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Cite This: J. Chem. Eng. Data 2018, 63, 2219−2227

Solubility Modeling, Solvent Effect, and Preferential Solvation of Thiamphenicol in Cosolvent Mixtures of Methanol, Ethanol, N,NDimethylformamide, and 1,4-Dioxane with Water Xinbao Li,† Yu Liu,† Yong Cao,† Yang Cong,‡ Ali Farajtabar,§ and Hongkun Zhao*,‡

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†

School of Environmental & Municipal Engineering, North China University of Water Resources and Electric Power, ZhengZhou, He’nan 450011, People’s Republic of China ‡ College of Chemistry & Chemical Engineering, YangZhou University, YangZhou, Jiangsu 225002, People’s Republic of China § Department of Chemistry, Jouybar Branch, Islamic Azad University, Jouybar, Iran S Supporting Information *

ABSTRACT: The thiamphenicol solubility in aqueous cosolvent solutions of ethanol (1), methanol (1), 1,4-dioxane (1), and N,N-dimethylformamide (DMF, 1) was measured via the isothermal dissolution equilibrium method at temperatures ranging from 278.15 to 318.15 K under local pressure (101.1 kPa). At fixed composition of ethanol (methanol, 1,4-dioxane, or DMF) and temperature, the solubility of thiamphenicol was larger in DMF + water mixtures than in the ethanol/methanol/1,4-dioxane mixtures. The local solvent proportions were acquired with the method of inverse Kirkwood−Buff integrals. The absolute value of these preferential solvation parameters were all lower than 1.0 × 10−2 for ethanol (1) + water (2) and 1,4-dioxane (1) + water (2) solutions in water-rich compositions and for methanol (1) + water (2) solutions in whole compositions. In the former two cosolvent mixtures in intermediate compositions and cosolvent-rich regions, thiamphenicol was preferentially solvated by cosolvent. However, for the DMF (1) + water (2) solutions, water solvated preferentially thiamphenicol in water-rich compositions and by DMF in intermediate and DMF-rich compositions. This case by cosolvent might be illustrated based on higher basic behavior of water, which interacted with Lewis acidic groups of thiamphenicol. In addition, the solubility of thiamphenicol was described with the van’t Hoff−Jouyban−Acree, Jouyban−Acree, and Apelblat−Jouyban−Acree models. The obtained average relative deviations were no greater than 1.85%. Furthermore, the solvent effect treatment through the KATLSER model indicated that the solubility variation was significantly affected by the cavity term.

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INTRODUCTION The drug solubility in aqueous cosolvent solutions is of great importance for purifying raw material, designing liquid dosage, and comprehending the mechanism concerning chemical and physical stability for drug dissolution.1−4 In addition, the dependence of solubility on temperature permits carrying out deep analysis to understand the molecular mechanism regarding the drug dissolution process.5 Furthermore, the solubility of drugs in mixed solvents is used in calculating the preferential solvation of a solute by solvent compositions in solution, which can help us to understand the interactions of molecules in relation to the drug dissolution process.5,8 Thiamphenicol (Figure S1, CAS registry no. 15318-45-3) is an important antibiotic used in animals. It is bacteriostatic for the Gram-positive aerobes and some anaerobes.9,10 Currently, it is used as a human and veterinary antibiotic. Owing to high activity in vivo, thiamphenicol has been employed in the clinic.11 Furthermore, it plays a crucial role in the treatment of infection in some less-developed countries.12,13 However, although there is wide usage of thiamphenicol, the physicochemical property of the drug in organic and aqueous © 2018 American Chemical Society

mixtures has not been investigated systematically in the literature. Up until now, the solubility of thiamphenicol in only 13 pure solvents has been determined.14 Many semiempirical and theoretical equations may be used in predicting the drug solubility in mixed solvents; nevertheless, the solubility data obtained via experiment is essential for chemical and pharmaceutical scientists.2,15 The solubility of thiamphenicol in neat water is low. Although cosolvency technique has been widely used to solubilize drugs in pharmacies long ago,1 in recent years the mechanisms regarding the decrease or increase in solubility of drugs start to be studied.5−8 The solubility is governed by the interactions that take place at the microscopic level between the solute and solvent. The polarity is used as a general definition for the overall capacity of the solvent to dissolve the solute. In attempts to describe this definition, Kamlet, Abboud, and Taft (KAT) employ the Received: March 7, 2018 Accepted: May 18, 2018 Published: May 24, 2018 2219

DOI: 10.1021/acs.jced.8b00179 J. Chem. Eng. Data 2018, 63, 2219−2227

Journal of Chemical & Engineering Data

Article

Table 1. Experimental Mole Fraction Solubility (xeT,W × 102) of Thiamphenicol in Mixed Solvent of Methanol (w) + Water (1− w) with Various Mass Fractions within the Temperature Range of 278.15−318.15 K at 101.1 kPaa w T/K

0b

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1b

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.002501 0.003423 0.004959 0.007300 0.009523 0.01325 0.01872 0.02532 0.03391

