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Oct 19, 2016 - Songgu Wu,. †,‡. Shijie Xu,. †,‡. Kangli Li,. †,‡ ...... (22) Abbott, M. M.; Smith, J. M.; Van Ness, H. C. Introduction to ...
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Solubility Correlation and Thermodynamic Analysis of Sorafenib Free Base and Sorafenib Tosylate in Monosolvents and Binary Solvent Mixtures Shuang Jiang,†,‡ Yujia Qin,†,‡ Songgu Wu,†,‡ Shijie Xu,†,‡ Kangli Li,†,‡ Peng Yang,†,‡ Kaifei Zhao,†,‡ Lanlan Lin,†,‡ and Junbo Gong*,†, ‡ †

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China ‡ The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin 300072, China S Supporting Information *

ABSTRACT: The solubility of sorafenib free base (SFB) and sorafenib tosylate (ST) in five monosolvents and binary solvents of 2-propanol + 1,4-dioxane was measured over the temperature ranged from 283.15 to 333.15 K by using a UV spectroscopy method. The solubility of SFB and ST in different monosolvents increases with increasing temperature, while in the binary solvents, the solubility shows the maximum value at 0.50 and 0.75 2-propanol mole fraction for SFB and ST, respectively. The Apelblat model and the CNIBS/R-K model were applied to correlate the solubility data, which shows that the two selected thermodynamic models could give satisfactory results. Moreover, mixing thermodynamic properties of enthalpy, entropy, and Gibbs free energy of SFB and ST were obtained based on the nonrandom two-liquid model for further understanding of the mixing behavior.

1. INTRODUCTION

trials, including hepatocellular, renal cell, breast and colorectal carcinomas, and melanoma.3 Further, sorafenib has been combined with other active agents producing higher efficacy and lower side effects.4,5 As a kind of significant anticarcinogen, sorafenib has attracted considerable attention in the field of pharmacy and medicinal chemistry. Salt formation6,7 is the most common and effective method to increase solubility and dissolution rates of acidic or basic drugs. During the past years, plenty of work has been done to understand the behavior of salts and their free acid (base) in water or mixed-aqueous solvents,8,9 while only little attention is paid to the solubility in organic solvents. Given that pharmaceutical salts are usually prepared and purified from organic solvents, it is essential to get the solubility data of acidic or basic drugs and their salts, which is directly relevant to the design and optimization of the crystallization procedure. However, few studies have investigated the solubility of SFB and ST in organic solvents to date. In this work, a UV spectroscopy method was used to determine the solubility of SFB and ST in five monoalcoholic solvents and 2-propanol + 1,4-dioxane mixtures from 283.15 to 333.15 K at atmospheric pressure. The experimental data were correlated by the Apelblat model and the CNIBS/R-K model. Moreover, the mixing enthalpy, entropy, and Gibbs free energy

Sorafenib, an oral multitarget tyrosine kinase inhibitor directing to tumor cell proliferation and angiogenesis,1,2 has been crystallized currently as sorafenib free base (SFB, C21H16ClF3N4O3, CAS Registry No: 284461-73-0, Figure 1) and sorafenib tosylate (ST, C21H16ClF3N4O3·C7H8O3S, CAS Registry No: 475207-59-1, Figure 1). Sorafenib has shown promise as an efficacious therapeutic acting on various tumor types in clinical and preclinical

Received: July 13, 2016 Accepted: October 19, 2016

Figure 1. Chemical structure of SFB (a) and ST (b). © XXXX American Chemical Society

A

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of SFB and ST were calculated and discussed based on the nonrandom two-liquid (NRTL) model.

2. EXPERIMENT 2.1. Materials. SFB was supplied by Wuhan Hongxinkang Fine Chemical Co., Ltd. with mass purity >0.99, and ST was supplied by Huai’an Xinlicheng Chemical Co., Ltd. with mass purity >0.998. The solvents used in the experiment, including 1-propanol, 2-propanol, 1-butanol, 2-methyl-1-propanol, 1-pentanol, and 1,4-dioxane, were analytical grade provided by Tianjin Jiangtian Chemical Technique Co., Ltd. All chemicals mentioned above were used without further purification. More detailed information about materials used in this study has been listed in Table 1. Table 1. Detailed Description of Materials Used in Experiments chemical name Sorafenib free base Sorafenib tosylate 1-propanol 2-propanol 1-butanol 2-methyl-1propanol 1-pentanol 1,4-dioxane a

source Wuhan Hongxinkang Fine Chemical Co., Ltd. Huai’an Xinlicheng Chemical Co., Ltd. Tianjin Jiangtian Chemical Technique Co., Ltd. Tianjin Jiangtian Chemical Technique Co., Ltd. Tianjin Jiangtian Chemical Technique Co., Ltd. Tianjin Jiangtian Chemical Technique Co., Ltd. Tianjin Jiangtian Chemical Technique Co., Ltd. Tianjin Jiangtian Chemical Technique Co., Ltd.

mass fraction purity

analysis method

>0.99

HPLCa

>0.998

HPLCa

>0.995

GCb

>0.995

GCb

>0.995

GCb

>0.995

GCb

>0.995

GCb

>0.995

GCb

Figure 2. Absorbance versus concentration (μg/mL) calibration curve: red ●, SFB; blue ■, ST.

