Measurement and modeling correlation of capecitabine solubility in n-hexane + ethyl acetate and n-heptane + ethyl acetate at various temperatures

Journal of Molecular Liquids 295 (2019) 111716

Contents lists available at ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Measurement and modeling correlation of capecitabine solubility in n-hexane þ ethyl acetate and n-heptane þ ethyl acetate at various temperatures Rui Zhao a, b, Yameng Wan a, Pengshuai Zhang a, Ning Wu a, Jiao Sha a, Tao Li a, *, Baozeng Ren a, * a b

School of Chemical Engineering, Zhengzhou University, Zhengzhou, He’nan 450001, People’s Republic of China Henan chemical Technician College, Kaifeng, He’nan 475000, People’s Republic of China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 June 2019 Received in revised form 4 September 2019 Accepted 6 September 2019 Available online 7 September 2019

In this work, by using laser dynamic isothermal method, the solubilization behavior and thermodynamics of capecitabine solubility in the binary mixtures of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate from (278.15 to 323.15) K were measured under atmospheric pressure. The measured results showed that the experimental solubility of capecitabine increased non-linearly with increasing temperature and ethyl acetate content (w1) in the studied mixture solvents. Six cosolvency mathematical models including the modified Apelblat equation, combined nearly ideal binary solvent/ Redlich-Kister (CNIBS/R-K) equation, Wilson model, non-random two liquid (NRTL) model, UNIQUAC model, and the modified Jouyban-Acree-van’t Hoff model were fitted to the experimental results. The maximum relative average deviation (ARD) was 0.27, the maximum root-mean-square deviation (RMSD) was 0.0007. The order of the relative average deviation (ARD) of the six cosolvency mathematical models is CNIBS/R-K > modified Jouyban-Acree-van’t Hoff > NRTL > Wilson > modified Apelblat > UNIQUAC. Basically speaking, the measured solubility data in this study can be well correlated with the six thermodynamic models, while the modified Jouyban-Acree-van’t Hoff model allowed the calculation of solubility of capecitabine at an arbitrary mixture composition and temperature in the studied binary solvent mixtures composition and temperature. Moreover, apparent thermodynamic properties of capecitabine dissolution process in the investigated mixed solvents including entropy, enthalpy and Gibbs free energy were computed using van’t Hoff and Gibbs equations. Besides, the logarithm of activity coefficient of capecitabine (lng1) in the studied saturated solutions were also calculated with the NRTL model, UNIQUAC model, and Wilson model, respectively. The positive values of lng1 means that the repulsive interactions exist between capecitabine and the corresponding mixture solvents, and the solutions system positively deviate from Raoult’s law. This work can give fundamental data for the crystallization and purification of capecitabine from ethyl acetate. © 2019 Elsevier B.V. All rights reserved.

Keywords: Capecitabine Solubility Ethyl acetate N-hexane N-heptane Binary solvent mixture

1. Introduction Capecitabine (CAS registry No. 154361-50-9) is a white to offwhite crystalline powder, which chemical structure is presented in Fig. 1. Its molecular formula and molar mass are C15H22FN3O6 and 359.35 g$mol1, respectively. Capecitabine is an important prodrug of fluoropyrimidine, which is used as first line treatment of patients with metastatic colorectal carcinoma. The industrial products of capecitabine always crystallize from acetic esters [1]. Therefore, the

* Corresponding authors. E-mail addresses: [email protected] (T. Li), [email protected] (B. Ren). https://doi.org/10.1016/j.molliq.2019.111716 0167-7322/© 2019 Elsevier B.V. All rights reserved.

experimental solubility data of capecitabine in acetic esters is significant for its crystallization process. In order to extend the practical database on capecitabine solubility data and select a suitable solvent system, the aims of this work were to (1) measure the experimental solubility data of capecitabine in n-hexane þ ethyl acetate and n-heptane þ ethyl acetate from (278.15 to 323.15) K; (2) fit and back-calculate the obtained solubility data with some cosolvency models; and (3) compute the apparent thermodynamic parameters of capecitabine dissolution in studied mixed solvents.

2

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

Fig. 1. Chemical structure of capecitabine.

2. Experimental 2.1. Materials The experimental capecitabine (0.99 mass fraction purity, batch number: 003160701, approval number: H20133364) used in this work was supplied by Lianyungang Guike Pharmaceutical Co., Ltd. of china. In the present study, all the organic solvents were used as received without further purification and the materials details were list in Table 1. 2.2. TG-DSC analysis The melting temperature Tm and fusion enthalpy DfusH are the basic thermodynamic properties of capecitabine and it is necessary for the correlation of the experimental solubility data with the thermodynamic models, such as NRTL model, Wilson model, and UNIQUAC model. The values of Tm and DfusH of capecitabine had been obtained in our previous literature [2]. 2.3. Experimental method

literature [3,4] and described here briefly. First, an amount of mixture solvent was accurately weighed by using a precision weighing balance (Sartorius, type BSA224S, Germany) with an uncertainty of ±0.0001 g, then injected them in a 200 mL doublejacketed glass crystallizer, in order to control the temperature of the crystallizer, a super thermostatically-controlled water bath (Bilang, type DCW0506, China) was used in this study and the standard uncertainty of the water bath is ±0.05 K. Second, an excess amount of capecitabine (m1) was also accurately weighed and added in the glass crystallizer, after the capecitabine was small amount dissolved with the help of a magnetic stirring apparatus (Jintan Huafeng, type 85-2A, China) for about 2 h and then continue to add small quantities of mixture solvent per 2 h in the glass crystallizer, the quality of solvent was recorded each time. When the electrical signal reached its maximum value until the last crystal of capecitabine was completely dissolved, then the solution was just reach the saturated point and calculated the total mass of the mixture solvent. The reported solubility data point was the average of three repeats. The mole fraction of capecitabine (x1), ethyl acetate (x2), and nalkanes (x3) in mixture solutions were expressed as:

The experimental method used in this work was similar to

Table 1 Sources and purity of the experiment materials used in this work. Chemical name

CAS registry number

Source

Mass fraction

Capecitabine Ethyl acetate n-Hexane n-Heptane

154361-50-9 141-78-6 110-54-3 142-82-5

Lianyungang Guike pharmaceutical co., LTD Sinopharm chemical reagent co., LTD Tianjin Fengchuan chemical reagent co., LTD Tianjin Fengchuan chemical reagent co., LTD

Mass Mass Mass Mass

a b

The purity was analyzed by High-performance liquid chromatography. The purity was determined by Gas chromatography.

purity purity purity purity

0.998a 0.995b 0.995b 0.985b

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

x1 ¼

m1 =M1 m1 =M1 þ m2 =M2 þ m3 =M3

(1)

x2 ¼

m2 =M2 m1 =M1 þ m2 =M2 þ m3 =M3

(2)

x3 ¼

m3 =M3 m1 =M1 þ m2 =M2 þ m3 =M3

(3)

3

The mole fraction of ethyl acetate (x10 ) in mixed solvents without capecitabine was expressed as:

x’1 ¼

m2 =M2 m2 =M2 þ m3 =M3

(4)

The mass fraction of ethyl acetate (w1) in mixed solvents without capecitabine can be expressed as:

w1 ¼

m2 m2 þ m3

(5)

where m1, m2 and m3 stand for the mass of capecitabine, ethyl acetate and n-alkanes, respectively; M1, M2 and M3 represent the molar mass of capecitabine, ethyl acetate and n-alkanes, respectively. 3. Results and discussion 3.1. Experimental solubility data and correlation The experimental solubility of capecitabine in the binary solvent mixtures of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate from (278.15 to 323.15) K under atmospheric pressure are listed in Table 3 and Table 4, and the corresponding diagram are demonstrated in Fig. 2 and Fig. 3. As can be seen, for the investigated mixed solvents the highest solubility value was observed in neat ethyl acetate at 323.15 K (0.3177 mol$L1), exhibiting a feature of low solubility. Capecitabine solubility profile represents an increase in solubility with increase in temperature, and at all temperatures the solubility rises as the ethyl acetate content increases in the mixed solvents. The solubility reaches a maximum value in neat ethyl acetate. The experimental solubility data of capecitabine in the mixed solutions of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate were correlated and back-calculated using some reported mathematical models namely the modified Apelblat equation, combined nearly ideal

Fig. 3. Experimental mole fraction solubility of capecitabine (x1) in binary mixed solvents of n-heptane þ ethyl acetate: x10 is the mole fraction of ethyl acetate in mixed solvents without capecitabine (The solid line was fitted by CNIBS/R-K equation).

binary solvent/Redlich-Kister (CNIBS/R-K) equation, Wilson model, non-random two liquid (NRTL) model, UNIQUAC model, and the modified Jouyban-Acree-van’t Hoff model, which are given here in brief. 3.1.1. The modified Apelblat equation The modified Apelblat equation is a semi-empirical equation to correlate the temperature and the solubility, which can be derived as follows [5,6]:

lnx1 ¼ A þ

B þ ClnðT=KÞ T=K

(6)

where A, B and C are the modified Apelblat equation parameters. 3.1.2. CNIBS/R-K equation The combined nearly ideal binary solvent/Redlich-Kister (CNIBS/R-K) equation was proposed by Acree and his co-workers [7e9]. This equation can be described as Eq. (7).


