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Dissolution behavior and thermodynamic properties of apixaban in pure and mixed solvents
J. Chem. Thermodynamics xxx (xxxx) xxx
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Dissolution behavior and thermodynamic properties of apixaban in pure and mixed solvents Cunbin Du a, Yang Cong a, Ying Zhang a, Yi Xue a,b, Bin Qiao a, Tingting Ye a, Mingliang Wang a,⇑ a b
School of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, PR China Southeast University – Red Sun Research Center for Intelligent Industry, Nanjing 211189, PR China
a r t i c l e
i n f o
Article history: Received 20 August 2019 Received in revised form 3 September 2019 Accepted 7 September 2019 Available online xxxx Keywords: Apixaban Solubility Co-solvency phenomenon Thermodynamic properties
a b s t r a c t The solubility profile of apixaban in pure and mixed solvents within the temperature range from (288.15 to 328.15) K under atmosphere pressure (101.3 kPa) was studied and evaluated by some thermodynamics models. The solid state of apixaban in equilibrated form was characterized using powder X-ray diffraction (PXRD) technique. The maximum mole solubility in pure solvents was obtained in 1, 4-dioxane (3.648 103) at 328.15 K, and followed by methanol (1.967 103), acetone (7.885 104),ethanol (6.049 104), isopropanol (3.806 104), ethyl acetate (2.266 104), n-hexane (1.883 104), water (3.989 105). The solubility was quite small. Therefore, the solubility profile of apixaban in mixtures of (1, 4-dioxane + water) was further studied. Moreover, it increased at first and then decreased with the increasing mass fraction of 1, 4-dioxane. Moreover, the extended Hildebrand solubility approach (EHSA) was applied to evaluate the co-solvency phenomenon in mixed solvent at 298.15 K. In the following, the analysis of apparent thermodynamic properties indicates that the dissolution process in all selected solvents is an endothermic and entropy driven process. Ó 2019 Published by Elsevier Ltd.
1. Introduction Atrial fibrillation (AF) is the most common cardiac arrhythmia which is associated with increased risk of stroke, the prevalence of the disease in the United States in 2010 was 5.2 million and is expected to rise to by 2030 [1]. Vitamin K antagonists are highly effective in preventing stroke in patients with AF [2,3]. However, many patients are not suitable candidates for or are unwilling to receive vitamin K antagonist therapy, and these patients have a high risk of stroke [4]. In recent years, the development of non-vitamin K antagonist oral anticoagulants (NOACs), including direct thrombin inhibitor and factor Xa inhibitors have increased therapeutic options for anticoagulation and could potentially overcome many drawbacks of Vitamin K [5]. Apixaban (CAS Reg. No. 503612-47-3; chemical structure shown in Fig. 1), an oral direct factor Xa inhibitor with a trade name of Eliquis and marketed by Bristol-Myers Squibb [6], is a novel anticoagulant [7] that a few studies have demonstrated its safety and efficacy profile [4]. Factor Xa catalyzes the conversion of prothrombin to thrombin, the final enzyme in the coagulation cascade that is responsible for fibrin clot formation [8]. Apixaban has no direct effect on platelet aggregation, but by inhibiting factor Xa, it ⇑ Corresponding author. E-mail address: [email protected] (M. Wang).
indirectly decreases clot formation induced by thrombin. In industry, the process of preparing apixaban is complicated owing to many intermediates need to be prepared [9]. Like many other pharmaceutical manufacturing processes, solution crystallization is the final step to obtain apixaban products with high purity and high yield. The recrystallization process of apixaban needs the solubility data urgently [10]. So it is important to know the solubility data to select the best solvent for recrystallization in industrial production. Drug solid can exist in crystalline, amorphous or partially crystalline powders. Crystalline structures have long range molecular order, while amorphous structures are more disordered. Crystalline and amorphous materials show significantly different physicochemical properties, due to differences in microstructure, this affecting the stability, bioavailability and curative effect of the drug. Therefore, it is very important to analyze the crystal form of solid drug substance for controlling the quality and efficacy of drugs [11,12]. In this work, the isothermal saturation method was adopted to measure the solubility of apixaban in water, methanol, ethanol, isopropanol, ethyl acetate, n-hexane, 1,4-dioxane, acetone and (water + 1,4-dioxane) mixtures at temperatures ranging from 288.15 K to 328.15 K under atmospheric pressure. The modified Apelblat equation and kh equation were employed to correlate the experimental solubility in pure solvents, and the solubility in binary solvent mixtures was correlated by the Jouyban-Acree
https://doi.org/10.1016/j.jct.2019.105949 0021-9614/Ó 2019 Published by Elsevier Ltd.
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recrystallization in methanol and the final purity was 0.994 in mass fraction, which was confirmed by a high-performance liquid chromatography (HPLC). The solvents, including methanol, ethanol, isopropanol, ethyl acetate, n-hexane, 1,4-dioxane, and acetone with analytical grade were provided by Sinopharm Chemical Reagent Co., Ltd., China. The mass fraction purities of these solvents were all higher than 0.994, which were provided by supplier. The water used in the experiment is the secondary distilled water prepared by our laboratory. The purity and source information of the chemicals employed in this work is tabulated in Table 1. 2.2. Characterization of apixaban The X-ray diffractometer (XRD) used in this work is a Rigaku D/max-2500 (Rigaku, Japan) using Cu Ka radiation (1.5405 Å). In this work, a step size of 0.02°and a scanning rate of 10°/min over a diffraction angle (2h) range of 5°–50° were used before and after the experiments to confirm the form of apixaban. The patterns are shown in Fig. 2.
Fig. 1. Chemical structure of apixaban.
model, Modified Apelblat-Jouyban-Acree model and a combination of the Jouyban-Acree model with the van’t Hoff equation. The extended Hildebrand solubility approach (EHSA) was applied to evaluate the co-solvency phenomenon in mixed solvent at 298.15 K. Moreover, some apparent thermodynamic properties of dissolution process in all selected solvents were discussed. 2. Experimental section 2.1. Materials and apparatus Apixaban (with a mass fraction of 0.975) was purchased from MOLBASE Chemical Reagent Co., Ltd., China. It was purified by
2.3. Solubility measurement In this work, the solubility of apixaban in pure solvents including water, methanol, ethanol, isopropanol, ethyl acetate, n-hexane, 1,4-dioxane, acetone and binary solvent mixtures of water + 1,4dioxane were determined by the isothermal saturation method [13,14]. Saturated solutions of apixaban were prepared in the jacketed glass vessel. The temperature of the vessel was kept at the desired value through circulating water, which temperature was controlled by the smart thermostatic bath (model: DZKW-4) through the outer jacket of the jacketed glass vessel. The real temperature was displayed by using a mercury glass micro thermometer, which standard uncertainty is 0.02 K. For each
Table 1 Detailed information on the materials used in the work.
a b
Chemicals
Molar mass gmol1
Source
Initial mass fraction purity
Final mass fraction purity
Purification method
Analytical method
Apixaban
459.50
0.975
0.994
Recrystallization
HPLCa
Methanol Ethanol Isopropanol Ethyl acetate n-Hexane 1,4-Dioxane Acetone
32.04 46.07 60.06 88.11 86.18 88.11 58.08
MOLBASE Chemical Reagent Co., Ltd., China Sinopharm Chemical Reagent Co., Ltd.,China
0.995 0.996 0.994 0.995 0.996 0.994 0.995
0.995b 0.996b 0.994b 0.995b 0.996b 0.994b 0.995b
— — — — — — —
None
High-performance liquid phase chromatograph. the result was provided by supplier.
Fig. 2. X-ray powder diffraction patterns of apixaban in pure and mixed solvents.