High-performance liquid chromatography. bGas chromatography.

2.2. Characterization. The SFB and ST samples before and after experiments were tested by X-ray power diffraction (PXRD) to ensure the crystal form remained the same, which was carried out on Rigaku D/max-2500 (Rigaku, Japan) using Cu Kα radiation (0.15405 nm) over the 2-theta range from 2° to 50° with the scanning rate of 1 step per second. The melting properties of SFB and ST were determined by differential scanning calorimetry (DSC, 1/500, Mettler Toledo, Switzerland) under a nitrogen atmosphere. Approximately 6 mg of sample (SFB or ST) was added to a standard DSC aluminum pan and heated from 298.15 to 523.15 K at the rate of 10 K min−1. The experiment of DSC was conducted for three times. 2.3. Solubility Measurement. The saturated concentrations of SFB and ST in different solvents were determined via a UV spectroscopy method. Before measuring the solubility of the samples, the calibration curves of the two solutes in 2-propanol were obtained on a UV-3010 spectrophotometer (HITACHI, Japan) at 298.15 K and atmospheric pressure. The maximal absorptions of SFB and ST are both 265 nm, which shows great agreement with Shimada and his co- workers’ work.10 The linear calibration curves for SFB and ST are given in Figure 2 with R2 = 0.9995 and 0.9993, respectively. The apparatus and procedures used in this research were similar to those employed in previous studies.11 Briefly, an excess mount of solid (SFB or ST) was added into a 50 mL flask containing approximately 20 g of mixed or neat solvent

Figure 3. PXRD patterns of SFB and ST.

Figure 4. DSC curves of SFB and ST at a heating rate of 10 K min−1.

prepared in advance. Then the sealed flasks were put into a thermostatic bath shaker (type 501A, Shanghai Laboratory B

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Table 2. Experimental and Correlated Mole Fraction Solubility of SFB and ST in Monosolvents (p = 0.1 MPa)a SFB T/K

10

3

xexp SFB

283.15 293.15 303.15 313.15 323.15 333.15

0.6778 0.8879 1.369 2.045 3.134 4.565

283.15 293.15 303.15 313.15 323.15 333.15

0.5092 0.6380 1.039 1.520 2.261 3.251

283.15 293.15 303.15 313.15 323.15 333.15

0.6453 0.8159 1.298 1.933 2.881 4.165

283.15 293.15 303.15 313.15 323.15 333.15

0.2525 0.3792 0.7154 1.044 1.553 2.164

283.15 293.15 303.15 313.15 323.15 333.15

0.5994 0.8188 1.222 1.731 2.560 3.774

ST 10

3

xcal SFB

1-Propanol 0.6235 0.9303 1.388 2.071 3.084 4.583 2-Propanol 0.4626 0.6940 1.033 1.526 2.239 3.260 1-Butanol 0.5866 0.8776 1.306 1.935 2.851 4.177 2-Methyl-1-propanol 0.2357 0.4155 0.6836 1.058 1.551 2.164 1-Pentanol 0.5784 0.8230 1.188 1.736 2.562 3.811

xexp ST

103 xcal ST

0.1392 0.1752 0.2584 0.3444 0.4557 0.6217

0.1356 0.1850 0.2517 0.3412 0.4609 0.6202

0.0781 0.1087 0.1604 0.2293 0.3105 0.4417

0.0777 0.1116 0.1589 0.2248 0.3156 0.4402

0.1317 0.1626 0.2379 0.3162 0.4192 0.5410

0.1247 0.1730 0.2357 0.3158 0.4168 0.5423

0.0618 0.0967 0.1489 0.2155 0.2840 0.4225

0.0660 0.0980 0.1436 0.2076 0.2964 0.4185

0.0578 0.0876 0.1482 0.2089 0.2717 0.3942

0.0603 0.0933 0.1395 0.2020 0.2843 0.3900

10

3

Figure 5. Experimental and calculated solubility data of SFB in monosolvents at temperature ranging from 283.15 to 333.15 K: black ■, 1-propanol; red ●, 2-propanol; blue ▲, 1-butanol; green ▼, 2-methyl-1-propanol; pink ◀, 1-pentanol; , calculated data by the Apelblat equation.

a exp xSFB

cal cal and xexp ST are the experimental solubility. xSFB and xST are the calculated solubility according to the Apelblat equation. The standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.08. The relative standard uncertainty of pressure is ur(p) = 0.05.

Figure 6. Experimental and calculated solubility data of ST in monosolvents at temperature ranging 283.15 to 333.15 K: black ■, 1-propanol; red ●, 2-propanol; blue ▲, 1-butanol; green ▼, 2-methyl1-propanol; pink ◀, 1-pentanol; , calculated data by the Apelblat equation.

