Measurement and Modeling of the Solubility of Genistin in Water +

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Measurement and Modeling of the Solubility of Genistin in Water + (Ethanol or Acetone) Binary Solvent Mixtures from T= (278.2 to 313.2) K Jie-Ping Fan, Dan-Dan Liao, Bing Zhen, Xiao-Kang Xu, and Xue-Hong Zhang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03393 • Publication Date (Web): 08 Dec 2015 Downloaded from http://pubs.acs.org on December 15, 2015

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Industrial & Engineering Chemistry Research

Measurement and Modeling of the Solubility of Genistin in Water + (Ethanol or Acetone) Binary Solvent Mixtures from T= (278.2 to 313.2) K Jie-Ping Fana*, Dan-Dan Liaoa, Bing Zhena, Xiao-Kang Xua, Xue-Hong Zhangb a

Key Laboratory of Poyang Lake Ecology and Bio-Resource Utilization of Ministry of Education,

Department of Chemical Engineering, Nanchang University, Nanchang 330031, China.

b

School of

Foreign Language, Nanchang University, Nanchang 330031, China. *

Correspondence

to:

Jie-Ping

Fan

([email protected]);

Tel:

086-791-83968583;

Fax:

086-791-83968594 ABSTRACT The solubilities of genistin in the binary solvent mixtures (ethanol + water, acetone + water) with various initial mole fractions were measured by the high performance liquid chromatography (HPLC) analysis method at the different temperatures ranging from 278.2 K to 313.2 K. An interesting phenomenon was observed, i.e., a synergistic effect of the binary solvent mixtures on solubility; in this synergistic effect the solubility of genistin reached maximum, and was higher than the solubility of the separate constituent when the initial mole fraction of ethanol or acetone was 0.5 within the whole range of the studied temperatures. The solubility of genistin in the mixtures increased with the temperature. The simplified thermodynamic model, the modified Apelblat model and λh model were used to correlate the solubility data of genistin with temperatures. Among the three models, the modified Apelblat model showed the best correlation in describing the dependence of solubility on temperatures. Furthermore, to illustrate the effects of both the temperature and the initial mass fraction of ethanol or acetone on the changes of the solubility of genistin, NRTL (Non-Random Two-Liquid) model, Sun model and Ma model were also used to correlate the data. The results showed that the calculated solubility by the Sun model showed better agreement with the experimental data than those by other two models. Keywords: Genistin; Solubility; Binary solvent mixtures; Correlation; NRTL model; Jouyban−Acree model

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1. Introduction Genistin (C21H20O10, Molar mass: 432.37 g mol-1, CAS number: 529-59-9, Figure 1), one of isoflavones, a member of the phytoestrogen family and is mainly isolated from dietary plants , such as soybean1 and Radix Puerariae Lobatae2. Genistin is the 7-O-β-D-glucoside form of genistein, which can be converted to genistein by digestive enzymes in the digestive system to exert their biological effects. Therefore, recently genistin has received considerable attention because its various biological activities, such as anticancer activity,3,4 antioxidant activity,5,6 antibacterial activity,7 preventing bone loss8 and relieving intestinal hypercontractility9. So genistin is widely used in pharmaceutical and food industries, for instance, as a potent inhibitor of breast cancer10 and as dietary supplements 11. Extraction and crystallization were important separation methods for industrial manufacturing genistin. In order to find a proper solvent system for crystallization or extraction, it is essential to understand their solubilities in various solvents. In our previous work,12,13 only in pure organic solvents the solubilities of genistin were reported. However, the solubility data of genistin in the binary solvent mixtures have not been systematically studied. The solvents, i.e., ethanol, acetone, and binary solvent mixtures consisting of (ethanol + water) and (acetone + water), are very important, and often used to extract or purify genistin from the medicine plants. Therefore, in this work the solubility data of genistin in the binary solvent mixtures consisting of (ethanol + water) and (acetone + water) with different mole fractions were measured by HPLC analysis method from 278.2 to 313.2 K. The simplified thermodynamic model, the modified Apelblat model and λh model were used to correlate the solubility data of genistin with temperature. Furthermore, to illustrate the effects of both the temperature and the initial solvent composition on the solubility of genistin, NRTL (Non-Random Two-Liquid) model, Sun model and Ma model were also employed to correlate the solubility data. 2. Experimental 2.1. Materials Genistin (mass fraction purity ≥ 0.98) was purchased from Xi’an Haoxuan Biotechnology Co. Ltd, Shanxi, China. Its structure was confirmed by UV and 1HNMR spectra. Ethanol and acetone were