2
3
4 lnx1 ¼ B0 þ B1 x’1 þ B2 x’1 þ B3 x’1 þ B4 x’1

(7)

Where, B0eB4 are the equation’s parameters which were obtained by least-squares analysis. 3.1.3. The modified Jouyban-Acree-van’t Hoff model The Jouyban-Acree model combined with van’t-Hoff model could give an accurate method to prediction of the solubility in the mixed solvents. The Jouyban-Acree-van’t Hoff model [10,11] is represented as:

    2 B B w ,w X lnx1;T ¼ w1 A1 þ 1 þ w2 A2 þ 2 þ 1 2 Ji ,ðw1  w2 Þi T T T i¼0 (8) In Eq. (8), A1, B1 and A2, B2 are coefficient of the van’t Hoff model computed by drawing lnx1 against 1/T in the mono-solvents 1 and 2 at different temperatures, respectively. Ji terms are then calculated using the above equation as the model constants of multiple linear regression of (lnx1,T-w1(A1 þ B1/T)-w2(A2 þ B2/T)) against w1$w2/T, w1$w2(w1-w2)/T and w1$w2(w1-w2)2/T. Eq. (8) could be rearranged as Eq. (9) [12] to correlate the solubility data in solvent mixtures at different temperatures. Fig. 2. Experimental mole fraction solubility of capecitabine (x1) in binary mixed solvents of n-hexane þ ethyl acetate: x10 is the mole fraction of ethyl acetate in mixed solvents without capecitabine (The solid line was fitted by CNIBS/R-K equation).

lnx1;T ¼ D1 þ

w2 w3 w4 D2 w þ D3 w1 þ D4 1 þ D5 1 þ D6 1 þ D7 1 T T T T T

(9)

4

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

Here, D1eD7 are the model’s parameters which were computed with a simple with an intercept regression analysis. 3.1.4. Local composition model According to the traditional theory, when the solid-liquid phase reaches equilibrium at constant temperature T and pressure P, the fugacity of the solute 1 (capecitabine in this work) in the pure solid phase fS1(T, P) is same with the fugacity of the solute 1 in the liquid phase fL1(T, P, xL) at a certain condition. The fugacity relationship between the solid and liquid phase can be described as:



f1S ðT; PÞ ¼ f1L T; P; xL



(10)

The fugacity of the solute in the liquid phase fL1(T, P, xL) can also be expressed as follows

(11)

where x1 is the mole fraction solubility of capecitabine in mixture solution and g1 is the activity coefficient of the solute at the solidliquid equilibrium; fL1(T, P) is the fugacity of the solute 1 in the pure liquid phase. Further deduction and assumptions can result in the simplified equation as follows [13,14].

lnx1 ¼



R

    DCp 1 1 T Tm  lng1  1  þ ln Tm T Tm R,T T

(12)

where x1 is the mole fraction solubility of capecitabine in mixture solvents at absolute temperature T; Tm ¼ 393.05 K, DfusH ¼ 27.19 kJ$mol1; The value of △Cp is negligible and can be ignored. To back-calculate the value of x1, it is necessary to calculate the value of lng1. The logarithm of activity coefficient of capecitabine (lng1) in the studied saturated solutions could be calculated with the NRTL model, UNIQUAC model, and Wilson model. The NRTL model was derived by Renon and Prausnitz [15]. Combine with the local composition model, it is widely used to correlate the solid-liquid equilibrium [16e18]. The form of NRTL in the multicomponent system is as follows [14,19]: m P

GE RT

¼

m X

xi

i¼1

tji xj Gji

j¼1 m P

(17)

where aij represents the non-randomness of the mixture and the value of aij usually varies from 0.20 to 0.47; the values Dgij stands for the adjustable interaction energy parameters. The UNIQUAC (universal quasichemical) model was proposed by Abrams in 1975 [20,21]. The expression of UNIQUAC model for multicomponent mixtures of m components could be given as follows [14,22]:

GE GE ðcombinatorialÞ GE ðresidualÞ þ ¼ R,T R,T R,T

(18)

m m GE ðcombinatorialÞ X f z X q ¼ xi ln i þ xi qi ln i R,T xi 2 fi

(19)

i¼1

  f1L T; P; xL ¼ x1 g1 ðT; P; x1 Þf1L ðT; PÞ

Dfus H


 Gij ¼ exp  aij tij

(13) xl Gli

i¼1

1 0 m m X X GE ðresidualÞ ¼  qi xi ln@ qj tji A R,T i¼1 j¼1

(20)

m fi z q f X þ qi ln i þ li  i xl xi 2 fi xi j¼1 j j 2 0 1 m m 6 X X qj tji 6 þ qi 61  ln@ qj tji A  m P 4

lngi ¼ ln

j¼1

qj tkj

j¼1

3 (21)

7 7 7 5

k¼1

For ternary system, the logarithm of activity coefficient of solute (capecitabine in this work) in the studied saturated solutions could be expressed as:

lng1 ¼ ln

    f1 z q r r þ q1 ln 1 þ f2 l1  1 l2 þ f3 l1  1 l3 x1 2 f1 r2 r3

 q1 lnðq1 þ q2 t21 þ q3 t31 Þ  q1 q2 t21 þ q1 q3 t31 q1 q2 t12 þ  q1 þ q2 t21 þ q3 t31 q1 t12 þ q2 þ q3 t32  q1 q2 t13  q1 t13 þ q2 t23 þ q3

(22)

l¼1 m P

lngi ¼

0

tji xj Gji

j¼1 m P

þ xl Gli

l¼1

m X j¼1

m P

1

trj xr Grj C

xj Gij B B C r¼1 Btij  m C m P P @ A xl Glj xl Gli l¼1

(14)

l¼1

For ternary system, the logarithm of activity coefficient of solute (capecitabine in this work) in the studied saturated solutions could be expressed as:

lng1 ¼

ðt21 x2 G21 þ t31 x3 G31 Þðx2 G21 þ x3 G31 Þ ðx1 þ x2 G21 þ x3 G31 Þ2 þ

þ

tij ¼

x2 G12 ðt12 x2 þ t12 x3 G32  t32 x3 G32 Þ ðx1 G12 þ x2 þ x3 G32 Þ2

(15)

x3 G13 ðt13 x3 þ t13 x2 G23  t23 x2 G23 Þ

Dgij RT

ðx1 G13 þ x2 G23 þ x3 Þ2 (16)

Table 2 Calculated van der Waals molar volume and surface area of capecitabine using elements and chemical bonds method. Element and chemical bond

Number

Volume/ (cm3$mol1)

Surface area/ (109 cm2$mol1)

C H F N O CeF CeC CeO C]O C]N CeN NeH OeH CeH CeC (ring) CeO (ring) C]C (ring) CeN (ring) SUM

15 22 1 3 6 1 5 3 2 1 2 1 2 19 4 2 1 2

185.85 95.92 8.01 28.17 51.06 4.44 21.50 14.46 9.74 5.41 7.52 2.95 5.18 60.23 19.08 9.38 5.55 7.40 196.17

32.85 23.98 1.63 5.46 10.20 0.96 5.80 3.39 2.30 1.34 2.14 0.66 1.66 17.48 4.84 2.14 1.31 2.36 27.74

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

5

Table 3 Experimental and calculated mole fraction solubility of capecitabine and relative deviations (RD) in binary mixed solvents of n-hexane þ ethyl acetate at different temperature and under p ¼ 101.3 kPa.a,b T/K

100xexp 1

Apelblat

Wilson

NRTL

100xcal 1

100xcal 1

100xcal 1

100RD

100RD

UNIQUAC 100RD

100xcal 1

100RD

w1c¼0.1019 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0032 0.0044 0.0061 0.0083 0.0111 0.0148 0.0196 0.0257 0.0335 0.0433

0.0034 0.0046 0.0062 0.0083 0.0111 0.0147 0.0194 0.0255 0.0334 0.0435

7.71 4.86 2.67 1.07 0.03 0.66 0.89 0.75 0.28 0.50

0.0033 0.0045 0.0061 0.0081 0.0108 0.0144 0.0191 0.0254 0.0340 0.0457

3.63 2.18 0.71 2.24 2.47 2.69 2.37 0.98 1.38 5.44

0.0032 0.0044 0.0061 0.0083 0.0112 0.0150 0.0198 0.0259 0.0338 0.0436

0.33 0.86 0.09 0.14 0.90 1.02 0.91 0.96 0.79 0.73

0.0032 0.0044 0.0061 0.0082 0.0111 0.0148 0.0196 0.0257 0.0336 0.0435

0.25 0.81 0.44 0.74 0.19 0.16 0.22 0.002 0.16 0.58

w1 ¼ 0.2044 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0037 0.0051 0.0069 0.0092 0.0122 0.0160 0.0208 0.0268 0.0344 0.0437

0.0039 0.0052 0.0070 0.0092 0.0122 0.0159 0.0207 0.0267 0.0343 0.0438

4.24 2.64 1.41 0.51 0.09 0.44 0.54 0.44 0.15 0.31

0.0038 0.0051 0.0069 0.0091 0.0120 0.0157 0.0205 0.0267 0.0347 0.0452

3.33 0.71 0.72 1.34 1.98 2.00 1.52 0.41 0.98 3.50

0.0035 0.0048 0.0066 0.0090 0.0121 0.0161 0.0213 0.0280 0.0364 0.0469

6.53 5.75 4.25 2.35 0.85 0.83 2.53 4.31 5.68 7.40

0.0038 0.0051 0.0069 0.0091 0.0121 0.0159 0.0207 0.0268 0.0346 0.0443

1.78 0.02 0.70 0.74 1.00 0.86 0.50 0.11 0.53 1.46

w1 ¼ 0.3047 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0121 0.0150 0.0185 0.0226 0.0274 0.0331 0.0398 0.0475 0.0564 0.0667

