Experimental Determination and Thermodynamic Models for Solid

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

pubs.acs.org/jced

Experimental Determination and Thermodynamic Models for Solid−Liquid Equilibrium of 4‑(4-Aminophenoxy)‑N‑methylpyridine2-carboxamide in Pure and Binary Solvent Mixtures for T = (278.15−328.15) K Huace Sheng,† Shimin Fan,‡ Wangdan Zhao,† Jian Zhang,† Xinxin Zhao,† Yonghong Hu,†,‡ Yonggen Qian,§ and Wenge Yang*,† †

School of Pharmaceutical Sciences and ‡The Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, No. 30, South Puzhu Road, Nanjing 211816, China § Jiangsu Fengyuan Biological Engineering Co. Ltd., No. 6, Hongqi Road, Sheyang Xian, Jiangsu Sheng 224300, China ABSTRACT: In this study, the solubility of 4-(4-aminophenoxy)-N-methylpyridine-2-carboxamide (APMC) in pure tetrahydrofuran, ethyl acetate, acetonitrile, n-butanol, n-propanol, ethanol, methanol, and three binary solvent mixtures (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol) was first experimentally determined within the temperature range from (278.15 to 328.15) K under atmosphere pressure by the gravimetric method. The results reveal that the solubility of APMC increases with an increase in temperature in all of the solvents selected. The modified Apelblat equation and the Buchowski−Ksiazaczak λh equation were used to correlate the experimental solubility in pure solvents while the modified Apelblat equation, the CNIBS/R−K model, and the Jouyban−Acree model were applied to correlate the solubility in binary solvent mixtures. All of the models could be well applied, and the modified Apelblat equation stood out to be more suitable with a higher accuracy compared to that of the other three models.

1. INTRODUCTION Sorafenib, an oral multikinase inhibitor, was developed by German pharmaceutical company Bayer.1−3 In the multicenter, double-blind, randomized phase III Sorafenib hepatocellular carcinoma assessment randomized protocol (SHARP) study, Sorafenib was shown to be efficacious and well tolerated in patients with advanced hepatocellular carcinoma.4−6 Compared with other drugs, Sorafenib was generally well tolerated and had manageable side effects.7−10 4-(4-Aminophenoxy)-N-methylpyridine-2-carboxamide (also named APMC, CASRN: 284462-37-9, M = 243.26 g·mol−1, Figure 1) is an important intermediate for the synthesis of

To establish an ideal crystallization strategy for the separation and purification as well as to obtain APMC with high purity and yield, it is of great importance to acquire the solubility of APMC in appropriate solvents. To the best of our knowledge, though much work has been done on this compound, most research mainly focused on its synthesis and application,19−21 and the information on its solubility in commonly used solvents has not been reported yet. The lack of solubility data makes it difficult to design and optimize the manufacturing process of APMC. Therefore, it is essential to measure the solubility of APMC in pure solvents and binary mixtures. Continuing on our research in this direction, we hope to provide some useful data for the crystallization process of APMC because the purity is a significant part of a pharmaceutical intermediate. In the present study, we employed a gravimetric method to determine the solubility of APMC in tetrahydrofuran, ethyl acetate, acetonitrile, n-butanol, n-propanol, ethanol, methanol, and (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol) binary solvent mixtures from 278.15 to 328.15 K under atmospheric pressure. We also adopted four commonly used models, including the modified Apelblat equation, Buchowski−Ksiazaczak λh equation, CNIBS/R−K model,

Figure 1. Chemical Structure of APMC.

Sorafenib.11−16 As one of the most basal physiochemical properties, solubility has a wide variety of applications in different areas such as in the pharmaceutical, biological, and chemical industries. The solubility of organic compounds in different solvents is important for understanding the (solid + liquid) equilibrium or phase equilibrium of a crystallization process.17,18 © XXXX American Chemical Society

Received: February 28, 2018 Accepted: April 24, 2018

A

DOI: 10.1021/acs.jced.8b00165 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Provenance and Purity of the Materials Used material 4-(4-aminophenoxy)-N-methylpyridine-2carboxamide methanol ethanol n-propanol n-butanol ethyl acetate acetonitrile tetrahydrofuran a

source

mass fraction purity

molar mass (g·mol−1)

purification method

analysis method

≥0.980

243.3

none

HPLCa

none none none none none none none

GCb GC GC GC GC GC GC

Nanjing Chemlin Chemical Industrial Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals Shenbo Chemicals

≥0.997 ≥0.990 ≥0.995 ≥0.995 ≥0.995 ≥0.990 ≥0.990

32.04 46.07 60.10 74.12 88.11 41.05 72.11

High-performance liquid chromatography. bGas chromatography.

and Jouyban−Acree model, to correlate the obtained solubility values. Computational results showed that the four models fitted the experiment data well, and the modified Apelblat equation had a higher accuracy than that of the other three.

2. EXPERIMENTAL SECTION 2.1. Materials. 4-(4-Aminophenoxy)-N-methylpyridine-2carboxamide with a mass fraction purity of >0.98 was purchased from Nanjing Chemlin Chemical Industrial Co., Ltd. Its purity was measured by high-performance liquid chromatography (HPLC-type Agilent 1260 Infinity LC, Agilent Technologies). Meanwhile, all of the solvents (Shenbo Chemicals) used for experiments were analytical reagent grade, and their mass fraction purities were higher than 0.99. More details about the purity of solvents were revealed in Table 1. All of the solvents were utilized without further purification. 2.2. Apparatus and Procedures. The crystal form of APMC used in this work was analyzed by X-ray powder diffraction (PXRD), differential scanning calorimetry (DSC), and scanning electron microscopy with elemental microanalysis (SEM/EDS). PXRD was performed on an X-ray diffractometer (ARL XTRA, USA) with Cu Kα radiation at 40 mA and 40 kV. The samples were scanned from 5° to 50° (2θ) at a scanning rate of 0.02° s−1. The diffractogram of APMC is shown in Figure 2, which can confirm that it is APMC with high polymorphic purity.