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analytical reagent and purchased from Tianjin Hengxin Chemical Preparation Co. Ltd. and Shanghai Rich Joint Chemical Reagents Co. Ltd., China, respectively. The double-distilled water was prepared from a SZ-93 automatic dual water distiller (Shanghai Yarong biochemical instrument plant, China) and its purity was testified by pH and conductivity. More details of the materials are listed in Table 1. 2.2. Apparatus and Procedures According to the literatures,12,14-15 the solubilities of genistin in binary solvent mixtures were measured by the HPLC analysis method. Briefly, a saturated solution of genistin (about 8 mL) with excess genistin solid was prepared in a glass vial which was stoppered and sealed up with tape to avoid evaporation of the solvent during the experimental steps. The vial was laid in a low temperature thermostatic reaction bath (type DFY5/40, China) with an uncertainty of ± 0.1 K. The solution was stirred continuously by an electric magnetic stirrer for at least 48 h to ensure solid-liquid equilibrium, and then the solution was allowed to settle for another 12 h to obtain a clear saturated solution before sampling. Three samples (each for approximately 0.5 mL) were taken out from upper clear saturated solution in each vial by a preheated and pre-weighted disposable syringe equipped with a filter. The syringe with saturated solution was weighed on an analytical balance (type FA1104N, Shanghai, China) with an uncertainty of ± 0.1 mg. During the weighing process, the syringe needle was closed by a silicon rubber to prevent the solvent from evaporating. Then the sample solution was injected into a volumetric flask, and the syringe was thoroughly eluted by methanol and all elutions were also transferred into the volumetric flask. Finally the sample solution was diluted to the mark before the HPLC determination. The concentration of genistin in the sample solution was determined by HPLC according to the literatures.12,16-17 Each experiment was repeated at least twice to check the repeatability and three samples were taken for each solution. In this study, the relative uncertainties of the experimental solubility data were calculated by using relative standard deviation (RSD) and all of them were within ± 0.10. The mole fraction solubility of genistin (x1) in pure solvent and binary solvent mixtures can be calculated by eqs. 1 and 2, respectively. x1 =

m1 / M 1 m1 / M 1 + m2 / M 2

(1)

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x1 =

m1 / M 1 m1 / M 1 + m2 / M 2 + m3 / M 3

(2)

where m1, m2, and m3 represent the mass of genistin and each solvent used in the solution, respectively, and M1, M2, and M3 are the molar mass of genistin and each solvent.

2.3. HPLC Conditions According to our previous study,12 the determination of genistin was carried out on an Agilent 1100 HPLC system (Agilent Technologies, USA) equipped with a vacuum degasser (type G1379A), a quaternary pump (type G1311A), an auto-sampler (type G1313A) and a diode-array detector (type G1315A). The detection wavelength of genistin was 260 nm. The separation was performed on a Sharpsil-T-C18 column (4.6 × 250 mm, 5 µm) at 303.2 K with a mobile phase composed of methanol and water (40:60, v/v) at a flow rate of 1.0 mL min-1.

2.4. PXRD Conditions Genistin standard and precipitates in different solvents were determined by the powder X-ray diffraction (PXRD, Bede D1, UK), using Cu Kα (λ=1.54056) as source. The results were presented in Figures S1.