0.0126 0.0153 0.0186 0.0226 0.0273 0.0328 0.0394 0.0472 0.0564 0.0672

4.03 2.27 0.95 0.01 0.59 0.87 0.87 0.60 0.09 0.64

0.0100 0.0130 0.0168 0.0214 0.0272 0.0343 0.0430 0.0537 0.0668 0.0828

16.97 13.17 9.44 5.32 0.90 3.49 8.01 13.04 18.45 24.21

0.0086 0.0116 0.0154 0.0204 0.0266 0.0344 0.0443 0.0565 0.0716 0.0903

27.94 22.57 14.19 11.52 1.55 4.34 10.66 17.71 27.92 34.73

0.0123 0.0151 0.0184 0.0224 0.0272 0.0328 0.0395 0.0474 0.0568 0.0677

1.47 0.38 0.56 0.92 0.89 0.85 0.69 0.11 0.68 1.57

w1 ¼ 0.4054 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0273 0.0325 0.0385 0.0454 0.0531 0.0619 0.0717 0.0828 0.0951 0.1087

0.0284 0.0332 0.0388 0.0452 0.0526 0.0612 0.0709 0.0822 0.0950 0.1098

4.18 2.31 0.81 0.37 0.88 1.21 1.06 0.75 0.05 0.99

0.0199 0.0256 0.0327 0.0415 0.0523 0.0656 0.0818 0.1016 0.1257 0.1550

27.22 21.30 15.12 8.66 1.53 5.91 14.07 22.67 32.14 42.58

0.0144 0.0195 0.0262 0.0348 0.0458 0.0597 0.0773 0.0993 0.1267 0.1605

47.29 39.99 32.05 23.45 13.84 3.54 7.81 19.94 33.21 47.68

0.0278 0.0327 0.0383 0.0449 0.0524 0.0611 0.0712 0.0827 0.0959 0.1109

1.79 0.50 0.48 1.18 1.26 1.22 0.73 0.14 0.80 2.06

w1 ¼ 0.5059 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0343 0.0416 0.0503 0.0603 0.0719 0.0853 0.1005 0.1179 0.1375 0.1597

0.0353 0.0423 0.0505 0.0602 0.0714 0.0844 0.0995 0.1170 0.1372 0.1604

2.90 1.70 0.46 0.25 0.74 1.04 0.96 0.74 0.21 0.45

0.0271 0.0349 0.0445 0.0564 0.0710 0.0889 0.1107 0.1373 0.1697 0.2090

20.89 16.16 11.54 6.50 1.27 4.20 10.18 16.48 23.40 30.88

0.0217 0.0293 0.0390 0.0515 0.0673 0.0874 0.1125 0.1438 0.1826 0.2304

36.61 29.65 22.48 14.64 6.33 2.46 11.97 22.00 32.82 44.28

0.0346 0.0418 0.0501 0.0599 0.0714 0.0846 0.1000 0.1177 0.1382 0.1617

0.98 0.40 0.31 0.59 0.74 0.78 0.49 0.13 0.50 1.23

w1 ¼ 0.6053 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0752 0.0936 0.1156 0.1417 0.1725 0.2087 0.2509 0.2998 0.3563 0.4212

0.0785 0.0960 0.1168 0.1418 0.1714 0.2067 0.2485 0.2978 0.3559 0.4242

4.45 2.52 1.06 0.04 0.61 0.95 0.97 0.67 0.11 0.71

0.0687 0.0871 0.1097 0.1373 0.1708 0.2114 0.2604 0.3194 0.3904 0.4758

8.63 6.90 5.06 3.08 0.96 1.30 3.78 6.53 9.56 12.96

0.0461 0.0612 0.0806 0.1052 0.1362 0.1749 0.2231 0.2826 0.3559 0.4457

38.72 34.58 30.26 25.75 21.05 16.19 11.09 5.73 0.12 5.81

0.0761 0.0939 0.1153 0.1408 0.1711 0.2070 0.2494 0.2994 0.3580 0.4268

1.19 0.34 0.28 0.65 0.81 0.81 0.59 0.14 0.49 1.33

w1 ¼ 0.7045 278.15 283.15

0.1034 0.1308

0.1086 0.1344

5.02 2.76

0.1023 0.1292

1.02 1.20

0.0867 0.1142

16.13 12.71

0.1048 0.1313

1.37 0.42

(continued on next page)

6

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

Table 3 (continued ) 100xexp 1

T/K

Apelblat 100xcal 1

Wilson 100RD

100xcal 1

NRTL 100RD

UNIQUAC

100xcal 1

100RD

100xcal 1

100RD

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.1641 0.2042 0.2523 0.3096 0.3774 0.4571 0.5503 0.6587

0.1658 0.2039 0.2499 0.3054 0.3721 0.4521 0.5477 0.6618

1.04 0.15 0.94 1.35 1.40 1.10 0.47 0.46

0.1621 0.2020 0.2502 0.3084 0.3784 0.4624 0.5631 0.6838

1.24 1.10 0.82 0.38 0.27 1.16 2.32 3.80

0.1491 0.1931 0.2484 0.3175 0.4035 0.5101 0.6422 0.8056

9.15 5.42 1.53 2.56 6.91 11.60 16.69 22.30

0.1636 0.2028 0.2500 0.3067 0.3747 0.4561 0.5532 0.6690

0.28 0.71 0.93 0.94 0.71 0.22 0.53 1.57

w1 ¼ 0.8033 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.1299 0.1704 0.2216 0.2855 0.3647 0.4622 0.5812 0.7256 0.8995 1.1077

0.1421 0.1801 0.2278 0.2876 0.3624 0.4558 0.5722 0.7169 0.8964 1.1188

9.36 5.67 2.79 0.73 0.63 1.38 1.55 1.20 0.34 1.00

0.1333 0.1721 0.2209 0.2820 0.3582 0.4534 0.5722 0.7209 0.9078 1.1446

2.62 1.02 0.31 1.24 1.78 1.91 1.55 0.65 0.93 3.33

0.1262 0.1651 0.2144 0.2764 0.3539 0.4504 0.5703 0.7190 0.9032 1.1317

2.86 3.09 3.24 3.20 2.97 2.55 1.87 0.91 0.41 2.16

0.1325 0.1717 0.2209 0.2826 0.3596 0.4553 0.5743 0.7223 0.9065 1.1370

1.99 0.74 0.30 1.01 1.41 1.49 1.18 0.46 0.78 2.64

w1 ¼ 0.9019 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.2016 0.2679 0.3525 0.4595 0.5937 0.7606 0.9666 1.2190 1.5263 1.8977

0.2233 0.2854 0.3642 0.4641 0.5903 0.7497 0.9504 1.2030 1.5201 1.9175

10.78 6.54 3.33 0.99 0.57 1.44 1.67 1.31 0.41 1.04

0.2092 0.2718 0.3511 0.4516 0.5787 0.7398 0.9448 1.2072 1.5466 1.9917

3.75 1.44 0.38 1.72 2.52 2.73 2.26 0.97 1.33 4.95

0.2166 0.2810 0.3619 0.4629 0.5888 0.7451 0.9388 1.1789 1.4769 1.8480

7.46 4.90 2.66 0.75 0.82 2.04 2.87 3.29 3.23 2.62

0.2078 0.2710 0.3512 0.4526 0.5808 0.7429 0.9482 1.2095 1.5448 1.9808

3.09 1.16 0.38 1.50 2.17 2.33 1.91 0.78 1.21 4.38

w1 ¼ 1.0000 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.3000 0.3900 0.5200 0.6784 0.9191 1.1199 1.4900 1.9000 2.3679 3.0100

0.3144 0.4100 0.5327 0.6896 0.8895 1.1435 1.4649 1.8705 2.3808 3.0209

4.80 5.13 2.45 1.66 3.22 2.11 1.68 1.55 0.55 0.36

0.3046 0.3997 0.5214 0.6767 0.8747 1.1275 1.4512 1.8681 2.4100 3.1231

1.53 2.50 0.28 0.48 4.92 0.67 2.61 1.68 1.69 3.76

0.3310 0.4253 0.5433 0.6909 0.8750 1.1050 1.3930 1.7553 2.2146 2.8038

10.32 9.04 4.49 1.60 4.89 1.34 6.51 7.62 6.56 6.85

0.3062 0.4004 0.5205 0.6739 0.8696 1.1203 1.4435 1.8641 2.4201 3.1715

2.08 2.66 0.10 0.67 5.38 0.04 3.12 1.89 2.20 5.37

a exp Standard uncertainties are u(T) ¼ 0.05 K and u(p) ¼ 0.5 kPa; Relative standard uncertainty ur is ur(xexp is experimental mole fraction solubility of capecitabine 1 ) ¼ 0.03, x1 in the binary mixed solvents. b xcal 1 stand for the calculated mole fraction solubility of capecitabine in the binary mixed solvents by the modified Apelblat equation, Wilson model, non-random two liquid (NRTL) model, or UNIQUAC model. c w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.


