Article pubs.acs.org/jced
Solubility Determination and Modeling for 4,4′-Dihydroxydiphenyl Sulfone in Mixed Solvents of (Acetone, Ethyl Acetate, or Acetonitrile) + Methanol and Acetone + Ethanol from (278.15 to 313.15) K Yong Xie,† Hongwei Shi,† Cunbin Du,‡ Yang Cong,‡ and Hongkun Zhao*,‡ †
School of Chemistry & Chemical Engineering, Suzhou University, Suzhou, Anhui 234000, People’s Republic of China College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jia1 ngsu 225002, People’s Republic of China
‡
ABSTRACT: In the present study, the solubility of 4,4′-dihydroxydiphenyl sulfone in mixed solvents of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + methanol) were determined experimentally by using the isothermal dissolution equilibrium method within the temperature range from (278.15 to 313.15) K under atmosphere pressure. The solubility increased with increasing temperature in the binary solvent mixtures at constant solvent composition. At constant temperature and solvent composition, the dissolving capacity of 4,4′-dihydroxydiphenyl sulfone in the four binary solvent mixtures ranked as (acetone + ethanol) > (acetone + methanol) > (ethyl acetate + methanol) > (acetonitrile + methanol). The obtained solubility data were correlated by employing the Jouyban−Acree model, modified Apelblat−Jouyban−Acree model, Ma model and Sun model. The four models were proven to give good representation of the experimental solubility data. The largest value of relative average deviations (RAD) was 4.97 × 10−2, and that of root-mean-square deviations (RMSD) was 6.49 × 10−4. The experimental solubility and the models in this study could be helpful in separating 4,4′-dihydroxydiphenyl sulfone from its isomeric mixtures.
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INTRODUCTION Because of the uniqueness of the diphenyl sulfone linkage, 4,4′-dihydroxydiphenyl sulfone (CAS Reg. No. 80-09-1; chemical structure shown in Figure 1) has a heat resistance, a resistance to
byproduct. So the obtained crude product contains 20 to 30% by weight of 2,4′-dihydroxydiphenyl sulfone as an impurity, which decreases the purity and the yield of 4,4′-dihydroxydiphenyl sulfone. Further, it has been recently recognized that trihydroxytriphenyldisulfone is produced as a byproduct along with 2,4′-dihydroxydiphenyl sulfone. As the properties of polymers prepared from 4,4′-dihydroxydiphenyl sulfone are highly dependent on the degree of purity and the isomer ratio of the monomers used, a demand for 4,4′-dihydroxydiphenyl sulfone with extremely high-purity has arisen to improve the quality of products in the field. According to the manufacturing processes, however, it is impossible to avoid the formation as the side reaction product of 2,4′-dihydroxydiphenyl sulfone, an isomer of 4,4′-dihydroxydiphenyl sulfone, and it is not easy to isolate 4,4′-dihydroxydiphenyl sulfone from this isomer mixture. The solubilities of 4,4′-dihydroxydiphenyl sulfone in pure and mixed solvents not only are useful for the products′ characteristics such as crystal size distribution, crystal habits, purity, and yields, but also provide the fundamental data for the modeling of solubility and understanding of interactions between 4,4′-dihydroxydiphenyl sulfone and various solvents. In the industrial purification process, many solvent crystallization methods have been put forward to separate the dihydroxydiphenyl sulfone isomers.15−19 Recently we reported the solubility of 4,4″-dihydroxydiphenyl sulfone in nine pure solvents.20
Figure 1. Chemical structure of 4,4′-dihydroxydiphenyl sulfone.
oxidation, and a stability to light. Therefore, it is an important chemical which is in increasing use in recent years as a substitute for bisphenol A in the fields of polyester resins, epoxy resins, and polycarbonate resins.1−4 In addition, 4,4′-dihydroxydiphenyl sulfone can now be found in a variety of common consumer products.5−7 In recent years, the demand for 4,4′-dihydroxydiphenyl sulfone has increased in the chemical industry in such fields as fibers, resins, or the like. Various processes have been proposed for preparing 4,4′-dihydroxydiphenyl sulfone.8−14 The industrial processes heretofore known for producing 4,4′-dihydroxydiphenyl sulfone include one in which a phenol and a sulfonating agent are subjected to dehydration reaction in the presence of a solvent. However, when the dehydration reaction is conducted in a solvent, the desired 4,4′-dihydroxydiphenyl sulfone as dissolved in the reaction product has an isomerization equilibrium with an isomer, that is, 2,4′-dihydroxydiphenylsulfone produced as a © XXXX American Chemical Society
Received: May 24, 2016 Accepted: August 30, 2016
A
DOI: 10.1021/acs.jced.6b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Source and Properties of 4,4′-Dihydroxydiphenyl Sulfone and the Selected Solvents chemical name 4,4′-dihydroxydiphenyl sulfone acetonitrile methanol acetone ethyl acetate ethanol a
molar mass g·mol−1 250.27 41.05 32.04 58.05 88.11 46.07
source
initial mass fraction purity
purification method
0.987
recrystallization
0.996 0.995 0.993 0.994 0.997
none none none none none
Nantong Baisheng Chemical Co., Ltd. Sinopharm Chemical Reagent Co., Ltd., China
final mass fraction purity
analysis method HPLCa
0.996 0.995 0.993 0.994 0.997
GCb GC GC GC GC
High-performance liquid chromatography. bGas chromatography.