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experiment, an excess amount of apixaban was introduced to the glass vessel. Continuous stirring was obtained for intensive mixing the suspension by means of a magnetic stirrer at a certain temperature. In order to determine the equilibration time of the solid–liquid system, about 0.5 mL liquid phase was taken out every an hour by using a 2 mL syringe connected with a 0.2 lm pore filter, and then analyzed by a the high-performance liquid phase chromatograph (HPLC). The same content of liquid phase indicated that the solution reached equilibrium. The results show that 12 h can ensure that the system is completely saturated. When the solid– liquid system arrived at equilibrium, the stirring was stopped and the solution was permitted to settle for 1 h before sampling. The upper portion was taken out with a 5 mL of preheated syringe connected with a filter (PTFE 0.2 lm), and transferred into a volumetric flask of 25 mL preweighed with the balance. The volumetric flask with sample was covered quickly with a rubber stopper. The total amount of the solution and flask was weighed again by using the balance. Then the sample was diluted to 25 mL with methanol, and analyzed with a high-performance liquid chromatography. All the experiments were carried out three times, and the average value was employed to calculate the mole fraction solubility. The saturated mole fraction solubility of apixaban (xw;T ) in pure and binary solvents are obtained by using Eqs. (1) and (2).
xw;T ¼
m1 =M1 m1 =M 1 þ m2 =M 2
ð1Þ
xw;T ¼
m1 =M 1 m1 =M 1 þ m2 =M 2 þ m3 =M 3
ð2Þ
Here x1 is the mole fraction solubility of apixaban; m1 refers to the mass of solute, m2 and m3 represent the mass of the solvents that constitute the solution. M1, M2 and M3 are the corresponding molecule mass of each solvent.
2.4. Analysis method The content of apixaban was analyzed using the Agilent-1260 high-performance liquid-phase chromatograph (HPLC). It was equipped with a reverse phase column with a type of LP-C18 (250 mm 4.6 mm). The temperature of reverse phase column was 303.15 K. The wavelength of the UV detector was set to 280 nm. Pure methanol was used as mobile phase with a flow rate of 1 mLmin1. Each analysis was repeated three times to check the repeatability and three samples were taken for each equilibrium solution at a given temperature. The average value was regarded as the final solubility data.
3. Results and discussion
3.2. Solubility data The measured mole fraction solubility of apixaban in pure and binary solvents were presented in Tables 2 and 3, and plotted in Figs. 3 and 4. It can be found that the solubility of apixaban is a function of temperature and solvent composition. The solubility of apixaban monotonically increased with an increasing temperature, and The maximum mole solubility in pure solvents was obtained in 1, 4-dioxane (3.648 103) at 328.15 K, and followed by methanol (1.967 103), acetone (7.885 104), ethanol (6.049 104), isopropanol (3.806 104), ethyl acetate (2.266 104), n-hexane (1.883 104), water (3.989 105). In three alcohols, it decreased with the increase of carbon chain length. While, in other solvents, it increased with the rising solubility parameters except for water. The influencing factors are comparatively complex, including the polarity of the studied solvents, intermolecular interactions between the solute and the solvent, hydrogen bonding interaction, and so on [15]. For the mixtures of (1, 4-dioxane + water), Fig. 4 show that the solubility increased monotonically with the temperature at all studied composition, but the composition dependence of the solubility had a maximum around the 1, 4-dioxane mass fraction w = 0.8302. After that, with the increase of co-solvent (1, 4-dioxane), the intermolecular force increases gradually, resulting in an increase of solubility while w 5 0.8302, however, it is vice versa at w﹥0.8302. It is acknowledged that solutes reach their maximum solubility value in solvents with the same solubility parameter. In order to estimate maximum solubility at certain mixture ratio, the extended Hildebrand solubility approach (EHSA) was applied to evaluate the cosolvency phenomenon in mixed solvent at 298.15 K. [16] The relevant calculation process is shown in Table S1. In this work, Hilde
brand solubility parameter is 30.02 MPa0.5, and the D d factor between this drug and mixed solvent is presented in Table 4. The minimum value is founded at w = 0.88 (in mass fraction). It is very close to the composition of the mixed solvent when the solubility data reach the maximum (at w = 0.8302). It may be the deviation of estimating the molar volume and partial solubility parameters of solute. 3.3. Solubility modeling In this work, some models were employed to correlated the solubility of apixaban in pure and binary solvents, which correspond to the modified Apelblat equation [17–19], kh equation [20], Jouyban-Acree model [21,22], Modified Apelblat-Jouyban-Acree model [23,24] and a combination of the Jouyban-Acree model with the van’t Hoff equation [23,24]. 3.3.1. Modified Apelblat equation The modified Apelblat equation is a semi-empirical equation. It describes the dependence of mole fraction solubility on the absolute temperature T, and expressed as equation (3) [17–19].
3.1. XRD analysis The results of XRD were presented in Fig. 2. From Fig. 2, it can be seen that all the XPRD patterns of solid phase of apixaban in equilibrium with its solution have the same characteristic peaks with the raw material. Therefore, no polymorph transformation or solvate formation is observed during the whole experiment. In addition, compared the analysis of X-ray powder diffraction in references 11 and 12, in this work, the characteristic peaks of Xray powder diffraction are expressed at 2h angle of 8.5°, 10.0°, 10.5°, 11.2°, 12.3°, 16.3°, 17.0°, 18.5°, 18.9°, 19.6°, 21.1°, 21.5°, 22.0 ± 0.2°, 22.3°, 24.8°, 27.0°, 29.9°, and 32.7°, it is almost the same as the XRD curves of apixaban form I in references 11 and 12.
lnx ¼ A þ
B þ ClnT T
ð3Þ
where x is the mole fraction solubility of apixaban in pure organic solvents; A, B and C are the adjustable parameters in the modified Apelblat equation. 3.3.2. Buchowski–Ksiazaczak kh equation The Buchowski–Ksiazaczak kh equation, expressed as Eq. (4), is another equation to describe the solubility of solid in pure solvent. [20]. The Buchowski–Ksiazaczak kh equation has two parameters k and h, and Tm is the melting temperature of apixaban in Kelvin.
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Table 2 Experimental (xe) and calculated (xcal) mole fraction solubility of apixaban in different solvents at the temperature range from T = (288.15 To 328.15) K under 101.3 kPa.a T/K
Water 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Methanol 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Ethanol 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Isopropanol 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Ethyl acetate 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 n-Hexane 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 1,4-Dioxane 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Acetone 288.15
1000xe
Table 2 (continued) T/K
1000xe
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
0.2821 0.3279 0.3862 0.4569 0.5345 0.6121 0.7003 0.7885
1000xcal Modified Apelblat equation
kh equation
9.225e-3 1.094e-2 1.328 e-2 1.632 e-2 1.995 e-2 2.411 e-2 2.870 e-2 3.395 e-2 3.989 e-2
8.899 1.102 1.353 1.649 1.995 2.397 2.860 3.391 3.998
9.270 9.880 1.053 1.124 1.199 1.280 1.369 1.464 1.568
0.3103 0.3981 0.5176 0.6687 0.8620 1.090 1.344 1.637 1.967
0.2976 0.3987 0.5245 0.6785 0.8641 1.084 1.340 1.635 1.970
0.3129 0.4057 0.5216 0.6653 0.8425 1.060 1.324 1.645 2.032
0.1076 0.1373 0.1799 0.2256 0.2806 0.3456 0.4203 0.5035 0.6049
0.1076 0.1395 0.1783 0.2250 0.2803 0.3451 0.4201 0.5061 0.6035
0.1106 0.1403 0.1768 0.2211 0.2748 0.3395 0.4170 0.5096 0.6198
5.716e-2 7.205 e-2 9.583 e-2 0.1297 0.1752 0.2194 0.2652 0.3229 0.3806
5.207 e-2 7.324 e-2 0.1000 0.1328 0.1718 0.2168 0.2673 0.3224 0.3809
5.771 e-2 7.573 e-2 9.851 e-2 0.1271 0.1627 0.2068 0.2610 0.3275 0.4084
5.098 e-2 5.925 e-2 7.210 e-2 8.852 e-2 0.1054 0.1285 0.1563 0.1884 0.2266
4.973 e-2 6.013 e-2 7.271 e-2 8.794 e-2 0.1064 0.1286 0.1555 0.1879 0.2271
4.851 e-2 5.981 e-2 7.327 e-2 8.925 e-2 0.1081 0.1303 0.1564 0.1869 0.2225
1.241 e-2 1.845 e-2 2.879 e-2 4.180 e-2 5.760 e-2 7.754 e-2 0.1048 0.1427 0.1883
1.328 e-2 1.959 e-2 2.837 e-2 4.040 e-2 5.659 e-2 7.806 e-2 0.1061 0.1422 0.1882
1.319 e-2 1.922 e-2 2.764 e-2 3.930 e-2 5.524 e-2 7.682 e-2 0.1058 0.1442 0.1949
1.138 1.302 1.556 1.824 2.159 2.507 2.867 3.263 3.648
1.100 1.322 1.571 1.850 2.157 2.493 2.857 3.248 3.665
0.9954 1.246 1.549 1.913 2.348 2.866 3.480 4.205 5.060
0.2523
0.2410
0.2447
e-3 e-2 e-2 e-2 e-2 e-2 e-2 e-2 e-2
e-3 e-3 e-2 e-2 e-2 e-2 e-2 e-2 e-2
1000xcal Modified Apelblat equation
kh equation
0.2855 0.3361 0.3932 0.4573 0.5289 0.6084 0.6965 0.7934
0.2872 0.3357 0.3910 0.4538 0.5250 0.6058 0.6973 0.8010
a Standard uncertainties u are u(T) = 0.02 K, u(p) = 400 Pa; Relative standard uncertainty ur is ur (x) = 0.045.