!     Duij aij uij  ujj ≡exp  tij ¼ exp  ¼ exp  RT T RT
!     Duji aji uji  uii ≡exp  tji ¼ exp  ¼ exp  RT T RT

(23)

(24)

where the character energies Duij and Duji are only weakly dependent on temperature T. The segment fraction fi and area fraction qi for component i could be given by:

fi ¼

xi ri m P xj rj

(25)

j

qi ¼

xi qi m P xj q j j

(26)

li ¼

z ðr  qi Þ  ðri  1Þ 2 i

(27)

The coordination number z is set equal to 10. Parameters ri and qi stand for the volume parameter and surface area parameter for component i, which can be calculated with:ri ¼ Qi/VVW, qi ¼ Ri/AVW. Where Ri and Qi are Van der Waals area and volume, VVW is the standard segment volume (15.17cm3$mol1), AVW is the standard segment area (2.5  109 cm2$mol1). The values of ri and qi for the selected solvents can be obtained from literature [14]. The value of r1 and q1 of capecitabine can be calculated based on the method of functional groups [23,24]. Y.J. Zhao et al. had introduced a new method based on elements and chemical bonds for fast calculation of molecular volume and surface [25]. The corresponding values of elements and chemical bonds of capecitabine are listed in Table 2, and the calculated results are: Q1 ¼196.17 cm3$mol1, 9 2 1 R1 ¼ 27.74  10 cm $mol , therefore, r1 ¼12.93144; q1 ¼11.096. The Wilson model for multicomponent mixtures could be expressed as [14,26]:

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

7

Table 4 Experimental and calculated mole fraction solubility of capecitabine and relative deviations (RD) in binary mixed solvents of n-heptane þ ethyl acetate at different temperature and under p ¼ 101.3 kPa.a,b T/K

100xexp 1

Apelblat

Wilson

NRTL

100xcal 1

100RD

100xcal 1

100xcal 1

100RD

UNIQUAC 100RD

100xcal 1

100RD

w1c¼0.2737 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0053 0.0072 0.0097 0.0128 0.0169 0.0220 0.0285 0.0366 0.0467 0.0591

0.0061 0.0079 0.0103 0.0133 0.0172 0.0222 0.0284 0.0364 0.0463 0.0589

13.81 9.69 6.43 3.89 1.98 0.63 0.23 0.66 0.70 0.40

0.0054 0.0073 0.0096 0.0127 0.0166 0.0217 0.0281 0.0364 0.0470 0.0607

2.37 0.78 0.71 0.81 1.57 1.44 1.24 0.49 0.72 2.73

0.0049 0.0068 0.0093 0.0125 0.0168 0.0222 0.0293 0.0382 0.0494 0.0635

7.36 5.82 4.50 2.15 0.77 1.12 2.67 4.29 5.82 7.49

0.0054 0.0072 0.0096 0.0127 0.0167 0.0219 0.0284 0.0366 0.0469 0.0599

1.38 0.27 0.76 0.47 0.93 0.64 0.50 0.06 0.47 1.32

w1 ¼ 0.3696 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0126 0.0149 0.0203 0.0240 0.0282 0.0350 0.0410 0.0490 0.0574 0.0710

0.0130 0.0159 0.0193 0.0235 0.0284 0.0342 0.0411 0.0492 0.0588 0.0701

3.14 6.92 4.75 2.25 0.71 2.35 0.17 0.43 2.48 1.30

0.0103 0.0134 0.0173 0.0222 0.0283 0.0358 0.0451 0.0566 0.0707 0.0880

18.41 10.14 14.77 7.52 0.29 2.36 10.08 15.49 23.12 23.88

0.0095 0.0126 0.0166 0.0216 0.0280 0.0359 0.0458 0.0579 0.0729 0.0911

27.26 16.19 17.23 9.99 0.16 2.56 11.59 18.20 27.82 28.34

0.0127 0.0157 0.0192 0.0234 0.0284 0.0343 0.0413 0.0495 0.0591 0.0702

1.02 5.16 5.45 2.50 0.71 1.96 0.69 0.96 2.88 1.08

w1 ¼ 0.4679 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0226 0.0290 0.0370 0.0470 0.0580 0.0720 0.0885 0.1080 0.1320 0.1590

0.0247 0.0305 0.0378 0.0467 0.0576 0.0709 0.0873 0.1071 0.1313 0.1607

9.08 5.24 2.09 0.69 0.72 1.48 1.40 0.81 0.51 1.09

0.0217 0.0279 0.0358 0.0455 0.0575 0.0723 0.0903 0.1124 0.1393 0.1722

4.18 3.64 3.28 3.16 0.83 0.37 2.07 4.08 5.55 8.27

0.0202 0.0262 0.0338 0.0431 0.0546 0.0688 0.0860 0.1070 0.1324 0.1631

12.15 9.56 8.77 8.30 5.81 4.47 2.22 0.89 0.34 2.59

0.0231 0.0292 0.0368 0.0461 0.0574 0.0712 0.0880 0.1083 0.1327 0.1620

2.01 0.67 0.63 1.99 0.99 1.04 0.55 0.25 0.52 1.90

w1 ¼ 0.5686 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0340 0.0430 0.0550 0.0742 0.0860 0.1055 0.1346 0.1672 0.1948 0.2425

0.0368 0.0458 0.0567 0.0702 0.0867 0.1070 0.1317 0.1619 0.1986 0.2433

8.29 6.41 3.14 5.35 0.87 1.39 2.13 3.16 1.97 0.33

0.0332 0.0426 0.0543 0.0688 0.0866 0.1085 0.1351 0.1675 0.2068 0.2547

2.44 0.89 1.18 7.22 0.76 2.80 0.34 0.15 6.18 5.02

0.0348 0.0444 0.0561 0.0704 0.0879 0.1090 0.1346 0.1654 0.2023 0.2466

2.49 3.17 1.95 4.86 2.17 2.86 0.30 0.97 3.75 1.89

0.0346 0.0439 0.0552 0.0692 0.0864 0.1073 0.1327 0.1635 0.2008 0.2458

1.89 1.99 0.42 6.71 0.41 1.67 1.43 2.21 3.07 1.36

w1 ¼ 0.6723 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.0681 0.0870 0.1166 0.1420 0.1750 0.2181 0.2754 0.3388 0.4222 0.5141

0.0727 0.0909 0.1134 0.1414 0.1760 0.2190 0.2721 0.3377 0.4186 0.5182

6.81 4.44 2.76 0.45 0.60 0.41 1.19 0.32 0.85 0.80

0.0690 0.0882 0.1119 0.1411 0.1770 0.2209 0.2744 0.3397 0.4192 0.5162

1.32 1.35 4.02 0.60 1.16 1.28 0.35 0.27 0.70 0.41

0.0681 0.0871 0.1106 0.1396 0.1752 0.2188 0.2719 0.3364 0.4146 0.5095

0.21 0.13 5.44 1.66 0.14 0.36 1.14 0.78 1.75 0.87

0.0692 0.0882 0.1118 0.1409 0.1768 0.2207 0.2745 0.3400 0.4198 0.5168

1.57 1.35 4.15 0.77 1.01 1.20 0.34 0.35 0.58 0.52

w1 ¼ 0.7786 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.1227 0.1540 0.2030 0.2513 0.3228 0.4091 0.5250 0.6385 0.8062 0.9700

0.1285 0.1626 0.2053 0.2586 0.3250 0.4075 0.5098 0.6364 0.7927 0.9853

4.73 5.60 1.14 2.91 0.69 0.38 2.89 0.32 1.67 1.58

0.1220 0.1570 0.2007 0.2551 0.3227 0.4064 0.5101 0.6386 0.7984 0.9981

0.53 1.96 1.12 1.52 0.04 0.67 2.85 0.02 0.96 2.89

0.1203 0.1555 0.1995 0.2542 0.3221 0.4058 0.5088 0.6352 0.7904 0.9808

2.19 0.95 1.74 1.28 0.29 0.79 3.09 0.59 1.94 1.11

0.1219 0.1568 0.2006 0.2552 0.3230 0.4071 0.5110 0.6394 0.7981 0.9947

0.66 1.85 1.17 1.56 0.07 0.50 2.67 0.15 1.00 2.54

w1 ¼ 0.8879 278.15 283.15

0.1552 0.1986

0.1707 0.2202

9.97 10.90

0.1578 0.2071

1.70 4.27

0.1601 0.2099

3.29 5.49

0.1559 0.2061

0.47 3.77

(continued on next page)

8

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

Table 4 (continued ) 100xexp 1

T/K

Apelblat 100xcal 1

Wilson 100RD

NRTL

100xcal 1

100RD

100xcal 1

UNIQUAC 100RD

100xcal 1

100RD

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.2704 0.3605 0.4563 0.6240 0.7688 1.0314 1.2572 1.5800

0.2838 0.3652 0.4692 0.6018 0.7707 0.9855 1.2580 1.6031

4.96 1.30 2.82 3.56 0.25 4.45 0.06 1.46

0.2703 0.3512 0.4550 0.5885 0.7614 0.9872 1.2864 1.6911

0.05 2.58 0.29 5.68 0.97 4.29 2.33 7.03

0.2737 0.3552 0.4593 0.5928 0.7648 0.9887 1.2846 1.6852

1.37 1.61 0.73 5.00 0.54 4.10 2.20 6.66

0.2706 0.3531 0.4587 0.5938 0.7670 0.9903 1.2810 1.6651

0.06 2.04 0.53 4.84 0.24 3.98 1.9 5.39

w1 ¼ 1.0000 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

0.3000 0.3900 0.5200 0.6784 0.9191 1.1199 1.4900 1.9000 2.3679 3.0100

0.3144 0.4100 0.5327 0.6896 0.8895 1.1435 1.4649 1.8705 2.3808 3.0209

4.80 5.13 2.45 1.66 3.22 2.11 1.68 1.55 0.55 0.36

0.3046 0.3997 0.5214 0.6767 0.8747 1.1275 1.4512 1.8681 2.4100 3.1231

1.53 2.50 0.28 0.48 4.92 0.67 2.61 1.68 1.69 3.76

0.3310 0.4253 0.5433 0.6909 0.8750 1.1050 1.3930 1.7553 2.2146 2.8038

10.32 9.04 4.49 1.60 4.89 1.34 6.51 7.62 6.56 6.85

0.3062 0.4004 0.5205 0.6739 0.8696 1.1203 1.4435 1.8641 2.4201 3.1715

2.08 2.66 0.10 0.67 5.38 0.04 3.12 1.89 2.20 5.37

a exp Standard uncertainties are u(T) ¼ 0.05 K and u(p) ¼ 0.5 kPa; Relative standard uncertainty ur is ur(xexp is experimental mole fraction solubility of capecitabine 1 ) ¼ 0.03, x1 in the binary mixed solvents. b cal x1 stand for the calculated mole fraction solubility of capecitabine in the binary mixed solvents by the modified Apelblat equation, Wilson model, non-random two liquid (NRTL) model, or UNIQUAC model. c w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

Table 5 Average relative deviations (ARD) of the four models for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate. Solvents