0.003707 0.005252 0.007709 0.01108 0.01482 0.02079 0.02855 0.03838 0.05105

0.005022 0.007260 0.01074 0.01522 0.02061 0.02902 0.03914 0.05282 0.07057

0.006466 0.009450 0.01405 0.01977 0.02697 0.03810 0.05144 0.06891 0.09195

0.008081 0.01190 0.01774 0.02484 0.03402 0.04815 0.06417 0.08734 0.1162

0.009895 0.01462 0.02183 0.03044 0.04188 0.05933 0.08017 0.1074 0.1428

0.01188 0.01768 0.02640 0.03669 0.05062 0.07180 0.09456 0.1307 0.1733

0.01413 0.02108 0.03154 0.04375 0.06050 0.08588 0.1137 0.1569 0.2077

0.01669 0.02494 0.03740 0.05180 0.07172 0.1018 0.1357 0.1858 0.2458

0.01954 0.02937 0.04412 0.06091 0.08457 0.1200 0.1625 0.2188 0.2894

0.02297 0.03451 0.05181 0.07155 0.09933 0.1411 0.1893 0.2586 0.3413

a

Standard uncertainties u are u(T) = 0.02 K and u(p) = 0.4 kPa. Relative standard uncertainty ur is ur (x) = 0.045. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of methanol in mixed solvents of methanol (w) + water (1−w). bTaken from ref 14.

of organic solvent in binary solutions changed from 0.1 to 0.9. The local pressure was ∼101.1 kPa during the experiment. Experimental Apparatus and Procedure. The diagram of the determination apparatus and the experimental procedure were similar to those described in our previous publication.8,14,21,22 They were illustrated briefly here. The apparatus for solubility measurement is shown in Figure S2. It included a magnetic stirrer, a 100 mL jacketed glass vessel, and a circulating isopropanol + water mixture, the temperature of which was governed using a thermostatic bath (QYHX-1030; standard uncertainty: 0.05 K) purchased from Shanghai Joyn Electronic Co., Ltd., China. Prior to testing, the apparatus’ reliability was confirmed by determining the benzoic acid solubility in toluene.21,22 The solubilities of thiamphenicol in mixed solvents of methanol + water, ethanol + water, 1,4-dioxane + water, and DMF + water were measured using the method of isothermal dissolution equilibrium.8,14,21,22 The saturated mixtures of thiamphenicol were obtained in the vessel. An excess thiamphenicol was placed to ∼60 mL mixed solvents. Approximately 0.5 mL of liquor was taken out at intervials of 2 h and then analyzed using HPLC. If the content of liquid phase did not change, the system was assumed to be in equilibrium. Analytical results indicated that ∼12 h was enough to be in equilibration for all of the investigated mixtures. Then, stirring was stopped for 1 h. The clear liquor was withdrawn and transferred immediately to a preweighed volumetric flask. Finally, the extracted sample was diluted using methanol, and 1 μL was taken out for testing. The thiamphenicol solubility in mole fraction (xw,T) in the four cosolvent solutions are calculated using eq 1. In addition, the initial composition of the mixed solvents (w) is computed using eqs 2 and 3.

solvatochromic comparison method to measure separately the solvent ability making the specific interaction and nonspecific interaction with solute.16−18 They scale the polarity into three terms including α, β, and π* to describe the acidity of hydrogen bond, the basicity of hydrogen bond, and the polarizability/ dipolarity of solvent, respectively.16−18 Because the parameters of KAT are deduced from direct determination of solventinduced energy changes occurring at the solvation shell of the probe, the concept regarding linear solvation energy relationships (KAT-LSER) is proposed, which assumes that the Gibbs energy relating to the solvent properties, e.g., the solubility, is linearly related to these solvent descriptors.19,20 The solvent effect treatment through KAT-LSER offers a convenient approach to shed light on how the solvent interacts with the solute. This work tries to give an idea about the relative stabilization of thiamphenicol in aqueous−organic mixtures with respect to water and the comprehensive solvent−solvent and solvent− solute interactions therein. Thus, the objectives of the present work are to report the thiamphenicol (component 3) solubility in binary mixed solvents of ethanol + water, methanol + water, 1,4-dioxane + water, and DMF + water at several temperatures so as to obtain respective thermodynamic quantities of the mixed solutions and the preferential solvation of thiamphenicol by the cosolvents.

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EXPERIMENTAL SECTION Materials and Apparatus. The mass fraction of thiamphenicol purchased from Beijing HWRK Chemical Co. Ltd., China was 0.975. It was crystallized three times in a water + ethanol mixture, which had a volume ratio of 60:40. The mass fraction of thiamphenicol used in the experiments was 0.996 analyzed using high-performance liquid chromatography (HPLC, Agilent 1260).14 The ethanol, methanol, 1,4-dioxane, and DMF were purchased from Sinopharm Chemical Reagent Co., Ltd., China, which had mass fraction purities no less than 0.994 confirmed using gas chromatography (Smart (GC2018)). The twice-distilled water (conductivity < 2 μS cm−1) used in this work was prepared in our lab. Detailed aspects of these compounds are tabulated in Table S1. Preparation of Mixed Solvents. An analytical balance (BSA224S) provided by Satorius Scientific Instruments was used to prepare the mixed solvents, the estimated relative standard uncertainty of which was ∼0.0002. The compositions

x w,T =

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

w1 = w =

w2 =

m2 m 2 + m3

m3 m 2 + m3

(1)

(2)

(3)

where m1 denotes the mass of thiamphenicol, m2 denotes the mass of methanol, ethanol, 1,4-dioxane, or DMF, and m3 denotes the mass of water. M1, M2, and M3 are the 2220



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Table 2. Experimental Mole Fraction Solubility (xeT,W × 102) of Thiamphenicol in Mixed Solvent of Ethanol (w) + water (1−w) with Various Mass Fractions within the Temperature Range of 278.15−318.15 K at 101.1 kPaa w T/K

0b

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1b

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.002501 0.003423 0.004959 0.007300 0.009523 0.01325 0.01872 0.02532 0.03391