relationship between the solubility (ln x) and reciprocal of absolute temperature (1/T). The modified Apelblat equation is given as follows:
Nevertheless, to the best of the authors’ present knowledge, no work has been carried out for determining the solubility of 4,4′-dihydroxydiphenyl sulfone in cosolvent mixtures. It is wellknown that temperature alteration of a solvent mixture is a usual way to change the compound solubility in crystallization studies. Knowledge of the solubilities enable the acquisition of the most appropriate solvent system for purifying 4,4′-dihydroxydiphenyl sulfone via the crystallization method. We find that the solubilities of 4,4′-dihydroxydiphenyl sulfone are larger in acetone, ethyl acetate, and acetonitrile than in methanol or ethanol.20 The mixed solvents can change the solubility of 4,4′-dihydroxydiphenyl sulfone. To provide the comprehensive basic data for engineering application and more systematic and useful thermodynamic information on the crystallization of 4,4′-dihydroxydiphenyl sulfone from some mixed solvents, the aims of this work are to (1) determine the solubility of 4,4″-dihydroxyphenyl sulfone in four mixed solvents of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol) with different solvent compositions at temperatures ranging from (278.15 to 313.15) K; and (2) correlate the experimental solubility data with the Jouyban−Acree model,21,22 modified Apelblat−Acree model,23,24 Ma model25 and Sun model.25
ln x = A +
⎛ ⎞ B ln xm , T = w1⎜A1 + 1 + C1 ln T ⎟ ⎝ ⎠ T ⎛ ⎞ B + w2⎜A 2 + 2 + C2 ln T ⎟ ⎝ ⎠ T +
w1w2 T
2
∑ Ji (w1 − w2)i i=0
(3)
Equation 3 can describe the solubility of solute in binary mixed solvents with various compositions at different temperatures. To evaluate the equation parameters, the model needs the solute solubility in pure solvents at the lowest and highest temperatures. The modification of eq 1 is used to correlate the solubility of 4,4′-dihydroxydiphenyl sulfone in binary solvent mixtures at different temperatures. It is proposed by Ma and co-workers25 and expressed as eq 4.
SOLUBILITY MODELING Several models have been proposed to correlate the solubility of a solid in mixed solvents. In this work, four models are employed to correlated the solubility of 4,4′-dihydroxydiphenyl sulfone in binary solvent mixtures of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol) at different temperatures, which are the Jouyban−Acree model,21,22 a combination of the Jouyban−Acree model with the modified Apelblat equation,23,24 Ma model,25 and Sun model.25 The Jouyban−Acree model is widely used to describe both temperature and composition of solvent mixtures effect on solubility of solute.23,24 The general form of the Jouyban−Acree model can be expressed as eq 1. w1w2 T
(2)
In eq 2, x is the mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone in pure solvent at absolute temperature T, and A, B, and C are regression parameters acquired by correlating the experimental solubility data. Combining eq 2 with eq 1 gives eq 3.23,24
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ln xm , T = w1 ln x1, T + w2 ln x 2, T +
B + C ln(T /K) T /K
D2 w + D3w1 + D4 1 T T w12 w13 w4 + D5 + D6 + D7 1 T T T
ln xm , T = D1 +
(4)
Here D1 to D7 are equation parameters. On the other hand, Ma and co-workers25 put forward another modified version on eq 3 to correlate the solubility of a solute in mixed solvents at different temperatures, which is expressed as
2
∑ Ji (w1 − w2)i
E2 w w + E3 ln T + E4w1 + E5 1 + D5 1 T T T w12 w13 w14 + E6 + E7 + E8 + E9w1ln T (5) T T T
i=0
ln xm , T = E1 +
(1)
In formula 1, x m,T is the mole fraction solubility of 4,4′-dihydroxyphenyl sulfone in binary solvent mixtures at absolute temperature T; w1 and w2 are the mass fraction of solvents 1 (acetone, ethyl acetate, or acetonitrile) and 2 (methanol or ethanol) in the absence of the solute (4,4′-dihydroxydiphenyl sulfone), respectively, w1 = 1 − w2; x1,T and x2,T are the mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone in pure solvents, and Ji terms are the Jouyban−Acree model parameters. The modified Apelblat equation, which was previously used by Apelblat,26,27 may be employed to describe a nonlinear
where E1 to E9 are parameters. The detailed discussion about eqs 4 and 5 can be found in ref 25.