3. RESULTS AND DISCUSSION 3.1. Characterization of Genistin Figure S1 illustrates the representative PXRD patterns of genistin standard and precipitates in different solvents. Compared with the PXRD patterns of genistin standard, the PXRD patterns of precipitates in each solvent had no significant changes, which indicated that genistin was very stable and had no polymorphism throughout the experiments.

3.2. Synergistic Effect of the Solvents on Solubility The mole fraction solubility data of genistin in ethanol, acetone, water and their binary solvent mixtures were reported in Table S1 and also plotted in Figures 2 and 3. From Table S1, Figures 2 and 3 it can be seen that in all the studied solvents the solubility of genistin increased with the temperature. Especially, an interesting phenomenon was observed: the solubility increased and then decreased with the initial mole fraction of ethanol or acetone in the binary solvent mixtures; the

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solubility reached maximum and was higher than the solubility of the separate constituents when the mole fraction of ethanol or acetone was 0.5 at the whole range of the temperatures studied. The phenomenon occurred due to the synergistic effect of mixed solvents on the solubility, which relied on the properties of solute and the solvents. Similar phenomenon was also observed in other reports.18 The maximum solubility exhibited in ethanol + water and acetone + water binary solvent mixtures may be attributed to a strong intermolecular association of solute molecule with solvent mixtures. Especially, the hydrogen bond in the solution might play an important role in the maximum solubility effect. Genistin has several hydroxy groups and one carbonyl group which generate hydrogen bond donation (HBD) and hydrogen bond acceptance (HBA) ability. Water can form hydrogen bond with genistin, and however water also can form strong hydrogen bonds between solvent molecules because not only HBD ability but also HBA ability of water are strong. 12 In ethanol + water and acetone + water binary solvent mixtures, strong hydrogen bonds can be easily formed between solvent molecular and genistin, and therefore genistin was more easily dissolved in the binary solvent mixtures. On the other hand, another reason for the maximum solubility was that the polarities of the solute and mixture of solvents are closest to each other.18,19

3.3. Correlation of Solubility Data with Temperature In this work, the solubility data of genistin in different solvents were correlated by several models in order to quantitatively describe the solid−liquid equilibrium. For a fixed solvent the simplified thermodynamic model (eq. S1),12,20 the modified Apelblat model (eq. 3)21,22 and λh model (eq. S2)23 were used to correlate the solubility with temperature. The modified Apelblat equation is described as eq. 3. lnx1 = a +

b + c ln(T / K ) T /K

(3)

where x1 is the molar fraction solubility of genistin; T is the experimental temperature; a, b, and c are the parameters of the modified Apelblat equation. The parameters of the simplified thermodynamic model (eq. S1), the modified Apelblat model (eq. 3) and λh model (eq. S2) could be obtained by using a non-linear regression from the experimental solubility data, and all parameters were listed in Tables S2 and S3. 6


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3.4. Correlation of Solubility Data with Both Temperature and Initial Solvent Composition of Binary Solvent Mixtures As described above, the simplified thermodynamic model, the modified Apelblat model and λh model can be used to predict the solubility at different temperature in a fixed initial solvent composition of binary solvent mixtures. However, when both temperature and initial solvent composition of binary solvent mixtures need to be considered, the more versatile models should be adopted. In this work, a combination of the Jouyban−Acree model with the simplified thermodynamic model and the modified Apelblat model has been proposed to correlate the solubility data in the solvent mixtures at different temperatures and different initial solvent compositions, i.e., Sun model and Ma model.24,25 The Jouyban−Acree model is one of the most important models that can predict the solubility accurately with acceptable deviation from experimental data. For a binary solvent mixture, the Jouyban−Acree model could be expressed as eq. 4.25,26 ln x1 = m2 ln x2 + m3 ln x3 +