Figure 3. Scanning electron microscopy image of APMC.

DSC data were collected on a Netzsch DSC 204 differential scanning calorimeter. Indium (melting temperature, 156.6 ± 1.0 °C; heat of fusion, 28.5 ± 1.5 J·g−1) was used for the calibration. An empty pan was used as the reference. Accurately weighed samples were placed in aluminum crucibles and heated at the rate of 10 K·min−1 under the protection of nitrogen at 50 mL·min−1. The thermogram of APMC is shown in Figure 4. 2.3. Solubility Measurements. The solubility of APMC in seven pure solvents and three binary solvent mixtures (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol) was measured from 278.15 to 328.15 K by the gravimetric method under atmosphere pressure.22 The method has been validated in our previous publication.23 For each measurement, 7 mL of solvent and a specified amount of APMC were put in a 10 mL cuvette with a glass plug (to prevent the evaporation of solvent). The mixture was stirred continuously for 24 h with a magnetic stirrer to make sure the solution reached solid−liquid equilibrium. The experimental temperature was monitored by an intelligent water-circulating thermostatic bath. As the solid−liquid system reached equilibrium, the magnetic stirrer was switched off. Five hours later, 1 mL of the clear upper saturated solution was taken by a pipet gun and quickly transferred into a previously weighed 5 mL beaker with a cover. The total weight was measured immediately; the beaker was put into a dryer, and the sampling was recorded repeatedly until getting a constant weight. Each experiment was replicated at least three times to check the repeatability of the solubility determination. We noticed that APMC before and after the measurements in different solvent systems is an light-brown crystalline powder.

Figure 2. Diffractogram of APMC.

SEM data was collected by using a variable pressure field emission FEI QUANTA 200 FEG microscope on gold-coated and uncoated samples at 15 kV. The microphotograph of APMC is depicted in Figure 3. B



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Figure 4. DSC scan of APMC.

this work is the melting temperature of APMC with a standard uncertainty of 0.50 K. 3.2. Solubility Data and Correlation Models. To discover a suitable model to represent the solubility for APMC in different solvents and extend the use of the solubility values obtained, four correlation models were employed in this work, which correspond to the modified Apelblat equation, Buchowski− Ksiazaczak λh equation, CNIBS/R−K equation, and Jouyban− Acree equation. 3.2.1. In Pure Solvents. The modified Apelblat equation and the Buchowski−Ksiazaczak λh equation were used to correlate the experimental solubility for APMC in pure solvents. The mole fraction solubility (x) of APMC in different pure solvents from 278.15 to 328.15 K was presented in Table 2 and shown graphically in Figure 5. 3.2.1.1. Modified Apelblat Equation. The modified Apelblat equation,24−29 a widely used semiempirical model, is used to correlate the solubility of APMC against temperature. This equation is expressed as eq 4

The saturated mole fraction solubility of APMC in pure solvents was calculated by eq 1

x=

m1/M1 m1/M1 + m2/M 2

(1)

where m1 and M1 denote the mass and molar mass of APMC while m2 and M2 denote that of the solvents. The mole fraction solubility of APMC (x) in three binary solvent mixtures (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol) is calculated by eq 2. The mole fraction of ethyl acetate (xA) in the binary solvent mixtures is calculated by eq 3 x=

xA =

m1/M1 m1/M1 + m2/M 2 + m3/M3 m2 /M 2 m2 /M 2 + m3 /M3

(2)

(3)

where m1, m2, and m3 represent the mass of APMC, ethyl acetate, and the other organic solvent (methanol, ethanol, or n-butanol), respectively, and M1, M2, and M3 represent the molar masses of APMC, ethyl acetate, and the other organic solvent (methanol, ethanol, or n-butanol), respectively. All molar quantities are based on the IUPAC relative atomic mass table.

ln x = A +

B + C ln(T /K) T /K

(4)

where x represents the solubility mole fraction of APMC, T represents the experimental temperature, and A, B, and C are the model parameters determined by the experimental solubility data. 3.2.1.2. Buchowski−Ksiazaczak λh Equation. The Buchowski− Ksiazaczak λh equation was first proposed by Buchowski et al.30−37 This equation has two parameters, λ and h, and is expressed as eq 5

3. RESULTS AND DISCUSSION 3.1. Melting Thermodynamics. As fundamental and basic data, the melting temperature is necessary for the Buchowski− Ksiazaczak λh equation adopted in this work to correlate the solubility, but melting temperature Tm of APMC has not been reported so far. As shown in the DSC thermogram (Figure 4), there is a sharp endothermic peak at the temperature of 390.15 K. It is generally acknowledged that the process of melting should be endothermic, and hence we can draw a conclusion that the mean extrapolated onset temperature (390.15 K) determined in

⎡ 1 ⎛ λ(1 − x) ⎞ 1 ⎤ ln⎜1 + ⎟ = λh⎢ − ⎥ ⎝ ⎠ (Tm/K) ⎦ x ⎣ (T /K)

(5)

where λ and h are two equation constants and Tm is the melting temperature of APMC. The value of λ reflects the nonideality of the solution system, while λh estimates the enthalpy of solution. C