During calculation, it is cited from reference 12, and the value is 511.15 K.
kð1 xÞ 1 1 ¼ kh ln 1 þ x T Tm
ð4Þ
3.3.3. Jouyban-Acree model The Jouyban-Acree model provides accurate mathematical descriptions for the solubility dependence on both temperature and solvent composition for binary and ternary mixed solvents [21,22], and is described as Eq. (5).
lnxw;T ¼ w1 lnx1;T þ w2 lnx2;T þ
2 w1 w2 X J ðw1 w2 Þi T i¼0 i
ð5Þ
where xw,T is the solubility of solute in mole fraction in the binary solvent mixtures at temperature T in Kelvin; w1 and w2 denote the mass fraction of solvents 1 (1,4-dioxane) and 2 (water) in the absence of the solute (apixaban), respectively; x1,T and x2,T are the mole fraction solubility of solute in pure solvent, and Ji stands for the Jouyban-Acree model parameters. 3.3.4. Van’t Hoff-Jouyban-Acree model A linear van’t Hoff equation is established for providing precise predictions of a solute dissolved in a solvent at a limited temperature range. It describes the dependence of the natural logarithm of the mole fraction solubility on the reciprocal of absolute temperature and is expressed as Eq. (6) [24]. The solubility of a solute in pure solvent at different temperatures can be calculated with the van’t Hoff equation.
lnx ¼ A þ B=TðKÞ
ð6Þ
where A and B are equation constants. Substituting Eqs. (6) into (5), one can obtain the Van’t Hoff-Jouyban-Acree model expressed as Eq. (7) [23,24].
lnxw;T ¼ w1 ðA1 þ
2 B1 B2 w1 w2 X J ðw1 w2 Þi Þ þ w2 ðA2 þ Þþ T=K T=K T=K i¼0 i
ð7Þ Here A1, B1, A2, B2 and Ji are the model constants. This model can provide an estimation of the solute solubility in binary solvent mixtures at different temperatures and composition of solvents. 3.3.5. Modified Apelblat-Jouyban-Acree model Similarly, substituting Eqs. (3) into (5), the Apelblat-JouybanAcree model is acquired and described as Eq. (8) [23,24].
lnxw;T ¼ w1 ½A1 þ
B1 B2 þ C 1 lnðT=KÞ þ w2 ½ðA2 þ T=K T=K
þ C 2 lnðT=KÞ þ
2 w1 w2 X J ðw1 w2 Þi T=K i¼0 i
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ð8Þ
0.7653 0.8302 0.8800 0.9514 1.000
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A 1.138 1.302 1.556 1.824 2.159 2.507 2.867 3.263 3.648 0.5500 2.622 2.913 3.364 3.855 4.443 5.043 5.644 6.290 6.918
1.101 1.323 1.574 1.852 2.160 2.497 2.861 3.253 3.670 0.3520 2.534 2.952 3.410 3.908 4.444 5.019 5.629 6.274 6.950
1.095 1.292 1.515 1.767 2.051 2.369 2.724 3.119 3.556 0 2.602 2.987 3.413 3.882 4.398 4.962 5.577 6.246 6.972
2.476 2.999 3.551 4.212 4.885 5.660 6.494 7.335 8.300
2.543 2.863 3.366 3.890 4.539 5.199 5.869 6.595 7.288
2.459 2.908 3.404 3.949 4.539 5.175 5.854 6.573 7.328
2.499 2.900 3.349 3.849 4.403 5.016 5.691 6.432 7.242
4.289 4.862 5.658 6.536 7.522 8.536 9.708 10.94 12.29
4.413 4.906 5.690 6.505 7.502 8.504 9.503 10.58 11.59
4.266 4.979 5.757 6.599 7.502 8.463 9.477 10.54 11.64
4.405 5.050 5.762 6.546 7.407 8.347 9.371 10.48 11.69
4.903 5.385 6.052 6.891 7.776 8.781 9.964 11.30 12.71
4.721 5.231 6.041 6.888 7.919 8.954 9.981 11.08 12.12
4.564 5.306 6.114 6.986 7.919 8.910 9.953 11.04 12.18
4.729 5.404 6.148 6.965 7.858 8.832 9.890 11.04 12.27
3.514 4.065 4.734 5.476 6.304 7.211 8.169 9.154 10.24
4.034 4.468 5.152 5.878 6.756 7.641 8.520 9.462 10.36
3.899 4.530 5.217 5.960 6.756 7.603 8.496 9.434 10.41
4.034 4.611 5.248 5.946 6.711 7.544 8.450 9.431 10.49 1.585 1.765 1.998 2.255 2.534 2.812 3.121 3.444 3.783
1.412 1.576 1.824 2.102 2.434 2.777 3.124 3.499 3.873
1.364 1.596 1.851 2.131 2.435 2.763 3.116 3.492 3.89
1.387 1.601 1.840 2.105 2.398 2.719 3.072 3.457 3.877
0.9040 1.019 1.163 1.317 1.493 1.705 1.934 2.164 2.443
0.9055 1.009 1.162 1.341 1.550 1.769 1.991 2.231 2.477
0.8747 1.020 1.181 1.358 1.551 1.760 1.986 2.228 2.487
0.8924 1.031 1.184 1.355 1.543 1.751 1.978 2.226 2.497
9.225e-3 1.094e-2 1.328 e-2 1.632 e-2 1.995 e-2 2.411 e-2 2.870 e-2 3.395 e-2 3.989 e-2
9.2 e-3 1.09e-2 1.33e-2 1.63e-2 2.00e-2 2.41e-2 2.87e-2 3.40e-2 3.99e-2
8.9 e-3 1.10e-2 1.40e-2 1.70e-2 2.00e-2 2.40e-2 2.90e-2 3.40e-2 4.00e-2
9.0 e-3 1.11e-2 1.36e-2 1.65e-2 1.99e-2 2.39e-2 2.86e-2 3.39e-2 4.01e-2
a Standard uncertainties u are u(T) = 0.02 K, u(p) = 400 Pa; Relative standard uncertainty ur is ur (x) = 0.047. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.001. w represents the mass fraction of 1,4-dioxane in mixed solvents of 1,4-dioxane (w) + water(1-w)
1 0 c e 1 X @xw;T xw;T A e N xw;T
N
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN uP 2 c e u ti¼1 ðxw;T xw;T Þ
@lnxw;T @lnxw;T ¼ R @ð1=TÞ p @ ½ð1=TÞ ð1=T hm Þ p
o o DHsol DGsol T hm
5
ð9Þ
ð10Þ
ð11Þ ð12Þ ð13Þ ð14Þ where Thm refers to the mean harmonic temperature, nis the number of temperature points. R is the universal gas constant. Ti is the experiment temperature. o o o The results includingDHsol , DGsol and DSsol at Thm = 307.61 K were tabulated in Table 5. The obtained values are all positive. As expected, the values of dissolution enthalpy in each solvent are all positive, and with the range from 17.22 kJmol1 to 53.11 kJmol1. The dissolution process in pure and mixed solvents o values are from 12.41 to 27.73 kJmol1. is endothermic. The DGsol Apparently, the solubility of apixaban increases with decreasing o o DGsol in solution. Moreover, the values DSsol are all positive as well,
1 i¼1 T i
n T hm ¼ Pn
o DSsol ¼
o DGsol ¼ RT hm intercept
o DHsol ¼ R
Thermodynamic properties of solute dissolved in solvent mixtures may give essential information for the dissolution process. o The apparent dissolution enthalpy (DHsol ), apparent molar stano o dard Gibbs energy (DGsol ) and DSsol of apixaban dissolved in solvents can be computed by the famous van’t Hoff, [25,26] moreover, the results including intercept and slope of van’t Hoff plots was presented in Table S4.
