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Solubility Modeling and Mixing Thermodynamics of Thiamphenicol in Water and Twelve Neat Organic Solvents from T = (278.15 to 318.15) K Xinbao Li,† Mengqian Wu,† Yang Cong,‡ Cunbin Du,‡ and Hongkun Zhao*,‡ †

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 S Supporting Information *

ABSTRACT: The solid−liquid equilibrium for thiamphenicol in 13 neat solvents (ethanol, methanol, n-propanol, isopropyl alcohol, n-butanol, acetone, acetonitrile, ethyl acetate, 2-butanone, toluene, water, N,Ndimethylformamide, and 1,4-dioxane) was built with the static method at temperatures T = (278.15 to 318.15) K under pressure of 101.2 kPa, and the thiamphenicol solubilities in the selected solvents were measured by using high-performance liquid chromatography. Generally, the solubility data in mole fraction in the selected solvents ranked as N,N-dimethylformamide > acetone > methanol >1,4-dioxane >2-butanone > ethanol > acetonitrile > ethyl acetate > n-propanol > isopropyl alcohol > water > n-butanol > toluene. The nonrandom two-liquid model, Wilson model, modified Apelblat equation, and λh equation were employed to describe the solubility behavior of thiamphenicol in theses solvents. The maximum values of the RMSD and RAD were 4.08 × 10−4 and 2.02%, respectively, and the correlation results by using the modified Apelblat equation were best among the studied models. Additionally, the mixing properties, activity coefficient at infinitesimal concentration and reduced excess enthalpy were derived.

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INTRODUCTION Solubility is a significant physicochemical property in pharmaceutical science. In the developing liquid dosage forms and in the pharmaceutical industry, the solubility of the drugs plays an essential role because the knowledge of solubility makes it possible to select the suitable solvents for drug dissolution and solve different problems such as low bioavailability, medical solutions, and injectable formulations of drugs.1 Besides it is important for the properties of solids and the correlation between in vivo and in vitro data. Changing the solubility of a drug may affect the bioavailability and cause its improvement. Moreover, in the pharmaceutical industry, aqueous solubility is one of the most significant properties of a drug. The solubility of a drug in water is needed to make a solution for toxicological and pharmacological tests of drug screening, and solubility in an organic solvent is also significant in drug production and crystallization for the purification procedure and progression of pharmaceutical analysis.2 Thiamphenicol (CAS No. 15318-45-3; structure shown in Figure 1) is a potent antibiotic employed particularly for veterinary uses against infectious diseases. It has high in vivo action of release with glucuronic acid in the liver and has been employed clinically. At present, it is used as a veterinary and human antibiotic.3,4 It has remarkable activity against both Gram positive microorganisms and Gram negative.5−11 It also © XXXX American Chemical Society

Figure 1. Chemical structure of thiamphenicol.

plays an important role in dealing with infectious disease, especially in developing countries.12,13 The solubility is a fundamental issue for numerous in vivo uses, and the solubility of thiamphenicol in water is very small. Conversely, the total asymmetric synthesis of derivatives of thiamphenicol remains an attractive field at present, since they show the probable enhanced biological activities in comparison with the parent substrate. Organic solvents, for example, ethyl acetate, diethyl ether, or carbon trichloride permit its comprehensive solubility at high substrate concentrations.14 The thiamphenicol solubility in solvents affects the conversion rate and the yield of target compound. To develop the further application of thiampheniReceived: June 13, 2017 Accepted: September 13, 2017

A

DOI: 10.1021/acs.jced.7b00542 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

where R is the universal gas constant (8.314 J·K−1·mol−1), p denotes experimental pressure, and γ denotes the activity coefficient of a solute. ΔCp and ΔV denote the difference of heat capacity and volume of a solute between the liquid state and the solid state at the fusion temperature, respectively. The terms comprising ΔCp in eq 3 are less significant than the first term on the right side, so they can be neglected.23 In addition, small changes of pressure do not affect importantly on equilibrium.24 Furthermore, it is not easy to get the triple point temperature Ttp and pressure ptp (where the three phases of a substance coexist in thermodynamic equilibrium) and corresponding enthalpy ΔHtp for many solids. Instead, the triple point temperature Ttp equals approximately to the fusion temperature Tm. Hence, by substituting the triple point temperature Ttp and ΔHtp with the normal fusion temperature Tm and corresponding fusion enthalpy ΔfusH, respectively, a simplified equation expressing the solute solubility in neat solvents may be derived from eq 3.23