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Table 2. Mole Fraction Solubility x of 4-(4-Aminophenoxy)-N-methylpyridine-2-carboxamide in Different Pure Solvents in the Temperature Range from 278.15 K to 328.15 K under 101.3 kPaa tetrahydrofuran

ethyl acetate 100RD

100RD

T/K

100x

eq 4

eq 5

100x

eq 4

eq 5

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

8.976 9.782 10.77 11.85 12.93 14.31 15.79 17.27 19.22 21.09 23.31

0.23 −0.29 0.060 0.26 −0.48 0.12 0.31 −0.48 0.42 −0.13 −0.0086

1.7 0.34 0.10 −0.07 −0.99 −0.42 −0.14 −0.76 0.36 0.047 0.39

5.276 6.369 7.730 9.190 11.03 12.90 15.15 17.91 20.73 23.85 28.02

−0.78 −0.77 0.34 −0.073 0.94 −0.047 −0.27 0.66 −0.053 −1.0 0.52 n-butanol

2.1 1.0 1.2 0.11 0.60 −0.72 −1.1 −0.059 −0.50 −0.99 1.2

acetonitrile 100RD

100RD

T/K

100x

eq 4

eq 5

100x

eq 4

eq 5

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

2.730 3.172 3.942 4.905 5.947 7.369 8.975 10.93 13.28 16.15 19.50

4.0 −2.0 −1.1 0.21 −0.91 0.37 0.12 0.031 −0.021 0.20 −0.12

13 4.4 2.5 1.5 −1.2 −1.0 −1.8 −1.8 −1.3 0.069 1.3

0.3220 0.4400 0.5630 0.7810 0.9860 1.316 1.714 2.217 2.868 3.657 4.663

0.56 2.1 −2.1 2.3 −1.9 −0.038 −0.0058 −0.10 0.37 −0.082 −0.028 ethanol

4.4 4.6 −0.69 2.9 −1.9 −0.30 −0.40 −0.47 0.14 −0.11 0.16

n-propanol 100RD

100RD

T/K

100x

eq 4

eq 5

100x

eq 4

eq 5

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.4510 0.5930 0.7780 1.114 1.349 1.813 2.365 3.076 3.964 5.025 6.382

2.6 −0.084 −2.2 5.2 −3.3 −0.69 −0.41 0.23 0.58 −0.12 −0.061

5.3 1.7 −1.1 5.6 −3.3 −0.87 −0.69 −0.036 0.40 −0.15 0.085 methanol

0.5390 0.7070 0.9140 1.359 1.792 2.493 3.314 4.398 5.873 7.640 9.987

7.9 1.4 −6.1 1.7 −1.8 0.94 −0.036 −0.40 0.61 −0.27 0.025

14 6.0 −2.7 3.5 −0.93 1.0 −0.48 −1.1 −0.015 −0.53 0.46

100RD T/K

100x

eq 4

eq 5

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

0.8090 1.174 1.576 2.029 2.760 3.694 4.880 6.336 8.205 10.52 13.43

−1.5 3.6 2.1 −2.7 −0.97 −0.019 0.47 0.035 0.11 −0.10 0.010

3.9 7.4 4.7 −1.1 −0.30 −0.054 −0.020 −0.67 −0.52 −0.35 0.50

a

x is the mole fraction solubility of APMC at system temperature T. Standard uncertainties for temperature and pressure are u(T) = 0.05 K and u(P) = 0.58 kPa, respectively. The relative standard uncertainty for solubility is ur(x) = 0.03. D



Article

RD =

x − xc x

RAD =

1 N

(6)

N

x − xc x

∑ i=1

(7)

N

RMSD =

Table 3. Parameters of the Modified Apelblat Model for 4-(4Aminophenoxy)-N-methylpyridine-2-carboxamide in Different Pure Solvents B

C

102RMSD

102RAD

2678.02 −2163.33 1380.58 −1696.21 −2720.41 −3710.78 −4336.21

14.66 2.850 16.72 10.58 7.180 5.860 2.533

0.045 0.10 0.046 0.0098 0.024 0.029 0.026

0.35 0.50 0.82 0.88 1.4 1.9 1.0

A

THF −94.55 EA −11.22 acetonitrile −102.7 n-butanol −59.21 n-propanol −36.03 ethanol −24.95 methanol −3.470 average(100RAD) = 0.99

Table 4. Parameters of the Buchowski−Ksiazaczak λh Model for 4-(4-Aminophenoxy)-N-methylpyridine-2-carboxamide in Different Pure Solvents solvent

λ

THF 0.218 EA 1.29 acetonitrile 1.22 n-butanol 0.430 n-propanol 0.590 ethanol 1.43 methanol 1.66 average(100RAD) = 1.6

h

102RMSD

102RAD

5322.20 2443.20 3180.36 11 353.9 8227.02 3946.02 3173.14

0.068 0.14 0.17 0.013 0.026 0.040 0.047

0.37 0.76 2.6 1.4 1.7 2.7 1.6

N

(8)