m2 m3 2 + ∑ J i (m2 − m3 )i T i =0

(4)

where x1 is the mole fraction solubility of solute in the mixed solvent at temperature T (K); x2 and x3 represent the mole fraction solubility of the solute in pure solvents 2 and 3; m2 and m3 represent the mass fractions of solvents 2 and 3 in the absence of the solute; Ji is the model constant. Substituting the simplified thermodynamic equation (eq. S1) or eq. 3 into eq 4, eqs. 5 and 6 can be obtained, respectively. 24,25 2 A  A  mm ln x1 = m2  2 + B2  + m3  3 + B3  + 2 3 + ∑ J i (m2 − m3 ) i T T  T  i=0

(5)

2 b b     mm ln x1 = m2  a2 + 2 + c2 ln T  + m3  a3 + 3 + c3 ln T  + 2 3 + ∑ J i (m2 − m3 )i T T T     i =0

(6)

After introducing a constant term in eq. 5, Sun and co-workers employed the modified model (eq. 7) to fit the solubility data in mixed solvents at different temperatures.27 D2 m2 m22 m23 m24 ln x1 = D1 + + D3m2 + D4 + D5 + D6 + D7 T T T T T

(7)

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Ma and co-workers introduced a constant term to eq. 6, a further simplified model was obtained as eq. 8.28 ln x1 = E1 +

E2 m m2 m3 m4 + E3 ln T + E4 m2 + E5 2 + E6 2 + E7 2 + E8 2 + E9 m2 ln T T T T T T

(8)

where Di and Ei are the model parameters of eqs. 7 and 8, respectively; x1 , T and m2 are the same as those in eq. 4. NRTL (Non-Random Two-Liquid) model29 is a versatile activity coefficient model which can be applied to correlate and/or predict the properties of multicomponent systems. NRTL model has been successfully used to correlate solid -liquid equilibrium properties for many nonideal solutions in wide temperature ranges. When the (solid + liquid) phase system reaches the equilibrium state, the fugacity of a component i in the solid phase should be equal to that in the liquid phase. After a reasonable simplification, a simplified equation (eq. 9) can be obtained from the rigorous thermodynamics equation. 30

∆ fus H m  1 1   −  R  T Tm 

lnγ i xi = −

(9)

where ∆fusHm is the fusion enthalpy, Tm is the melting temperature, γi represent activity coefficient of the component i and xi is the mole fraction of the component i. In this work, the value of ∆fusHm and Tm for genistin are equal to 21.30 kJ mol-1 and 547.47 K, respectively, which are cited from our previous work12. The activity coefficient of solute in eq. 9 can be calculated by the activity coefficient equation (NRTL model). The general NRTL model for the component i in a mixture of n components could be expressed as eq. 10.29,31 n

∑ τ ji G ji x j ln γ i =

j =1

n

∑G k =1

ki

xk

n  τ mj Gmj x m  ∑ n Gij x j  m =1 +∑ n τ − n  ij j =1 Gkj x k  Gkj x k ∑ ∑ k =1 k =1 

     

(10)

The NRTL model for a binary solvent mixture can be described by eq. 11.32

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ln γ1 =

τ 21G21 x2 + τ 31G31 x3 x1 (1 − ) x1 + G21 x2 + G31 x3 x1 + G21 x2 + G31 x3

+

τ G x +τ G x G12 x2 ( τ12 − 12 12 1 32 32 3 ) G12 x1 + x2 + G32 x3 G12 x1 + x2 + G32 x3

+

τ G x +τ G x G13 x3 ( τ13 − 13 13 1 23 23 2 ) G13 x1 + G23 x2 + x3 G13 x1 + G23 x2 + x3

where, τ ji =

g ji − g ii RT

(11)

, G ji = exp(−α ji τ ji ) , α ji = α ij , i,j=1,2,3;

where αij is the parameter related to the non-randomness of the solution, and gij−gjj is the cross-interaction energy parameter. In this work, the subscript of 1 represents genistin, 2 represents ethanol or acetone, and 3 represents water. For the two solvents (components 2 and 3), the solvent-solvent interaction parameters, g23−g33, g32−g23, α23 were taken from the literature.33 In this work, eqs. 7, 8 and 11 were employed to correlated the solubility of genistin in binary solvent mixtures, and the parameters of eqs. 7, 8 and 11 were obtained by using a non-linear regression from the experimental solubility data and all parameters were presented in Table 2.