0.002819 0.004070 0.005492 0.008283 0.01113 0.01530 0.02161 0.02890 0.03885

0.003190 0.004639 0.006264 0.009402 0.01238 0.01785 0.02430 0.03314 0.04466

0.003596 0.005060 0.007152 0.01094 0.01421 0.02056 0.02756 0.03800 0.05131

0.004084 0.006059 0.008473 0.01190 0.01690 0.02315 0.03246 0.04452 0.05991

0.004666 0.006633 0.009441 0.01424 0.01918 0.02678 0.03732 0.05033 0.06817

0.005339 0.007618 0.01159 0.01568 0.02257 0.03110 0.04314 0.05862 0.07935

0.006156 0.009277 0.01349 0.01816 0.02630 0.03631 0.05018 0.06994 0.09421

0.007191 0.01084 0.01484 0.02168 0.03096 0.04279 0.05888 0.08071 0.1094

0.008476 0.01172 0.01817 0.02625 0.03626 0.05214 0.06877 0.09370 0.1273

0.01017 0.01480 0.02195 0.03090 0.04383 0.06246 0.08374 0.1153 0.1567

a

Standard uncertainties u are u(T) = 0.02 K and u(p) = 0.4 kPa. Relative standard uncertainty ur is ur (x) = 0.045. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of ethanol in mixed solvents of ethanol (w) + water (1−w). bTaken from ref 14.

Table 3. Experimental Mole Fraction Solubility (xeT,W × 102) of Thiamphenicol in Mixed Solvents of DMF (w) + water (1−w) with Various Mass Fractions within the Temperature Range of 278.15−318.15 K at 101.1 kPaa w T/K

0b

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1b

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.002501 0.003423 0.004959 0.007300 0.009523 0.01325 0.01872 0.02532 0.03391

0.01739 0.02301 0.03237 0.04583 0.05835 0.07860 0.1073 0.1407 0.1831

0.05219 0.06843 0.09410 0.1277 0.1670 0.2194 0.2920 0.3752 0.4761

0.09368 0.1221 0.1660 0.2267 0.2843 0.3707 0.4886 0.6221 0.7874

0.1283 0.1671 0.2263 0.3064 0.3969 0.5034 0.6486 0.8262 1.031

0.1618 0.2114 0.2847 0.3736 0.4888 0.6091 0.7900 1.011 1.255

0.2124 0.2774 0.3713 0.4819 0.6091 0.8040 1.004 1.279 1.576

0.3022 0.3954 0.5255 0.6913 0.8705 1.101 1.397 1.730 2.136

0.4642 0.6046 0.7989 1.024 1.306 1.620 2.037 2.533 3.084

0.7066 0.9187 1.204 1.546 1.944 2.412 2.990 3.637 4.421

0.9203 1.197 1.561 1.987 2.501 3.082 3.786 4.575 5.529

a

Standard uncertainties u are u(T) = 0.02 K and u(p) = 0.4 kPa. Relative standard uncertainty ur is ur (x) = 0.045. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of DMF in mixed solvents of DMF (w) + water (1−w). bTaken from ref 14.

Table 4. Experimental mole Fraction Solubility (xeT,W × 102) of Thiamphenicol in Mixed Solvents of 1,4-Dioxane (w) + Water (1−w) with Various Mass Fractions within the Temperature Range of 288.15−318.15 K at 101.1 kPaa w b

T/K

0

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1b

288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.004959 0.007300 0.009523 0.01325 0.01872 0.02532 0.03391

0.005980 0.008711 0.01148 0.01591 0.02236 0.03019 0.04037

0.006928 0.009994 0.01330 0.01838 0.02572 0.03471 0.04634

0.007929 0.01133 0.01524 0.02100 0.02925 0.03945 0.05261

0.009157 0.01296 0.01761 0.02419 0.03355 0.04521 0.06023

0.01164 0.01598 0.02190 0.02958 0.04041 0.05405 0.07127

0.01385 0.01925 0.02635 0.03559 0.04879 0.06578 0.08734

0.01841 0.02504 0.03418 0.04689 0.06317 0.08470 0.1118

0.02426 0.03252 0.04461 0.06169 0.08169 0.1090 0.1431

0.03078 0.04118 0.05812 0.07764 0.1032 0.1390 0.1822

0.03844 0.05082 0.07285 0.09734 0.1302 0.1732 0.2272

a

Standard uncertainties u are u(T) = 0.02 K and u(p) = 0.4 kPa. Relative standard uncertainty ur is ur (x) = 0.045. Solvent mixtures were prepared by mixing different masses of the solvents with relative standard uncertainty ur(w) = 0.0002. w represents the mass fraction of 1,4-dioxane in mixed solvents of 1,4-dioxane (w) + water (1−w). bTaken from ref 14.

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RESULTS AND DISCUSSION X-ray Powder Diffraction Analysis. The XPRD of the raw thiamphenicol and the solids in equilibrium with the mixed solvents are given as Figure S3. As is shown in Figure S3, all XPRD patterns of solid phase in mixed solvents and raw thiamphenicol have identical characteristic peaks. Thus, no transformation of polymorph or solvation is found in the experiment. Solubility Data. The thiamphenicol solubility in mole fraction in mixed solutions of methanol + water, ethanol + water, 1,4-dioxane + water, and DMF + water is tabulated in

corresponding molar masses. The relative standard uncertainty is estimated to be 4.5% for the solubility in mole fraction. X-ray Powder Diffraction. For validating the existence of polymorph transformation or solvation of thiamphenicol in solubility determination, the solid in equilibration with liquor is collected and analyzed with X-ray powder diffraction (XRPD). The experiment was made on a HaoYuan DX-2700B instrument at room temperature. The solids were tested using Cu Kα radiation at 1.54184 nm with a rate of 6 deg min−1. The tube current and voltage were set to 30 mA and 40 kV, respectively. The data were gathered from 5° to 80° (2θ). 2221



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Tables 1−4. Moreover, the relationship between the solubility data and solvent composition and temperature is shown graphically in Figures 1−4. These indicate that the mole

Figure 3. Mole fraction solubility (x) of thiamphenicol in DMF (w) + water (1−w) mixed solutions with various mass fractions at different temperatures: w, mass fraction of DMF; □, w = 1; ○, w = 0.9000; ◇, w = 0.8000; ☆, w = 0.7000; △, w = 0.6000; ■, w = 0.5000; ●, w = 0.4000; ▲, w = 0.3000; ◆, w = 0.2000; ★, w = 0.1000; ▼; w = 0; , calculated curves by the Jouyban−Acree model.