where N represents the number of experimental points and x and xc represent the experimental and calculated values, respectively. The RD values between the experimental values and the calculated values are also listed in Table 2. Using the solubility values in Table 2, the parameters of A, B, and C were presented in Table 3, and the parameters of λ and h are presented in Table 4 with the root-mean-square deviations (RMSDs) and the relative average deviation (RAD). From the data listed in Tables 3 and 4, we can see that the relative average deviations of the modified Apelblat equation and the Buchowski−Ksiazaczak λh equation are 0.99% and 1.59%, respectively. The small RMSDs show that the calculated values for APMC in seven pure solvents are in good agreement with the experimental values. As stated previously, the Apelblat equation and the λh equation can all be employed to correlate the solubility of APMC, but the modified Apelblat equation has a higher accuracy than that of the λh equation. As shown in Figure 5, the solubility of APMC in these selected pure solvents increases with an increase in temperature, and the solubility values are relatively high in tetrahydrofuran and ethyl acetate but low in n-butanol. The solubility rank has the following order: ethyl acetate > tetrahydrofuran > acetonitrile > methanol > ethanol > n-propanol > n-butanol. Besides, the solubility of APMC in ethyl acetate shows the strongest positive dependency on temperature. At temperatures below 313.15 K, the solubility of APMC in ethyl acetate is less than that of APMC in tetrahydrofuran; however, at above 313.15 K, the solubility is much greater in ethyl acetate than in tetrahydrofuran. Some properties of the solvents,38 including the polarities, dipole moments (μ), dielectric constants (ε), and Hildebrand solubility parameters (δH), are shown in Table 5, which are employed to illustrate the difference in solubility. From the alcohol systems in Table 5, it can be found that the sequence of the solubility is approximately in accordance with the changing trend in the polarities, dipole moments (μ), dielectric constants (ε), and Hildebrand solubility parameters (δH). Besides, the solubility sequence in pure tetrahydrofuran and ethyl acetate is in accordance with the dipole moments (μ) and dielectric constants (ε) at temperatures below 313.15 K. At temperatures above 313.15 K, the sequence of the solubility is in accordance with the

Figure 5. Plot of the mole fraction solubility (x) of APMC versus temperature (T) in different pure solvents.

solvent

∑i = 1 (x − x c)2

3.2.1.3. Deviation. The relative deviation (RD), the relative average deviation (RAD), and the root-mean-square deviation (RMSD) were applied to evaluate the applicability of this model Table 5. Physical properties for the selected solventa

a

solvent

polarityb

dipole moment μ/D

dielectric constant ε (T = 293.15 K)

Hildebrand solubility parameter δH/(J·m−3)1/2

n-butanol n-propanol ethanol methanol ethyl acetate acetonitrile tetrahydrofuran

60.2 61.7 65.4 76.2 23 46 21

1.66 1.7 1.7 1.7 1.7 3.2 1.75

18.2 20.1 22.4 32.6 6.02 37.5 7.6

11.4 11.9 13.4 14.5 9.1 11.9 9.1

Taken from the literature.38 bValues of polarity are relative to water, with a polarity of 100. E



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Table 6. Mole Fraction Solubility x of 4-(4-Aminophenoxy)-N-methylpyridine-2-carboxamide in (Ethyl Acetate + n-Butanol) Binary Solvent Mixtures in the Temperature Range from 278.15 K to 328.15 K under 101.3 kPaa xA

100x

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.3220 0.5940 1.241 1.940 2.397 3.356 4.031 5.276

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.4400 0.7600 1.498 2.306 2.917 3.976 4.951 6.369

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.5630 0.9590 1.847 2.731 3.506 4.737 5.938 7.730

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.7810 1.217 2.228 3.297 4.173 5.618 7.157 9.190

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.9860 1.542 2.723 3.957 5.060 6.655 8.548 11.03

0.0000 0.1394 0.2823 0.4289

1.316 1.939 3.282 4.637

100RD (eq 4)

100RD (eq 10)

T = 278.15 0.56 0.10 −0.15 −0.44 0.50 1.1 0.16 −0.78 T = 283.15 2.1 0.59 −0.86 −0.40 0.75 0.16 0.94 −0.77 T = 288.15 −2.1 −0.14 0.59 −0.82 0.12 0.025 −0.12 0.34 T = 293.15 2.3 −0.16 −0.11 0.60 −1.1 −0.31 −0.20 −0.073 T = 298.15 −1.9 −0.18 0.55 1.4 −0.19 −0.52 −0.72 0.94 T = 303.15 −0.038 −0.80 −0.12 −0.27

xA

100RD (eq 13)

100x

K 0.00 −11 3.4 3.5 −6.7 4.4 −1.8 0.00

−41 −22 11 18 8.3 11 −1.7 0.82

0.00 −11 2.5 3.1 −4.5 2.6 −0.87 0.00

−33 −22 7.1 14 6.4 7.6 −1.2 0.26

0.00 −9.5 3.6 1.6 −3.8 2.5 −0.94 0.00

−33 −22 5.5 9.4 3.9 5.1 −2.3 0.91

0.00 −11 2.5 2.8 −3.6 1.7 −0.45 0.00

−22 −21 2.5 7.4 1.2 2.8 −2.3 0.14

0.00 −8.5 2.2 1.9 −2.5 1.1 −0.25 0.00

−22 −19 1.4 5.4 0.89 0.95 −2.6 0.89

0.00 −8.4 2.4 1.4

−14 −17 −0.44 1.8

K

K

K

K

K

0.5793 0.7336 0.8920 1.000

6.048 7.899 10.29 12.90

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

1.714 2.494 3.993 5.530 7.282 9.365 12.30 15.15

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

2.217 3.112 4.814 6.596 8.641 11.02 14.40 17.91

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

2.868 3.908 5.830 7.868 10.24 13.00 17.20 20.73

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

3.657 4.935 7.096 9.383 12.07 15.30 20.17 23.85

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

4.663 6.183 8.545 11.20 14.29 17.79 23.54 28.02

100RD (eq 4)

100RD (eq 10)

T = 303.15 −0.37 −0.29 0.042 −0.047 T = 308.15 −0.01 1.0 0.21 −0.20 0.51 0.049 0.47 −0.27 T = 313.15 −0.10 −0.055 −0.30 −0.14 0.22 −0.086 −0.73 0.66 T = 318.15 0.37 −0.32 −0.28 −0.086 0.093 0.19 0.44 −0.053 T = 323.15 −0.082 0.14 0.32 −0.058 −0.25 0.44 0.22 −1.0 T = 328.15 −0.028 −0.021 −0.068 0.087 0.053 −0.29 −0.18 0.52