3.5. Evaluation of Data Correlation by the Models The relative average deviations (RAD) and the root-mean-square deviations (RMSD) were used to evaluate the accuracy of the model correlations. RAD and RMSD were defined as eqs. 12 and 13, respectively. RAD =

1 N

N

∑ i =1

xic − xi xi

(

 ∑N x c − x i i RMSD =  i =1 N  

(12)

)

2

   

1/ 2

(13)

where xic and xi are calculated solubility and experimental solubility, respectively; N is the number of experimental data for each system. In this work, the fitting results of the simplified thermodynamic model (eq. S1) and the modified Apelblat model (eq. 3) were presented in Table S2 by correlating the solubility data with the temperatures, and the result of λh model (eq. S2) was listed in Table S3. The results indicated that all 9



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the three modes could well fit the experimental data. Overall, both RAD and RMSD of the modified Apelblat model were the lowest in comparision with the other two models, which indicated that the modified Apelblat model showed the best fit to the solubility data of genistin among the simplified thermodynamic model, the modified Apelblat model and λh model. The Sun model, Ma model and NRTL model can correlate the solubility data of genistin with the temperatures and initial solvent compositions. Compared with the simplified thermodynamic model, the modified Apelblat model and λh model, the Sun model, Ma model and NRTL model are more versatile, especially for industrial application, because they can predict the solubility of genistin at any temperatures and at any initial solvent compositions within the experiment condition ranges. The fitting results of the Sun model, Ma model and NRTL model were presented in Table 2. The RAD and RMSD of the calculated and experimental values for eqs. 7, 8 and 11 were very low, and their correlation coefficients (R2) were all above 0.97. The results showed that the Sun model, Ma model and NRTL model could be used to correlate the experimental solubility data of genistin in the binary solvent mixtures (ethanol + water, acetone + water) within all initial solvent composition ranges. Among the three models the Sun model had the lowest RMSD and the highest R2, which indicated that Sun model showed the best correlation in describing the dependence of solubility on the temperatures and the initial solvent compositions in the binary solvent mixtures (ethanol + water, acetone + water).

4. CONCLUSION The solubilities of genistin in (ethanol+water) and (acetone+water) with different initial mole fractions were measured in thetemperature range from 278.2 K to 313.2 K. The solubility of genistin increased with the increase of temperature. A synergistic effect of the binary solvent mixtures on solubility was observed, the solubility of genistin reached maximum and was higher than the solubility of the separate constituents when the mole fraction of ethanol or acetone was 0.5 in the whole range of the studied temperatures. The polarities and hydrogen bond abilities of the solvents played an important role in the dissolution process. To correlate the solubilities with temperature, the simplified thermodynamic model, the modified Apelblat model and λh model were used and the

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results showed that the modified Apelblat model had a better correlation than the other two models. Furthermore, the Sun model, Ma model and NRTL model were applied to correlate the solubility data in the solvent mixtures at different temperatures and different initial solvent compositions; the results showed that the three modes could well correlate the experimental solubility data of genistin, and the Sun model was more accurate than the other two models. The experimental solubilities and the parameters in this study were useful for the purification of genistin.

