of Ethanol with Ethyl Acetate, Acetone, And Acetonitrile As Functions of the Ethanol Mole Fraction xEtOH ′ on the Solute-Free Basis at Temperature T = 298.15 K and Pressure p = 0.10 MPaa AcOEt + EtOH

acetone + EtOH

CH3CN + EtOH

x′EtOH

x2

x′EtOH

x2

x′EtOH

x2

0.000 0.091 0.175 0.289 0.389 0.507 0.610 0.700 0.817 0.916 1.000

0.00111 0.0197 0.0248 0.0272 0.0300 0.0266 0.0252 0.0206 0.0134 0.00725 0.00441

0.000 0.123 0.240 0.351 0.457 0.558 0.654 0.746 0.835 0.919 1.000

0.0234 0.0328 0.0377 0.0396 0.0390 0.0329 0.0273 0.0210 0.0147 0.00740 0.00441

0.000 0.090 0.182 0.276 0.373 0.471 0.572 0.675 0.781 0.889 1.000

0.00239 0.00608 0.0109 0.0169 0.0199 0.0202 0.0205 0.0188 0.0132 0.00934 0.00441

Figure 11. Solubility x2 of indomethacin in various organic solvents at 298.15 K plotted against the Hildebrand solubility parameter δ1 of the solvent. The solubility shows a marked increase with increasing δ1 up to the gray bar (δ1 = (20 to 23) MPa1/2), whereas it turns to decrease at larger δ1.

a

Standard uncertainties for temperature, pressure, and ethanol mole fraction are u(T) = 0.2 K, u(p) = 5 kPa, and u(x′EtOH) = 0.001, respectively. Relative standard uncertainty for solubility is ur(x2) = 0.05. Figure 12. Geometry of the HSPs of indomethacin, ethanol, ethyl acetate, acetone, and acetonitrile. The blue, green, and red solid lines denote the solvent mixtures of ethanol with ethyl acetate, acetone, and acetonitrile, respectively, on which the points a, b, and c provide a minimum HSP distance Ra from indomethacin, as shown by the dotted lines.

mixture lines, a minimum Hansen distance R a from indomethacin is obtained not at the pure solvents but at the points a, b, and c, respectively, indicating that a maximum solubility appears in the mixture at the corresponding solvent composition. It should be noted, for the CH3CN + EtOH mixture, that the solvent mixing reduces the excess δP of CH3CN as well as the excess δH of EtOH, giving the (δP, δH) values close to those of indomethacin. The mechanism demonstrates that the decomposition of molecular interaction into polarity and hydrogen bonding contributions plays an essential role in the thermodynamic modeling of the solubility maximum in solvent mixtures. Such a solubility maximum is reported for many pharmaceuticals in binary mixtures of nonpolar or weakly polar solvent (cyclohexane, dichloromethane, dioxane, and AcOEt) with a protic one (alcohols and water).5,25,28,29,53,55−62 The solubility maximum is found also in alcohol + water mixture for solutes with higher hydrophilicity, such as acetaminophen (paracetamol).9,56,63 These solubility maxima have been often used for the validation of solubility models,5,8,9,11,12,14,63 although most of the maxima can be explained even by the Hildebrand δ,59 as shown in Figure 11. In contrast, solubility enhancement in the mixture of a polar aprotic solvent with a protic one, such as the CH3CN + EtOH mixture in Figure 10c, has been rarely investigated so far, except for the recent research by Duereh et al.64−66 They proposed an application of the mixture of polar aprotic solvent (ketones, lactones, nitriles, and dimethyl sulfoxide) with protic one for pharmaceutical and polymer industries as alternative solvents replacing hazardous ones. This type of solvent mixture is expected to be a novel category of good solvent as well as a

Figure 10. Solubilities x2 of indomethacin in solvent mixtures of ethanol with (a) ethyl acetate, (b) acetone, and (c) acetonitrile at ′ on the 298.15 K as functions of the ethanol mole fraction xEtOH solute-free basis. The solubilities measured in this work are compared with those reported by Hellsten et al.28 and Martinez et al.29 The solid and dashed lines are the solubilities calculated with eqs 4 and 5 assuming the mole fraction (x)-weighted HSP in eq 11 and the volume fraction (ϕ)-weighted HSP in eq 12, respectively.