Figure 1. Mole fraction solubility (x) of thiamphenicol in methanol (w) + water (1−w) mixed solutions with various mass fractions at different temperatures: w, mass fraction of methanol; □, w = 1; ○, w = 0.9000; ◇, w = 0.8000; ☆, w = 0.7000; △, w = 0.6000; ■, w = 0.5000; ●, w = 0.4000; ▲, w = 0.3000; ◆, w = 0.2000; ★, w = 0.1000; ▼; w = 0; , calculated curves by the Jouyban−Acree model.

Figure 4. Mole fraction solubility (x) of thiamphenicol in 1,4-dioxane (w) + water (1−w) mixed solutions with various mass fractions at different temperatures: w, mass fraction of 1,4-dioxane; □, w = 1; ○, w = 0.9000; ◇, w = 0.8000; ☆, w = 0.7000; △, w = 0.6000; ■, w = 0.5000; ●, w = 0.4000; ▲, w = 0.3000; ◆, w = 0.2000; ★, w = 0.1000; ▼; w = 0; , calculated curves by the Jouyban−Acree model.

Figure 2. Mole fraction solubility (x) of thiamphenicol in ethanol (w) + water (1−w) mixed solutions with various mass fractions at different temperatures: w, mass fraction of ethanol; □, w = 1; ○, w = 0.9000; ◇, w = 0.8000; ☆, w = 0.7000; △, w = 0.6000; ■, w = 0.5000; ●, w = 0.4000; ▲, w = 0.3000; ◆, w = 0.2000; ★, w = 0.1000; ▼; w = 0; , calculated curves by the Jouyban−Acree model.

ln x w,T = w1ln x1,T + w2 ln x 2,T +

w1w2 T /K

2

∑ Ji (w1 − w2)i i=0

(4)

where xw,T refers to the solute solubility in mole fraction in mixed solvents, w1 and w2 denote the mass fraction of solvent 1 (ethanol, methanol, 1,4-dioxane, or DMF) and 2 (water), respectively, in solute (thiamphenicol)-free solutions, x1,T and x2,T are the mole fraction solubilities of thiamphenicol in neat solvents, and Ji are equation parameters. The van’t Hoff equation is described as eq 5

fraction solubility of thiamphenicol increases with a rise of cosolvent composition and temperature for the four binary systems. The largest solubility values are observed in neat organic solvents. Tables 1−4 also show that, with the same solvent composition and temperature, the thiamphenicol solubility is higher in DMF + water mixtures than in methanol + water, 1,4-dioxane + water, and ethanol + water. Solubility Modeling. Some solubility models in mixed solvents are summarized in ref 15. Here, three are used to fit the solubility of thiamphenicol in mixed solvents of methanol + water, ethanol + water, 1,4-dioxane + water, and DMF + water, which are Jouyban−Acree,15,22 van’t Hoff−Jouyban-Acree,22 and Apelblat−Jouyban−Acree models.22 The Jouyban−Acree model expressed as eq 4 presents precise expression for solute solubility in ternary and binary solvent mixtures.15,22

ln x T = A +

B T /K

(5)

where xT is the solubility of thiamphenicol in the solvent mixtures. Combining eqs 4 and 5, the van’t Hoff−Jouyban− Acree model is acquired and described as22 ⎛ ⎛ B1 ⎞ B2 ⎞ ww ⎟ + w2⎜A 2 + ⎟+ 1 2 ln x w,T = w1⎜A1 + ⎝ ⎝ T /K ⎠ T /K ⎠ T /K

2

∑ Ji (w1 − w2)i i=0

(6) 2222



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⎛ Vδ 2 ⎞ ln(xi) = c0 + c1π* + c 2β + c3α + c4⎜ s H ⎟ ⎝ 100RT ⎠

where Ai and Bi are parameters in the van’t Hoff equation. The Apelblat equation describes a nonlinear dependence of mole fraction solubility (ln xT) in neat solvents on temperature (1/T) expressed as B ln x T = A + + C ln(T /K) T /K