100RD (eq 13)

K −1.3 0.20 0.13 0.00

−0.19 −0.11 −1.5 −0.29

0.00 −6.3 1.8 0.77 −0.24 −0.52 0.39 0.00

−8.5 −12 −0.66 0.35 0.065 −0.70 −0.52 −0.61

0.00 −5.1 1.7 0.54 −0.21 −0.41 0.31 0.00

−3.4 −9.9 −1.1 −0.45 −0.55 −1.4 −1.1 0.30

0.00 −5.6 1.2 1.1 0.29 −1.2 0.72 0.00

2.1 −6.2 −0.57 −0.67 −0.75 −1.4 0.81 −0.36

0.00 −4.9 0.95 1.1 0.34 −1.3 0.77 0.00

6.6 −1.5 1.1 −0.35 −0.92 −1.2 1.4 −1.2

0.00 −3.6 0.25 1.1 0.75 −1.7 0.91 0.00

11 2.8 2.2 0.60 −0.20 −1.6 2.0 0.51

K

K

K

K

K

a

xA is the mole fraction of ethyl acetate in the (ethyl acetate + n-butanol) binary solvent mixtures. x is the mole fraction solubility of APMC. Standard uncertainties for temperature, pressure, and mole fraction of ethyl acetate are u(T) = 0.05 K, u(P) = 0.58 kPa, and u(xA) = 0.0001, respectively. The relative standard uncertainty for solubility is ur(x) = 0.03.

correlate the solubility of APMC in three binary solvent mixtures (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol). The mole fraction solubility of APMC in three binary solvent mixtures over the temperature range from 278.15 to 328.15 K was presented in Tables 6−8 and shown graphically in Figures 6−8.

polarity. However, it can be found that the solubility of APMC in acetonitrile does not follow this principle. The reason may be due to the intermolecular comprehensive interaction between solvent and solute molecules. 3.2.2. In Binary Solvent Mixtures. The modified Apelblat, CNIBS/R−K, and the Jouyban−Acree models were applied to F



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Table 7. Mole Fraction Solubility x of 4-(4-Aminophenoxy)-N-methylpyridine-2-carboxamide in (Ethyl Acetate + Ethanol) Binary Solvent Mixtures in the Temperature Range from 278.15 K to 328.15 K under 101.3 kPaa xA

100x

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.5390 0.8760 1.380 1.851 2.658 3.701 4.436 5.276

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.7070 1.125 1.746 2.306 3.202 4.253 5.218 6.369

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.9140 1.446 2.200 2.909 3.857 4.919 6.060 7.730

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

1.359 1.876 2.757 3.635 4.708 5.754 7.208 9.190

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

1.792 2.427 3.502 4.535 5.731 6.838 8.592 11.03

0.0000 0.1394 0.2823 0.4289

2.493 3.153 4.429 5.636

100RD (eq 4)

100RD (eq 10)

T = 278.15 7.9 0.59 0.65 0.80 0.73 0.61 0.47 −0.78 T = 283.15 1.4 0.40 0.63 −0.26 0.27 0.43 0.54 −0.77 T = 288.15 −6.1 −0.054 0.23 0.20 −0.45 −0.17 −0.98 0.34 T = 293.15 1.7 0.14 0.70 −0.012 −0.076 −0.58 −0.37 −0.073 T = 298.15 −1.8 −0.22 0.27 −0.14 −0.19 −0.33 0.22 0.94 T = 303.15 0.94 −0.41 0.26 −0.39

xA

100RD (eq 13)

100x

K 0.00 3.9 5.7 −4.5 −2.0 3.4 −2.0 0.00

−0.49 13 20 15 19 22 11 1.1

0.00 1.8 4.3 −3.8 −0.84 2.3 −1.4 0.00

−7.2 7.1 15 10 13 15 6.6 0.51

0.00 1.5 2.9 −2.7 −0.68 2.0 −1.2 0.00

−15 1.9 10 7.2 7.9 7.6 1.5 1.2

0.0 −1.4 2.0 −1.3 0.16 0.32 −0.21 0.00

−5.5 −1.5 5.8 4.2 4.5 2.0 −0.72 0.39

0.00 −1.9 1.7 −1.0 0.38 −0.13 0.043 0.00

−8.3 −4.2 3.3 1.7 1.6 −1.6 −2.1 1.2

0.00 −2.7 1.7 −0.70

−4.4 −5.6 1.1 −0.34

K

K

K

K

K

0.5793 0.7336 0.8920 1.000

7.026 8.174 10.21 12.90

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

3.314 4.152 5.628 7.016 8.517 9.890 12.14 15.15

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

4.398 5.361 7.083 8.786 10.51 12.05 14.37 17.91

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

5.873 7.069 8.976 10.71 12.95 14.57 17.27 20.73

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

7.640 9.271 11.29 13.35 15.75 17.98 20.63 23.85

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

9.987 12.12 14.25 16.36 19.42 22.18 24.65 28.02

100RD (eq 4)

100RD (eq 10)

T = 303.15 0.23 −0.32 0.28 −0.047 T = 308.15 −0.036 0.56 0.26 −0.22 −0.66 0.15 0.23 −0.27 T = 313.15 −0.40 −0.63 0.13 0.78 0.12 0.63 −0.50 0.66 T = 318.15 0.61 0.14 0.24 −0.66 0.62 −0.37 0.16 −0.053 T = 323.15 −0.27 0.23 0.064 0.39 −0.34 0.12 0.10 −1.0 T = 328.15 0.025 −0.091 0.018 −0.11 0.029 −0.045 −0.057 0.52

100RD (eq 13)