100ARD

Solvents

Apelblat w1a¼0.1019

a

Wilson

1.94 1.08 1.09 1.26 0.94 1.21 1.47 2.46 2.81 1.58

w1 ¼ 0.2044 w1 ¼ 0.3047 w1 ¼ 0.4054 w1 ¼ 0.5059 w1 ¼ 0.6053 w1 ¼ 0.7045 w1 ¼ 0.8033 w1 ¼ 0.9019 Average value

2.41 1.65 11.30 19.12 14.15 5.88 1.33 1.53 2.21 6.62

NRTL 0.67 4.05 17.31 26.88 22.32 18.93 10.50 2.33 3.06 11.78

UNIQUAC w1a¼0.1019

0.36 0.77 0.81 1.02 0.62 0.66 0.77 1.20 1.89 0.90

w1 ¼ 0.2044 w1 ¼ 0.3047 w1 ¼ 0.4054 w1 ¼ 0.5059 w1 ¼ 0.6053 w1 ¼ 0.7045 w1 ¼ 0.8033 w1 ¼ 0.9019 Average value

w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

Table 6 Average relative deviations (ARD) of the four models for capecitabine in binary mixed solvents of n-heptane þ ethyl acetate. Solvents

100ARD

w1a¼0.2737 w1 ¼ 0.3696 w1 ¼ 0.4679 w1 ¼ 0.5686 w1 ¼ 0.6723 w1 ¼ 0.7786 w1 ¼ 0.8879 Average value a

Wilson

NRTL

UNIQUAC

3.84 2.45 2.31 3.30 1.86 2.19 3.97 2.85

1.29 12.61 3.54 2.70 1.15 1.26 2.92 3.64

4.20 15.93 5.51 2.44 1.25 1.40 3.10 4.83

0.68 2.24 1.06 2.12 1.18 1.22 2.32 1.55

8 0 19 = m < m X X GE ¼  xj Lij A xi ln@ ; : RT j¼1

lngi ¼  ln@

j¼1

1 xj Lij A þ 1 

m X j¼1

xi Lji m P xk Lik k¼1

(29)

Apelblat

Wilson

NRTL

UNIQUAC

0.02 0.01 0.03 0.07 0.07 0.21 0.37 0.79 1.42 0.33

0.08 0.05 0.66 1.92 2.03 2.18 0.92 1.30 3.27 1.38

0.02 0.13 0.96 2.16 2.90 2.93 5.87 1.09 2.84 2.10

0.01 0.02 0.04 0.09 0.07 0.21 0.38 1.03 2.87 0.52

Table 8 Root-mean-square deviation (RMSD) of the four models for capecitabine in binary mixed solvents of n-heptane þ ethyl acetate.

w1 ¼ 0.3696 w1 ¼ 0.4679 w1 ¼ 0.5686 w1 ¼ 0.6723 w1 ¼ 0.7786 w1 ¼ 0.8879 Average value

(28)

104RMSD

w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

w1a¼0.2737

i¼1

m X

a

Solvents

Apelblat

w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

0

Table 7 Root-mean-square deviation (RMSD) of the four models for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate.

a

104RMSD Apelblat

Wilson

NRTL

UNIQUAC

0.04 0.08 0.12 0.30 0.30 0.91 2.05 0.54

0.06 0.75 0.51 0.58 0.23 1.05 4.08 1.04

0.18 0.89 0.29 0.33 0.37 0.83 3.85 0.96

0.03 0.08 0.11 0.31 0.23 0.95 3.24 0.71

w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

For binary mixture solvents, the logarithm of activity coefficient of solute (capecitabine in this work) in the saturated solutions could be expressed as:

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

9

Table 9 Parameters of the modified Apelblat equation for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate. n-Hexane þ ethyl acetate

w1

0.1019 0.2044 0.3047 0.4054 0.5059 0.6053 0.7045 0.8033 0.9019

n-Heptane þ ethyl acetate

w1

A

B

C

R2

101.72 59.53 75.44 82.57 57.49 71.28 82.60 129.61 143.36

177.80 1853.68 160.48 1059.05 325.61 37.17 354.84 2037.04 2526.45

16.36 9.96 11.71 12.54 9.01 11.37 13.24 20.56 22.77

0.9998 0.9999 0.9997 0.9992 0.9997 0.9996 0.9995 0.9993 0.9993

0.2737 0.3696 0.4679 0.5686 0.6723 0.7786 0.8879 1.0000

A

B

C

R2

115.20 74.68 124.54 121.01 141.62 119.79 152.71 108.98

901.62 115.30 2046.81 1887.81 2711.49 1638.70 2781.89 817.32

18.17 11.61 19.34 18.89 22.15 19.05 24.23 17.82

0.9993 0.9981 0.9992 0.9979 0.9995 0.9989 0.9979 0.9980

Table 10 Parameters of Wilson model for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate. w1

Wilson △l13

△l21

△l23

△l31

△l32

n-Hexane þ ethyl acetate 0.1019 7554.09 0.2044 8156.44 0.3047 6064.43 0.4054 5153.28 0.5059 4949.42 0.6053 3219.92 0.7045 2653.74 0.8033 3366.40 0.9019 3352.78

△l12

23,800.99 23,006.43 58,870.76 57,164.59 53,494.30 51,322.86 45,829.20 22,532.87 26,048.83

1090.47 18.50 18,528.47 16,259.43 14,088.61 11,591.94 8318.01 4031.10 2843.78

2811.58 6193.61 28,099.14 30,980.92 33,652.64 34,936.48 34,237.43 62.62 36.23

1.57 793.16 7126.82 6903.92 8098.11 9722.00 10,731.96 3859.29 2777.85

7853.88 6977.55 42,443.30 42,737.15 40,612.22 36,131.51 29,208.41 296.33 115.05

n-Heptane þ ethyl acetate 0.2737 8200.28 0.3696 6676.58 0.4679 5469.48 0.5686 4904.03 0.6723 3671.10 0.7786 3230.60 0.8879 4333.22 1.0000 2707.37

36,525.66 60,220.32 53,661.83 47,763.20 32,636.07 31,703.76 27,436.17 e

3037.99 17,499.56 13,029.34 10,514.06 2809.53 3482.25 2422.26 2228.86

4064.58 31,710.46 28,593.63 29,354.54 8272.38 3234.50 29.45 e

1334.99 6326.50 6914.25 7702.71 3138.88 2107.45 2398.44 e

5188.47 45,345.84 36,327.56 31,881.16 7338.46 3511.25 58.73 e

Table 11 Parameters of NRTL model for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate. w1

w1

NRTL

Dg12

Table 12 Parameters of UNIQUAC model for capecitabine in binary mixed solvents of nhexane þ ethyl acetate and n-heptane þ ethyl acetate.

Dg13

Dg23

Dg21

Dg31

Dg32

n-Hexane þ ethyl acetate 0.1019 265.52 79.93 98.10 0.2044 949.93 0.00 134.45 0.3047 258.49 260.31 0.87 0.4054 255.17 1.71 403.57 0.5059 234.97 230.00 1.23 0.6053 253.32 107.72 232.21 0.7045 1023.92 1020.17 6.64 0.8033 1270.17 1137.63 0.05 0.9019 1897.36 864.15 1775.11

15,352.32 13,160.53 39,946.25 12,341.18 11,685.81 9598.58 9505.18 9056.37 8169.31

15,990.06 1.12 15,973.79 1175.31 12,858.36 3.09 12,350.57 267.86 11,685.81 9.52 9598.58 215.97 9505.19 2.91 8437.02 288.75 10,808.35 628.71

n-Heptane þ ethyl acetate 0.2737 235.14 231.00 0.3696 300.84 295.48 0.4679 702.70 706.22 0.5686 83.25 50.66 0.6723 320.53 198.85 0.7786 307.06 695.44 0.8879 1855.08 1721.38 1.0000 3289.27 e

15,229.67 40,393.71 39,387.92 29,511.64 18,140.39 11,712.35 9182.10 9740.02

15,229.73 12,215.36 10,196.81 6439.55 3370.88 2122.18 12,596.61 e

0.59 5.21 3.78 366.25 441.33 1186.12 773.23 e

5.97 14.95 3.39 634.09 517.80 175.99 5.88 e

UNIQUAC

a13

a31

a23

a32

n-Hexane þ ethyl acetate 0.1019 511.75 392.10 0.2044 707.76 356.42 0.3047 4457.81 414.67 0.4054 4285.27 352.62 0.5059 1304.05 175.70 0.6053 558.74 62.34 0.7045 337.91 3.38 0.8033 186.73 44.99 0.9019 165.21 8.63

a12

a21

142.51 144.95 186.79 199.33 142.92 97.93 73.26 9.84 6.75

372.57 341.24 316.13 280.48 177.37 58.28 9.88 1.14 6.44

58.37 126.15 149.37 160.75 143.43 65.99 31.27 175.72 136.71

732.46 660.59 3359.79 3105.27 5.19 174.96 279.92 136.80 0.03

n-Heptane þ ethyl acetate 0.2737 686.48 321.78 0.3696 2626.08 276.04 0.4679 697.08 205.33 0.5686 551.58 175.01 0.6723 495.61 80.52 0.7786 413.47 8.02 0.8879 127.64 18.54 1.0000 139.99 16.11

143.24 164.66 140.03 146.08 115.82 63.44 2.67 e

307.22 269.57 203.61 175.45 85.80 7.35 20.33 e

123.90 138.05 129.53 127.43 90.89 36.32 1.30 e

789.94 1891.29 451.46 566.79 852.19 2196.05 13.28 e

10

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

Table 13 Parameters of CNIBS/R-K model for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate. T/K

CNIBS/R-K B1

B2

B3

B4

R2

102ARD

104RMSD

n-Hexane þ ethyl acetate 278.15 12.87 283.15 12.56 288.15 12.05 293.15 11.59 298.15 10.75 303.15 10.59 308.15 9.60 313.15 8.91 318.15 8.44 323.15 7.80 Average value