ASSOCIATED CONTENT Supporting Information Experimental mole fraction solubility of genistin (x) in mixed solvents with different temperature from (278.2 to 313.2) K are listed in Table S1. The parameters of the simplified thermodynamic model (eq. S1) and modified Apelblat model (eq. 3) are givne in Tables 2S, and Tables 3S shows the parameters of the λh model (eq. S2). The representative PXRD patterns of genistin standard and precipitates are presented in Figure S1.

ACKNOWLEDGMENTS Financial support from the National Natural Science Foundation of China (Nos. 21366019, 20806037 and 20876131), Jiangxi Province Young Scientists (Jinggang Star) Cultivation Plan (20112BCB23002), Jiangxi Province Higher School Science and Technology Landing Plan Projects (No. KJLD13012), Special Funds for Graduate Student Innovation in Jiangxi Province (No. YC2014-S013), and Jiangxi Province Undergraduate Innovation and Entrepreneurship Training Program (No. 201310403040) are gratefully acknowledged.

REFERENCES: (1) Lee, C. H.; Yang, L.; Xu, J. Z.; Yeung, S. Y. V.; Huang, Y.; Chen, Z. Y. Relative Antioxidant Activity of Soybean Isoflavones and Their Glycosides. Food Chem. 2005, 90, 735–741. (2) Xiao, W.; Wang, F.-Q.; Li, C.-H.; Zhang, Q.; Xia, Z.-N.; Yang, F.-Q. Determination of Eight Isoflavones in Radix Puerariae by Capillary Zone Electrophoresis with an Ionic Liquid as an Additive. Anal. Methods 2015, 7 , 1098–1103.

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(3) Choi, E. J.; Kim, T.; Lee, M. S. Pro-Apoptotic Effect and Cytotoxicity of Genistein and Genistin in Human Ovarian Cancer SK-OV-3 Cells. Life Sci. 2007, 80, 1403–1408. (4) Gruca, A.; Krawczyk, Z.; Szeja, W.; Grynkiewicz, G.; Rusin, A. Synthetic Genistein Glycosides Inhibiting EGFR Phosphorylation Enhance the Effect of Radiation in HCT 116 Colon Cancer Cells. Molecules 2014, 19, 18558–18573. (5) Russo, A.; Cardile, V.; Lombardo, L.; Vanella, L.; Acquaviva, R. Genistin Inhibits UV Light-Induced Plasmid DNA Damage and Cell Growth in Human Melanoma Cells. J. Nutr. Biochem. 2006, 17, 103–108. (6) Mi, J. C.; Kang, A. Y.; Kyung, M. L.; Oh, E.; Jun, H. J.; Kim, S. Y.; Joong, H. A.; Moon, T. W.; Lee, S. J.; Park, K. H. Water-Soluble Genistin Glycoside Isoflavones up-Regulate Antioxidant Metallothionein Expression and Scavenge Free Radicals. J. Agric. Food Chem. 2006, 54, 3819–3826. (7) Wu, T.; He, M.; Zang, X.; Zhou, Y.; Qiu, T.; Pan, S.; Xu, X. A Structure-Activity Relationship Study of Flavonoids as Inhibitors of E. Coli by Membrane Interaction Effect. Biochim. Biophys. Acta 2013, 1828, 2751–2756. (8) Hooshmand, S.; Juma, S.; Arjmandi, B. H. Combination of Genistin and Fructooligosaccharides Prevents Bone Loss in Ovarian Hormone Deficiency. J. Med. Food 2010, 13, 320–325. (9) Xiong, Y.; Chen, D.; Lv, B.; Liu, F.; Wang, L.; Lin, Y. The Characteristics of Genistin-Induced Inhibitory Effects on Intestinal Motility. Arch. Pharm. Res. 2013, 36, 345–352. (10) Hamdy, S. M.; Latif, a. K. M. a.; Drees, E. a.; Soliman, S. M. Prevention of Rat Breast Cancer by Genistin and Selenium. Toxicol. Ind. Health 2012, 28, 746–757. (11) Liggins, J.; Bluck, L. J. C.; Runswick, S.; Atkinson, C.; Coward, W. A.; Bingham, S. a. Daidzein and Genistein Content of Fruits and Nuts. J. Nutr. Biochem. 2000, 11, 326–331. (12) Fan, J.-P.; Xu, X.-K.; Shen, G.-L.; Zhang, X.-H. Measurement and Correlation of the Solubility of Genistin in Eleven Organic Solvents from T=(283.2 to 323.2)K. J. Chem. Thermodyn. 2015, 89, 142–147.