K 0.73 −0.85 0.46 0.00

−0.047 −4.0 −3.1 −0.063

0.00 −2.1 1.4 −0.43 0.25 −0.39 0.25 0.00

−4.2 −4.7 0.26 −1.5 −2.1 −4.5 −3.5 −0.33

0.00 −1.1 1.1 −0.50 −0.031 0.15 −0.068 0.00

−3.3 −4.9 −0.80 −1.3 −1.7 −3.6 −3.8 0.58

0.00 −0.37 1.2 −1.6 1.1 −0.45 0.079 0.00

−0.91 −2.1 −0.39 −3.2 −0.71 −2.9 −2.0 −0.12

0.00 0.61 0.40 −1.0 0.28 0.48 −0.45 0.00

−0.35 0.81 −0.0071 −2.01 −0.52 0.44 −0.22 −0.96

0.00 2.1 0.33 −2.4 0.61 1.4 −1.3 0.00

1.5 4.1 1.3 −2.0 1.7 4.1 2.0 0.76

K

K

K

K

K

a xA is the mole fraction of ethyl acetate in (ethyl acetate + ethanol) binary solvent mixtures. x is the mole fraction solubility of APMC. Standard uncertainties for temperature, pressure, and mole fraction of ethyl acetate are u(T) = 0.05 K, u(P) = 0.58 kPa, and u(xA) = 0.0001, respectively. The relative standard uncertainty for solubility is ur(x) = 0.02.

3.2.2.1. Modified Apelblat Equation. The model parameters determined by the experimental solubility data are listed in Table 9. ln x = A +

theoretical models for calculating the solute solubility in binary solvents.39−44 This equation is expressed as eq 9 N

B + C ln(T /K) T /K

ln x = xA ln XA + x B ln XB + xAx B∑ Si(xA − x B)i i=0

3.2.2.2. CNIBS/R−K Model. The combined nearly ideal binary solvent/Redich−Kister (CNIBS/R−K) model is one of the

(9)

where xA and xB represent the initial mole fraction compositions of the binary solvents when the solute was not added. XA is the G



Article

Table 8. Mole Fraction Solubility x of 4-(4-Aminophenoxy)-N-methylpyridine-2-carboxamide in (Ethyl Acetate + Methanol) Binary Solvent Mixtures in the Temperature Range from 278.15 to 328.15 K under 101.3 kPaa xA

100x

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

0.8090 1.330 1.778 2.051 2.738 3.546 4.524 5.276

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

1.174 1.699 2.235 2.626 3.433 4.242 5.321 6.369

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

1.576 2.153 2.790 3.321 4.241 5.124 6.319 7.730

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

2.029 2.768 3.508 4.203 5.260 6.135 7.540 9.190

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

2.760 3.528 4.374 5.286 6.490 7.450 8.903 11.03

0.0000 0.1394 0.2823 0.4289

3.694 4.508 5.472 6.543

100RD (eq 4)

100RD (eq 10)

T = 278.15 −1.5 −0.80 0.74 −0.63 0.48 0.81 −0.92 −0.78 T = 283.15 3.6 −0.45 0.47 −0.34 0.35 −0.082 −0.97 −0.77 T = 288.15 2.1 −0.89 −0.26 −0.59 −0.53 0.020 −0.29 0.34 T = 293.15 −2.7 0.049 −0.064 −0.10 −0.35 −0.72 0.63 −0.073 T = 298.15 −0.97 0.11 −0.48 0.39 −0.034 −0.00093 0.30 0.94 T = 303.15 −0.019 0.43 −0.34 −0.11

xA

100RD (eq 13)

100x

K 0.00 2.9 2.6 −5.4 1.3 1.4 −1.1 0.00

−15 12 15 4.4 8.4 10 7.9 0.92

0.00 1.8 2.2 −4.3 1.5 0.72 −0.72 0.00

−8.2 7.8 11 3.3 7.0 6.0 3.8 0.39

0.00 1.7 1.6 −3.5 1.2 0.78 −0.74 0.00

−8.4 3.6 6.8 1.9 5.0 3.4 1.1 1.1

0.00 2.1 0.48 −2.8 1.7 −0.050 −0.35 0.00

−12 1.6 4.2 1.3 4.0 0.50 −0.50 0.32

0.00 2.5 0.074 −2.3 1.2 0.42 −0.61 0.00

−8.6 −0.36 1.6 1.0 3.3 −0.31 −2.5 1.1

0.00 1.7 −0.026 −1.7

−6.0 −1.2 0.031 −0.15

K

K

K

K

K

0.5793 0.7336 0.8920 1.000

7.895 8.992 10.64 12.90

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

4.880 5.758 6.870 8.153 9.707 10.81 12.56 15.15

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

6.336 7.278 8.513 10.02 11.73 13.03 14.91 17.91

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

8.205 9.277 10.57 12.17 13.95 15.60 17.70 20.73

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

10.52 11.72 13.09 14.75 16.72 18.85 21.02 23.85

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.000

13.43 15.05 16.17 18.08 19.97 22.55 25.44 28.02

100RD (eq 4)

100RD (eq 10)

T = 303.15 −0.53 0.17 0.98 −0.047 T = 308.15 0.47 0.70 0.38 0.60 0.64 −0.0045 0.28 −0.27 T = 313.15 0.035 −0.053 0.0080 0.49 0.62 0.13 0.020 0.66 T = 318.15 0.11 0.072 0.055 −0.24 −0.48 −0.27 −0.37 −0.053 T = 323.15 −0.10 −0.66 −0.0086 −0.75 −0.21 0.28 −0.82 −1.0 T = 328.15 0.010 0.27 −0.021 0.37 0.14 −0.10 0.50 0.52