Instrument Works Co., Ltd., China) with a temperature uncertainty of ±0.05 K for 20 h, which had been confirmed long enough to reach the equilibrium by a preliminary experiment. Agitation was stopped and the slurry was kept still for about 1 h to ensure the solid precipitated to the bottom. Subsequently, m g of saturated supernatant was filtered through an organic membrane (0.22 μm) and diluted to an appropriate concentration that was favorable for UV assay. Following that, the concentration of dilution was investigated by measuring the UV light absorbance at 265 nm with a 1 cm path length cell and interpolation from previously constructed UV spectrophotometric calibration curves. All the solubility experiments were run in triplicate at least for average. According to the measured data, the mole fraction solubility xSFB (for SFB) and xST (for ST) can be calculated by the following equations: A ×V ms = (1) α

x=

ms /Ms ms /Ms + ∑ m1/M1

(2)

where x refers to mole fraction solubility of solute. A represents absorbance obtained from the UV spectrophotometer. α is the slope of calibration curve with value of 0.1058 and 0.0780 for the solute of SFB and ST, respectively. V is the diluted volume. ms, ml respectively stand for the mass of solute and solvents, and Ms, Ml are the corresponding molar masses.

3. RESULTS AND DISCUSSION 3.1. Characterization of Samples. The PXRD patterns of SFB and ST are given in Figure 3. The identical patterns obtained before and after the experiments suggests that there is no phase transition during the solubility measurement, which guarantees the correctness and availability of the experimental data. C

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Table 3. Experimental and Correlated Mole Fraction Solubility of SFB and ST in the (2-Propanol + 1,4-Dioxane) Binary Solvents (p = 0.1 MPa)a SFB x0A

103 xexp SFB

0.14 0.27 0.39 0.49 0.59 0.69 0.77 0.85 0.93 1.00

1.3682 2.4980 3.2913 3.5809 3.4665 3.0837 2.2916 1.5212 0.9325 0.5092

0.14 0.27 0.39 0.49 0.59 0.69 0.77 0.85 0.93 1.00

1.7426 2.9082 3.8089 4.3388 4.2025 3.7383 2.8645 1.9438 1.2769 0.6380

0.14 0.27 0.39 0.49 0.59 0.69 0.77 0.85 0.93 1.00

2.2383 3.6701 4.7247 5.2774 5.0424 4.3942 3.4343 2.5743 1.7598 1.0386

SFB

ST 103 xcal SFB T = 283.14 K 1.3673 2.4743 3.3038 3.6406 3.4928 2.9811 2.2758 1.5515 0.9398 0.5045 T = 293.14 K 1.7104 2.9515 3.8609 4.2732 4.1895 3.6831 2.8929 2.0107 1.2227 0.6455 T = 303.14 K 2.2406 3.6796 4.7462 5.1975 5.0353 4.4047 3.5119 2.5630 1.7138 1.0524

103 xexp ST

103 xcal ST

x0A

103 xexp SFB

0.0240 0.0495 0.0779 0.1031 0.1165 0.1344 0.1319 0.1222 0.1032 0.0781

0.0230 0.0512 0.0787 0.1011 0.1184 0.1297 0.1324 0.1240 0.1042 0.0772

0.14 0.27 0.39 0.49 0.59 0.69 0.77 0.85 0.93 1.00

2.8374 4.8369 5.9569 6.3216 6.0515 5.4088 4.3595 3.2690 2.2585 1.5200

0.0305 0.0630 0.0990 0.1202 0.1407 0.1611 0.1672 0.1514 0.1321 0.1087

0.0303 0.0638 0.0964 0.1231 0.1436 0.1572 0.1616 0.1545 0.1353 0.1069

0.14 0.27 0.39 0.49 0.59 0.69 0.77 0.85 0.93 1.00

3.7129 6.3593 7.6028 8.0674 7.5684 6.8104 5.6445 4.1329 3.1139 2.2610

0.0404 0.0854 0.1215 0.1574 0.1870 0.2019 0.2080 0.1942 0.1733 0.1604

0.0421 0.0799 0.1227 0.1610 0.1882 0.2017 0.2025 0.1934 0.1778 0.1587

0.14 0.27 0.39 0.49 0.59 0.69 0.77 0.85 0.93 1.00

5.2359 8.2097 9.8713 10.4686 9.9959 8.8965 7.7063 6.0927 4.7560 3.2512

ST 103 xcal SFB T = 313.14 K 2.9256 4.6616 5.9222 6.4097 6.1530 5.3686 4.3225 3.2439 2.2833 1.5166 T = 323.14 K 3.8538 6.0359 7.6146 8.1700 7.7646 6.7377 5.4613 4.2082 3.1225 2.2560 T = 333.14 K 5.3929 8.0235 9.7728 10.4176 10.0938 9.0769 7.6614 6.1072 4.6113 3.3074

103 xexp ST

103 xcal ST

0.0555 0.1122 0.1562 0.2092 0.2499 0.2774 0.2827 0.2712 0.2457 0.2293

0.0585 0.1031 0.1583 0.2126 0.2540 0.2759 0.2789 0.2681 0.2495 0.2286

0.0785 0.1445 0.2009 0.2746 0.3252 0.3659 0.3733 0.3681 0.3421 0.3105

0.0817 0.1361 0.2043 0.2738 0.3305 0.3646 0.3744 0.3642 0.3412 0.3122

0.1262 0.2093 0.2907 0.3933 0.4487 0.4954 0.5073 0.4857 0.4659 0.4417

0.1274 0.2047 0.2973 0.3868 0.4550 0.4929 0.5018 0.4899 0.4667 0.4408

a 0 xA

exp is the initial mole fraction of 2-propanol in (2-propanol +1,4-dioxiane) binary solvents. xexp FSB and xST are the experimentally determined solubility cal cal for SFB and ST. xFSB and xST are the calculated solubility according to CNIBS/R−K model for SFB and ST. The standard uncertainty of T is u(T) = 0.05 K. The relative standard uncertainty of the solubility measurement is ur(x) = 0.05. The relative standard uncertainty of the initial mole fraction of methanol is ur(x0A) = 0.01. The relative standard uncertainty of pressure is ur(p) = 0.05.