col and improve the yield of thiamphenicol derivatives, it is necessary to know the solubility of thiamphenicol in different solvents. The physicochemical properties of thiamphenicol in mixtures has been studied, but despite the usefulness of this drug, its solubility data in aqueous and organic solvents remain uncomplete.15,16 The solubility data of thiamphenicol in methanol, acetonitrile, ethanol, acetone, water and ethyl acetate at 303.15 K have been reported only by Indrayanto and coworkers.15 From numerous species of solvents employed in the pharmaceutical industry, we select water and 12 organic solvents including ethanol, methanol, isopropyl alcohol, npropanol, n-butanol, acetone, acetonitrile, 2-butanone, ethyl acetate, toluene, water, 1,4-dioxane, and N,N-dimethylformamide (DMF). On the basis of the considerations mentioned above, the aims of the present work are to (1) determine the thiamphenicol solubility in these solvents at the temperatures ranging from (278.15 to 318.15) K; (2) correlate the thiamphenicol solubility with different solubility models; and (3) compute the mixing properties for the dissolution procedure of thiamphenicol in these solvents. It is noteworthy that the melting point of 1,4-dioxane is about 284.4 K. In this work, the solubility for thiamphenicol in 1,4-dioxane is determined at temperatures T = (288.15 to 318.15) K.

THERMODYNAMIC MODELS With the purpose of finding a suitable model to describe the solubility behavior for thiamphenicol in the selected solvents and extend the application of the solubility, the λh equation,17 modified Apelblat equation,18−20 Wilson21 and nonrandom two-liquid (NRTL)22 models are employed to correlate the thiamphenicol solubility in the studied solvents. λh Equation. The λh equation17 expressed as eq 1 is a semiempirical equation, which includes two parameters, λ and h. This model is employed to correlate the solubility data with temperature.

⎤ ⎡ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎢ − ⎥ x 2 + Λ 21x1 ⎦ ⎣ x1 + Λ12x 2 (5)

(1)

here, x is the solubility of thiamphenicol in mole fraction in 13 neat solvents; Tm is the fusion temperature of thiamphenicol in Kelvin. Modified Apelblat Equation. The modified Apelblat equation having three parameters is also a semiempirical model.18−20 It is a quite accurate mathematical model to fit the solubility of solute with temperature in neat solvents, and is expressed as eq 2. ln x = A + B /(T /K) + C ln(T /K)

(4)

It should be noted that the value of ln (γi) is zero for an ideal system. With the object of fitting the solubility (x) of thiamphenicol using different models, the activity coefficient γ should be needed. For a binary system, the activity coefficient (ln γ) described by the Wilson model21 is given as eqs 5−7. The Wilson model is usually used to correlate the dependence of solute solubility on temperature.

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

ΔfusH ⎛ 1 1 ⎞ − ⎟ ⎜ R ⎝ Tm/K T /K ⎠

ln(xi·γi) =

Λ12 =

⎛ ⎛ λ − λ11 ⎞ V2 Δλ12 ⎞ V2 ⎟= exp⎜ − 12 exp⎜ − ⎟ ⎝ V1 RT ⎠ V1 ⎝ R(T /K) ⎠

(6)

Λ 21 =

⎛ ⎛ λ − λ 22 ⎞ Δλ 21 ⎞ V1 V ⎟ = 1 exp⎜ − exp⎜ − 21 ⎟ ⎝ V2 RT ⎠ V2 ⎝ R(T /K) ⎠

(7)

where x1 is the mole fraction of solute in equilibrium liquor, and x2, solvent. V1 and V2 stand for the molar volume of the solute and the solvent, respectively. Δλij are adjustable parameters (J·mol−1) in Wilson model which is in relation to interaction energy between the components i and j. NRTL Model. The NRTL model22 expressed as eqs 8−11 has been employed extensively in expressing the liquid−liquid, vapor−liquid, and solid−liquid equilibrium. Similar to the Wilson model, the NRTL model is also employed to correlate the solute solubility with temperature.