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EXPERIMENTAL SECTION Materials. 4,4′-Dihydroxydiphenyl sulfone with a mass fraction of 0.987 was produced by Nantong Baisheng Chemical Co., Ltd., China. Purification of 4,4″-dihydroxydiphenyl sulfone
B
DOI: 10.1021/acs.jced.6b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Saturated solutions of 4,4′-dihydroxydiphenyl sulfone were prepared in the jacketed glass vessel, the temperature of which was kept at the desired value through circulating water from the smart thermostatic bath (model: DZKW-4). An excess amount of 4,4′-dihydroxydiphenyl sulfone was placed in the glass vessel filled with about 40 mL of solvent mixtures. Continuous stirring was obtained with a magnetic stirrer for intensive mixing of the solution at a fixed temperature. To determine the equilibration time of the studied systems, about 0.5 mL of liquid phase was taken out with a pore syringe filter (PTFE 0.2 μm) every hour and then analyzed by HPLC. If the composition of liquid phase became constant, the solution was assumed to be in equilibrium. Results indicated that it took about 14 h to reach equilibrium for the studied systems. Once the system reached equilibrium, the stirring was stopped and the solution was permitted to settle for at least 1 h before sampling. The upper liquid phase was taken out with a 5 mL preheated syringe attached to a filter (PTFE 0.2 μm), and then transferred into a 25 mL volumetric flask preweighed with the analytical balance. The volumetric flask was covered quickly with a rubber stopper. The total amount of the sample and volumetric flask was weighed again with the analytical balance. Subsequently, the sample was diluted to 25 mL with methanol, and analyzed by HPLC. Three samples were taken for every equilibrium solution at a given temperature, and each analysis was carried out three times to check the repeatability. The average value was employed to calculate the final solubility value. The relative standard uncertainty of the determined solubility data was estimated to be 0.0467 in mole fraction. The saturated mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone (xm,T) in the binary mixed solvents are calculated by using eq 6, and the composition of binary mixed solvents (w) is defined with eq 7.
was performed by recrystallization in acetone for three times. The purified 4,4′-dihydroxydiphenyl sulfone was dried in vacuum until the mass became constant, and then reserved in a desiccator. The final purity in mass fraction of 4,4′-dihydroxydiphenyl sulfone used in solubility determination was 0.993, which was additionally confirmed by using a normalization method in the high-performance liquid chromatography (HPLC) system. The solvents acetonitrile, methanol, ethanol, acetone, and ethyl acetate were analytical grade. The mass fraction purity of the four solvents, analyzed by gas chromatography (FULI 9790, China), were higher than 0.993. They were used in the experiment without further purification. The properties and source of the chemicals used in the solubility determination were presented in Table 1. Apparatus. The experimental apparatus is shown graphically in Figure 2. It comprises a 100 mL jacketed glass vessel, a circulating
xm,T =
Figure 2. Schematic diagram of experimental apparatus: I, smart thermostatic water bath; II, mercury-in-glass thermometer; III, magnetic stirrer; IV, stirrer controller; V, jacketed glass vessel; VI, sampling port; VII, condenser.
w=
water system, and a magnetic stirrer. The system temperature was controlled by the circulating water, which was provided from a DZKW-4 smart thermostatic bath produced by Ningbo Scientz Biotechnology Co., Ltd., and had a standard uncertainty of 0.02 K. A condenser was connected to the jacketed glass vessel to prevent the solvent from escaping. A mercury thermometer with a standard uncertainty of 0.02 K inserted in the vessel was used to display the true temperature of solutions. An analytical balance (model: BSA224S; standard uncertainty of 0.0001 g) was employed to determine the mass of solute, solvent, and mixed solvents. Solubility Measurement. In the present work, the solid− liquid equilibrium of 4,4′-dihydroxydiphenyl sulfone in binary solvent mixtures of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol) were reached by the isothermal dissolution equilibrium method,11,22 and the solubilities were determined using a highperformance liquid phase chromatograph. The experimental apparatus and method were validated by measuring the benzoic acid solubility in toluene in advance.28 The solvent mixtures were prepared by using an analytical balance (model: BSA224S) in the experiment with a standard uncertainty of 0.0001 g. The amount of mixed solvent was about 40 mL, and the mass fractions of ethyl acetate, acetone, or acetonitrile in the binary mixtures varied from 0.1 to 0.9. During the experiment, the atmosphere pressure was about 101.1 kPa.
w1/M1 w1/M1 + w2 /M 2 + w3/M3
w2 w2 + w3
(6)
(7)
where w1 is the mass fraction of 4,4′-dihydroxydiphenyl sulfone; w2 is the mass fraction of acetone, ethyl acetate, or acetonitrile, respectively; and w3 is the mass fraction of methanol or ethanol. M1, M2, and M3 are the corresponding molar mass. Analysis Method. The concentration of 4,4′-dihydroxydiphenyl sulfone was analyzed by using the Waters 2695 HPLC, which was equipped with a Waters 1525 pump, a Waters 2487 UV detector, and a Waters 717 plus autosampler. The detective wavelength was set to 254 nm. Pure methanol was used as mobile phase at a flow rate of 1 mL·min−1. The chromatographic column was a Waters C18 reverse phase column (250 mm × 4.6 mm), at a temperature of 303 K.