The melting properties of SFB and ST were analyzed using DSC. The onset point was chosen as the melting temperature. According to the plots shown in Figure 4, the melting temperature Tm,SFB (for SFB) and Tm,ST (for ST) are 479.97 ± 0.5 K and 507.30 ± 0.5 K (expanded uncertainty with 0.95 level of confidence), and the enthalpy of fusion ΔfusHSFB and ΔfusHST are measured as 35.73 ± 1.15 kJ mol−1 and 43.54 ± 1.21 kJ mol−1 (expanded uncertainty with 0.95 level of confidence), respectively. 3.2. Equilibrium Solubility. 3.2.1. Solubility in Monosolvents. The measured mole fraction solubility data of SFB and ST in five monosolvents are presented in Table 2 and Figures 5 and 6. It can be seen that the solubility of ST is far lower than the solubility of SFB at the same state, and the solubility in all selected solvents increases with the temperature rising. This apparent tendency indicates that cooling crystallization is an appropriate recrystallization method both for SFB and ST. As shown in Figures 5 and 6, the solubility of SFB can be ranked as 1-propanol > 1-butanol > 1-pentanol > 2-propanol >

2-methyl-1-propanol at a given temperature, and the solubility of ST occurs in the following order: 1-propanol > 1-butanol > 2-propanol > 2-methyl-1-propanol > 1-pentanol. It is obvious that the polarity of solvents is not the only factor on the process of dissolution. According to Gu and his coauthors,12 the polarity of solvents used in experiment is ranked as 1-propanol (0.52) > 2-propanol (0.48) > 1-butanol (0.47) > 2-methyl-1propanol (0.4) = 1-pentanol (0.4). Although the polarity of 2-propanol is little larger than that of 1-butanol, the solubility values of SFB and ST in 1-butanol are both much higher compared with that in 2-propanol. The case of 2-methyl-1propanol and 1-pentanol is similar. Thus, it can be concluded that the steric hindrance of solvents plays a negative role in solvent−solute interaction. Another vital element that may influence the solubility is hydrogen bonding. The solute molecular structure contains many hydrogen donor and hydrogen acceptor groups (see Figure 1), which will contribute to the formation of a hydrogen bond between solvent and solute molecules, thereby impacting the capacity of dissolution. Actually, the solubility greatly depends on the mutual competition D

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points did not change with temperature. Compared with that of ST, the mole fraction solubility of SFB is much higher. The curve of solubility shows a maximum point at 0.50 and 0.75 2-propanol mole fraction for SFB and ST, respectively. On the basis of the “like dissolves like” theory, the solubility of the polar solute will increase when introducing the 2-propanol into nonpolar 1,4-dioxane. However, the solubility is not a positive correlation with an increase in the content of 2-propanol. The maximum solubility and a positive synergistic effect is observed. The cosolvency in this case may be not caused by van der Waals interactions, and the hydrogen bonding might be the primarily effect. When the mole fraction of 2-propanol is increased, the hydrogen-bonding may become stronger before reaching the maximal solubility. Then strong hydrogen-bonding interactions between 2-propanol molecules are formed as the mole fraction of 2-propanol is subsequently increased, which might weaken the interaction between the solvent and solute. Additionally, the maximal value of SFB and ST is at different 2-propanol mole fractions at a certain temperature. So it is possible that cosolvency should be more relative to the structure of solute. The ion-dipole interaction also could play important roles in the cosolvency behavior. 3.3. Data Correlation. One main purpose of this paper is to provide necessary data for industrial application; simplicity of the models is of great importance for the correlation or calculation of solid−liquid equilibrium data in industry. In this work, two widely used solid−liquid phase equilibrium models, the Apelblat model and the CNIBS/R-K model were selected to correlate and analyze the experimental data. 3.3.1. Apelblat Model. The Apelblat model15,16 is a frequently used semiempirical model, which is extensively applied to correlate the mole fraction solubility and the absolute temperature in monosolvents and binary solvent mixtures. Its simplified form can be described as eq 3

of the interaction between the solute−solvent and solvent− solvent, and weaker solvent−solvent interactions and stronger solute−solvent interactions will give higher solubility. 3.2.2. Solubility in Binary Solvents. Co-solvency, a common phenomenon described by previous studies,13,14 is a feasible and effective method to improve the solubility for poorly soluble drugs that contribute to increase the productivity of the crystallization process. In this work, 1,4-dioxane was chosen as a cosolvent and the mole fraction solubility of SFB and ST in binary solvents (1,4-dioxane + 2-propanol) was listed in Table 3 and graphically plotted in Figures 7 and 8. It can be observed