(2)

where, also x is the mole fraction solubility of thiamphenicol in 13 solvents; A, B, and C are adjustable parameters in the modified Apelblat equation. Wilson Model. At a given pressure and temperature, a general (liquid−solid) equilibrium model can be described as eq 3 for a liquid−solid system in equilibrium.23

N

ln γi =

∑ j = 1 τjiiGjiixj N

∑k = 1 Gkixk N

+

⎞ ΔHtp ⎛ 1 Ttp 1 ⎞ ΔCp ⎛ Ttp ⎜⎜ ln(x·γ ) = − ⎟⎟ − − + 1⎟ ⎜ln R ⎝ Ttp T⎠ R ⎝ T T ⎠ ΔV − (p − ptp ) (3) RT

∑ j=1

N ⎡ ∑ x τ G ⎤ ⎢τ − m = 1 m mj mj ⎥ ijj N N ∑k = 1 Gkjxk ⎢⎣ ∑k = 1 Gkjxk ⎥⎦

xjGijj

Gjii = exp( −αjiiτjii) αijj = αjii = α B

(8) (9) (10)


Journal of Chemical & Engineering Data τijj =

gijj − gjj R(T /K)

=

Article

Δgijj R(T /K)

was completely mixed. The equilibration time was confirmed by analyzing the liquid phase repeatedly using the HPLC, which was withdrawn every 2 h by a 3 mL syringe equipped with a 0.2 μm pore syringe filter. If the content of thiamphenicol did not change, the system was believed to reach equilibrium. The analytical results showed that 13 h was enough to put the studied systems at equilibrium. As soon as the system was in equilibrium, the magnetic stirring was halted to let any solid precipitate from the system. Thirty min later, about 2 mL (standard uncertainty: 0.01 mL) of the upper equilibrium liquor was withdrawn by using the 3 mL precooled (or preheated) syringe, and transferred rapidly into a preweighed volumetric flask of 25 mL. The flask was quickly covered with a rubber stopper. The total mass was determined on an analytical balance with a standard uncertainty of 0.0001 g. The density of the equilibrium liquor was obtained. Then the sample was diluted to 25 mL with chromatographic grade methanol, and 2 μL of solution was employed to analyze the concentration of thiamphenicol by HPLC. Before measurement, a series of solutions with known concentration of thiamphenicol were prepared, and 2 μL of solution was withdrawn to analyze with the same HPLC. The relationship between peak area and concentration of thiamphenicol was acquired, which was shown graphically in Figure S2 of the Supporting Information. Once the determination process was performed at one temperature, the residue containing an excess amount of solid was heated to another temperature, and the experiment procedure was performed repeatedly. The local atmospheric pressure was about 101.2 kPa during our experiment process. The saturated solubility (x) of thiamphenicol in mole fraction was acquired by eq 12.

(11)

here, Δgij are adjustable parameters in the NRTL model, which relate to interaction energy. α is the parameter varying from (0.20 to 0.47).23,25

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EXPERIMENTAL SECTION Materials and Apparatus. Thiamphenicol having a purity of 0.975 in mass fraction was bought from Beijing HWRK Chemical Co., Ltd., China. The crude sample was recrystallized three times in the mixtures of (acetone + ethyl acetate) with a volume ratio of 10:90.25 The content of the purified thiamphenicol was 0.996 in mass fraction, which was confirmed using a high-performance liquid phase chromatograph (HPLC, Agilent-1260). The solvents (ethanol, methanol, n-propanol, isopropyl alcohol, n-butanol, acetone, ethyl acetate, 2-butanone, toluene, acetonitrile, DMF, and 1,4-dioxane) were all of analytical grade. They were provided by Sinopharm Chemical Reagent Co., Ltd., China, and employed in experiment without extra purification. The contents of the organic solvents were no lower than 0.993 (mass fraction) confirmed by gas chromatography (GC Smart (GC-2018)). The twice distilled water was prepared in our laboratory, the conductivity of which was below 2 μS·cm−1 . The details of the selected solvents and thiamphenicol were collected and tabulated in Table S1 of Supporting Information. The experimental apparatus (Figure S1 of Supporting Information) comprised a 100 mL jacketed glass vessel, a magnetic stirrer, and a circulating (isopropyl alcohol + water) system. The temperature of (isopropyl alcohol + water) was controlled with a thermostatic bath (model: QYHX-1030) having a standard uncertainty of 0.05 K. It was provided by Shanghai Joyn Electronic Co., Ltd., China. The exact temperature of solution was shown by using a mercury glass microthermometer with a standard uncertainty of 0.02 K, which was inserted in the inner chamber of the vessel. A condenser connecting with the vessel was used to prevent the solvent from escaping. The reliability of the apparatus was verified by measuring the benzoic acid solubility in toluene in advance.26,27 Melting Properties Determination. The fusion temperature (T m ) of thiamphenicol was determined in the literature,4,7,11,28 nevertheless the fusion enthalpy (ΔfusH) of thiamphenicol has not been reported up to now. With the purpose of correlating the thiamphenicol solubility using thermodynamic models, the ΔfusH of thiamphenicol was measured by using a DSC instrument (Pyris-Diamond, PerkinElmer) in a nitrogen gas. With indium as the reference material, this instrument was recalibrated before determination. About 3 mg of thiamphenicol was introduced into a DSC pan, and heated at a heating rate of 5 K·min−1. The standard uncertainties were estimated to be 0.5 K for temperature and 0.40 kJ·mol−1 for fusion enthalpy. Solubility Determination. The liquid−solid equilibria for the thiamphenicol + solvent mixtures were reached using the static technique26,27 over the temperature range from (278.15 to 318.15) K, and the thiamphenicol solubility in equilibrium liquor was determined with theHPLC. The details of the experiment process were described in our previous works.26,27 Here it was illustrated briefly. About 60 mL solvent and an excessive amount of thiamphenicol were placed in the 100 mL vessel. The mixture was stirred until the system