17.21 17.18 15.37 14.06 9.55 10.95 5.33 2.12 0.54 2.74

17.29 19.30 16.08 14.45 3.72 10.20 3.14 9.75 12.05 19.55

6.46 10.89 8.92 8.96 1.71 8.16 5.12 10.59 11.25 18.29

0.68 1.75 1.43 1.98 1.94 2.81 2.05 3.66 3.36 5.78

0.9970 0.9973 0.9978 0.9981 0.9986 0.9986 0.9989 0.9991 0.9992 0.9993

14.58 13.53 12.79 12.05 10.88 10.47 9.00 8.08 7.74 6.47 10.56

0.51 0.64 0.77 0.93 1.07 1.35 1.53 1.78 2.11 2.41 1.31

n-Heptane þ ethyl 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 Average value

10.70 10.58 9.17 0.61 5.41 4.45 2.55 6.20 2.16 5.27

26.42 26.68 26.60 31.31 29.17 33.78 30.33 35.30 33.06 35.28

54.45 54.95 52.06 46.15 50.40 40.23 46.58 39.82 42.58 41.45

26.97 27.31 25.45 20.65 23.96 15.97 21.05 15.41 17.70 16.53

0.9945 0.9953 0.9962 0.9983 0.9973 0.9987 0.9979 0.9994 0.9987 0.9993

23.80 23.41 22.40 12.58 19.73 11.03 17.82 8.24 14.26 10.33 16.36

0.70 0.83 1.01 0.89 1.50 1.29 2.18 1.53 2.71 2.60 1.52

acetate 15.46 15.18 14.42 11.41 12.84 9.56 11.56 8.65 9.76 8.60

Table 14 Parameters of the modified Jouyban-Acree-van’t Hoff model for capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate. Jouyban-Acree-van’t Hoff

n-Hexane þ ethyl acetate

n-Heptane þ ethyl acetate

D1 D2 D3 D4 D5 D6 D7 100ARD 10000RMSD

3.73 3781.56 4.98 2919.11 10,037.85 12,393.52 5060.36 12.31 6.74

2.42 3376.60 7.91 3890.15 9000.96 10,068.53 3845.22 7.85 3.08

was used to correlate the experimental solubility of capecitabine. The relative deviation (RD), relative average deviation (ARD) and root-mean-square deviation (RMSD) of the modified Apelblat equation, CNIBS/R-K equation, NRTL model, Wilson model and UNIQUAC model are expressed as

RD ¼

xexp  xcal 1 1

ARD ¼

exp



1Xn

x1  xcal 1



exp i¼1

x

n 1 "

lng1 ¼ 1  lnðx1 þ x2 L12 þ x3 L13 Þ 

2 1Xn  exp RMSD ¼ x  xcal 1 n i¼1 1

x1 x1 þ x2 L12 þ x3 L13

x2 L21 x3 L31   x1 L21 þ x2 þ x3 L23 x1 L31 þ x2 L32 þ x3 



lji  ljj Dlji ni n ¼ i exp  exp  nj R,T nj R,T



Lji ¼











#1 2 (35)



n P m xexp xcal

P

i;j i;j

xexp

i;j i¼1 j¼1

(31)

ARD ¼

(32)

2P 2 3 n P m  exp xi;j  xcal i;j 6i¼1 j¼1 71 6 7 2 RMSD ¼ 6 7 4 5 m,n

where Lij and Lji are adjustable parameters of Wilson equation and they are related to the molar volumes of pure-component (ni, nj) and the characteristic energy differences (Dlij, Dlji). 3.1.5. Model accuracy For the modified Apelblat equation and CNIBS/R-K equation the software Origin was used to calculate the solubility of capecitabine with the least-squares method. For the NRTL model, Wilson model, UNIQUAC model and modified Jouyban-Acree-van’t Hoff model, the software Mathcad

(36)

m,n

=

nj lij  lii nj Dlij ¼ exp  exp  ni R,T ni R,T

(34)

The ARD and RMSD of modified Jouyban-Acree-van’t Hoff model can be calculated by following equations.

(30) Lij ¼

(33)

exp

x1

=

B0

(37)

where xexp and xcal are the experimental and calculated mole fraction solubility values of capecitabine, respectively; n and m stand for the number of experimental points and the number of mass fractions in each solvent. The obtained experimental mole fraction solubility data for capecitabine in the n-hexane þ ethyl acetate and n-heptane þ ethyl acetate mixed solvents were correlated with Eqs. (6), (7), (9), (12) and (13)e(32). The calculated mole fraction solubility data of

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

11

Table 15 Calculated logarithm values (lng1) of capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate under p ¼ 101.3 kPa.a T/K

lng1 NRTL

n-Hexane þ ethyl acetate w1b¼0.1019 278.15 6.9223 283.15 6.7995 288.15 6.6807 293.15 6.5658 298.15 6.4545 303.15 6.3465 308.15 6.2416 313.15 6.1396 318.15 6.0402 323.15 5.9432 w1 ¼ 0.4054 278.15 5.2755 283.15 5.1814 288.15 5.0906 293.15 5.0026 298.15 4.9176 303.15 4.8351 308.15 4.7552 313.15 4.6777 318.15 4.6025 323.15 4.5294 w1 ¼ 0.7045 278.15 3.6079 283.15 3.5405 288.15 3.4746 293.15 3.4100 298.15 3.3465 303.15 3.2839 308.15 3.2220 313.15 3.1606 318.15 3.0996 323.15 3.0387 n-Heptane þ ethyl acetate w1 ¼ 0.2737 278.15 6.4812 283.15 6.3659 288.15 6.2544 293.15 6.1465 298.15 6.0419 303.15 5.9404 308.15 5.8416 313.15 5.7456 318.15 5.6519 323.15 5.5604 w1 ¼ 0.5686 278.15 4.5374 283.15 4.5036 288.15 4.4694 293.15 4.4337 298.15 4.4007 303.15 4.3659 308.15 4.3291 313.15 4.2922 318.15 4.2569 323.15 4.2172 w1 ¼ 0.8879 278.15 3.0095 283.15 2.9478 288.15 2.8804 293.15 2.8103 298.15 2.7427 303.15 2.6591 308.15 2.5864 313.15 2.4900 318.15 2.4083 323.15 2.3115 a b

Uniquac

Wilson

6.9102 6.7938 6.6800 6.5686 6.4595 6.3524 6.2471 6.1434 6.0410 5.9395

6.8786 6.7814 6.6822 6.5818 6.4799 6.3744 6.2649 6.1513 6.0321 5.9075

5.0049 4.9914 4.9749 4.9552 4.9319 4.9048 4.8736 4.8379 4.7973 4.7514

5.0779 5.0339 4.9908 4.9484 4.9069 4.8660 4.8257 4.7858 4.7464 4.7074

3.4237 3.4056 3.3862 3.3653 3.3431 3.3193 3.2941 3.2672 3.2386 3.2082

3.4472 3.4215 3.3954 3.3689 3.3417 3.3137 3.2847 3.2545 3.2230 3.1899

6.3945 6.3067 6.2193 6.1327 6.0464 5.9608 5.8755 5.7905 5.7058 5.6212

6.3855 6.3019 6.2185 6.1357 6.0518 5.9675 5.8817 5.7941 5.7043 5.6121

4.5309 4.5027 4.4724 4.4392 4.4061 4.3705 4.3322 4.2925 4.2529 4.2092

4.5736 4.5309 4.4880 4.4423 4.4030 4.3608 4.3150 4.2694 4.2283 4.1790

3.0265 2.9565 2.8834 2.8093 2.7365 2.6539 2.5777 2.4855 2.4022 2.3078

3.0152 2.9531 2.8845 2.8133 2.7439 2.6583 2.5835 2.4847 2.4008 2.3021

NRTL w1 ¼ 0.2044 6.8323 6.7106 6.5931 6.4793 6.3691 6.2622 6.1584 6.0575 5.9591 5.8633 w1 ¼ 0.5059 4.9469 4.8585 4.7729 4.6900 4.6097 4.5318 4.4563 4.3828 4.3114 4.2419 w1 ¼ 0.8033 3.2170 3.1558 3.0953 3.0352 2.9753 2.9152 2.8548 2.7935 2.7311 2.6673 w1 ¼ 0.3696 5.8165 5.7402 5.6652 5.5933 5.5239 5.4554 5.3897 5.3252 5.2628 5.1999 w1 ¼ 0.6723 3.8428 3.8050 3.7653 3.7271 3.6878 3.6471 3.6044 3.5612 3.5155 3.4692 w1 ¼ 1.0000 2.2782 2.2356 2.1892 2.1409 2.0848 2.0361 1.9705 1.9043 1.8357 1.7549

Uniquac

Wilson

6.7499 6.6540 6.5593 6.4656 6.3730 6.2813 6.1905 6.1004 6.0109 5.9218

6.7358 6.6474 6.5592 6.4709 6.3816 6.2911 6.1991 6.1050 6.0079 5.9083

4.6279 4.6256 4.6214 4.6152 4.6070 4.5967 4.5840 4.5690 4.5513 4.5310

4.7688 4.7260 4.6839 4.6424 4.6013 4.5606 4.5203 4.4802 4.4402 4.4003

3.1896 3.1380 3.0859 3.0330 2.9790 2.9236 2.8665 2.8072 2.7453 2.6805

3.1841 3.1356 3.0859 3.0348 2.9819 2.9268 2.8691 2.8085 2.7446 2.6771

5.5320 5.5321 5.5288 5.5244 5.5183 5.5097 5.5001 5.4887 5.4762 5.4610

5.7403 5.6857 5.6269 5.5741 5.5224 5.4683 5.4178 5.3662 5.3161 5.2606

3.8393 3.8043 3.7671 3.7293 3.6899 3.6488 3.6056 3.5612 3.5142 3.4658

3.8420 3.8045 3.7646 3.7274 3.6889 3.6486 3.6055 3.5621 3.5149 3.4671

2.3523 2.2924 2.2291 2.1639 2.0905 2.0241 1.9404 1.8555 1.7680 1.6670

2.0914 2.0437 1.9927 1.9399 1.8798 1.8269 1.7580 1.6889 1.6178 1.5359

lng1 is the logarithm of activity coefficient of the solute (capecitabine) in binary mixed solvents. w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