Figure 7. Experimental and calculated solubility data of SFB in the (2-propanol + 1,4-dioxane) binary solvents at temperature ranging from 283.15 to 333.15 K: black ■, 283.15 K; red ●, 293.15 K; blue ▲, 303.15 K; green ▼, 313.15 K; pink ◀, 323.15 K; chartreuse ▶, 333.15 K; , calculated data by the CNIBS/R−K model.

ln x = A +

B + C ln T T

(3)

where x is the mole fraction solubility of solute (SFB or ST) at absolute temperature T (K), and A, B, and C are the empirical constants. The value of A and B reflects the nonidealities of the real solution in terms of variation of activity coefficient in the solution, and C represents the effect of temperature on the fusion enthalpy. 3.3.2. CNIBS/R−K Model. The CNIBS/R−K model is one of the theoretical models for predicting the relationship between isothermal solubility and solvent composition.17,18 It can be express as eq 4 N

ln x = xA0 ln XA + x B0 ln XB + xA0x B0 ∑ Si(xA0 − x B0)i i=0

(4)

where x0A and x0B refer to the initial mole fraction of 2-propanol and 1,4-dioxane in a binary solvent mixture without solute, respectively, XA and XB represent the mole fraction solubility of the solute in 2-propanol and 1,4-dioxane. Si is the model parameter and N represents the number of “curve-fit” parameters. When N = 2, the equation can be simplified as19

Figure 8. Experimental and calculated solubility data of ST in the (2-propanol +1, 4-dioxane) binary solvents at temperature ranging from 283.15 to 333.15 K: black ■, 283.15 K; red ●, 293.15 K; blue ▲, 303.15 K; green ▼, 313.15 K; pink ◀, 323.15 K; chartreuse ▶, 333.15 K; , calculated data by the CNIBS/R−K model.

ln x = B0 + B1xA0 + B2 (xA0 )2 + B3(xA0 )3 + B4 (xA0 )4

that at a given solvent composition, the solubility value is positively correlated with temperature, indicating that the dissolution process is endothermic. During the increase of the initial mole fraction of 2-propanol in mixtures, the solubility reached a maximum, and then decreased. Meanwhile, the maximum

(5)

where B0, B1, B2, B3, and B4 are model parameters which can be obtained by least-squares regression. In this study, the Apelblat model was used to correlate the experimental solubility of SFB and ST in monosolvents and the E

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Table 4. Calculated Values of Mixing Thermodynamic Properties of SFB in (2-Propanol +1,4-Dioxane) Binary Mixture Solventsa ΔmixH

ΔmixS

ΔmixG

ΔmixH

ΔmixS

ΔmixG

x0A

kJ mol−1

J mol−1 K−1

kJ mol−1

x0A

kJ mol−1

J mol−1 K−1

kJ mol−1

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−1.6200 −2.6560 −3.2279 −3.4248 −3.3197 −2.9732 −2.4281 −1.7324 −0.9200

−2.5427 −3.9662 −4.7157 −4.9586 −4.8055 −4.3354 −3.6022 −2.6466 −1.4826

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−1.6113 −2.6505 −3.2275 −3.4302 −3.3299 −2.9877 −2.4484 −1.7565 −0.9440

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−1.6174 −2.6516 −3.2235 −3.4248 −3.3213 −2.9759 −2.4326 −1.7368 −0.9258

−2.5799 −4.0168 −4.7732 −5.0198 −4.8650 −4.3902 −3.6501 −2.6842 −1.5073

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−1.6075 −2.6522 −3.2346 −3.4433 −3.3439 −3.0042 −2.4673 −1.7704 −0.9613

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−1.6146 −2.6499 −3.2240 −3.4271 −3.3244 −2.9782 −2.4366 −1.7461 −0.9348

−2.6182 −4.0706 −4.8340 −5.0821 −4.9250 −4.4447 −3.6977 −2.7239 −1.5335

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−1.6026 −2.6541 −3.2466 −3.4639 −3.3722 −3.0327 −2.5013 −1.8079 −0.9956

T = 283.15 K 3.2587 4.6273 5.2544 5.4168 5.2472 4.8109 4.1465 3.2287 1.9869 T = 293.15 K 3.2833 4.6569 5.2865 5.4409 5.2658 4.8244 4.1532 3.2318 1.9838 T = 303.15 K 3.3108 4.6864 5.3109 5.4593 5.2802 4.8376 4.1599 3.2255 1.9750

T = 313.15 K 3.3409 4.7164 5.3304 5.4749 5.2884 4.8355 4.1511 3.2170 1.9663 T = 323.15 K 3.3780 4.7471 5.3440 5.4717 5.2793 4.8189 4.1280 3.2021 1.9440 T = 333.15 K 3.4312 4.7781 5.3491 5.4528 5.2406 4.7773 4.0745 3.1427 1.8919

−2.6575 −4.1275 −4.8967 −5.1447 −4.9860 −4.5020 −3.7483 −2.7639 −1.5597 −2.6991 −4.1862 −4.9615 −5.2115 −5.0499 −4.5614 −3.8013 −2.8051 −1.5895 −2.7457 −4.2460 −5.0287 −5.2805 −5.1181 −4.6243 −3.8588 −2.8549 −1.6259

a

The relative standard uncertainty of mole fraction of 2-propanol in the binary solvent mixture is ur (x0A) = 0.01. The expanded uncertainties are U(ΔmixH) = 0.05 ΔmixH, U(ΔmixS) = 0.06 ΔmixS, U(ΔmixG) = 0.06 ΔmixG (0.95 level of confidence).