x=

m1/M1 m1/M1 + m2 /M 2

(12)

where m1 and m2 stand for the mass of thiamphenicol and the solvent, respectively; and M1 and M2 are the molar mass of thiamphenicol and corresponding solvent. Analysis Method. The compositions of the equilibrium liquor were analyzed on an Agilent 1260 HPLC system (Agilent Technologies, USA), which included a quaternary pump (type G1311C), a UV detector (type G1314F), and an autosampler (type G1329B). The wavelength of the UV detector was 220 nm. The chromatographic analysis was carried out on a unimicro-Kromasil C18, 5 μm (250 mm × 4.6 mm) column, the temperature of which was about 303 K. The mobile phase was neat methanol, the flow rate of which was 1.0 mL·min−1. Three samples were taken for every equilibrium liquor at a given temperature. In addition, we repeated each analysis three times to check the repeatability. The mean value was regarded as the final solubility. The relative standard uncertainty for the determined solubility values was estimated to be 2.6% in mole fraction. X-ray Powder Diffraction. The crystal forms of thiamphenicol were confirmed by X-ray powder diffraction (XPRD). It was performed on a HaoYuan DX-2700B instrument (HaoYuan, China). The samples were measured by Cu Ka radiation, the wavelength of which was 1.54184 nm. The tube current and voltage were 30 mA and 40 kV, respectively. The XPRD data were collected from 10° to 80° (2-theta) at a scan speed of 6 deg·min−1 under normal pressure. C



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RESULTS AND DISCUSSION X-ray Powder Diffraction Analysis. With the intention of demonstrating the existence of the solvate formation or polymorphic transformation of thiamphenicol during the experiment process, the collected equilibrium solid is dried under vacuum and tested by XPRD. The patterns of the raw material thiamphenicol and the solid formed in the studied solvents are shown graphically in Figure S3 of the Supporting Information. It can be seen that the XPRD pattern of all of the solid phase equilibrating with its mixture has the same characteristic peaks as the raw material thiamphenicol. Thus, the conclusion can be made that there is no solvate formation or polymorphic transformation during the experiment procedure. Melting Properties of Thiamphenicol. Figure 2 is the DSC scan of thiamphenicol. The fusion temperature Tm and

that reported in ref 28; however, within the range of those given in refs 4, 7, and 11. This result perhaps results from the differences in samples, equipment, and/or determined conditions. On the basis of the fusion enthalpy ΔfusH of thiamphenicol, the fusion entropy ΔfusS for thiamphenicol is computed to be 107.3 J·(K·mol)−1 with eq 13.

ΔfusS =

ΔfusH Tm

(13)

Solubility Data. The mole fraction solubility (x) of thiamphenicol in methanol, ethanol, n-propanol, isopropyl alcohol, n-butanol, acetone, ethyl acetate, acetonitrile, 2butanone, toluene, water, DMF, and 1,4-dioxane within the temperature range from (278.15 to 318.15) K are listed in Table 1 and plotted in Figure 3. Additionally, the plots of ln(x) versus 1/T in 13 solvents are shown graphically in Figure S4 of the Supporting Information. The solubilities of thiamphenicol increase with an increase temperature for a certain solvent. At a certain temperature, the mole fraction solubility of thiamphenicol is highest in DMF, and lowest in toluene. It can also be seen from Figure 3 that the solubilities of thiamphenicol in mole fraction decrease based on the following order: DMF > acetone > methanol >1,4-dioxane >2-butanone > ethanol > acetonitrile > ethyl acetate > n-propanol > isopropyl alcohol > water > n-butanol > toluene. The solubility data of thiamphenicol in methanol, acetonitrile, ethanol, acetone, water, and ethyl acetate at 303.15 K have been reported in ref 15, which are 3.33 mg·mL−1 for acetonitrile, 12.50 mg·mL−1 for methanol, 3.85 mg·mL−1 for ethanol, 7.14 mg·mL−1 for acetone, 2.50 mg·mL−1 for water, and 1.25 mg·mL−1 for ethyl acetate. However, the densities of the solutions are not provided. In this work, the mole fraction solubilities of thiamphenicol in the six neat solvents are approximately calculated by assuming that the densities of the