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1978.

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Table 1. The sample provenance and mass fraction purity of genistin.

1

Chemicals Mass fraction purity

Method of purification Analysis method

genistin

≥ 0.980

None

a

ethanol

≥ 0.997

None

b

acetone

≥ 0.995

None

GC

a

High-performance liquid chromatography.

b

Gas chromatography.

HPLC GC

Provenance Xi’an Haoxuan Bio-technique Co., Ltd, Shanxi, China Tianjin Hengxin Chemical Preparation Co. Ltd. Shanghai Rich Joint Chemical Reagents Co., Ltd.

2 3 4

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1

Table 2. Parameters of the Sun model (eq. 7), the Ma model (eq. 8) and the NRTL model (eq. 11) correlated from the experimental

2

data of genistin in the investigated solvents. Binary

solvent Sun model

Ma model

NRTL model

mixtures

Parameters

Value

Parameters

Value

Parameters

Value

Ethanol+Water

D1

4.02711

E1

-73.42278

(g21-g11)/R

4303.17497

D2

-5507.43295

E2

-1948.12645

(g31-g11)/R

5501.34963

D3

-8.64486

E3

11.55594

(g32-g22)/R

199.0009

D4

6513.53270

E4

24.74622

(g12-g22)/R

-824.49044

D5

-1204.89559

E5

4401.68549

(g13-g33)/R

-752.33726

D6

-2370.21147

E6

127.77137

(g23-g33)/R

-44.59241

D7

832.84079

E7

-3648.34269

α12

0.37549

E8

1282.86580

α13

0.42809

E9

-4.97248

α23

0.2941

Acetone+Water

RAD

0.11982

RAD

0.18687

RAD

0.07340

104RMSD

0.01905

104RMSD

0.01936

104RMSD

0.04606

a

0.99680

a

0.99658

a

0.99684

D1

-0.84279

E1

72.83441

(g21-g11)/R

4796.19344

D2

-5364.42488

E2

-11271.36968

(g31-g11)/R

5501.34963

D3

-0.66094

E3

-10.65566

(g32-g22)/R

109.56535

D4

21127.89214

E4

-120.03630

(g12-g22)/R

-1047.40383

R2

R2

R2

17



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a

Page 18 of 21

D5

-53811.92927

E5

36195.92677

(g13-g33)/R

-752.33726

D6

63283.43415

E6

-67856.33966

(g23-g33)/R

110.34318

D7

-27667.17664

E7

72213.70221

α12

0.28466

E8

-29493.52398

α13

0.42809

E9

17.38230

α23

0.5916

RAD

0.50612

RAD

0.54690

RAD

0.34034

104RMSD

0.23981

104RMSD

0.24182

104RMSD

1.10465

a

0.98588

a

0.98512

a

0.97043

R2

R2

R2

R2 is the correlation coefficient of the correlation by the models.

18


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1 2

Figure 1. Chemical structure of genistin.

3 4

19



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Page 20 of 21

1

2 3

Figure 2. Mole fraction solubility x of genistin in (ethanol+ water) mixed solvents with various

4

initial mole fractions (φ) of ethanol at different temperatures

5 6

20


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1

2 3

Figure 3. Mole fraction solubility x of genistin in (acetone+ water) mixed solvents with various

4

initial mole fractions (φ) of acetone at different temperatures

5

21


Measurement and Modeling of the Solubility of Genistin in Water +

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