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RESULTS AND DISCUSSION Solubility Data. Table 2 presents the measured mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone in binary solvent mixtures of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol). It is noted that the mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone in pure solvents (acetone, ethyl acetate, acetonitrile, methanol, and ethanol) are also presented in Table 2, which are taken from ref 20. For comparison with the experimental points, the dependence of mole fraction solubility on temperature and solvent composition are shown graphically in Figures 3, 4, 5, and 6 C
DOI: 10.1021/acs.jced.6b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. Experimental Mole Fraction Solubility (xT,me·103) of 4,4′-Dihydroxydiphenyl Sulfone (cr) in Mixed Solvents of (Acetone + Methanol), (Ethyl Acetate + Methanol) and (Acetonitrile + Methanol) with Different Mass Fractions within the Temperature Range from T/K = (278.15 to 313.15) under 101.1 kPaa acetone (w) + methanol (1 − w) T/K
w=
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 T/K
w=
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
T/K
w=
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 T/K 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15
w=
b
0
0.1010
0.1996
0.1789 0.2446 0.3421 0.4698 0.6480 0.8707 1.124 1.411
0.2718 0.4052 0.6018 0.8001 1.061 1.322 1.750 2.231
0.5961 0.7609 1.010 1.341 1.720 2.213 2.891 3.841
0.6017
0.7019
0.8019
0.9009
1b
0.9618 1.411 2.018 2.652 1.251 1.730 2.570 3.438 1.568 2.219 3.421 4.691 2.011 2.959 4.418 6.014 2.537 3.911 5.919 7.602 3.169 5.008 7.576 9.679 3.951 6.430 9.310 12.16 5.121 7.819 11.28 15.46 ethyl acetate (w) + methanol (1 − w)
4.048 5.061 6.206 7.895 10.08 12.37 15.25 19.02
5.411 7.096 8.913 11.27 14.03 17.15 20.95 24.98
7.4875 9.180 11.43 14.45 18.23 22.39 26.83 31.99
10.26 12.70 15.29 18.87 22.79 26.81 30.79 35.13
w = 0.3018
0.4042
0.5025
0b
0.1020
0.2011
0.3000
0.5987
0.6997
0.7991
0.8998
1b
0.1789 0.2446 0.3421 0.4698 0.6480 0.8707 1.124 1.411
0.2733 0.4634 0.6996 0.9246 1.223 1.548 1.918 2.352
0.5527 0.7975 1.061 1.387 1.849 2.338 2.912 3.711
0.9208 1.378 1.721 2.658 1.202 1.783 2.567 3.762 1.551 2.217 3.462 4.974 1.958 2.843 4.481 6.250 2.510 3.629 5.402 7.764 3.413 4.741 6.572 9.722 4.448 6.083 8.170 11.83 5.692 7.668 9.979 14.43 acetonitrile (w) + methanol (1 − w)
3.927 5.161 6.586 8.288 10.23 12.88 16.12 19.77
4.547 6.072 7.821 9.943 12.28 15.65 19.59 24.32
5.878 7.431 9.564 12.22 15.47 19.45 23.34 27.5
5.390 6.603 8.427 10.66 13.64 17.40 21.45 26.09
0b
0.0993
0.1988
0.2985
0.5982
0.6985
0.7988
0.8993
1b
0.1789 0.2446 0.3421 0.4698 0.6480 0.8707 1.124 1.411
0.4259 0.6015 0.8010 1.061 1.358 1.682 2.087 2.610
0.7300 0.9698 1.220 1.513 1.879 2.386 3.038 3.859
0.9604 1.060 1.291 1.238 1.431 1.968 1.568 2.029 2.803 2.071 2.701 3.671 2.668 3.552 4.692 3.387 4.568 5.951 4.341 5.811 7.589 5.466 7.312 9.841 acetone (w) + ethanol (1 − w)
1.961 2.638 3.469 4.692 5.966 7.642 9.574 12.51
2.292 3.153 4.181 5.590 7.465 9.412 11.55 14.26
3.419 4.288 5.662 7.163 9.040 11.23 13.95 17.43
3.740 4.802 6.323 8.114 9.952 12.05 14.84 18.62
3.163 3.910 4.892 6.548 8.195 10.10 12.59 15.28
0b
0.0996
0.2008
0.2992
0.4013
0.4981
0.5991
0.6993
0.7994
0.8997