100RD (eq 13)

K 1.1 0.20 −0.42 0.00

1.9 −1.1 −2.7 −0.087

0.00 1.8 −0.20 −1.7 1.2 0.078 −0.40 0.00

−3.9 −1.3 −0.39 0.075 2.2 −1.6 −3.6 −0.33

0.00 1.8 −0.36 −1.4 0.81 0.42 −0.58 0.00

−2.8 −1.7 −1.4 −0.38 1.4 −1.2 −3.3 0.60

0.00 1.4 −0.39 −0.89 0.34 0.65 −0.65 0.00

−1.2 −0.43 −1.5 −1.3 −0.33 −0.92 −2.4 −0.081

0.00 1.1 −0.20 −0.86 0.037 1.0 −0.85 0.00

0.14 0.63 −1.2 −1.9 −0.66 0.80 −1.0 −0.90

0.00 1.2 −1.2 0.30 −0.14 0.44 −0.38 0.00

1.8 3.9 −0.43 −0.74 −0.83 2.0 2.7 0.84

K

K

K

K

K

a

xA is the mole fraction of ethyl acetate in (ethyl acetate + methanol) binary solvent mixtures. x is the mole fraction solubility of APMC. Standard uncertainties for temperature, pressure, and mole fraction of ethyl acetate are u(T) = 0.05 K, u(P) = 0.58 kPa, and u(xA) = 0.0001, respectively. The relative standard uncertainty for solubility is ur(x) = 0.03.

saturated mole solubility of APMC in ethyl acetate. XB is the saturated mole solubility of APMC in methanol, ethanol, and n-butanol, respectively. Si is the model constant, and N can be equal to 0, 1, 2, and 3. When N = 2 and substituting (1 − xA) for xB, eq 9 can be written as eq 10

ln x − (1 − xA ) ln XB − xA ln XA = (1 − xA)xA[S0 + S1(2xA − 1) + S2(2xA − 1)2 ]

(10)

This is a variant of the CNIBS/R−K model. Parameter Si can be obtained by regressing {ln x − (1 − xA) ln XB − xA ln XA} versus H



Article

Figure 6. Plot of the mole fraction solubility (x) of APMC versus temperature (T) in (ethyl acetate + n-butanol) binary solvent mixtures.

Figure 8. Plot of the mole fraction solubility (x) of APMC versus temperature (T) in (ethyl acetate + methanol) binary solvent mixtures.

Table 9. Parameters of the Modified Apelblat Model for APMC in Three Binary Solvent Mixtures

Figure 7. Plot of the mole fraction solubility (x) of APMC versus temperature (T) in (ethyl acetate + ethanol) binary solvent mixtures.

{(1 − xA)xA[S0 + S1(2xA − 1) + S2(2xA − 1)2 ]}

The values of the parameters are given in Table 10. However, the CNIBS/R−K model can be used to describe only the solubility data and to predict solubility data for different concentrations of a mixed solvent at a fixed temperature. To describe the effect of both solvent composition and temperature on the solubility of APMC, we adopt another equation. 3.2.2.3. Jouyban−Acree Model. The Jouyban−Acree model is widely used to describe the solubility of a solute with the variation of both temperature and the initial composition of binary solvent mixtures.45−58 This equation is expressed as eq 11 N

ln x = xA ln XA + x B ln XB + xAx B∑ i=0

Ji (xA − x B)i T

(11)

xA

A

B

C

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.0000

−59.21 −140.8 −133.0 −143.2 −59.98 −71.95 −27.68 −11.22

Ethyl Acetate + n-Butanol −1696.21 2511.31 2828.84 3586.41 −210.650 507.000 −1605.72 −2163.33

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.0000

−24.95 −253.7 −170.1 −105.7 −193.5 −328.8 −180.2 −11.22

Ethyl Acetate + Ethanol −3710.78 7159.81 3872.98 1222.10 5480.11 11 880.1 5325.53 −2163.33

0.0000 0.1394 0.2823 0.4289 0.5793 0.7336 0.8920 1.0000

−24.95 −183.2 −116.0 −24.52 −6.911 −127.5 −171.2 −11.22

Ethyl Acetate + Methanol −3710.78 4346.02 1640.98 −2387.60 −2897.60 2735.72 4935.07 −2163.33

100RAD

10.58 0.88 22.50 0.32 21.04 0.32 22.46 0.37 10.13 0.38 11.85 0.31 5.370 0.38 2.850 0.50 average(100RAD) = 0.43 5.860 1.9 39.66 0.31 26.99 0.31 17.29 0.36 30.23 0.34 50.24 0.34 28.05 0.35 2.850 0.50 average(100RAD) = 0.55 5.860 1.0 29.01 0.41 18.84 0.26 5.192 0.42 2.439 0.40 20.31 0.23 26.71 0.55 2.850 0.50 average(100RAD) = 0.47

or (N = 2)

where Ji is the model constant, T is the absolute temperature, and the other symbols have the same meaning as in eq 9. In these works, we expressed the variation in ln XA and ln XB values in eq 11 as

⎛ ⎛ B ⎞ B ⎞ ln x = xA ⎜A1 + 1 ⎟ + x B⎜A 2 + 2 ⎟ ⎝ ⎝ T⎠ T⎠ xAx B + [J + J1(xA − x B) + J2 (xA − x B)2 ] (13) T 0 where the A1, B1, A2, B2, and Ji terms are the model constants, which are listed in Table 11.