Figure 2. DSC scan of thiamphenicol.

fusion enthalpy ΔfusH of thiamphenicol are observed to be 437.36 K and 46.91 kJ·mol−1, respectively. The fusion temperature Tm measured in the present work is smaller than

Table 1. Experimental Mole Fraction Solubility (x) of Thiamphenicol in Different Solvents at the Temperature Range from T= (278.15 to 318.15) K under 101.2 kPaa 100x T/K

acetonitrile

ethyl acetate

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15

0.007958 0.01192 0.01771 0.02587 0.03633 0.05023 0.07158 0.09796 0.1343 DMF

0.006238 0.009090 0.01244 0.01715 0.02457 0.03481 0.04709 0.06432 0.08611 methanol

0.01017 0.01480 0.02195 0.03090 0.04383 0.06246 0.08374 0.1153 0.1567 2-butanone

0.9203 1.197 1.561 1.987 2.501 3.082 3.786 4.575 5.529

0.02297 0.03451 0.05181 0.07155 0.09933 0.1411 0.1893 0.2586 0.3413

0.01385 0.01970 0.02858 0.03792 0.05096 0.07043 0.09521 0.1248 0.1664

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 a

ethanol

n-propanol

isopropyl alcohol

0.005106 0.007345 0.01035 0.01473 0.01991 0.02853 0.03799 0.05095 0.06866 n-butanol

0.003460 0.005196 0.007131 0.01037 0.01458 0.02015 0.02689 0.03642 0.04926 acetone

0.0009545 0.001382 0.002079 0.003104 0.004461 0.006393 0.008424 0.01228 0.01647

0.02832 0.04248 0.05851 0.08403 0.1116 0.1486 0.2018 0.2683 0.3523

1,4-dioxane

toluene

0.03844 0.05082 0.07285 0.09734 0.1302 0.1732 0.2272 water

0.0003958 0.0006031 0.0008894 0.001281 0.001893 0.002696 0.003805 0.005528 0.007604 xidl

0.002501 0.003423 0.004959 0.007300 0.009523 0.01325 0.01872 0.02532 0.03391

0.2893 0.3640 0.4562 0.5694 0.7081 0.8774 1.083 1.333 1.635

Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.45 kPa; relative standard uncertainty ur is ur(x) = 0.026. D



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Figure 3. Solubility (x) of thiamphenicol in mole fraction in organic solvents at different temperature: (a) ∗, DMF. (b) ●, Methanol; ▲, ethanol; ▶, 1,4-dioxane; ▼, n-propanol; ◀, water; ◆, n-butanol. (c) □, Acetone; ▷, 2-butanone; ○, acetonitrile; ◁, ethyl acetate; ◇, isopropyl alcohol; △, toluene. +, ☆, ▽, × , ★, and ■, solubility of thiamphenicol in methanol, ethanol, water, acetone, acetonitrile, and ethyl acetate at 303.15 K, respectively, taken from ref 15. Solid line, , calculated curves from modified Apelblat equation.

Solubility Correlation and Calculation. The thiamphenicol solubilities in the studied solvents are correlated with the four models mentioned above. The nonlinear least-squares method31 is employed in the regression procedure. For the Wilson model and the NRTL model, the object function is

solutions ares equal to that of the corresponding neat solvent, and shown graphically in Figure 3. It can be found that the determined solubilities at 303.15 K in this work are almost the same with the values reported in the literature. It can be observed from Figure 3 and Table 1 that, for the mixtures of thiamphenicol + alcohol, the order of the solubility values in mole fraction is consistent with the polarities of the solvents except for isopropyl alcohol.29 The solvent polarities appear to be an important factor to effect the solubility of thiamphenicol in the studied alcohols. A similar case can also be observed for the acetone, 2-butanone, and toluene. Although the water polarity is the largest among the selected solvents, the solubility of thiamphenicol is smaller in water than in methanol. This case may be due to the molecular interactions between thiamphenicol and water. On the other hand, the thiamphenicol molecule has large dipole moments owing to the −NH− group, and therefore may provide strong nonspecific dipole− dipole interactions with the solvents.30 It can form H-bonds with solvent, which have a direct influence on the solute solubility. The solubilities of thiamphenicol are larger in DMF than in the other solvents. This case is apparently caused by the formation of H-bonds between the N−H groups of thiamphenicol and (one of) the free electron pairs of the oxygen atoms in DMF molecules. By and large, it is too complicated to clarify the solubility behavior tabulated in Table 1 according to a single reason. This behavior may be caused by many factors, for instance, solvent−solvent interactions, solvent−solute interactions, and molecular sizes and shapes and so on.