NRTL w1 ¼ 0.3047 5.9022 5.8151 5.7311 5.6492 5.5705 5.4936 5.4188 5.3461 5.2757 5.2063 w1 ¼ 0.6053 4.0078 3.9349 3.8642 3.7954 3.7285 3.6633 3.5995 3.5372 3.4761 3.4161 w1 ¼ 0.9019 2.7036 2.6507 2.5977 2.5442 2.4898 2.4341 2.3768 2.3174 2.2553 2.1903 w1 ¼ 0.4679 5.0108 4.9588 4.9077 4.8576 4.8089 4.7606 4.7131 4.6656 4.6181 4.5710 w1 ¼ 0.7786 3.2778 3.2297 3.1804 3.1325 3.0826 3.0323 2.9796 2.9288 2.8731 2.8196

Uniquac

Wilson

5.5682 5.5716 5.5716 5.5686 5.5627 5.5543 5.5433 5.5302 5.5151 5.4979

5.7637 5.7122 5.6615 5.6117 5.5625 5.5137 5.4652 5.4170 5.3689 5.3207

3.7439 3.7411 3.7365 3.7302 3.7222 3.7125 3.7012 3.6882 3.6736 3.6573

3.8438 3.8138 3.7838 3.7537 3.7233 3.6924 3.6610 3.6289 3.5960 3.5622

2.7399 2.6818 2.6224 2.5615 2.4984 2.4327 2.3637 2.2909 2.2136 2.1313

2.7344 2.6793 2.6224 2.5631 2.5009 2.4353 2.3658 2.2919 2.2134 2.1298

4.9381 4.9095 4.8792 4.8472 4.8139 4.7791 4.7429 4.7054 4.6663 4.6261

4.9996 4.9521 4.9051 4.8580 4.8120 4.7653 4.7185 4.6714 4.6228 4.5743

3.2726 3.2284 3.1822 3.1357 3.0868 3.0363 2.9828 2.9295 2.8710 2.8131

3.2712 3.2278 3.1814 3.1365 3.0879 3.0376 2.9829 2.9307 2.8700 2.8123

12

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

capecitabine in binary mixed solvents are also listed in Table 3 and Table 4. The calculated RD, ARD and RMSD of the modified Apelblat equation, CNIBS/R-K equation, Wilson model, NRTL model, UNIQUAC model and the modified Jouyban-Acree-van’t Hoff model are shown in Tables 3e14. The computed parameters of the investigated equations are reported in Tables 9e14. The calculated results indicated that all the six thermodynamic models correlated the solubility of capecitabine well. The total average values of RMSD of the modified Apelblat equation, Wilson model, NRTL model, UNIQUAC model, CNIBS/R-K model and the modified Jouyban-Acreevan’t Hoff model are 0.44  104, 1.21  104, 1.53  104, 0.62  104, 1.42  104 and 4.91  104, respectively. The order of the relative average deviation (ARD) of the six cosolvency mathematical models is CNIBS/R-K > modified Jouyban-Acree-van’t Hoff > NRTL > Wilson > modified Apelblat > UNIQUAC. For the modified Apelblat equation and CNIBS/R-K model, the values of R2 of the two models are all >0.99. Combined with the lower values of RMSD, ARD and higher values of R2, it could be seen that all the six thermodynamic models can correlate the solubility data well and the UNIQUAC model and the modified Apelblat equation correlate the experimental values better than the other models relatively. The logarithm of activity coefficient of capecitabine (lng1) in the studied saturated solutions were back-calculated with the NRTL model, UNIQUAC model, and Wilson model, respectively. The calculated values are listed in Table 15. The positive values of lng1 means that the repulsive interactions exist between capecitabine and the corresponding mixture solvents, and the solutions system positively deviate from Raoult’s law.

3.2. Apparent thermodynamic properties for capecitabine dissolution The dissolution behavior of capecitabine in the mixed solutions of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate was studied by calculating the apparent thermodynamic parameters of the dissolution process, namely, the standard enthalpy (ΔHB), entropy (ΔSB) and Gibbs free energy change (ΔGB) using van’t Hoff and Gibbs equations. The modified version of van’t Hoff equation is represented as:

vlnx1 DH +  ¼   R v T1  T1hm

(38)

zTS

(41)

The apparent thermodynamic properties of ΔHB, ΔSB and ΔGB that were computed for the capecitabine dissolution in the mixture of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate at Thm are summarized in Table 16. The values of ΔGB and ΔHB of capecitabine dissolution in the mixed solvent of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate are positive in all cases, and ΔGB values reduce with the increasing mass fraction of ethyl acetate to obtain a minimum value in pure ethyl acetate illustrating that the dissolving is more favorable with increasing the capecitabine solubility. ΔSB values are also positive in all systems. The results demonstrate that capecitabine dissolving in the mixed solutions of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate are always endothermic and entropy-driven. zH and zTS are also listed in Table 16. In all studied solutions, the main contributor of ΔGB of solution is the enthalpy (zH > zTS and zH > 0.6). The results indicate the high energetic need for overcoming the cohesive forces of the

Table 16 Apparent thermodynamic parameters for dissolution behavior of capecitabine in binary mixed solvents of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate at Thm.

DG

DH

DS

(kJ$mol1)

(kJ$mol1)

(J$K1$mol1)

TDS (kJ$mol1)

zH

zTS

n-Hexane þ ethyl acetate 0.1019 22.44 43.36 0.2044 22.23 40.83 0.3047 20.28 28.36 0.4054 18.67 22.96 0.5059 17.89 25.56 0.6053 15.69 28.61 0.7045 14.73 30.75 0.8033 13.78 35.60 0.9019 12.56 37.23

69.74 62.03 26.94 14.31 25.56 43.05 53.39 72.71 82.26

20.92 18.61 8.08 4.29 7.67 12.91 16.02 21.81 24.67

0.67 0.69 0.78 0.84 0.77 0.69 0.66 0.62 0.60

0.33 0.31 0.22 0.16 0.23 0.31 0.34 0.38 0.40

n-Heptane þ ethyl acetate 0.2737 21.41 39.94 0.3696 20.17 28.34 0.4679 18.39 32.34 0.5686 17.37 32.49 0.6723 15.57 33.36 0.7786 14.06 34.79 0.8879 13.13 39.08

61.77 27.21 46.50 50.43 59.30 69.14 86.49

18.53 8.16 13.95 15.13 17.79 20.74 25.94

0.68 0.78 0.70 0.68 0.65 0.63 0.60

0.32 0.22 0.30 0.32 0.35 0.37 0.40

w1a

a

P



T DS+



 ¼


+

DH þ T DS+

w1 is the mass fraction of ethyl acetate in mixed solvents without capecitabine.

where x1 denotes the mole fraction capecitabine solubility, T and R are the absolute temperature (K) and the ideal gas constant, respectively. Thm is the average harmonic temperature calculated as:

Thm ¼

n P i¼1

n 



(39)

1

=T

where n is the number of definite temperatures. In this work, the calculated Thm value is 299.96 K. By drawing ln x1 vs 1/T  1/Thm, the values of ΔSB and ΔGB of solutions can be calculated from the intercept and the slope, respectively [27], and ΔSB can also be computed from Gibbs equation. The relative contributions of entropy (zTS) and enthalpy (zH) to ΔGB of dissolution is obtained by using Eqs. (40) and (41) [28].





DH+

 zH ¼


+



DH þ T DS+

(40)

Fig. 4. Enthalpy-entropy compensation plot for the solubility of capecitabine in nhexane þ ethyl acetate mixtures at 299.96 K. The points represent the mass fraction of ethyl acetate in the n-hexane þ ethyl acetate mixtures in the absence of capecitabine.

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

13

Research Projects of Henan Higher Education Institutions (No. 19A530004). References

Fig. 5. Enthalpy-entropy compensation plot for the solubility of capecitabine in nheptane þ ethyl acetate mixtures at 299.96 K. The points represent the mass fraction of ethyl acetate in the n-heptane þ ethyl acetate mixtures in the absence of capecitabine.

capecitabine molecules and those of n-hexane, n-heptane and ethyl acetate molecules in the capecitabine dissolution procedure [29]. The diagram of ΔHB against ΔGB was employed to study the mechanism of co-solvency at different temperatures [30]. The plot in Fig. 4 shows that capecitabine in the n-hexane þ ethyl acetate solvent systems show a non-linear, ΔHB against ΔGB plot with positive slope region (0.1  w1  0.4) and enthalpy driving mechanism, and negative slope region (0.4  w1  0.9) with entropy driving mechanism. The plot in Fig. 5 shows that capecitabine in the n-heptane þ ethyl acetate solvent systems show a non-linear, ΔHB against ΔGB plot with positive slope region (0.27  w1  0.37) and enthalpy driving mechanism, and region with negative slope (0.37  w1  0.89) with entropy driving mechanism. 4. Conclusion The solubility of capecitabine in the binary mixtures of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate from (278.15 to 323.15) K were measured by the laser dynamic isothermal method under atmospheric pressure. Results shows that the solubility of capecitabine increases with increasing temperature and ethyl acetate content (w1) in the studied mixture solvents. The experimental solubility values of capecitabine are well correlated with the modified Apelblat equation, combined nearly ideal binary solvent/RedlichKister (CNIBS/R-K) equation, Wilson model, non-random two liquid (NRTL) model, UNIQUAC model, and the modified Jouyban-Acreevan’t Hoff model. From deviation analysis, the UNIQUAC model and the modified Apelblat equation can give satisfactory correlation results relatively. The values of lng1 that back-calculated with the NRTL model, UNIQUAC model, and Wilson model are relatively close and all positive, which indicated that the repulsive interactions exist between capecitabine and the corresponding solvents, and the solutions system positively deviate from Raoult’s law. The values of ΔGB, ΔHB and ΔSB of capecitabine dissolution in the mixed solvent of n-hexane þ ethyl acetate and n-heptane þ ethyl acetate are positive in all cases, which indicated that the dissolution of capecitabine in the selected solvents is an endothermic and entropy-driven process. This work can give fundamental data for the crystallization and purification of capecitabine from acetic esters. Acknowledgments This research work was financially supported by the Science and Technology Project of Henan province (No. 182102210002) and Key