1b
0.2134 0.2909 0.3887 0.5305 0.7146 0.9241 1.177 1.420
0.7469 0.9968 1.338 1.717 2.151 2.574 2.979 3.453
1.250 1.738 2.176 2.673 3.755 3.911 5.195 5.981
1.744 2.283 2.983 3.642 4.896 5.435 6.692 8.001
2.245 2.955 3.857 4.582 6.193 6.783 8.693 10.53
2.869 3.574 4.710 5.601 7.600 8.304 11.03 12.99
3.619 4.463 6.027 7.184 8.787 10.65 13.21 15.97
4.613 5.809 7.659 9.148 11.569 13.270 16.726 20.62
5.898 7.395 9.407 11.624 13.94 16.49 19.69 24.07
7.492 9.092 11.801 14.55 17.72 20.92 24.63 29.65
10.26 12.70 15.29 18.87 22.79 26.81 30.79 35.13
0.3981
0.3982
0.4994
0.4982
a
Standard uncertainties u are u(T) = 0.02 K, u(p) = 400 Pa; relative standard uncertainty ur is ur(x) = 0.0467. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.003. w represents the mass fraction of acetone, ethyl acetate, or acetonitrile in mixed solvents of (acetone + methanol), (ethyl acetate + methanol), or (acetonitrile + methanol). bTaken from ref 20.
the solubility of 4,4′-dihydroxydiphenyl sulfone in the four binary solvent mixtures rank as (acetone + ethanol) > (acetone + methanol) > (ethyl acetate + methanol) > (acetonitrile + methanol). The hydroxyl group of methanol and ethanol acts as a hydrogen-bond donor, while the sulfone group of 4,4′-dihydroxydiphenyl sulfone, carbonyl group of acetone, and ester group in ethyl acetate act as a hydrogen-bond acceptor. Thus, a hydrogen bond could also be formed between 4,4′-dihydroxydiphenyl sulfone and solvent molecules. The polarity order of the selected the solvents is methanol > ethanol > acetonitrile > acetone > ethyl acetate. Besides, the polarity of 4,4′-dihydroxydiphenyl sulfone is very weak. So the solubility of 4,4′-dihydroxydiphenyl sulfone is larger in (acetone + ethanol)
as well. Table 2 shows that, for the studied mixed solvents, the solubility of 4,4′-dihydroxydiphenyl sulfone is a function of solvent composition and temperature. The solubility of 4,4′-dihydroxydiphenyl sulfone increases with the increase in temperature and mass fraction of acetone for the systems (acetone + methanol) and (acetone + ethanol), and the maximum solubility of 4,4′-dihydroxydiphenyl sulfone is observed in pure acetone. At the same temperature and mass fraction of solvent, the mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone in the (acetone + ethanol) mixture are larger than those in (acetone + methanol), (acetonitrile + methanol), or (ethyl acetate + methanol) mixed solvents. At constant temperature and solvent composition, D
DOI: 10.1021/acs.jced.6b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 3. Mole fraction solubility (x) of 4,4′-dihydroxydiphenyl sulfone in acetone (w) + methanol (1 − w) mixed solutions with different mass fractions at elevated temperatures: ◇, w = 0.9009; ▼, w = 0.8019; △, w = 0.7019; ●, w = 0.6017; □, w = 0.5025; ★, w = 0.4042; ▽, w = 0.3018; ▲, w = 0.1996; ○, w = 0.1010; solid curve, calculated by the Jouyban−Acree model.
Figure 6. Mole fraction solubility (x) of 4,4′-dihydroxydiphenyl sulfone in acetone (w) + ethanol (1 − w) mixed solutions with different mass fractions at elevated temperatures: ◇, w = 0.8997; ▼, w = 0.7994; △, w = 0.6993; ●, w = 0.5991; □, w = 0.4981; ★, w = 0.4013; ▽, w = 0.2992; ▲, w = 0.2008; ○, w = 0.0996; solid curve, calculated by the Jouyban−Acree model.