F=

∑ (ln γie − ln γic)2

(14)

i=1

and for modified Apelblat equation and λh equation, it is expressed as F=

∑ (xie − xic)2

(15)

i=1

Additionally, so as to evaluate the selected models, relative average deviation (RAD), the relative deviation (RD), and the root-mean-square deviation (RMSD) are empoyed and described as eqs 16, 17, and 18, respectively. RAD =

RD =

1 N

N

∑ i=1

xie − xic xie

(16)

xe − xc xe

(17)

⎡ ∑N (x c − x e)2 ⎤1/2 i i ⎥ RMSD = ⎢ i = 1 ⎢⎣ ⎥⎦ N E

(18)



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constant. In this manner, γ3 will depend essentially upon e11, e33, and e13.34,38 It has been confirmed that the e11 and e33 terms are unfavorable for the dissolution procedures, while the e13 term favors these procedures.33,38 In general, the contribution of the term containing e33 may be regarded as constant. As a qualitative method, the following analysis can be performed on the basis the energetic quantities and magnitudes expressed in eq 21. The term e11 is highest in toluene and it was lowest in DMF (exhibiting a γ3 value < 1). The values of e11 are similarly attained in acetonitrile, ethyl acetate, ethanol, n-propanol, isopropyl alcohol, and 2-butanone because their mole fraction solubilities are also similar. The e11 values are much lower in methanol, acetone, and 1,4-dioxane in comparison with toluene and n-butanol. Neat toluene and n-butanol have larger γ values suggesting high e11 and low e13 values. However, in DMF, methanol, acetone, and 1,4-dioxane (having low γ values), the values of e11 are relatively low while the values of e13 may be higher. Thus, the solvation of thiamphenicol can be higher in DMF, methanol, acetone, and 1,4-dioxane. Besides, for the system of thiamphenicol + water, γ values are relative high, which indicates high e11 and low e13 values. Mixing Properties. The evaluation of thermodynamic functions of mixtures is essential for modeling liquid−solid equilibrium investigations. The mixing enthalpy (ΔmixH°) varies on the basis of the interactions of solvent−solvent, solvent−solute, and solute−solute, whereas the entropy change (ΔmixS°) is a function of the disorder degree or randomness of a mixture.39 Thus, so as to understand the solubility behavior of thiamphenicol in the selected neat solvents, the thermodynamic properties of mixtures are evaluated. Since all the mixtures under consideration are nonideal, the mixing enthalpy (ΔmixH), mixing entropy (ΔmixS), and the Gibbs energy change of mixing (ΔmixG) may be evaluated as the following equation.39,40

here ln γie denotes the logarithm of activity coefficient computed using eq 4; and ln γci , calculated using solubility models. N refers to the number of data points; xci is the calculated values of thiamphenicol solubility; and xei represents experimental ones. The densities of the selected solvents tabulated in Table S1 are cited in ref 29. The density of thiamphenicol is cited in ref 32, and the fusion temperature (Tm) and fusion enthalpy (ΔfusH) of thiamphenicol are taken from the present work. The obtained parameters’ values of A, B, and C in the modified Apelblat equation, λ and h in λh equation, Δgij in NRTL and Δλij in Wilson models, together with the values of RMSD are listed in Table S2 of the Supporting Information. In light of the obtained parameters’ values, the values of RD and RAD are calculated and tabulated in Table S3 of the Supporting Information. In addition, a graphic display of the difference between the experimental solubility and the calculated values using the modified Apelblat equation is given in Figure 3. It can be found from Tables 1 and S2 and S3 that the computed solubilities of thiamphenicol in 13 neat solvents agree well with the determined ones. The largest RMSD value is 4.08 × 10−4, which is obtained with λh equation for the solvent of DMF, and the maximum RAD value is 2.02 × 10−2. The values of RAD obtained using the modified Apelblat equation are no more than 1.73 × 10−2. The conclusion may be made that the selected models may all be used to correlate the thiamphenicol solubility in these solvents. Activity Coefficients. The ideal solubility of thiamphenicol (xid) is evaluated by using eq 19.33,34 ln x id =