where δH and Vs stand for solvent Hildebrand solubility parameter and solute molar volume in hypothetical subcooled state, respectively. The term δH is a measure of the cohesive energy density illustrating the strength of the solvent−solvent intermolecular forces. The product of δH2 and Vs accounts for the cavity term, which is the energy necessary to overcome the intermolecular solvent−solvent forces for providing a cavity with the size of the solute. A dimensionless quantity is acquired for the cavity term by dividing it by RT. The number 100 in the denominator is used to scale the cavity term in the comparable range with the other descriptors to achieve a reliable comparison between them. In eq 12, c0 refers to the intercept value at which all descriptors are zero; c1 and c4 reveal the sensitivity of the solubility to the nonspecific solvent−solute and solvent−solvent interactions, respectively, and c2 and c3 denote the solute’s susceptibility to the specific solute−solvent interactions. The KAT parameters α, β, and π* for ethanol + water, methanol + water, 1,4-dioxane + water, and DMF + water and δH for the pure solvents were gathered from different sources.23−27 Literature data are corrected by referencing to the pure solvents and then tabulated in Table S3. The δH values for mixed solvents are obtained from the δH values of neat solvents 1 (methanol, ethanol, DMSO, and n-propanol) and 2 (water) in the solute-free mixtures as ϕ1δH1 + ϕ2δH2, where ϕi denotes the volume fraction of solvent i in solution.6 A value of Vs = 229.82 cm3 mol−1 is calculated from the molar mass divided by the density.28 The thiamphenicol solubility is modeled based on the KATLSER in the form of 15 submodels as tabulated in Tables S4− S7. From the regression analysis, the best model that satisfies both the statistical and physical criteria is chosen. Because solute−solvent interactions and thecavity term have exoergic and endoergic effects on the solubility, respectively, models with negative coefficient for KAT parameters and positive coefficient for the cavity term are rejected. Then, as bolded in Tables S4−S7, one model having the lowest standard deviation, highest F-value, and squared correlation coefficient (r2) closest to unity is selected. Excellent correlation is observed for the solubility in methanol + water mixtures with the cavity term. It means that the Hildebrand solubility parameter can adequately describe the power of the solvent to solubilize thiamphenicol in this mixture. The triple-parametric KAT-LSER model containing π*, α, and cavity term gives also to somewhat good correlation. However, the standard deviations for two KAT parameters are high; it appears the effect of solvent− solute interaction is damped by the dominant role of the cavity term upon solubility. In the ethanol (1) + water (2) solutions, the α of solvent contributes together with the cavity term to the solubility. However, the cavity term explains 58% of the solubility variation with a very low standard deviation. Table S6 shows that, among KAT-LSER models, the single-parametric model of the cavity term gives the best result. Finally, results tabulated in Table S7 indicate that β and cavity term have a physically meaningful impact on the solubility in the mixed solvents of 1,4-dioxane + water; cavity and β term contribute by 33 and 67% to the solubility variation, respectively.

(7)

where A−C denote parameters. Combining eqs 4 and 7, the Apelblat−Jouyban−Acree equation is acquired and described as eq 8.22 ⎡ ⎤ B1 ln x w,T = w1⎢A1 + + C1ln(T /K )⎥ ⎣ ⎦ T /K ⎡ ⎤ B2 ww + w2⎢A 2 + + C2 ln(T /K )⎥ + 1 2 ⎦ T /K ⎢⎣ T /K

2

∑ Ji (w1 − w2)i i=0

(8)

The determined thiamphenicol solubilities in ethanol + water, methanol + water, 1,4-dioxane + water, and DMF + water mixtures are correlated with eqs 4, 6, and 8 based on the following function. F=

e c − lnww,T )2 ∑ (lnx w,T i=1

(9)

For assessing these models studied, the root-mean-square deviation (RMSD) and relative average deviation (RAD) described as eqs 10 and 11, respectively, are employed. N

RMSD =

RAD =

1 N

c e ∑i = 1 (x w,T )2 − x w,T

N c e ⎛ |x w,T − x w,T |⎞ ⎟⎟ e x w,T ⎠ ⎝

∑ ⎜⎜

(12)

(10)

(11)

where N refers to the number of temperature points. The superscript “e” denotes the experiment, and superscript “c” denotes computed using the different models. On the basis of the determined solubility values, the model parameters are computed with the software of Mathcad. The acquired equation parameters along with the values of RMSD and RAD are tabulated in Table S2. The thiamphenicol solubilities in the four binary solutions of methanol + water, ethanol + water, 1,4-dioxane + water, and DMF + water are evaluated based on the values of model parameters. The values calculated by the Jouyban−Acree model are plotted in Figures 1−4. The maximum RAD value is found to be 1.85% acquired using the van’t Hoff−Jouyban−Acree equation for methanol + water mixtures. In addition, all RMSD values are less than 1.56 × 10−4. The RMSD and RAD values attained using the Jouyban−Acree model are smaller than those obtained using other models. In general, all of the models selected may be used to describe the thiamphenicol solubility in mixed solvents of methanol + water, ethanol + water, 1,4-dioxane + water, and DMF + water. The Jouyban−Acree equation gives the best results among the three models. Solvent Effect. KAT-LSER is examined on the solubility data to obtain information on the types of solvent−solute interactions. In the general form, the Gibbs free energy of the solubility is presented as a linear combination of separated energy contributions from various solvent−solute and solvent− solvent interactions as eq 12.18 2223



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is the second derivative of the excess molar Gibbs energy of mixing for two neat solvents (G1 exc + 2) regarding the water composition in solutions (kJ mol−1). Vcor denotes the correlation volume, and r3 denotes the molecular radius of thiamphenicol computed using eq 21, where NAv is the Avogadro’s number.

The above description reveals that the thiamphenicol solubility is obviously affected by the solvent−solvent interactions in the studied aqueous solutions. It may be due to the big molecular size of the solute, which makes the solubility more favorable if the δH values of the solvent decrease when the content of cosolvent (ethanol, methanol, 1,4-dioxane, and DMF) increases in aqueous mixtures. Preferential Solvation of Thiamphenicol. The Inverse Kirkwood−Buff integrals (IKBI) method is valuable for evaluating the preferential solvation of nonelectrolyte in mixed solvents. The dealing relies upon the standard molar Gibbs energy of transfer of thiamphenicol (3) from water (2) to mixed solvents and also upon the excess molar Gibbs energy of mixing for mixed solvents in the absence of solute. Therefore, the outcomes are described as preferential solvation parameter (δx1,3) of thiamphenicol (3) by solvent molecules using the composition of mixed solvents. The IKBI equation is presented as eq 135−8 Gi ,3 =

∫0

rcor

(13)

(14)

G2,3 = RTκT − V3 +

x1V1D Q

(17)

(22)

(23)

0 −x1/ t1 Δtr G3,2 + A 2 e−x1/ t2 → 1 + 2 = A 0 + A1e

with, (16)

(21)

0 The computed values of ΔtrG3,2→1 + 2 at five temperatures are presented in Tables S8 and S9 and shown graphically in Figure S4. These values are correlated with eq 24. The regressed coefficients are presented in Table S10.