Figure 4. Mole fraction solubility (x) of 4,4′-dihydroxydiphenyl sulfone in ethyl acetate (w) + methanol (1 − w) mixed solutions with different mass fractions at elevated temperatures: ◇, w = 0.8998; ▼, w = 0.7991; △, w = 0.6997; ●, w = 0.5987; □, w = 0.4994; ★, w = 0.3981; ▽, w = 0.3000; ▲, w = 0.2011; ○, w = 0.1020; solid curve, calculated by the Jouyban−Acree model.
binary solvents is the same. The influencing factors of the solubility of solids in liquids are comparatively complex, and the formation of a hydrogen bond between solvents and solute is only one of the factors affecting the dissolution behavior. Further analysis of the dissolution process is complicated and beyond the scope of this article. Table 2 also illustrates that, for the systems of (ethyl acetate + methanol) and (acetonitrile + methanol), the solubility increases monotonically with the temperature at every composition, but the composition dependence of the solubility has a maximum around the ethyl acetate (acetonitrile) mass fraction of w = 0.9 at every temperature. This behavior may result from the hydrogen bond formed between 4,4′-dihydroxydiphenyl sulfone and solvent molecules and the polarity of solvent mixtures. At a certain temperature, the solubility of 4,4′-dihydroxydiphenyl sulfone is larger in ethyl acetate or acetonitrile than in methanol. With the increase in content of ethyl acetate or acetonitrile in binary mixed solvents, the polarity of solvent mixtures decreases. On the other hand, the strength of an intermolecular hydrogen in the two binary solvents decreases. As a result, the solubility of 4,4′-dihydroxydiphenyl sulfone in the two binary solvents increases at first, and then decreases. Solubility Correlation and Calculation. Four solution models are used to correlate the solubility of 4,4′-dihydroxydiphenyl sulfone in mixed solvents of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol), which are the Jouyban−Acree model (eq 1), a combination of the Jouyban−Acree model with the modified Alphabat eq (eq 3), Ma model (eq 4), and Sun model (eq 5). In the present work, the objective function is defined as eq 8. F=
Figure 5. Mole fraction solubility (x) of 4,4′-dihydroxydiphenyl sulfone in acetonitrile (w) + methanol (1 − w) mixed solutions with different mass fractions at elevated temperatures: ◇, w = 0.8993; ▼, w = 0.7988; △, w = 0.6985; ●, w = 0.5982; □, w = 0.4982; ★, w = 0.3982; ▽, w = 0.2985; ▲, w = 0.1988; ○, w = 0.0993; solid curve, calculated by the Jouyban−Acree model.
∑ (ln xie − ln xic)2 i=1
(8)
xei
Here ln signifies the logarithm of experimental mole fraction solubility, and ln xei is the calculated values. To judge the error calculated with different models, the relative average deviation (RAD) and root-mean-square deviation (RMSD) are introduced, which are described as eqs 9 and 10, respectively.
than in (acetone + methanol). In addition, the strength of an intermolecular hydrogen in the binary solvents was in the following order: (methanol + acetone) > (methanol + ethyl acetate) > (methanol + acetonitrile). Consequently, the solubility order of 4,4′-dihydroxydiphenyl sulfone in the three
RAD = E
1 N
⎛ |xmc , T − xme , T | ⎞ ⎟⎟ ∑ ⎜⎜ xme , T ⎠ ⎝
(9) DOI: 10.1021/acs.jced.6b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. Parameters’ Values in Different Solubility Models Jouyban−Acree parameter J0 J1 J2
value 453.75 −99.14 −11.07
RAD·102 RMSD·104
Apelblat−Jouyban−Acree parameter
value
acetone + methanol 256.44 E1 −14146.87 E2 −37.34 E3 327.78 E4 −19316.01 E5 −47.45 E6 453.31 E7 −152.82 E8 −12.68 E9 4.43 6.45 ethyl acetate + methanol 49.72 E1 −5870.02 E2 −6.02 E3 327.78 E4 −19316.01 E5 −47.45 E6 738.31 E7 183.35 E8 554.48 E9 4.20 3.53 acetonitrile + methanol 70.98 E1 −6789.04 E2 −9.304 E3 327.78 E4 −19316.01 E5 −47.45 E6 813.19 E7 −99.72 E8 1116.39 E9 4.45 2.50 acetone + ethanol 256.44 E1 −14146.87 E2 −37.34 E3 364.08 E4 −20554.51 E5 −53.07 E6 691.27 E7 −1062.80 E8 946.05 E9 4.97 5.75
A1 B1 C1 A2 B2 C2 J0 J1 J2
3.86 6.49 J0 J1 J2
732.05 224.44 539.20
RAD·102 RMSD·104
A1 B1 C1 A2 B2 C2 J0 J1 J2
3.80 3.29 J0 J1 J2
803.0005 −65.7294 1090.67
RAD·102 RMSD·104
A1 B1 C1 A2 B2 C2 J0 J1 J2