J



Article

minimum HSP distance from indomethacin in Figure 12. This is consistent with the overestimation in the maximum solubility in Figure 10c. The positive deviations in π* and α are reported also for (acetonitrile + methanol or 1-propanol)68 and (cyclic ketone + methanol or ethanol)66 systems, and thus are considered to be a common feature for (aprotic polar + alcohol) solvent mixtures. The excess polarity and hydrogen bonding ability of mixed solvent are interpreted in terms of the preferential solvation, that is, a local solvent composition around the solute different from the bulk one. A better knowledge on the local environment around the solute will improve the solubility prediction in the mixed solvents.

touchstone to test the solubility models suited for solvent screening. Finally we elucidate why the maximum solubility in CH3CN + EtOH was overestimated by the calculation with eqs 5 and 11. To examine the linear composition dependence of HSP assumed in eq 11, we measured the two Kamlet−Taft solvatochromic parameters of the CH3CN + EtOH mixture: the π*-parameter is a measure of the solvent polarity and the α-parameter is that of the hydrogen bond donating ability,67 corresponding to δP and δH, respectively, in the framework of HSP. The Kamlet−Taft parameters were determined from the wavelength λmax of the maximum absorbance of the indicators, N,N-dimethyl-4-nitroaniline (NMe2) and Reichardt’s dye (RD):66 π * = 7.98 −

NMe2 2841/(λmax /nm)

5. CONCLUSIONS Solubilities of organic semiconductors and NSAIDs were systematically measured in a set of seven representative organic solvents and were correlated with the extended Hansen model to determine the HSP values of the solutes. The organic semiconductors were characterized by large δD = 21.0 ± 0.8 and small δP = 4.7 ± 1.2 and δH = 5.4 ± 0.5, whereas the NSAIDs had smaller δD = 18.4 ± 1.2 and larger δP = 9.9 ± 0.5 and δH = 11.6 ± 0.8. The HSP analysis allowed us to estimate the solubilities in other solvents and to predict the solubility maximum in mixed solvents. The solubility maximum of indomethacin in the CH3CN + EtOH mixture newly found in this study was explained by HSP but not by the Hildebrand δ, indicating that the decomposition of molecular interaction into polarity and hydrogen bonding contributions plays an essential role in the solubility modeling. The solubility data obtained here will help us to validate and improve other thermodynamic models based on the activity coefficient or the equation of state, which is examined in our subsequent works.

(13)

and RD α = 1856/(λmax /nm) − 2.03 − 0.72π *

(14)

The details are presented in Table S10. Figure 13 shows the composition dependence of the π*- and α-parameters of the

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00536.

■

Figure 13. Kamlet−Taft solvatochromic parameters, (a) π* and (b) α, of acetonitrile + ethanol mixture at 298.15 K as functions of the ethanol mole fraction xEtOH. The dashed line shows ideal composition dependence calculated from the linear combination of the value of pure acetonitrile and that of pure ethanol. The literature value of pure acetonitrile by Nunes et al.68 and that of pure ethanol by Duereh et al.66 are plotted for comparison.

Densities of the saturated solutions, comparison of the solubilities measured in this work and those in literature, and Kamlet−Taft solvatochromic parameters of the acetonitrile + ethanol mixture (PDF)

AUTHOR INFORMATION

Corresponding Author

*Phone: +81-29-861-9272. E-mail: [email protected]. ORCID

Yoshihiro Takebayashi: 0000-0002-3338-7470 Funding

This work was supported by JSPS KAKENHI JP16K06840. CH3CN + EtOH mixture. For pure CH3CN and EtOH, the Kamlet−Taft parameters obtained here are in good agreement with the literature ones determined by Nunes et al.68 and Duereh et al.,66 respectively, using the same indicators. For the CH3CN + EtOH mixture, an increase in the EtOH mole fraction gives a decrease in π* and an increase in α, as expected. Both parameters, however, exhibit nonlinear composition dependence with positive deviations. The excess π* and α suggest that the actual (δP, δH) values of the CH3CN + EtOH mixture are larger than those estimated by the linear combination in eq 11 or 12. The underestimation in the solvent (δP, δH) values will lead to an underestimation in the

Notes

The authors declare no competing financial interest.

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REFERENCES

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