(15)

x 2 V2D Q

3 × 1021V3 4πNAv

⎛ x3,2 ⎞ 0 ⎟⎟ Δtr G3,2 ⎜ → 1 + 2 = RT ln⎜ ⎝ x3,1 + 2 ⎠

x1x 2(G1,3 − G2,3)

G1,3 = RTκT − V3 +

3

where xi denotes the mole fraction of i in solute-free mixtures, o and κT,i denotes the isothermal compressibility of pure component i. The RTκT values can be acquired by using the available values of κoT,i for methanol (1.248 GPa−1), ethanol (1.153 GPa−1), 1,4-dioxane (0.738 GPa−1), DMF (0.653 GPa−1), and water (0.457 GPa−1) at 298.15 K.29 o The values of ΔtrG(3,2→1 + 2) of thiamphenicol from water (2) to methanol (1) + water (2), ethanol (1) + water (2), DMF (1) + water (2), and 1,4-dioxane (1) + water (2) solutions can be obtained by using eq 23 from the solubility values.

where stands for the local composition (mole fraction) of solvent (1) around thiamphenicol (3) and x1 denotes the bulk composition of cosolvent (1) in the initial solvent mixture. If δx1,3 is greater than 0, thiamphenicol is preferentially solvated by cosolvent (1); in contrast, if δx1,3 is < 0, water preferentially solvates thiamphenicol. The δx1,3 values can be achieved from the IKBI for the single solvent component as shown in the equations5−8 x1G1,3 + x 2G2,3 + Vcor

(20)

o o κT = x1κT,1 + x 2κT,2

xL1,3

δx1,3 =

⎡ ∂ 2G exc ⎤ 1+2 ⎥ Q = RT + x1x 2⎢ 2 ⎣ ∂x 2 ⎦T , p

where κT is dependent upon composition. On the other hand, the contribution of RTκT to the IKBI is minor, so the κT values can be computed approximately by5−8

where gi,3 is correlation function for solvent i in solvent (1) + water (2) solutions around thiamphenicol (3), r denotes the distance from the center of the thiamphenicol molecule (3) to that of water (2) or solvent (1), and rcor stands for the correlation distance. Hence, for r > rcor to infinity, the integral is essentially zero. The δx1,3 value of thiamphenicol (3) by compound 1 in cosolvent (1) + water (2) solutions can be expressed as5−8 L δx1,3 = x1,3 − x1 = −δx 2,3

(19)

r3 =

2

(gi ,3 − 1)4πr dr

o ⎞ ⎛ ∂Δtr G(3,2 → 1 + 2) ⎟ D=⎜ ∂x1 ⎠T , P ⎝

(24)

where A0, A1, A2, t1, and t2 are equation parameters. Therefore, the values of D are computed using the derivative of eq 24 according to the solvent composition in solutions at intervals of 0.05 in mole fractions of ethanol (1), methanol (1), DMF (1), or 1,4-dioxane (1). The attained values of D are presented in Table S11. Because of the lack of partial molar volumes of thiamphenicol (3) in the studied solutions in previous works, they are here believed to be similar to that of pure thiamphenicol. 5−8 In this way, the molar volume of thiamphenicol (3) can be obtained as 229.82 cm3 mol−1 by molar mass divided by the density.28 As a result, the solute radius value (r3) is computed with eq 21 as 0.450 nm. The values of RTκT and the partial molar volumes of two neat solvents in ethanol (1) + water (2), methanol (1) + water (2), and 1,4-dioxane (1) + water (2) solutions as well as the Q values at the studied temperatures5,8 and at 298.15 K30 have been reported. However, for the DMF (1) + water (2) mixture, these properties can only be found at 298.15 K.31 The values of G1exc+ 2 at the other studied temperatures are computed with eq

L L Vcor = 2522.5[r3 + 0.1363(x1,3 V1̅ + x 2,3 V2)1/3 − 0.085]3

(18)

where, κT denotes isothermal compressibility of cosolvent (1) + water (2) solutions (GPa−1) and V1 and V2 represent the partial molar volume of solvent in mixed solvents (cm3 mol−1); in the same way, V3 refers to the partial molar volume of thiamphenicol in the studied solutions. The D function expressed as eq 19 refers to the derivative of standard molar o Gibbs energy of transfer (ΔtrG(3,2→1 + 2)) of thiamphenicol from water (2) to cosolvent (1) + water (2) solutions regarding solvent content (kJ mol−1). The Q function expressed as eq 20 2224



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Figure 5. δx1,3 values of thiamphenicol (3) from water (2) to (a) methanol (1) + water (2), (b) ethanol (1) + water (2), (c) DMF (1) + water (2), and (d) 1,4-dioxane (1) + water (2) mixtures at several temperatures.