4.12 2.58 J0 J1 J2
709.94 −1042.41 992.62
RAD·102 RMSD·104
A1 B1 C1 A2 B2 C2 J0 J1 J2
4.34 5.24
∑i = 1 (xmc , T − xme , T )2 N
Sun value
parameter
value
−218.83 4889.16 34.23 472.26 −18582.64 −805.34 216.04 13.83 −70.97 3.74 4.92
D1 D2 D3 D4 D5 D6 D7
10.09 −5210.81 −2.38 2356.23 −799.65 206.32 18.87
45.99 −6725.59 −5.41 169.34 −5237.3 −2731.13 3806.66 −2118.59 −25.48 3.62 3.33
D1 D2 D3 D4 D5 D6 D7
78.9 −8036.732 −10.409 50.805 418.936 −6324.032 8680.379 −4280.831 −7.58 4.26 2.64
D1 D2 D3 D4 D5 D6 D7
139.14 −10268.33 −19.65 68.09 829.5 −8535.24 9788.68 −3915.76 −10.27 4.36 4.76
D1 D2 D3 D4 D5 D6 D7
3.41 5.62 9.85 −5133.34 −1.07 2279.43 −2712.85 3777.61 −2104.16
3.56 2.98 9.3 −4968.22 0.11 2661.29 −6343.98 8710.66 −4295.43
4.36 2.73 7.756 −4475.22 −0.6047 3860.21 −8521.87 9767.12 −3904.96
4.61 5.03
the model parameters of eqs 1 to 5 are acquired by the nonlinear least-squares method29 with Mathcad software. The obtained values of these model parameters are tabulated in Table 3 together with the RAD and the RMSD values. The solubility of 4,4′-dihydroxydiphenyl sulfone in the four binary mixtures of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol) are calculated based on the regressed model parameters. The calculated solubility by using the Jouyban−Acree model are shown graphically in Figures 3−6. Table 3 shows that for the studied binary mixed solvents, the RAD
N
RMSD =
Ma parameter
(10)
c where N signifies the number of a set of data points. xm,T denotes e the calculated values of solubility, and xm,T denotes the experimental ones. The mole fraction solubility of 4,4′-dihydroxydiphenyl sulfone in pure solvents of acetone, ethyl acetate, acetonitrile, methanol, and ethanol are cited in ref 20. According to the experimental solubility data of 4,4′-dihydroxydiphenyl sulfone in mixed solvents,
F
DOI: 10.1021/acs.jced.6b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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(5) Liao, C.; Liu, F.; Kannan, K. Bisphenol S, A New Bisphenol Analogue, in Paper Products and Currency Bills and its Association with Bisphenol A Residues. Environ. Sci. Technol. 2012, 46, 6515−6522. (6) Liao, C.; Liu, F.; Guo, Y.; Moon, H. B.; Nakata, H.; Wu, Q.; Kannan, K. Occurrence of Eight Bisphenol Analogues in Indoor Dust from the United States and Several Asian Countries: Implications for Human Exposure. Environ. Sci. Technol. 2012, 46, 9138−9145. (7) Kuruto-Niwa, R.; Nozawa, R.; Miyakoshi, T.; Shiozawa, T.; Terao, Y. Estrogenic Activity of Alkylphenols, Bisphenol S, and Their Chlorinated Derivatives using a GFP Expression System. Environ. Toxicol. Pharmacol. 2005, 19, 121−130. (8) Andreas, B. E.; Gunter, C. Process for Making 4,4′-Dihydroxydiphenyl Sulfone. US Patent 4,996,367, Feb 26, 1991. (9) Ogata, E.; Nate, N. Process for Preparation of 4,4′-Dihydroxydiphenylsulfone. US Patent 5,189,223, Feb 23, 1993. (10) Ogata, E.; Nate, N. Process for Producing High-purity 4,4′Dihydroxydiphenyl Sulfone. US Patent 7,456,321, Nov 25, 2008. (11) Akzo, N. V. Preparation of 4,4′-Dihydroxydiphenyl Sulfone. EP Patent 0,293,037, Nov 30, 1988. (12) Ogata, E.; Ono, K.; Nakagaki, S. 4,4′-Dihydroxydiphenylsulphone Preparation of High Purity from Phenol and Sulphuric Acid in Presence of Solvents. DE Patent 2,708,388, Aug 31, 1978. (13) Kitamura, H.; Shimizu, Y.; Ohura, O. Process for Isolating 4,4Dihydroxydiphenyl Sulfone from a Mixture of Dihydroxydiphenylsulfone Isomers. US Patent 4,382,147, May 3, 1983. (14) Brabander, M. M. D.; Geert, C. V. Separation and Purification of Isomeric Dihydroxy Diphenyl Sulfones. US Patent 3,065,274, Nov 20, 1962. (15) Mark, V.; Hedges, C. V. Process for Purifying Impure Diphenols. US Patent 4,113,974, Sep 12, 1978. (16) Scott, H. F. Separation and Purification of Isomeric Dihydroxy Diphenyl Sulphones. US Patent 2,392,137, Jan 1, 1946. (17) Thomas, W. S. Separation of Isomers of Dihydroxy Diphenyl Sulfone. US Patent 2,833,828, May 6, 1958. (18) Kuznetsov, L. L.; Belyaev, A. N.; Gromov, K. V. Method for Separation of 2,4′- and 4,4′-Dihydroxydiphenylsulfone. RU Patent 2,307,122, Sep 27, 