N J (xA − x B)i ⎛ ⎛ B ⎞ B ⎞ ln x = xA ⎜A1 + 1 ⎟ + x B⎜A 2 + 2 ⎟ + xAx B∑ i ⎝ ⎝ T⎠ T⎠ T i=0

(12) I



Article

Table 10. Parameters of the CNIBS/R−K Model for APMC in Thee Binary Solvent Mixtures T 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

S0

S1

S2

Table 11. Parameters of the Jouyban−Acree Model for APMC in Three Binary Solvent Mixtures T/K

100RAD

Ethyl Acetate + n-Butanol 2.1 −1.4 −0.73 3.9 1.8 −1.2 −0.63 3.1 1.6 −1.2 −0.66 2.8 1.3 −0.93 −0.61 2.7 1.2 −0.96 −0.64 2.1 1.0 −0.67 −0.45 1.7 0.86 −0.56 −0.30 1.3 0.71 −0.48 −0.47 1.0 0.57 −0.34 −0.16 1.3 0.47 −0.29 0.060 1.2 0.35 −0.30 −0.010 1.0 average(100RAD) = 2.0 Ethyl Acetate + Ethanol 1.2 −0.049 −0.37 2.7 1.1 −0.40 −0.38 1.8 1.0 −0.78 −0.66 1.4 0.66 −0.56 −0.94 0.67 0.57 −0.69 −0.95 0.64 0.43 −0.53 −1.0 0.89 0.36 −0.54 −0.90 0.60 0.34 −0.47 −1.1 0.37 0.28 −0.35 −0.80 0.61 0.30 −0.25 −0.47 0.41 0.28 −0.17 −0.31 1.0 average(100RAD) = 1.0 Ethyl Acetate + Methanol 0.59 −0.80 1.1 1.8 0.41 −0.59 0.26 1.4 0.32 −0.55 −0.21 1.2 0.35 −0.63 −0.30 0.93 0.26 −0.51 −0.77 0.89 0.18 −0.36 −0.73 0.64 0.15 −0.31 −0.89 0.66 0.088 −0.26 −0.92 0.66 0.0071 −0.20 −0.62 0.54 −0.023 −0.083 −0.35 0.51 −0.10 −0.091 0.051 0.45 average(100RAD) = 0.88

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15

RAD

parameters

Ethyl Acetate + n-Butanol 14 A1 8.03 11 B1 −3053.98 10 A2 9.10 7.4 B2 −4033.35 6.6 J0 210.29 4.4 J1 −155.73 3.0 J2 −49.670 2.3 1.6 1.8 2.7 average(100RAD) = 6.0 Ethyl Acetate + Ethanol 13 A1 8.03 9.2 B1 −3053.83 6.5 A2 13.81 3.1 B2 −5293.27 3.0 J0 101.81 2.3 J1 −91.12 2.6 J2 −206.75 2.5 1.5 0.66 2.2 average(100RAD) = 4.2 Ethyl Acetate + Methanol 9.3 A1 8.01 5.9 B1 −3049.66 3.9 A2 12.70 3.1 B2 −4833.31 2.4 J0 −0.47 1.7 J1 −48.93 1.7 J2 −131.27 1.6 1.0 0.91 1.7 average(100RAD) = 3.0

As shown in Figures 6−8, the solubility of APMC in binary solvent mixtures is a function of temperature and solvent composition. The solubility of APMC in the binary solvent mixtures increases rapidly with increasing temperature while it decreases with increasing methanol, ethanol, and n-butanol content at constant temperature; therefore, methanol, ethanol, and n-butanol could be used as effective antisolvents in the crystallization process of APMC.

3.2.2.4. Deviation. Similarly, RD and RAD were used to estimate the applicability of the models. The RD values in three binary solvent mixtures are listed in Tables 6−8. The parameter values of eqs 4, 10, and 13 are listed in Tables 9−11 together with the values of 100RAD. From the data listed in Tables 9−11, we can see that the maximum RAD values of the modified Apelblat equation, CNIBS/R−K model, and Jouyban−Acree model are 0.55%, 2.0%, and 6.0%, respectively. This result indicates that the modified Apelblat model proved to be more accurate and suitable for the description of the dissolution of APMC in the binary system at various temperatures while the CNIBS/R−K model and Jouyban−Acree model cause high deviations. Actually, the modified Apelblat model can be used to describe only the solubility data for different temperatures of mixed solvent at a fixed solvent composition. When both temperature and composition are taken into account, the CNIBS/R−K model and Jouyban−Acree model can be adopted and assisted with the modified Apelblat equation.

4. CONCLUSIONS We have employed a gravimetric method to determine the solubility of APMC in tetrahydrofuran, ethyl acetate, acetonitrile, n-butanol, n-propanol, ethanol, methanol, and (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol) binary solvent mixtures from T = (278.15 to 328.15) K under atmosphere pressure. In all solvents determined, the solubility of APMC increases with an increase in temperature to different extents. For the pure solvents, the solubility increment in ethyl acetate is the most remarkable. Moreover, our results have clearly demonstrated that the solubility of APMC in (ethyl acetate + methanol, ethyl acetate + ethanol, and ethyl acetate + n-butanol) binary solvent mixtures is low at low temperature but quickly J



Article

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increases at higher temperature. This phenomenon can be applied in the crystallization process of APMC. The experimental solubility of APMC was correlated by the modified Apelblat equation, λh equation, CNIBS/R−K model, and Jouyban−Acree model with satisfactory results, in which the modified Apelblat equation stood out to be more suitable than the other three models.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-25-83587108. Fax: +86-25-83587108. ORCID

Wenge Yang: 0000-0002-2501-3532 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (no. 31471693), Jiangsu Provincial Policy Guidance Plan (university−industry−research cooperation) prospective joint research projects (BY2016005-07), and the Jiangsu Agricultural Science and Technology Innovation Fund (CX(17)3052). We thank the editors and the anonymous reviewers.

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