−ΔfusH(Tfus − T ) RTfusT ⎛ T ⎞⎤ ΔCp ⎡ (Tfus − T ) ⎢ + + ln⎜ ⎟⎥ R ⎢⎣ T ⎝ Tfus ⎠⎥⎦

(19)

Δmix M = ME + Δmix M id

In general, ΔCp can be set approximately as the fusion entropy (ΔfusS).34−36 The reasons for this assumption have been provided in ref 37. The ΔfusS value for thiamphenicol is obtained as 107.3 J·(K· mol)−1. On the basis of these data, xidl values of thiamphenicol are evaluated and tabulated in Table 1. The activity coefficients (γ3) of thiamphenicol in the neat solvents are computed by using eq 20.33−35

γ3 = x idl /x3

where ME refers to the excess property in actual mixtures. ΔmixH, ΔmixS, and ΔmixG represent the mixing enthalpy, mixing entropy, and change of mixing Gibbs energy, respectively. Regarding an ideal mixture, the mixing properties in neat solvents are described as41

(20)

The calculated γ3 values of for solid thiamphenicol in the neat solvents are presented in Table S4 of the Supporting Information. The γ3 value is a measure of the error observed in actual solution processes from ideal solution processes. From γ3 values, the solvent−solute intermolecular interactions may be obtained with the help of eq 21.34,38 ln γ3 = (e11 + e33 − 2e13)

Δmix Gid = RT (x1 ln x1 + x 2 ln x 2)

(23)

Δmix S id = −R(x1 ln x1 + x 2 ln x 2)

(24)

Δmix H id = 0

(25)

where x1 denotes the mole fraction of solute; and x2 denotes the mole fraction of the solvent. Moreover, the excess functions are described as eqs 26−28 on the basis of the Wilson model.42

V3φ12 RT

(22)

GE = RT (x1 ln γ1 + x 2 ln γ2)

(21)

= −RT[x1 ln(x1 + x 2 Λ12) + x 2 ln(x 2 + x1Λ 21)]

where subscript 1 refers to the neat solvent; and 3 refers to the solute thiamphenicol. Therefore, e33, e11, and e13 signify the solute−solute, solvent−solvent, and solute−solvent interaction energies, respectively; V3 denotes the molar volume of thiamphenicol in the supercooled liquid state; and φ1 stands for the volume fraction of neat solvent. As for solids with low solubility, the term V3φ21/RT can be regarded almost as

(26)

⎡ ∂(GE /T ) ⎤ H E = − T 2⎢ ⎥ ⎣ ∂T ⎦ ⎛ Δλ12 Λ12 Δλ 21Λ 21 ⎞ = x1x 2⎜ + ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2 F

(27)


Journal of Chemical & Engineering Data SE =

HE − GE T

Article

Funding

This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

(28)

On the basis of the Wilson equation, the activity coefficient 43 (γ∞ 1 ) at infinitesimal concentration can be acquired by ln γ1∞ = −ln Λ12 + 1 − Λ 21

Notes

The authors declare no competing financial interest.

■

(29)

The dependence of excess enthalpy at infinite dilution upon temperature may be described as eq 30.44,45 ⎡ ∂ ln γ ∞ ⎤ 1 ⎢ ⎥ ⎣ ∂(1/T ) ⎦