[1] R. Kadaboina, S.M. Nariyam, V. Murki, R.R. Vinjamuri, S. Benda, S.K Komati, Preparation of capecitabine, United states patent application publication, US20110224422A1, 2011. [2] R. Zhao, M. Yu, P.S. Zhang, T. Li, B.Z. Ren, Solubility and dissolution characteristics of capecitabine in pure lower alcohols and water with methanol mixture solvents at atmospheric pressure and different temperatures, Fluid Phase Equilib. 460 (2018) 23e35, https://doi.org/10.1016/j.fluid.2017.12.024. [3] J.W. Mullin, M. Sipek, Solubility and density isotherms for potassium aluminum sulfate-water-alcohol systems, J. Chem. Eng. Data 26 (1981) 164e165, https://doi.org/10.1021/je00024a021. [4] M.A. Reus, A.E.D.M. Van Der Heijden, J.H. ter Horst, Solubility determination from clear points upon solvent addition, Org. Process. Res. Dev. 19 (2015) 1004e1011, https://doi.org/10.1021/acs.oprd.5b00156. [5] A. Apelblat, E. Manzurola, Solubilities of L-aspartic, DL-aspartic, DL-glutamic, p-hydroxybenzoic, o-anisic, p-anisic, and itaconic acids in water from T ¼ 278 K to T ¼ 345 K, J. Chem. Thermodyn. 29 (1997) 1527e1533, https:// doi.org/10.1006/jcht.1997.0267. [6] X. Li, X. Huang, Y.A. Luan, J. Li, N. Wang, X.L. Zhang, S. Ferguson, X.Z. Meng, H.X. Hao, Solubility and thermodynamic properties of 5-nitrofurazone form g in mono-solvents and binary solvent mixtures, J. Mol. Liq. 275 (2019) 815e828, https://doi.org/10.1016/j.molliq.2019.01.158. [7] W.E. Acree Jr., J.W. McCargar, A.I. Zvaigzne, I.L. Teng, Mathematical representation of thermodynamic properties. Carbazole solubilities in binary alkaneþ dibutyl ether and alkaneþ tetrahydropyran solvent mixtures, Phys. Chem. Liq. 23 (1991) 27e35, https://doi.org/10.1080/00319109108030630. [8] W.E. Acree Jr, A.I. Zvaigzne, Thermodynamic properties of non-electrolyte solutions: part 4. Estimation and mathematical representation of solute activity coefficients and solubilities in binary solvents using the NIBS and Modified Wilson equations, Thermochim. Acta 178(1991) 151-167. doi: https://doi.org/10.1016/0040-6031(91)80307-5. [9] W.E. Acree Jr., Mathematical representation of thermodynamic properties: part 2. Derivation of the combined nearly ideal binary solvent (NIBS)/RedlichKister mathematical representation from a two-body and three-body interactional mixing model, Thermochim. Acta 198 (1992) 71e79, https://doi.org/ 10.1016/0040-6031(92)85059-5. [10] A.B. Ochsner, R.J. Belloto Jr., T.D. Sokoloski, Prediction of xanthine solubilities using statistical techniques, J. Pharm. Sci. 74 (1985) 132e135, https://doi.org/ 10.1002/jps.2600740206. [11] A. Jouyban, M.A.A. Fakhree, W.E. Acree Jr., Comment on “measurement and correlation of solubilities of (z)-2-(2-aminothiazol-4-yl)-2methoxyiminoacetic acid in different pure solvents and binary mixtures of waterþ(ethanol, methanol, or glycol)”, J. Chem. Eng. Data 57 (2012) 1344e1346, https://doi.org/10.1021/je201340e. [12] H. Sun, M. Li, J. Jia, F. Tang, E. Duan, Measurement and correlation of the solubility of 2,6-diaminohexanoic acid hydro-chloride in aqueous methanol and aqueous ethanol mixtures, J. Chem. Eng. Data 57 (2012) 1463e1467, https://doi.org/10.1021/je300173v. [13] H. Renon, J.M. Prausnitz, Local composition in thermodynamic excess functions for liquid mixtures, AICHE J. 14 (1968) 135e144, https://doi.org/ 10.1002/aic.690140124. [14] J.M. Prausnitz, N.L. Linchtenthaler, E.G. Azevedo, Molecular Thermodynamics of Fluid-phase Equilibria, third ed., River-Prentice Hall, New Jersey, 1999. [15] H. Renon, J.M. Prausnitz, Estimation of parameters for the NRTL equation for excess Gibbs energies of strongly nonideal liquid mixtures, Ind. Eng. Chem. Process. Des. Dev. 8 (1969) 413e419, https://doi.org/10.1021/i260031a019. [16] Y. Tong, S.R. Zhai, K. Wang, H.S. Li, Q.D. An, Determination and correlation of solubility and solution thermodynamics of saccharin in different pure solvents, J. Chem. Thermodyn. 133 (2019) 70e78, https://doi.org/10.1016/ j.jct.2019.02.005. [17] P.S. Zhang, R. Zhao, C. Zhang, T. Li, B.Z. Ren, Solubility determination and correlation of cyromazine in sixteen pure solvents and mixing properties of solutions, Fluid Phase Equilib. 475 (2018) 77e88, https://doi.org/10.1016/ j.fluid.2018.07.024. [18] S.Y. Zong, J.K. Wang, Y. Xiao, H. Wu, Y.A. Zhou, Y.M. Guo, X. Huang, H.X. Hao, Solubility and dissolution thermodynamic properties of lansoprazole in pure solvents, J. Mol. Liq. 241 (2017) 399e406, https://doi.org/10.1016/ j.molliq.2017.06.037. [19] B.J. Fan, Q.S. Li, Y.F. Li, X.L. Song, J.P. Yin, Solubility measurement and correlation for 1-naphthoic acid in nine pure and binary mixed solvents from T ¼ (293.15 to 333.15) K, J. Mol. Liq. 273 (2019) 58e67, https://doi.org/ 10.1016/j.molliq.2018.09.114. [20] D.S. Abrams, J.M. Prausnitz, Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems, AICHE J. 21 (1975) 116e128, https://doi.org/10.1002/aic.690210115. [21] G. Maurer, J.M. Prausnitz, On the derivation and extension of the uniquac equation, Fluid Phase Equilib. 2 (1978) 91e99, https://doi.org/10.1016/03783812(78)85002-X. [22] Z. Bakher, M. Kaddami, Thermodynamic equilibrium study of phosphorus pentoxide-water binary system: the stability and solubility of 10H3PO4$H2O, Calphad 63 (2018) 148e155, https://doi.org/10.1016/j.calphad.2018.09.006.

14

R. Zhao et al. / Journal of Molecular Liquids 295 (2019) 111716

[23] A. Bondi, van der Waals Volumes and Radii, J. Phys. Chem. 68 (1964) 441e451, https://doi.org/10.1021/j100785a001.
, T. Brinck, J.S. Murray, P. Politzer, Quantitative [24] F.A. Bulat, A. Toro-Labbe analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies, J. Mol. Model. 16 (2010) 1679e1691, https://doi.org/10.1007/s00894-010-0692-x. [25] Y.J. Zhao, J.L. Si, L. Xia, S.G. Xiang, A new method based on elements and chemical bonds for fast calculation of molecular volume and surface, Computers and Applied Chemistry 07 (2013) 739e742, https://doi.org/10.11719/ com.app.chem20130708. [26] G.M. Wilson, Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing, J. Am. Chem. Soc. 86 (1964) 127e130, https://doi.org/ 10.1021/ja01056a002. [27] S. Vahdati, A. Shayanfar, J. Hanaee, F. Martínez, W.E. Acree Jr., A. Jouyban,

Solubility of carvedilol in ethanolþ propylene glycol mixtures at various temperatures, Ind. Eng. Chem. Res. 52 (2013) 16630e16636, https://doi.org/ 10.1021/ie403054z. [28] G.L. Perlovich, S.V. Kurkov, A. Bauer-Brandl, Thermodynamics of solutions: II. Flurbiprofen and diflunisal as models for studying solvation of drug substances, Eur. J. Pharm. Sci. 19 (2003) 423e432, https://doi.org/10.1016/S09280987(03)00145-3.
Pen ~ a, P. Bustamante, Thermodynamic analysis and [29] F. Martínez, M.A. enthalpyeentropy compensation for the solubility of indomethacin in aqueous and non-aqueous mixtures, Fluid Phase Equilib. 308 (2011) 98e106, https://doi.org/10.1016/j.fluid.2011.06.016. [30] M. Gantiva, F. Martínez, Thermodynamic analysis of the solubility of ketoprofen in some propylene glycolþ water co-solvent mixtures, Fluid Phase Equilib. 293 (2010) 242e250, https://doi.org/10.1016/j.fluid.2010.03.031.