3.4. Dissolution properties for the solution
c where N refers to the number of data points, and xw;T refers to the evaluated solubility. On the basis of the experimental solubility data, the parameters of Eqs. (3–10) are obtained by nonlinear least-squares method using Mathcad software. The obtained values of model parameters are tabulated in Tables S2 and S3, together with the values of RAD and RMSD. The solubility of apixaban in pure and binary mixed solvents was computed on the basis of the regressed model parameters. Tables S2 and S3 illustrate that for the pure solvents, the relative average deviations (RAD) between the calculated and experimental values are all no larger than 3.8 102, and the root-mean-square deviations (RMSD) are all smaller than 1.8510-4. For binary solvents mixture, the maximum value of relative average deviations (RAD) is 4.0102, and the root-meansquare deviations (RMSD) are all no larger than 2.8104. By comparison, the modified Apelblat equation and Jouyban-Acree model could be more suitable to correlate the result in pure and mixed solvents.
RMSD ¼
RAD ¼
where A1, B1, C1, A2, B2, C2 and Ji are the constants in the ApelblatJouyban-Acree model. In order to demonstrate the error calculated with different models, the relative average deviation (RAD) and root-meansquare deviation (RMSD) were used, which were described as Eqs. (9) and (10).
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J-A
1.138 1.302 1.556 1.824 2.159 2.507 2.867 3.263 3.648 0.6770 2.444 2.843 3.309 3.802 4.437 5.075 5.715 6.453 7.251 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
exp
288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
w T/K
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Table 3 Experimental (103xexp) and calculated (103xcal) mole fraction solubility of apixaban in mixed solvents of 1,4-dioxane (w) + water(1-w) with various mass fractions within the temperature range from T/K = (288.15 to 328.15) under 101.0 kPa.a
6
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Fig. 3. Mole fraction solubility (x) of apixaban in selected solvents at different temperature.
Fig. 4. Mole fraction solubility (x) of apixaban in binary mixed solvent 1,4-dioxane (w) + water(1-w) at different temperature.
Table 4 The comparison of Hildebrand solubility parameters between solute and 1,4-dioxane(w) + water (1-w).
w
Co-solvent composition in molar fraction
dMPa0.5,
Dd
x
0 0.352 0.55 0.677 0.7653 0.8302 0.88 0.9514 1 apixaban
0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1
47.86 45.12 42.38 39.64 36.90 34.17 31.43 25.95 20.47 30.02
17.84 15.1 12.36 9.62 6.88 4.15 1.41 4.07 9.55
1.328e-5 1.163e-3 1.998e-3 3.309 e-3 4.734 e-3 6.052 e-3 5.658 e-3 3.551 e-3 1.556 e-3
which indicate the dissolution process is apparently not only endothermic but also entropy-driving. 4. Conclusion The solubility profile of apixaban in pure and mixed solvents within the temperature range from (288.15 to 328.15) K under atmosphere pressure (101.3 kPa) was studied. The maximum mole
solubility in pure solvents was obtained in 1, 4-dioxane (3.648 103) at 328.15 K, and followed by methanol (1.967 103), acetone (7.885 104), ethanol (6.049 104), isopropanol (3.806 104), ethyl acetate (2.266 104), n-hexane (1.883 104), water (3.989 105). In mixtures of (1, 4-dioxane + water), it increased at first and then decreased with the increasing mass fraction of 1, 4-dioxane. Moreover, Hildebrand solubility parameter of solute is very close to the composition of
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C. Du et al. / J. Chem. Thermodynamics xxx (xxxx) xxx Table 5 The apparent dissolution standard enthalpy (DHosol ), apparent molar standard Gibbs energy (DGosol ) and DSosol of apixaban in pure and mixed solvents at mean harmonic temperature (307.61 K). Solvent
DGosol kJmol1
DHosol kJmol1
DSosol Jmol1K1
water methanol ethanol isopropanol n-hexane ethyl acetat acetone 1,4-dioxane 1,4-dioxane(w) + water (1-w) w = 0.352 w = 0.55 w = 0.677 w = 0.7653 w = 0.8302 w = 0.88 w = 0.9514
27.73 18.16 21.02 22.37 25.16 23.40 19.71 15.78
29.33 36.82 33.95 38.49 53.11 29.75 23.23 23.51
5.19 60.65 42.03 52.40 90.86 20.64 11.42 25.14
16.65 15.33 13.92 13.01 12.41 12.56 13.69
19.64 17.22 21.51 21.21 19.04 20.96 23.69
9.73 6.14 24.66 26.65 21.55 27.33 32.52
the mixed solvent when the solubility data reach the maximum. The analysis of apparent thermodynamic properties indicates that the dissolution process in all selected solvents is an endothermic and entropy driven process. Acknowledgement This project is supported by the priority academic program development of Jiangsu higher education institutions (1107047002). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jct.2019.105949. References [1] C.A. McHorney, E.D. Peterson, F. Laliberté, Comparison of adherence to rivaroxaban versus apixaban among patients with atrial fibrillation, Clin. Ther. 38 (2016) 2477–2488. [2] R.D. Lopes, J.H. Alexander, S.M. Al-Khatib, Apixaban for reduction in stroke and other ThromboemboLic events in atrial fibrillation (ARISTOTLE) trial: design and rationale, Am. Heart. J. 159 (2010) 331–339. [3] C.B. Granger, J.H. Alexander, J.J.V. McMurray, Apixaban versus warfarin in patients with atrial fibrillation, New. Engl. J. Med. 365 (2011) 981–992. [4] S.J. Connolly, J. Eikelboom, C. Joyner, Apixaban in patients with atrial fibrillation, New. Engl. J. Med. 364 (2011) 806–817. [5] Y. Bai, X.B. Shi, C.S. Ma, Meta-analysis of effectiveness and safety of oral anticoagulants in atrial fibrillation with focus on apixaban, Am. J. Cardiol. 120 (2017) 1689–1695. [6] Y. Chen, L. Li, J. Yao, Improving the solubility and bioavailability of apixaban via apixaban–oxalic acid cocrystal, Cryst. Growth. Des. 16 (2016) 2923–2930.
7
[7] J.H. Alexander, R.C. Becker, D.L. Bhatt, Apixaban, an oral, direct, selective factor Xa inhibitor, in combination with antiplatelet therapy after acute coronary syndrome: results of the Apixaban for prevention of Acute Ischemic and Safety Events (APPRAISE) trial, Circulation 119 (2009) 2877–2885. [8] C. Frost, J. Wang, S. Nepal, Apixaban, an oral, direct factor Xa inhibitor: single dose safety, pharmacokinetics, pharmacodynamics and food effect in healthy subjects, Brit. J. Clin. Pharmaco. 75 (2013) 476–487. [9] Z. Y. Xu, Q. Xu, Y. Qi, Method for synthesizing apixaban. CN 102675314 A, Jun 14, 2012. [10] W. Ji, D. Lu, S. Yang, Solubility and solution thermodynamics of cetilistat in water and (acetone, isopropyl alcohol, acetonitrile) binary solvent mixtures, J. Mol. Liq. 224 (2016) 1380–1387. [11] M H Zhang, Z T Zhang, Y Zhang, D Lin, X Y Xie, X Sui. Apixaban polymorph and preparation method thereof. CN 103,539,795, Jan 29, 2014. [12] R. Barbas, C. Puigjaner, R. Prohens, Assembling the Puzzle of Apixaban Solid Forms, Mol. Pharmaceut. 15 (2018) 1909–1916. [13] H. Yan, Z. Wang, J. Wang, Correlation of solubility and prediction of the mixing properties of capsaicin in different pure solvents, Ind. Eng. Chem. Res. 51 (2012) 2808–2813. [14] Y.M. Wang, Q.X. Yin, X.W. Sun, Y. Bao, J.B. Gong, B.H. Hou, Y.L. Wang, M.J. Zhang, C. Xie, H.X. Hao, Measurement and correlation of solubility of thiourea in two solvent mixtures from T = (283.15 to 313.15) K, J. Chem. Thermodyn. 94 (2016) 110–118. [15] I.M. Smallwood, Handbook of organic solvent properties, Amold, London, 1996. [16] D.M. Cristancho, D.R. Delgado, F. Martínez, Meloxicam solubility in ethanol + water mixtures according to the extended hildebrand solubility approach, J. Sol. Chem. 42 (2013) 1706–1716. [17] A. Apelblat, E. Manzurola, Solubilities of L-glutamic acid, 3-nitrobenzoic acid, p-toluic acid, calcium-l-lactate, calcium gluconate, magnesium-dl-aspartate, and magnesium-l-lactate in water, J. Chem. Thermodyn. 