CNIBS/R−K model was applied to correlate the solubility data in binary solvents. The correlated mole fraction solubilities are listed in Tables 2 and 3. The parameters of the models were obtained by the least-squares method and shown in Tables S1 and S2. To evaluate the accuracy and predictability of the models used in this paper, the average relative deviation (ARD %) defined as eq 6 was also calculated and presented in Tables S1 and S2. 100 ARD% = N

N

∑ i=1

xical − xiexp xiexp

four energetic steps from the kinetic perspective, namely, heating, fusion, cooling, and mixing processes.20,21 Among them, the mixing process is associated with the interaction between solute and solvent in nonideal solutions. Therefore, it is significant to explore and analyze the mixing thermodynamic properties, including the mixing Gibbs energy, mixing enthalpy, and mixing entropy, which is the essential data during the operation and optimization of crystallization procedure. In this work, the mixing thermodynamic properties ΔmixM in different solvents can be calculated by22 Δmix M = ME + Δmix M id

(6)

(7)

where M = G, H, and S, ME is the excess property, and ΔmixMid is the mixing property of ideal system. For the ideal solution, ΔmixHid = 0. The mixing Gibbs energy (ΔmixG), mixing enthalpy (ΔmixH) and mixing entropy (ΔmixS) of the nonideal solution can be determined by eq 8−1023

where N represents the number of experimental points, xexp i and refer to the experimental and calculated solubility data, xcal i respectively. As we can see from Tables S1 to S2, the average relative deviation (ARD %) between the experimental and calculated solubility values is below 5%, which indicates that the correlated values are in good agreement with experimental values at temperatures tested in this paper. The models selected could be used to predict the solubility of SFB and ST with satisfied accuracy. Since the accuracy of extrapolation of the two models was not tested, they were suggested for use only in the temperature ranging from 283.15 to 333.15 K. 3.4. Mixing Thermodynamics Properties. The dissolution process theoretically can be considered to be composed of

n

n

Δmix G = RT ∑ x i ln x i + RT ∑ x i ln γi i=1

i=1

n ⎛ ∂ ln γi ⎞ Δmix H = −RT 2 ∑ x i⎜ ⎟ ⎝ ∂T ⎠ p , x i=1

F

(8)

(9)

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Table 5. Calculated Values of Mixing Thermodynamic Properties of ST in (2-Propanol +1,4-Dioxane) Binary Mixture Solventsa ΔmixH

ΔmixS

−1

x0A

kJ mol

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−5.4313 −8.8659 −10.7510 −11.4151 −11.1019 −9.9958 −8.2364 −5.9319 −3.1660

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−5.4220 −8.8412 −10.7127 −11.3680 −11.0525 −9.9498 −8.1988 −5.9057 −3.1533

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−5.4130 −8.8174 −10.6757 −11.3229 −11.0054 −9.9061 −8.1632 −5.8814 −3.1419

J mol

−1

K

ΔmixH

ΔmixG −1

T = 283.15 K 2.8773 4.1980 4.8580 5.0185 4.7874 4.2588 3.5176 2.6218 1.5731 T = 293.15 K 2.9185 4.2846 4.9809 5.1633 4.9372 4.3986 3.6338 2.7056 1.6165 T = 303.15 K 2.9568 4.3644 5.0935 5.2947 5.0725 4.5248 3.7390 2.7804 1.6547

−1

x0A

kJ mol

kJ mol

−1

−6.2460 −10.0545 −12.1266 −12.8361 −12.4575 −11.2017 −9.2324 −6.6743 −3.6114

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−5.4042 −8.7944 −10.6399 −11.2796 −10.9604 −9.8650 −8.1302 −5.8595 −3.1323

−6.2776 −10.0973 −12.1729 −12.8816 −12.4998 −11.2392 −9.2641 −6.6989 −3.6272

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−5.3956 −8.7720 −10.6054 −11.2379 −10.9173 −9.8259 −8.0990 −5.8394 −3.1243