obtained. The calculated values of δx1,3 and Vcor are presented in Tables S16−S19 for methanol + water, ethanol + water, DMF + water, and 1,4-dioxane + water mixed solvents, respectively. Furthermore, the relationship between δx1,3 values and cosolvent composition is given in Figure 5. As can be shown from Figure 5, adding cosolvent (methanol, ethanol, DMF, or 1,4-dioxane) (1) makes δx 1,3 negative for thiamphenicol (3) from neat water to x1 = 0.31 of methanol, x1 = 0.25 of ethanol, x1 = 0.20 of DMF, and x1 = 0.20 of 1,4dioxane. Perhaps the ordering of water molecules near the aromatic ring of thiamphenicol (e.g., hydrophobic hydration) lowers net δx1,3 values to negative in the four cosolvent solutions. However, these absolute values of δx1,3 are all smaller than 1.0 × 10−2 except for the DMF (1) + water (2) system with content x1 = 0.05. Moreover, in methanol (1) + water (2) solutions with content 0.31 < x1 < 1, the absolute value of these δx1,3 values are also smaller than 1.0 × 10−2. These cases result from uncertainty of propagation rather than preferential solvation.37−39 In ethanol (1) + water (2) solutions with 0.25 < x1 < 1, DMF (1) + water (2) solutions with 0.20 < x1 < 1 and 1,4-dioxane (1) + water (2) solutions with 0.20 < x1 < 1.00, the local compositions of DMF (1,4-dioxane or ethanol) are greater than that of mixed solvents. Thus, the values of δx1,3 are positive, which demonstrates that thiamphenicol is preferentially solvated by the cosolvent. The case is perhaps due to breaking the structuring of water near thiamphenicol molecule that increases the solvation. The maximum positive values are δx1,3 = (1.525 to 1.748) × 10−2 in x1 = 0.65−0.70 for ethanol (1) + water (2), δx1,3 = (0.987 to 1.083) × 10−2 in x1 = 0.60 for DMF (1) + water (2) and δx1,3 = (9.940 to 13.44) × 10−2 in x1 = 0.55−0.60 for 1,4-dioxane (1) + water (2). It can also be seen that temperature shows little influence on the δx1,3 values for

25, where H1exc + 2 is the excess molar enthalpy in DMF (1) + water (2) solutions, T1 is the temperature at 298.15 K, and T2 is the studied temperature. H1exc+ 2 values for the DMF (1) + water (2) mixture (eq 26) are cited in ref 6. exc G1exc + 2(T2) = G1 + 2(T1) − T

∫T

T2

1

≈

⎛1⎞ ⎜ ⎟ H1exc + 2 d⎝ ⎠ T

⎛ T2 exc T2 ⎞ G1 + 2(T1) + H1exc ⎟ + 2 ⎜1 − T1 T1 ⎠ ⎝

(25)

2 H1exc + 2 = x1(1 − x1)[ − 7616 + 7751(1 − 2x1) − 1904(1 − 2x1) ]

(26)

The partial molar volumes for two neat solvents in methanol (1) + water (2), ethanol (1) + water (2), 1,4-dioxane (1) + water (2), and DMF (1) + water (2) solutions may be computed on the basis of eqs 27 and 28 using the reported densities for methanol + water,32,33 ethanol + water,34 DMF + water,35 and 1,4-dioxane + water solutions.36 V1 = V + x 2

dV dx1

(27)

V2 = V − x1

dV dx1

(28)

In eqs 17 and 18, V denotes the molar volume of solutions computed by using V = (x1·M1 + x2·M2)/ρ, where M1 refers to the molar mass of cosolvent and M2 to water. According to the determined solubility, the G1,3 and G2,3 values are obtained and presented in Tables S12−S15. The Vcor value needs iteration due to the dependence of Vcor upon the local mole fraction near thiamphenicol. The iteration process is performed via substituting δx1,3 and Vcor into eqs 14, 15, and 18 to recompute xL1,3 until nonvariant data of Vcor is 2225



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the DMF (1) + water (2) and methanol (1) + water (2) solutions. On the basis of functional group and structural investigation, thiamphenicol could serve as a Lewis acid in mixed solvents owing to capacity of the acidic hydrogen atom in −NH− and −OH groups (Figure S1), which form hydrogen bonds with oxygen atoms in O, −O−, and −OH groups of cosolvent. Moreover, thiamphenicol could also serve as a Lewis base due to free electron pairs in nitrogen of −N and the oxygen of  O and −OH, which act together toward acidic hydrogen atoms of water. On the basis of the preferential solvation analysis, it can be assumed that, in composition 0.25 < x1 < 1 for ethanol, 0.20 < x1 < 1 for DMF, and 0.20 < x1 < 1.00 for 1,4-dioxane, thiamphenicol serves as a Lewis acid with DMF, 1,4-dioxane, or ethanol molecules because the cosolvents are more basic than water except for 1,4-dioxane, as illustrated using the Kamlet− Taft parameters, e.g., β = 0.75 for ethanol, β = 0.69 for DMF, β = 0.37 for 1,4-dioxane, and β = 0.47 for water.29 Figure S5 shows the preferential solvation magnitudes of thiamphenicol in methanol + water, ethanol + water, DMF + water, and 1,4-dixoane + water at 298.15 K. The δx1,3 values of thiamphenicol by cosolvent are highest in 1,4-dioxane solutions, followed by ethanol and DMF solutions, and finally by methanol solutions in different mole fractions of cosolvent, i.e., x1 = 0.60, δx1,3 = 0.850 × 10−2 for methanol (1) + water (2), x1 = 0.65, δx1,3 = 1.604 × 10−2 for ethanol (1) + water (2), x1 = 0.60, δx1,3 = 1.074 × 10−2 for DMF (1) + water (2), and x1 = 0.60, δx1,3 = 11.01 × 10−2 for 1,4-dioxane (1) + water (2).