34 (2002) 1127–1136. [18] A. Apelblat, E. Manzurola, Solubilities of o-acetylsalicylic, 4-aminosalicylic, 3,5-dinitrosalicylic, and p-toluic acid, and magnesium-DL-aspartate in water from T = (278 to 348) K, J. Chem. Thermodyn. 31 (1999) 85–91. [19] A. Apelblat, E. Manzurola, Solubilities of L-aspartic, DL-aspartic, DL-glutamic, p-hydroxybenzoic, o-anistic, p-anisic, and itaconic acids in water from T=278K to T=345K, J. Chem. Thermodyn. 29 (1997) 1527–1533. [20] H. Buchowski, A. Ksiazczak, S. Pietrzyk, Solvent activity along a saturation line and solubility of hydrogen-bonding solids, J. Phys. Chem. 84 (1980) 975–979. [21] A. Jouyban, Review of the cosolvency models for predicting solubility of drugs in water-cosolvent mixtures, J. Pharm. Pharm. Sci. 11 (2008) 32–58. [22] S.H. Eghrary, R. Zarghami, F. Martinez, A. Jouyban, Solubility of 2-butyl-3benzofuranyl 4-(2-(diethylamino)ethoxy)-3,5-diiodophenyl ketone hydrochloride (amiodarone HCl) in ethanol + water and n-methyl-2pyrrolidone + water mixtures at various temperatures, J. Chem. Eng. Data 57 (2012) 1544–1550. [23] A. Jouyban, M.A.A. Fakhree, W.E. Jr, Acree, Comment on ‘‘Measurement and correlation of solubilities of (z)-2-(2-aminothiazol-4-yl)-2methoxyiminoacetic acid in different pure solvents and binary mixtures of water + (ethanol, methanol, or glycol), J. Chem. Eng. Data 57 (2012) 1344– 1346. [24] S. Vahdati, A. Shayanfar, J. Hanaee, F. Martínez, W.E. Jr, A. Jouyban Acree, Solubility of carvedilol in ethanol + propylene glycol mixtures at various temperatures, Ind. Eng. Chem. Res. 52 (2013) 16630–16636. [25] S. Han, L. Meng, C.B. Du, J. Xu, C. Cheng, J. Wang, H.K. Zhao, Solubility and solution thermodynamics of ethyl 5-amino-4-cyano-3-(2-ethoxy-2-oxoethyl)2-thiophenecarboxylate in nine organic solvents at elevated temperatures, J. Chem. Thermodyn. 97 (2016) 17–25. [26] A. Noubigh, C. Jeribi, A. Mgaidi, M. Abderrabba, Solubility of gallic acid in liquid mixtures of (ethanol + water) from (293.15 to 318.15) K, J. Chem. Thermodyn. 55 (2012) 75–78.
JCT 19-23
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J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Dissolution behavior and thermodynamic properties of apixaban in pure and mixed solvents Cunbin Du a, Yang Cong a, Ying Zhang a, Yi Xue a,b, Bin Qiao a, Tingting Ye a, Mingliang Wang a,⇑ a b
School of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, PR China Southeast University – Red Sun Research Center for Intelligent Industry, Nanjing 211189, PR China
a r t i c l e
i n f o
Article history: Received 20 August 2019 Received in revised form 3 September 2019 Accepted 7 September 2019 Available online xxxx Keywords: Apixaban Solubility Co-solvency phenomenon Thermodynamic properties
a b s t r a c t The solubility profile of apixaban in pure and mixed solvents within the temperature range from (288.15 to 328.15) K under atmosphere pressure (101.3 kPa) was studied and evaluated by some thermodynamics models. The solid state of apixaban in equilibrated form was characterized using powder X-ray diffraction (PXRD) technique. The maximum mole solubility in pure solvents was obtained in 1, 4-dioxane (3.648 103) at 328.15 K, and followed by methanol (1.967 103), acetone (7.885 104),ethanol (6.049 104), isopropanol (3.806 104), ethyl acetate (2.266 104), n-hexane (1.883 104), water (3.989 105). The solubility was quite small. Therefore, the solubility profile of apixaban in mixtures of (1, 4-dioxane + water) was further studied. Moreover, it increased at first and then decreased with the increasing mass fraction of 1, 4-dioxane. Moreover, the extended Hildebrand solubility approach (EHSA) was applied to evaluate the co-solvency phenomenon in mixed solvent at 298.15 K. In the following, the analysis of apparent thermodynamic properties indicates that the dissolution process in all selected solvents is an endothermic and entropy driven process. Ó 2019 Published by Elsevier Ltd.
1. Introduction Atrial fibrillation (AF) is the most common cardiac arrhythmia which is associated with increased risk of stroke, the prevalence of the disease in the United States in 2010 was 5.2 million and is expected to rise to by 2030 [1]. Vitamin K antagonists are highly effective in preventing stroke in patients with AF [2,3]. However, many patients are not suitable candidates for or are unwilling to receive vitamin K antagonist therapy, and these patients have a high risk of stroke [4]. In recent years, the development of non-vitamin K antagonist oral anticoagulants (NOACs), including direct thrombin inhibitor and factor Xa inhibitors have increased therapeutic options for anticoagulation and could potentially overcome many drawbacks of Vitamin K [5]. Apixaban (CAS Reg. No. 503612-47-3; chemical structure shown in Fig. 1), an oral direct factor Xa inhibitor with a trade name of Eliquis and marketed by Bristol-Myers Squibb [6], is a novel anticoagulant [7] that a few studies have demonstrated its safety and efficacy profile [4]. Factor Xa catalyzes the conversion of prothrombin to thrombin, the final enzyme in the coagulation cascade that is responsible for fibrin clot formation [8]. Apixaban has no direct effect on platelet aggregation, but by inhibiting factor Xa, it ⇑ Corresponding author. E-mail address: [email protected] (M. Wang).
indirectly decreases clot formation induced by thrombin. In industry, the process of preparing apixaban is complicated owing to many intermediates need to be prepared [9]. Like many other pharmaceutical manufacturing processes, solution crystallization is the final step to obtain apixaban products with high purity and high yield. The recrystallization process of apixaban needs the solubility data urgently [10]. So it is important to know the solubility data to select the best solvent for recrystallization in industrial production. Drug solid can exist in crystalline, amorphous or partially crystalline powders. Crystalline structures have long range molecular order, while amorphous structures are more disordered. Crystalline and amorphous materials show significantly different physicochemical properties, due to differences in microstructure, this affecting the stability, bioavailability and curative effect of the drug. Therefore, it is very important to analyze the crystal form of solid drug substance for controlling the quality and efficacy of drugs [11,12]. In this work, the isothermal saturation method was adopted to measure the solubility of apixaban in water, methanol, ethanol, isopropanol, ethyl acetate, n-hexane, 1,4-dioxane, acetone and (water + 1,4-dioxane) mixtures at temperatures ranging from 288.15 K to 328.15 K under atmospheric pressure. The modified Apelblat equation and kh equation were employed to correlate the experimental solubility in pure solvents, and the solubility in binary solvent mixtures was correlated by the Jouyban-Acree
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recrystallization in methanol and the final purity was 0.994 in mass fraction, which was confirmed by a high-performance liquid chromatography (HPLC). The solvents, including methanol, ethanol, isopropanol, ethyl acetate, n-hexane, 1,4-dioxane, and acetone with analytical grade were provided by Sinopharm Chemical Reagent Co., Ltd., China. The mass fraction purities of these solvents were all higher than 0.994, which were provided by supplier. The water used in the experiment is the secondary distilled water prepared by our laboratory. The purity and source information of the chemicals employed in this work is tabulated in Table 1. 2.2. Characterization of apixaban The X-ray diffractometer (XRD) used in this work is a Rigaku D/max-2500 (Rigaku, Japan) using Cu Ka radiation (1.5405 Å). In this work, a step size of 0.02°and a scanning rate of 10°/min over a diffraction angle (2h) range of 5°–50° were used before and after the experiments to confirm the form of apixaban. The patterns are shown in Fig. 2.