−6.3093 −10.1405 −12.2198 −12.9280 −12.5431 −11.2778 −9.2966 −6.7243 −3.6435

0.14 0.27 0.38 0.49 0.59 0.69 0.77 0.85 0.93

−5.3871 −8.7503 −10.5723 −11.1983 −10.8765 −9.7892 −8.0705 −5.8209 −3.1178

ΔmixS −1

J mol

ΔmixG −1

K

T = 313.15 K 2.9924 4.4377 5.1965 5.4145 5.1953 4.6377 3.8323 2.8456 1.6867 T = 323.15 K 3.0258 4.5054 5.2911 5.5238 5.3071 4.7401 3.9163 2.9035 1.7138 T = 333.15 K 3.0581 4.5683 5.3775 5.6224 5.4071 4.8313 3.9901 2.9548 1.7364

kJ mol−1 −6.3413 −10.1840 −12.2672 −12.9752 −12.5873 −11.3174 −9.3302 −6.7506 −3.6605 −6.3734 −10.2279 −12.3152 −13.0230 −12.6322 −11.3577 −9.3646 −6.7777 −3.6781 −6.4059 −10.2722 −12.3638 −13.0714 −12.6779 −11.3988 −9.3998 −6.8053 −3.6962

a

The relative standard uncertainty of mole fraction of 2-propanol in the binary solvent mixture is ur (x0A) = 0.01. The expanded uncertainties are U(ΔmixH) = 0.05 ΔmixH, U(ΔmixS) = 0.06 ΔmixS, U(ΔmixG) = 0.06 ΔmixG (0.95 level of confidence).

Δmix S =

Δmix H − Δmix G T

ln γi =

(10)

where xi represents the mole fraction of every component of solution and γi represents the activity coefficient of every component in real solution. The activity coefficient can be calculated by the NRTL mod24 el. On the basis of the theory of (solid + liquid) phase equilibrium, the solubility of one compound in the solution can be calculated as follow: ln x i =

ΔfusH ⎛ 1 1⎞ − ⎟ − ln γi ⎜ R ⎝ Tm T⎠

+

+

(x i + xjGji + xkG ki)2

[τijGijxj2 + GijG kjxjxk(τij − τkj)] (xj + x iGij + xkG kj)2 [τikGik xk2 + Gik Gjk xjxk(τik − τjk )] (xk + x iGik + xjGjk )2

(13)

where Gij, Gik, Gji, Gjk, Gki, Gkj, τij, τik, τji, τjk, τki, and τkj are parameters of this model. The definition of these terms can be expressed as

(11)

where enthalpy of fusion ΔfusH and melting point Tm were measured by DSC in section 3.1. For binary system (in monosolvents), the activity coefficient γi can be calculated as eq 12, and for a triplex mixture system (in binary solvents), the function of the activity coefficient γi can be expressed as eq 13:24 ⎡ ⎤ τjiGji2 τijGij2 ⎥ ln γi = xj2⎢ + ⎢⎣ (xi + Gjixj)2 (xj + Gijxi)2 ⎥⎦

(Gjixj + G kixk )(τjiGjixj + τkiG kixk )

Gij = exp( −αijτij)

(14)

τij = (gij − gjj)/RT

(15)

where τ is a constant which was assumed for the nonrandomness of the mixture, g represents the Gibbs energy of intermolecular interaction, and α is an adjustable empirical constant. After optimized fitting the solubility data using the NRTL model, the mixing thermodynamic properties were obtained. The mixing thermodynamic properties of SFB and ST in binary solvent mixtures are given in Tables 4 and 5, and the mixing thermodynamic properties of SFB and ST in monosolvents are shown in Tables S3 and S4, respectively. As can be seen, the

(12) G

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mole Gibbs energy ΔmixG is negative, which means the mixing of SFB and ST in all solvents is a spontaneous process. The negative value of ΔmixH indicates that the dissolution process is exothermic. The positive values of ΔmixS, in this paper, reflect the mixing process is entropy favorable. In brief, these results are beneficial for the design and optimization of crystallization processes of SFB and ST.