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86 514 87975568. Fax: +86 514 87975244. E-mail: [email protected]. ORCID

Ali Farajtabar: 0000-0002-5510-3782 Hongkun Zhao: 0000-0001-5972-8352 Funding

This research is financially supported by the Practice Innovation Project of Jiangsu Province for Post Graduate Students (Project numbers: XKYCX17_03 6 a nd XKYCX17_039) and the Science and Technology Research Key Project of the Education Department of Jiangsu Province (Project number: SJCX17_0621). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Rubino, J. T. Co-solvents and Cosolvency. In Encyclopedia of pharmaceutical technology; Swarbrick, J., Boylan, J. C., eds.; Marcel Dekker: New York, NY, 1988. (2) Jouyban, A. Handbook of Solubility Data for Pharmaceuticals; CRC Press: Boca Raton, FL, 2010. (3) Avdeef, A. Absorption and Drug Development, Solubility. In Permeability and Charge State; Wiley-Interscience: Hoboken, NJ, 2003. (4) Aulton, M. E. Pharmaceutics: The Science of Dosage Forms Design, 2nd ed.; Churchill Livingstone: London, 2002. (5) Li, X. B.; Wang, M. J.; Du, C. B.; Cong, Y.; Zhao, H. K. Preferential Solvation of Rosmarinic Acid in Binary Solvent Mixtures of Ethanol + Water and Methanol + Water According to the Inverse Kirkwood−Buff Integrals Method. J. Mol. Liq. 2017, 240, 56−64. (6) Marcus, Y. Solvent Mixtures: Properties and Selective Solvation; Marcel Dekker, Inc.: New York, NY, 2002. (7) Marcus, Y. Preferential Solvation in Mixed Solvents. In Fluctuation Theory of Solutions: Applications in Chemistry, Chemical Engineering, and Biophysics; Smith, P. E., Matteoli, E., O’Connell, J. P., eds.; CRC Press: Boca Raton, FL, 2013. (8) Chen, J.; Chen, G. Q.; Cong, Y.; Du, C. B.; Zhao, H. K. Solubility Modelling and Preferential Solvation of Paclobutrazol in Co-solvent Mixtures of (Ethanol, N-Propanol and 1,4-Dioxane) + Water. J. Chem. Thermodyn. 2017, 112, 249−258. (9) Perez, M.; Echeverria, P. G.; Martinez-Arripe, E.; Ez Zoubir, M.; Touati, R.; Zhang, Z. G.; Genet, J. P.; Phansavath, P.; Ayad, T.; Ratovelomanana-Vidal, V. An Efficient Stereoselective Total Synthesis of All Stereoisomers of the Antibiotic Thiamphenicol through Ruthenium-Catalyzed Asymmetric Reduction by Dynamic Kinetic Resolution. Eur. J. Org. Chem. 2015, 2015, 5949−5958. (10) Yunis, A. A. Chloramphenicol: Relation of Structure to Activity and Toxicity. Annu. Rev. Pharmacol. Toxicol. 1988, 28, 83−100. (11) Lu, W. Y.; Chen, P. R.; Lin, G. Q. New Stereoselective Synthesis of Thiamphenicol and Florfenicol from Enantiomerically Pure Cyanohydrin: A Chemo-Enzymatic Approach. Tetrahedron 2008, 64, 7822−7827. (12) Seiple, I. B.; Mercer, J. A. M.; Sussman, R. J.; Zhang, Z. Y.; Myers, A. G. Stereocontrolled Synthesis of syn-β-Hydroxy-α-Amino Acids by Direct Aldolization of Pseudoephenamine Glycinamide. Angew. Chem., Int. Ed. 2014, 53, 4642−4647. (13) Falagas, M. E.; Grammatikos, A. P.; Michalopoulos, A. Potential of Old-generation Antibiotics to Address Current Need for New Antibiotics. Expert Rev. Anti-Infect. Ther. 2008, 6, 593−600.

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CONCLUSIONS The solubility of thiamphenicol in four solvent mixtures over temperatures ranging from 278.15 to 318.15 K was determined. At the given temperature and composition of methanol, ethanol, 1,4-dioxane, or DMF, the solubility of thiamphenicol in mole fraction was highest in DMF (1) + water (2) solutions. By the Jouyban−Acree model, van’t Hoff−Jouyban−Acree model and Apelblat−Jouyban−Acree model, the mole fraction solubility of thiamphenicol was correlated, obtaining RAD values smaller than 1.85% and RMSD values smaller than 1.56 × 10−4. The dependence of thiamphenicol solubility on solvent properties was analyzed using the KAT-LSER equation. The local compositions of ethanol (methanol, 1,4-dioxane, or DMF) and water near thiamphenicol were derived with the method of IKBI. Thiamphenicol was preferentially solvated neither by water nor by methanol for the methanol solutions. In the case of the other mixed solvents in water-rich compositions, thiamphenicol was solvated preferentially by water; however, in cosolvent-rich and intermediate compositions, it was preferentially solvated by cosolvent.

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S9), equation coefficients (Table S10), values of D (Table S11), G2,3 and G1,3 values (Tables S12−S15), values of δx1,3, and correlation volume (Tables S16−S19) (PDF)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00179. Chemical structure of thiamphenicol (Figure S1), apparatus (Figure S2), XPRD (Figure S3), Gibbs energy of transfer (Figure S4), δx1,3 values at 298.15 K (Figure S5), detailed information on thiamphenicol and the selected solvents (Table S1), parameters of equations (Table S2), parameters α, β, π*, and δH (Table S3), multiple linear regression analysis of KAT-LSER model (Tables S4−S7), Gibbs energy of transfer (Tables S8− 2226



Article

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