Fig. 1. Chemical structure of apixaban.
model, Modified Apelblat-Jouyban-Acree model and a combination of the Jouyban-Acree model with the van’t Hoff equation. The extended Hildebrand solubility approach (EHSA) was applied to evaluate the co-solvency phenomenon in mixed solvent at 298.15 K. Moreover, some apparent thermodynamic properties of dissolution process in all selected solvents were discussed. 2. Experimental section 2.1. Materials and apparatus Apixaban (with a mass fraction of 0.975) was purchased from MOLBASE Chemical Reagent Co., Ltd., China. It was purified by
2.3. Solubility measurement In this work, the solubility of apixaban in pure solvents including water, methanol, ethanol, isopropanol, ethyl acetate, n-hexane, 1,4-dioxane, acetone and binary solvent mixtures of water + 1,4dioxane were determined by the isothermal saturation method [13,14]. Saturated solutions of apixaban were prepared in the jacketed glass vessel. The temperature of the vessel was kept at the desired value through circulating water, which temperature was controlled by the smart thermostatic bath (model: DZKW-4) through the outer jacket of the jacketed glass vessel. The real temperature was displayed by using a mercury glass micro thermometer, which standard uncertainty is 0.02 K. For each
Table 1 Detailed information on the materials used in the work.
a b
Chemicals
Molar mass gmol1
Source
Initial mass fraction purity
Final mass fraction purity
Purification method
Analytical method
Apixaban
459.50
0.975
0.994
Recrystallization
HPLCa
Methanol Ethanol Isopropanol Ethyl acetate n-Hexane 1,4-Dioxane Acetone
32.04 46.07 60.06 88.11 86.18 88.11 58.08
MOLBASE Chemical Reagent Co., Ltd., China Sinopharm Chemical Reagent Co., Ltd.,China
0.995 0.996 0.994 0.995 0.996 0.994 0.995
0.995b 0.996b 0.994b 0.995b 0.996b 0.994b 0.995b
— — — — — — —
None
High-performance liquid phase chromatograph. the result was provided by supplier.
Fig. 2. X-ray powder diffraction patterns of apixaban in pure and mixed solvents.
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experiment, an excess amount of apixaban was introduced to the glass vessel. Continuous stirring was obtained for intensive mixing the suspension by means of a magnetic stirrer at a certain temperature. In order to determine the equilibration time of the solid–liquid system, about 0.5 mL liquid phase was taken out every an hour by using a 2 mL syringe connected with a 0.2 lm pore filter, and then analyzed by a the high-performance liquid phase chromatograph (HPLC). The same content of liquid phase indicated that the solution reached equilibrium. The results show that 12 h can ensure that the system is completely saturated. When the solid– liquid system arrived at equilibrium, the stirring was stopped and the solution was permitted to settle for 1 h before sampling. The upper portion was taken out with a 5 mL of preheated syringe connected with a filter (PTFE 0.2 lm), and transferred into a volumetric flask of 25 mL preweighed with the balance. The volumetric flask with sample was covered quickly with a rubber stopper. The total amount of the solution and flask was weighed again by using the balance. Then the sample was diluted to 25 mL with methanol, and analyzed with a high-performance liquid chromatography. All the experiments were carried out three times, and the average value was employed to calculate the mole fraction solubility. The saturated mole fraction solubility of apixaban (xw;T ) in pure and binary solvents are obtained by using Eqs. (1) and (2).
xw;T ¼
m1 =M1 m1 =M 1 þ m2 =M 2
ð1Þ
xw;T ¼
m1 =M 1 m1 =M 1 þ m2 =M 2 þ m3 =M 3
ð2Þ
Here x1 is the mole fraction solubility of apixaban; m1 refers to the mass of solute, m2 and m3 represent the mass of the solvents that constitute the solution. M1, M2 and M3 are the corresponding molecule mass of each solvent.
2.4. Analysis method The content of apixaban was analyzed using the Agilent-1260 high-performance liquid-phase chromatograph (HPLC). It was equipped with a reverse phase column with a type of LP-C18 (250 mm 4.6 mm). The temperature of reverse phase column was 303.15 K. The wavelength of the UV detector was set to 280 nm. Pure methanol was used as mobile phase with a flow rate of 1 mLmin1. Each analysis was repeated three times to check the repeatability and three samples were taken for each equilibrium solution at a given temperature. The average value was regarded as the final solubility data.
3. Results and discussion
3.2. Solubility data The measured mole fraction solubility of apixaban in pure and binary solvents were presented in Tables 2 and 3, and plotted in Figs. 3 and 4. It can be found that the solubility of apixaban is a function of temperature and solvent composition. The solubility of apixaban monotonically increased with an increasing temperature, and The maximum mole solubility in pure solvents was obtained in 1, 4-dioxane (3.648 103) at 328.15 K, and followed by methanol (1.967 103), acetone (7.885 104), ethanol (6.049 104), isopropanol (3.806 104), ethyl acetate (2.266 104), n-hexane (1.883 104), water (3.989 105). In three alcohols, it decreased with the increase of carbon chain length. While, in other solvents, it increased with the rising solubility parameters except for water. The influencing factors are comparatively complex, including the polarity of the studied solvents, intermolecular interactions between the solute and the solvent, hydrogen bonding interaction, and so on [15]. For the mixtures of (1, 4-dioxane + water), Fig. 4 show that the solubility increased monotonically with the temperature at all studied composition, but the composition dependence of the solubility had a maximum around the 1, 4-dioxane mass fraction w = 0.8302. After that, with the increase of co-solvent (1, 4-dioxane), the intermolecular force increases gradually, resulting in an increase of solubility while w 5 0.8302, however, it is vice versa at w﹥0.8302. It is acknowledged that solutes reach their maximum solubility value in solvents with the same solubility parameter. In order to estimate maximum solubility at certain mixture ratio, the extended Hildebrand solubility approach (EHSA) was applied to evaluate the cosolvency phenomenon in mixed solvent at 298.15 K. [16] The relevant calculation process is shown in Table S1. In this work, Hilde
brand solubility parameter is 30.02 MPa0.5, and the D d factor between this drug and mixed solvent is presented in Table 4. The minimum value is founded at w = 0.88 (in mass fraction). It is very close to the composition of the mixed solvent when the solubility data reach the maximum (at w = 0.8302). It may be the deviation of estimating the molar volume and partial solubility parameters of solute. 3.3. Solubility modeling In this work, some models were employed to correlated the solubility of apixaban in pure and binary solvents, which correspond to the modified Apelblat equation [17–19], kh equation [20], Jouyban-Acree model [21,22], Modified Apelblat-Jouyban-Acree model [23,24] and a combination of the Jouyban-Acree model with the van’t Hoff equation [23,24]. 3.3.1. Modified Apelblat equation The modified Apelblat equation is a semi-empirical equation. It describes the dependence of mole fraction solubility on the absolute temperature T, and expressed as equation (3) [17–19].
3.1. XRD analysis The results of XRD were presented in Fig. 2. From Fig. 2, it can be seen that all the XPRD patterns of solid phase of apixaban in equilibrium with its solution have the same characteristic peaks with the raw material. Therefore, no polymorph transformation or solvate formation is observed during the whole experiment. In addition, compared the analysis of X-ray powder diffraction in references 11 and 12, in this work, the characteristic peaks of Xray powder diffraction are expressed at 2h angle of 8.5°, 10.0°, 10.5°, 11.2°, 12.3°, 16.3°, 17.0°, 18.5°, 18.9°, 19.6°, 21.1°, 21.5°, 22.0 ± 0.2°, 22.3°, 24.8°, 27.0°, 29.9°, and 32.7°, it is almost the same as the XRD curves of apixaban form I in references 11 and 12.
lnx ¼ A þ
B þ ClnT T
ð3Þ
where x is the mole fraction solubility of apixaban in pure organic solvents; A, B and C are the adjustable parameters in the modified Apelblat equation. 3.3.2. Buchowski–Ksiazaczak kh equation The Buchowski–Ksiazaczak kh equation, expressed as Eq. (4), is another equation to describe the solubility of solid in pure solvent. [20]. The Buchowski–Ksiazaczak kh equation has two parameters k and h, and Tm is the melting temperature of apixaban in Kelvin.