(3) Wilhelm, S. M.; Adnane, L.; Newell, P.; Villanueva, A.; Llovet, J. M.; Lynch, M. Preclinical overview of sorafenib, a multikinase inhibitor that targets both Raf and VEGF and PDGF receptor tyrosine kinase signaling. Mol. Cancer Ther. 2008, 7, 3129−3140. (4) Carter, C. A.; Chen, C.; Brink, C.; Vincent, P.; Maxuitenko, Y. Y.; Gilbert, K. S.; Waud, W. R.; Zhang, X. Sorafenib is efficacious and tolerated in combination with cytotoxic or cytostatic agents in preclinical models of human non-small cell lung carcinoma. Cancer Chemother. Pharmacol. 2006, 59, 183−195. (5) Benitez, A.; Yates, T. J.; Shamaldevi, N.; Bowen, T.; Lokeshwar, V. B. Dietary Supplement Hymecromone and Sorafenib: A Novel Combination for the Control of Renal Cell Carcinoma. J. Urol. 2013, 190, 285−290. (6) Paulekuhn, G. S.; Dressman, J. B.; Saal, C. Salt screening and characterization for poorly soluble, weak basic compounds: case study albendazole. Pharmazie 2013, 68, 555−564. (7) Serajuddin, A. T. M. Salt formation to improve drug solubility. Adv. Drug Delivery Rev. 2007, 59, 603−616. (8) Cox, B. G. Acids, Bases, and Salts in Mixed-Aqueous Solvents. Org. Process Res. Dev. 2015, 19, 1800−1808. (9) Cassens, J.; Prudic, A.; Ruether, F.; Sadowski, G. Solubility of Pharmaceuticals and Their Salts As a Function of pH. Ind. Eng. Chem. Res. 2013, 52, 2721−2731. (10) Shimada, M.; Okawa, H.; Maejima, T.; Yanagi, T.; Hisamichi, K.; Matsuura, M.; Akasaka, K.; Tsuchiya, M.; Kondo, Y.; Shimosegawa, T. A quantitative HPLC-UV method for determination of serum sorafenib and sorafenib N-oxide and its application in hepatocarcinoma patients. Tohoku J. Exp. Med. 2014, 233, 103−112. (11) Wang, J.; Xie, C.; Yin, Q.; Tao, L.; Lv, J.; Wang, Y.; He, F.; Hao, H. Measurement and correlation of solubility of cefmenoxime hydrochloride in pure solvents and binary solvent mixtures. J. Chem. Thermodyn. 2016, 95, 63−71. (12) Gu, C. H.; Li, H.; Gandhi, R. B.; Raghavan, K. Grouping solvents by statistical analysis of solvent property parameters: implication to polymorph screening. Int. J. Pharm. 2004, 283, 117− 125. (13) Miyako, Y.; Zhao, Y.; Takeshima, K.; Kataoka, T.; Handa, T.; Pinal, R. Solubility of hydrophobic compounds in water−cosolvent mixtures: Relation of solubility with water−cosolvent interactions. J. Pharm. Sci. 2010, 99, 293−302. (14) Gantiva, M.; Martínez, F. Thermodynamic analysis of the solubility of ketoprofen in some propylene glycol+ water cosolvent mixtures. Fluid Phase Equilib. 2010, 293, 242−250. (15) Apelblat, A.; Manzurola, E. Solubilities of o-acetylsalicylic, 4aminosalicylic, 3,5-dinitrosalicylic, and p-toluic acid, and magnesiumDLaspartate in water from T = (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (16) Apelblat, A.; Manzurola, E. Solubilities of L-aspartic, DLaspartic, DL-glutamic, p-hydroxybenzoic, o-anistic, p-anisic, and itaconic acids in water from T = (278 to 348) K. J. Chem. Thermodyn. 1997, 29, 1527−1533. (17) Acree, W. E., Jr; McCargar, J. W.; Zvaigzne, A. I.; Teng, I. L. Mathematical representation of thermodynamic properties. Carbazole solubilities in binary alkane+ dibutyl ether and alkane+ tetrahydropyran solvent mixtures. Phys. Chem. Liq. 1991, 23, 27−35. (18) Qin, Y.; Wang, H.; Yang, P.; Du, S.; Huang, C.; Du, Y.; Wu, S.; Gong, J.; Yin, Q. Measurement and correlation of solubility and dissolution properties of flunixin meglumine in pure and binary solvents. Fluid Phase Equilib. 2015, 403, 145−152. (19) Barzegar-Jalali, M.; Jouyban-Gharamaleki, A. A general model from theoretical cosolvency models. Int. J. Pharm. 1997, 152, 247− 250. (20) Li, K.; Du, S.; Wu, S.; Cai, D.; Wang, J.; Zhang, D.; Zhao, K.; Yang, P.; Yu, B.; Guo, B.; Li, D.; Gong, J. Determination and correlation of solubility and solution thermodynamics of oxiracetam in three (alcohol+water) binary solvents. J. Chem. Thermodyn. 2016, 96, 12−23. (21) Kondepudi, D. K. Introduction to modern thermodynamics; Wiley: Chichester, 2008.

4. CONCLUSION The solubility of SFB and ST was measured in five monosolvents and one binary solvent via UV spectroscopy method from T = (283.15 to 333.15) K. The solubility of SFB and ST increases with the increase of temperature in five monosolvents, and it is in the order of 1-propanol > 1-butanol > 1-pentanol > 2-propanol > 2-methyl-1-propanol and 1-propanol > 1-butanol > 2-propanol > 2-methyl-1-propanol > 1-pentanol, respectively. The solubility of SFB and ST in binary solvents also shows temperature dependence, while at a given temperature the solubility is mainly influenced by the solvent composition with the presence of a maximum. Particularly, the solubility of SFB is much higher than that of ST at the same temperature in all solvents used in this work. The experimental solubility data were correlated based on the Apelblat model and CNIBS/R−K model. It turns out that the two selected thermodynamic models show satisfactory correlation results. Also, the NRTL model was employed to calculate the thermodynamic properties containing the Gibbs energy, the enthalpy, and the entropy of mixing. These thermodynamic values obtained above indicated that the mixing processes of SFB and ST in different solvents are spontaneous and exothermic. All the experimental values provide good guidance for the crystallization and purification of SFB and ST.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00630. Calculated parameters for different models and mixing properties of SFB and ST in monosolvents (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-22-27405754. Fax: +86-22-27374971. E-mail: junbo_ [email protected]. Funding

The authors are grateful to the financial support of National Natural Science Foundation of China (81361140344 and 21376164), National 863 Program (2015AA021002), and Major National Scientific Instrument Development Project 21527812. Notes

The authors declare no competing financial interest.

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REFERENCES

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(22) Abbott, M. M.; Smith, J. M.; Van Ness, H. C. Introduction to chemical engineering thermodynamics; McGraw-Hill: Boston, 2001, 619−626. (23) Walas, S. M. Phase equilibria in chemical engineering; Butterworth-Heinemann: 2013. (24) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144.

I

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