2007. (19) Belyaev, A. N.; Vershinin, A. V.; Gromov, K. V.; Kuznetsov, L. L. Separation of 2,4′-and 4,4′-Dihydroxydiphenyl Sulfones. Russ. J. Appl. Chem. 2006, 79, 425−429. (20) Xie, Y.; Wang, H. Y.; Jiang, Q. Q.; Zhang, R. Solubility Measurement and Modeling of 4,4′-Dihydroxydiphenyl Sulfone in Nine Organic Solvents from T = (278.15 to 313.15) K and Thermodynamic Property of Dissolution. J. Chem. Eng. Data 2016, 61, 556−564. (21) Jouyban, A.; Shokri, J.; Barzegar-Jalali, M.; Hassanzadeh, D.; Acree, W. E.; Ghafourian, T.; Nokhodchi, A. Solubility of 7-Chloro-2methylamino-5-phenyl-3H-1,4-benzodiazepine-4-oxide, 7-Chloro-1,3dihydro-1-methyl-5-phenyl-2H-1,4-benzodiazepin-2-one, and 7Chloro-5-(2-chlorophenyl)-3-hydroxy-1,3-dihydro-1,4-benzodiazepin2-one in (Propane-1,2-diol + Water) at a Temperature of 303.2 K. J. Chem. Eng. Data 2009, 55, 539−542. (22) Jouyban, A. Review of the Cosolvency Models for Predicting Solubility of Drugs in Water-cosolvent Mixtures. J. Pharm. Pharm. Sci. 2008, 11, 32−58. (23) Jouyban, A.; Fakhree, M. A. A.; Acree, W. E. Comment on “Measurement and Correlation of Solubilities of (z)-2-(2-Aminothiazol4-yl)-2-methoxyiminoacetic Acid in Different Pure Solvents and Binary Mixtures of Water + (Ethanol, Methanol, or Glycol). J. Chem. Eng. Data 2012, 57, 1344−1346. (24) Vahdati, S.; Shayanfar, A.; Hanaee, J.; Martínez, F.; Acree, W. E.; Jouyban, A. Solubility of Carvedilol in Ethanol + Propylene Glycol Mixtures at Various Temperatures. Ind. Eng. Chem. Res. 2013, 52, 16630−16636. (25) Ma, H.; Qu, Y.; Zhou, Z.; Wang, S.; Li, L. Solubility of Thiotriazinone in Binary Solvent Mixtures of Water + Methanol and Water + Ethanol from (283 to 330) K. J. Chem. Eng. Data 2012, 57, 2121−2127. (26) Apelblat, A.; Manzurola, E. Solubilities of o-Acetylsalicylic, 4Aminosalicylic, 3,5-Dinitrosalicylic, and p-Toluic Acid, and Magnesium-
values and RMSD values between the calculated and experimental solubility are all least than 4.97 × 10−2 and 6.49 × 10−4, respectively. The four models provide almost the same RAD values and RMSD values. As a result, all the four models may be employed to correlate the solubility of 4,4′-dihydroxydiphenyl sulfone in the binary (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol) and (acetone + ethanol) mixtures at all initial composition ranges.
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CONCLUSION The solubility of 4,4′-dihydroxydiphenyl sulfone in four binary solvent mixtures of (acetone + methanol), (ethyl acetate + methanol), (acetonitrile + methanol), and (acetone + ethanol) with various compositions were determined experimentally at the temperature range from (278.15 to 313.15) K by using the isothermal dissolution equilibrium method under 101.1 kPa. For the four binary mixed solvents, the solubility of 4,4′-dihydroxydiphenyl sulfone increased with increasing temperature. At the same temperature, the solubility of 4,4′-dihydroxydiphenyl sulfone in (acetone + methanol), (acetone + ethanol), and (acetonitrile + methanol) increased with the increase in the mass fraction of acetone or acetonitrile. However, for the binary (ethyl acetate + methanol) mixtures, they increased initially and decreased afterward with increasing mass fraction of ethyl acetate. The dependence of 4,4′-dihydroxydiphenyl sulfone solubility on temperature and solvent composition was correlated by using the Jouyban−Acree model, Apelblat−Jouyban−Acree model, Ma model, and Sun model. The relative average deviations (RAD) and root-meansquare deviations (RMSD) were no greater than 4.97 × 10−2 and 6.49 × 10−4, respectively. So the calculated solubility data with the four models all provided good agreement with the experimental ones.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: + 86 514 87975568. Fax: + 86 514 87975244. Funding
This work is financial supported by the Natural Science Foundation of the Anhui Province (Project numbers: 1408085MB40 and KJ2016A888), the National Natural Science Foundation of China (Project number: 21406192) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. Notes
The authors declare no competing financial interest.
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