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Table 2 Experimental (xe) and calculated (xcal) mole fraction solubility of apixaban in different solvents at the temperature range from T = (288.15 To 328.15) K under 101.3 kPa.a T/K
Water 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Methanol 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Ethanol 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Isopropanol 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Ethyl acetate 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 n-Hexane 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 1,4-Dioxane 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 Acetone 288.15
1000xe
Table 2 (continued) T/K
1000xe
293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
0.2821 0.3279 0.3862 0.4569 0.5345 0.6121 0.7003 0.7885
1000xcal Modified Apelblat equation
kh equation
9.225e-3 1.094e-2 1.328 e-2 1.632 e-2 1.995 e-2 2.411 e-2 2.870 e-2 3.395 e-2 3.989 e-2
8.899 1.102 1.353 1.649 1.995 2.397 2.860 3.391 3.998
9.270 9.880 1.053 1.124 1.199 1.280 1.369 1.464 1.568
0.3103 0.3981 0.5176 0.6687 0.8620 1.090 1.344 1.637 1.967
0.2976 0.3987 0.5245 0.6785 0.8641 1.084 1.340 1.635 1.970
0.3129 0.4057 0.5216 0.6653 0.8425 1.060 1.324 1.645 2.032
0.1076 0.1373 0.1799 0.2256 0.2806 0.3456 0.4203 0.5035 0.6049
0.1076 0.1395 0.1783 0.2250 0.2803 0.3451 0.4201 0.5061 0.6035
0.1106 0.1403 0.1768 0.2211 0.2748 0.3395 0.4170 0.5096 0.6198
5.716e-2 7.205 e-2 9.583 e-2 0.1297 0.1752 0.2194 0.2652 0.3229 0.3806
5.207 e-2 7.324 e-2 0.1000 0.1328 0.1718 0.2168 0.2673 0.3224 0.3809
5.771 e-2 7.573 e-2 9.851 e-2 0.1271 0.1627 0.2068 0.2610 0.3275 0.4084
5.098 e-2 5.925 e-2 7.210 e-2 8.852 e-2 0.1054 0.1285 0.1563 0.1884 0.2266
4.973 e-2 6.013 e-2 7.271 e-2 8.794 e-2 0.1064 0.1286 0.1555 0.1879 0.2271
4.851 e-2 5.981 e-2 7.327 e-2 8.925 e-2 0.1081 0.1303 0.1564 0.1869 0.2225
1.241 e-2 1.845 e-2 2.879 e-2 4.180 e-2 5.760 e-2 7.754 e-2 0.1048 0.1427 0.1883
1.328 e-2 1.959 e-2 2.837 e-2 4.040 e-2 5.659 e-2 7.806 e-2 0.1061 0.1422 0.1882
1.319 e-2 1.922 e-2 2.764 e-2 3.930 e-2 5.524 e-2 7.682 e-2 0.1058 0.1442 0.1949
1.138 1.302 1.556 1.824 2.159 2.507 2.867 3.263 3.648
1.100 1.322 1.571 1.850 2.157 2.493 2.857 3.248 3.665
0.9954 1.246 1.549 1.913 2.348 2.866 3.480 4.205 5.060
0.2523
0.2410
0.2447
e-3 e-2 e-2 e-2 e-2 e-2 e-2 e-2 e-2
e-3 e-3 e-2 e-2 e-2 e-2 e-2 e-2 e-2
1000xcal Modified Apelblat equation
kh equation
0.2855 0.3361 0.3932 0.4573 0.5289 0.6084 0.6965 0.7934
0.2872 0.3357 0.3910 0.4538 0.5250 0.6058 0.6973 0.8010
a Standard uncertainties u are u(T) = 0.02 K, u(p) = 400 Pa; Relative standard uncertainty ur is ur (x) = 0.045.
During calculation, it is cited from reference 12, and the value is 511.15 K.
kð1 xÞ 1 1 ¼ kh ln 1 þ x T Tm
ð4Þ
3.3.3. Jouyban-Acree model The Jouyban-Acree model provides accurate mathematical descriptions for the solubility dependence on both temperature and solvent composition for binary and ternary mixed solvents [21,22], and is described as Eq. (5).
lnxw;T ¼ w1 lnx1;T þ w2 lnx2;T þ
2 w1 w2 X J ðw1 w2 Þi T i¼0 i
ð5Þ
where xw,T is the solubility of solute in mole fraction in the binary solvent mixtures at temperature T in Kelvin; w1 and w2 denote the mass fraction of solvents 1 (1,4-dioxane) and 2 (water) in the absence of the solute (apixaban), respectively; x1,T and x2,T are the mole fraction solubility of solute in pure solvent, and Ji stands for the Jouyban-Acree model parameters. 3.3.4. Van’t Hoff-Jouyban-Acree model A linear van’t Hoff equation is established for providing precise predictions of a solute dissolved in a solvent at a limited temperature range. It describes the dependence of the natural logarithm of the mole fraction solubility on the reciprocal of absolute temperature and is expressed as Eq. (6) [24]. The solubility of a solute in pure solvent at different temperatures can be calculated with the van’t Hoff equation.
lnx ¼ A þ B=TðKÞ
ð6Þ
where A and B are equation constants. Substituting Eqs. (6) into (5), one can obtain the Van’t Hoff-Jouyban-Acree model expressed as Eq. (7) [23,24].
lnxw;T ¼ w1 ðA1 þ
2 B1 B2 w1 w2 X J ðw1 w2 Þi Þ þ w2 ðA2 þ Þþ T=K T=K T=K i¼0 i
ð7Þ Here A1, B1, A2, B2 and Ji are the model constants. This model can provide an estimation of the solute solubility in binary solvent mixtures at different temperatures and composition of solvents. 3.3.5. Modified Apelblat-Jouyban-Acree model Similarly, substituting Eqs. (3) into (5), the Apelblat-JouybanAcree model is acquired and described as Eq. (8) [23,24].
lnxw;T ¼ w1 ½A1 þ
B1 B2 þ C 1 lnðT=KÞ þ w2 ½ðA2 þ T=K T=K
þ C 2 lnðT=KÞ þ
2 w1 w2 X J ðw1 w2 Þi T=K i¼0 i
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ð8Þ
0.7653 0.8302 0.8800 0.9514 1.000
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A
exp
J-A
A-J-A
V-J-A 1.138 1.302 1.556 1.824 2.159 2.507 2.867 3.263 3.648 0.5500 2.622 2.913 3.364 3.855 4.443 5.043 5.644 6.290 6.918
1.101 1.323 1.574 1.852 2.160 2.497 2.861 3.253 3.670 0.3520 2.534 2.952 3.410 3.908 4.444 5.019 5.629 6.274 6.950
1.095 1.292 1.515 1.767 2.051 2.369 2.724 3.119 3.556 0 2.602 2.987 3.413 3.882 4.398 4.962 5.577 6.246 6.972
2.476 2.999 3.551 4.212 4.885 5.660 6.494 7.335 8.300
2.543 2.863 3.366 3.890 4.539 5.199 5.869 6.595 7.288
2.459 2.908 3.404 3.949 4.539 5.175 5.854 6.573 7.328
2.499 2.900 3.349 3.849 4.403 5.016 5.691 6.432 7.242
4.289 4.862 5.658 6.536 7.522 8.536 9.708 10.94 12.29
4.413 4.906 5.690 6.505 7.502 8.504 9.503 10.58 11.59
4.266 4.979 5.757 6.599 7.502 8.463 9.477 10.54 11.64
4.405 5.050 5.762 6.546 7.407 8.347 9.371 10.48 11.69
4.903 5.385 6.052 6.891 7.776 8.781 9.964 11.30 12.71
4.721 5.231 6.041 6.888 7.919 8.954 9.981 11.08 12.12
4.564 5.306 6.114 6.986 7.919 8.910 9.953 11.04 12.18
4.729 5.404 6.148 6.965 7.858 8.832 9.890 11.04 12.27
3.514 4.065 4.734 5.476 6.304 7.211 8.169 9.154 10.24
4.034 4.468 5.152 5.878 6.756 7.641 8.520 9.462 10.36
3.899 4.530 5.217 5.960 6.756 7.603 8.496 9.434 10.41
4.034 4.611 5.248 5.946 6.711 7.544 8.450 9.431 10.49 1.585 1.765 1.998 2.255 2.534 2.812 3.121 3.444 3.783
1.412 1.576 1.824 2.102 2.434 2.777 3.124 3.499 3.873
1.364 1.596 1.851 2.131 2.435 2.763 3.116 3.492 3.89
1.387 1.601 1.840 2.105 2.398 2.719 3.072 3.457 3.877
0.9040 1.019 1.163 1.317 1.493 1.705 1.934 2.164 2.443
0.9055 1.009 1.162 1.341 1.550 1.769 1.991 2.231 2.477
0.8747 1.020 1.181 1.358 1.551 1.760 1.986 2.228 2.487
0.8924 1.031 1.184 1.355 1.543 1.751 1.978 2.226 2.497
9.225e-3 1.094e-2 1.328 e-2 1.632 e-2 1.995 e-2 2.411 e-2 2.870 e-2 3.395 e-2 3.989 e-2
9.2 e-3 1.09e-2 1.33e-2 1.63e-2 2.00e-2 2.41e-2 2.87e-2 3.40e-2 3.99e-2
8.9 e-3 1.10e-2 1.40e-2 1.70e-2 2.00e-2 2.40e-2 2.90e-2 3.40e-2 4.00e-2
9.0 e-3 1.11e-2 1.36e-2 1.65e-2 1.99e-2 2.39e-2 2.86e-2 3.39e-2 4.01e-2
a Standard uncertainties u are u(T) = 0.02 K, u(p) = 400 Pa; Relative standard uncertainty ur is ur (x) = 0.047. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.001. w represents the mass fraction of 1,4-dioxane in mixed solvents of 1,4-dioxane (w) + water(1-w)
1 0 c e 1 X @xw;T xw;T A e N xw;T
N
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN uP 2 c e u ti¼1 ðxw;T xw;T Þ
@lnxw;T @lnxw;T ¼ R @ð1=TÞ p @ ½ð1=TÞ ð1=T hm Þ p
o o DHsol DGsol T hm
5
ð9Þ
ð10Þ
ð11Þ ð12Þ ð13Þ ð14Þ where Thm refers to the mean harmonic temperature, nis the number of temperature points. R is the universal gas constant. Ti is the experiment temperature. o o o The results includingDHsol , DGsol and DSsol at Thm = 307.61 K were tabulated in Table 5. The obtained values are all positive. As expected, the values of dissolution enthalpy in each solvent are all positive, and with the range from 17.22 kJmol1 to 53.11 kJmol1. The dissolution process in pure and mixed solvents o values are from 12.41 to 27.73 kJmol1. is endothermic. The DGsol Apparently, the solubility of apixaban increases with decreasing o o DGsol in solution. Moreover, the values DSsol are all positive as well,
1 i¼1 T i
n T hm ¼ Pn
o DSsol ¼
o DGsol ¼ RT hm intercept
o DHsol ¼ R
Thermodynamic properties of solute dissolved in solvent mixtures may give essential information for the dissolution process. o The apparent dissolution enthalpy (DHsol ), apparent molar stano o dard Gibbs energy (DGsol ) and DSsol of apixaban dissolved in solvents can be computed by the famous van’t Hoff, [25,26] moreover, the results including intercept and slope of van’t Hoff plots was presented in Table S4.