= P ,x

(1) Dressman, J.; Reppas, C. Drug Solubility: How to Measure It, How to Improve It. Adv. Drug Delivery Rev. 2007, 59, 531−532. (2) Alsenz, J.; Kansy, M. High Throughput Solubility Measurement in Drug Discovery and Development. Adv. Drug Delivery Rev. 2007, 59, 546−567. (3) Balg, C.; Mieri, M. D.; Huot, J. L.; Blais, S. P.; Lapointe, J.; Chênevert, R. Inhibition of Helicobacter Pylori Aminoacyl-tRNA Amidotransferase by Chloramphenicol Analogs. Bioorg. Med. Chem. 2010, 18, 7868−7872. (4) 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. (5) 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. (6) Yunis, A. A. Chloramphenicol: Relation of Structure to Activity and Toxicity. Annu. Rev. Pharmacol. Toxicol. 1988, 28, 83−100. (7) Huang, X. B.; Li, Z. Z.; Zhou, Z.; Xie, S. J. Thiamphenicol Freezedried Powder. CN Patent 104,013,584, Sep 22, 2014. (8) Li, Q.; Zhang, H. B.; Li, C. G.; Xu, P. F. Stereoselective Synthesis of (−)-Chloramphenicol, (+)-Thiamphenicol and (+)-Sphinganine via Chiral Tricyclic Iminolactone. Chin. J. Chem. 2013, 31, 149−153 (Chinese). (9) Hajra, S.; Karmakar, A.; Maji, T.; Medda, A. K. Stereoselective Syntheses of (−)-Chloramphenicol and (+)-Thiamphenicol. Tetrahedron 2006, 62, 8959−8965. (10) Kaptein, B.; van Dooren, T. J. G. M.; Boesten, W. H. J.; Sonke, T.; Duchateau, A. L. L.; Broxterman, Q. B.; Kamphuis, J. Synthesis of 4-Sulfur-substituted (2 S, 3 R)-3-Phenylserines by Enzymatic Resolution. Enantiopure Precursors for Thiamphenicol and Florfenicol. Org. Process Res. Dev. 1998, 2, 10−17. (11) George, S.; Narina, S. V.; Sudalai, A. A Short Enantioselective Synthesis of (−)-Chloramphenicol and (+)-Thiamphenicol using Tethered Aminohydroxylation. Tetrahedron 2006, 62, 10202−10207. (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. (14) Da Silva, M. R.; Montenegro, T. G. C.; De Mattos, M. C.; De Oliveira, M. C. F.; De Lemos, T. L. G.; De Gonzalo, G.; Lavandera, I.; Gotor-Fernandez, V.; Gotor, V. Regioselective Preparation of Thiamphenicol Esters through Lipase-Catalyzed Processes. Tetrahedron 2014, 25, 987−994. (15) Indrayanto, G.; Trisna, D. L.; Santosa, M. H.; handajani, R.; Agustono, T.; Sucipto, P. Thiamphenicol. Anal. Profiles Drug Subst. Excipients 1993, 22, 461−488. (16) Jouyban, A. Handbook of Solubility Data for Pharmaceuticals; CRC Press: BocaRaton, FL, 2010. (17) Buchowski, H.; Ksiazczak, A.; Pietrzyk, S. Solvent Activity along a Saturation Line and Solubility of Hydrogen-Bonding Solids. J. Phys. Chem. 1980, 84, 975−979. (18) Apelblat, A.; Manzurola, E. Solubilities of o-Acetylsalicylic, 4Aminosalicylic, 3,5-Dinitrosalicylic, And p-toluic Acid, and Magne-

H1E, ∞ R

(30)

On the basis of the experimental solubility values and the parameters’ values in the Wilson model, the mixing functions of E,∞ ΔmixG, ΔmixH, ΔmixS, ln γ∞ are computed and 1 and H1 tabulated in Table S5 of the Supporting Information. It is obvious from Table S5 that all the ΔmixS° values are positive. Besides, the mixing Gibbs energy (Figure S5 of Supporting Information) is observed to decrease with increasing temperature. The lowest Gibbs free energy is acquired for the DMF system.

■

CONCLUSION The solubility of thiamphenicol in 13 neat solvents of methanol, ethanol, n-propanol, isopropyl alcohol, n-butanol, acetone, acetonitrile, ethyl acetate, 2-butanone, toluene, water, 1,4-dioxane, and DMF was determined by using the static method at the elevated temperatures under 101.2 kPa. With the rise in temperature, the thiamphenicol solubility in the neat solvents increased. At a fixed temperature, the sequence of mole fraction solubility in the studied solvents ranked as DMF > acetone > methanol > 1,4-dioxane > 2-butanone > ethanol > acetonitrile > ethyl acetate > n-propanol > isopropyl alcohol > water > n-butanol > toluene. Four thermodynamic models were used to correlate the determined solubility data. The maximum values of RAD and RMSD acquired with the four models were 2.02% and 4.08 × 10−4, respectively. Additionally, the mixing properties, reduced excess enthalpy (H1E,∞), and activity coefficient at infinitesimal concentration (γ∞ 1 ) were calculated on the bases of the experimental solubility values.

■

ASSOCIATED CONTENT

S Supporting Information *

Supporting Information Available: ). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00542. Experimental apparatus (Figure S1), relationship between peak area and concentration of thiamphenicol (Figure S2), XPRD patterns (Figure S3), van’t Hoff plots (Figure S4), mixing Gibbs energy (Figure S3), and detailed information on the materials (Table S1), parameters of the equations (Table S2), values of solubility, RD and RAD (Table S3), activity coefficients (Table S4), and mixing properties (Table S5) (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

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

Hongkun Zhao: 0000-0001-5972-8352 G



Article

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