3.4. Dissolution properties for the solution
c where N refers to the number of data points, and xw;T refers to the evaluated solubility. On the basis of the experimental solubility data, the parameters of Eqs. (3–10) are obtained by nonlinear least-squares method using Mathcad software. The obtained values of model parameters are tabulated in Tables S2 and S3, together with the values of RAD and RMSD. The solubility of apixaban in pure and binary mixed solvents was computed on the basis of the regressed model parameters. Tables S2 and S3 illustrate that for the pure solvents, the relative average deviations (RAD) between the calculated and experimental values are all no larger than 3.8 102, and the root-mean-square deviations (RMSD) are all smaller than 1.8510-4. For binary solvents mixture, the maximum value of relative average deviations (RAD) is 4.0102, and the root-meansquare deviations (RMSD) are all no larger than 2.8104. By comparison, the modified Apelblat equation and Jouyban-Acree model could be more suitable to correlate the result in pure and mixed solvents.
RMSD ¼
RAD ¼
where A1, B1, C1, A2, B2, C2 and Ji are the constants in the ApelblatJouyban-Acree model. In order to demonstrate the error calculated with different models, the relative average deviation (RAD) and root-meansquare deviation (RMSD) were used, which were described as Eqs. (9) and (10).
C. Du et al. / J. Chem. Thermodynamics xxx (xxxx) xxx
J-A
1.138 1.302 1.556 1.824 2.159 2.507 2.867 3.263 3.648 0.6770 2.444 2.843 3.309 3.802 4.437 5.075 5.715 6.453 7.251 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
exp
288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15
w T/K
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Table 3 Experimental (103xexp) and calculated (103xcal) mole fraction solubility of apixaban in mixed solvents of 1,4-dioxane (w) + water(1-w) with various mass fractions within the temperature range from T/K = (288.15 to 328.15) under 101.0 kPa.a
6
C. Du et al. / J. Chem. Thermodynamics xxx (xxxx) xxx
Fig. 3. Mole fraction solubility (x) of apixaban in selected solvents at different temperature.
Fig. 4. Mole fraction solubility (x) of apixaban in binary mixed solvent 1,4-dioxane (w) + water(1-w) at different temperature.
Table 4 The comparison of Hildebrand solubility parameters between solute and 1,4-dioxane(w) + water (1-w).
w
Co-solvent composition in molar fraction
dMPa0.5,
Dd
x
0 0.352 0.55 0.677 0.7653 0.8302 0.88 0.9514 1 apixaban
0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1
47.86 45.12 42.38 39.64 36.90 34.17 31.43 25.95 20.47 30.02
17.84 15.1 12.36 9.62 6.88 4.15 1.41 4.07 9.55
1.328e-5 1.163e-3 1.998e-3 3.309 e-3 4.734 e-3 6.052 e-3 5.658 e-3 3.551 e-3 1.556 e-3
which indicate the dissolution process is apparently not only endothermic but also entropy-driving. 4. Conclusion The solubility profile of apixaban in pure and mixed solvents within the temperature range from (288.15 to 328.15) K under atmosphere pressure (101.3 kPa) was studied. The maximum mole
solubility in pure solvents was obtained in 1, 4-dioxane (3.648 103) at 328.15 K, and followed by methanol (1.967 103), acetone (7.885 104), ethanol (6.049 104), isopropanol (3.806 104), ethyl acetate (2.266 104), n-hexane (1.883 104), water (3.989 105). In mixtures of (1, 4-dioxane + water), it increased at first and then decreased with the increasing mass fraction of 1, 4-dioxane. Moreover, Hildebrand solubility parameter of solute is very close to the composition of
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C. Du et al. / J. Chem. Thermodynamics xxx (xxxx) xxx Table 5 The apparent dissolution standard enthalpy (DHosol ), apparent molar standard Gibbs energy (DGosol ) and DSosol of apixaban in pure and mixed solvents at mean harmonic temperature (307.61 K). Solvent
DGosol kJmol1
DHosol kJmol1
DSosol Jmol1K1
water methanol ethanol isopropanol n-hexane ethyl acetat acetone 1,4-dioxane 1,4-dioxane(w) + water (1-w) w = 0.352 w = 0.55 w = 0.677 w = 0.7653 w = 0.8302 w = 0.88 w = 0.9514
27.73 18.16 21.02 22.37 25.16 23.40 19.71 15.78
29.33 36.82 33.95 38.49 53.11 29.75 23.23 23.51
5.19 60.65 42.03 52.40 90.86 20.64 11.42 25.14
16.65 15.33 13.92 13.01 12.41 12.56 13.69
19.64 17.22 21.51 21.21 19.04 20.96 23.69
9.73 6.14 24.66 26.65 21.55 27.33 32.52
the mixed solvent when the solubility data reach the maximum. The analysis of apparent thermodynamic properties indicates that the dissolution process in all selected solvents is an endothermic and entropy driven process. Acknowledgement This project is supported by the priority academic program development of Jiangsu higher education institutions (1107047002). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jct.2019.105949. References [1] C.A. McHorney, E.D. Peterson, F. Laliberté, Comparison of adherence to rivaroxaban versus apixaban among patients with atrial fibrillation, Clin. Ther. 38 (2016) 2477–2488. [2] R.D. Lopes, J.H. Alexander, S.M. Al-Khatib, Apixaban for reduction in stroke and other ThromboemboLic events in atrial fibrillation (ARISTOTLE) trial: design and rationale, Am. Heart. J. 159 (2010) 331–339. [3] C.B. Granger, J.H. Alexander, J.J.V. McMurray, Apixaban versus warfarin in patients with atrial fibrillation, New. Engl. J. Med. 365 (2011) 981–992. [4] S.J. Connolly, J. Eikelboom, C. Joyner, Apixaban in patients with atrial fibrillation, New. Engl. J. Med. 364 (2011) 806–817. [5] Y. Bai, X.B. Shi, C.S. Ma, Meta-analysis of effectiveness and safety of oral anticoagulants in atrial fibrillation with focus on apixaban, Am. J. Cardiol. 120 (2017) 1689–1695. [6] Y. Chen, L. Li, J. Yao, Improving the solubility and bioavailability of apixaban via apixaban–oxalic acid cocrystal, Cryst. Growth. Des. 16 (2016) 2923–2930.
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JCT 19-23
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