Determination and Correlation of Solubility Data and Dissolution

Dec 6, 2012 - ... K was determined by dynamic method with a laser monitoring technique. .... and digital monitor; (6) water bath; (7) photoelectric tr...
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Determination and Correlation of Solubility Data and Dissolution Thermodynamic Data of L‑Lactide in Different Pure Solvents Zhen Chen, Chuang Xie, Zhao Xu, Yongli Wang, Haiping Zhao, and Hongxun Hao* The National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China

ABSTRACT: The solubility of L-lactide in pure ethanol, ethyl acetate, acetone, isopropanol, methanol, and methylbenzene from (278.15 to 338.15) K was determined by dynamic method with a laser monitoring technique. It was found that L-lactide is sparingly soluble in ethanol, isopropanol, methanol, and methylbenzene while it has high solubility in ethyl acetate and acetone. The solubility data of L-lactide in different solvents increase with the increasing of temperature. The measured solubility data of Llactide were correlated by using the modified Apelblat, Wilson, nonrandom two-liquid (NRTL), and universal quasichemical (UNIQUAC) models, respectively. It was found that NRTL equations give the best correlation results for most solvents except for ethanol. The dissolution enthalpy, entropy of L-lactide, and the free Gibbs energy change of L-lactide in these solvents were obtained by using the van’t Hoff equation. From solubility data, melting point, fusion enthalpy, and entropy of L-lactide and Dlactide, it was proven that the thermodynamic data of D-lactide are the same with those data of L-lactide.

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INTRODUCTION 3,6-Dimethyl-1,4-dioxane-2,5-diketone (C6H8O4, lactide) is an important intermediate product for the synthesis of polylactic acid with a high molecular weight, which can be used to produce biodegradable materials.1,2 There are four kinds of lactide, which are L-lactide, D-lactide, meso-lactide, and D,Llactide. These compounds are optical isomers, and their structural formulas are given in Figure 1.3 Usually, L-lactide

commonly used lactide in industry because it can be found in the human body. L-Lactide produced by L-lactic acid usually carries impurities, such as lactic acid, oligomers of L-lactide, water, meso-lactide, Dlactide, and so on. These impurities will affect the properties of lactide and the further synthesis of polylactic acid with s high molecular weight. It has been reported that several methods, including crystallization, extraction, rectification, and hydrolyzation, can be applied to purify L-lactide.7−9 As reported, Llactide may be polymerized during the distillation process, and the equipment cost is usually high. When extraction and hydrolyzation techniques are used, the purity of final product is slightly lower than the product obtained by the other methods. Therefore, crystallization is potentially preferable in industry recently. Crystallization is an easy and environment-protecting method. Although L-lactide can be crystallized by both melt crystallization and solution crystallization, solution crystallization is more preferable due to the lower energy consumption.10 To develop a robust and reliable crystallization method to produce L-lactide with a high purity and yield, it is crucial to

Figure 1. Structure of three isomers of lactide. From left to right: Dlactide, meso-lactide, and L-lactide.

and D-lactide should have the same physical and chemical properties, such as the melting point (370.15 K) and solubility.4 However, D,L-lactide is often seen as one kind of mixture which is mixed with equimolar quantities of L-lactide and D-lactide. Moreover, D,L-lactide has a higher melting point (398.15 K) and no optical activity.5 Meso-lactide is a pure compound with two opposite optical activity carbon atoms, and its melting point (325.15 K) is lower than the others.6 L-lactide is the most © 2012 American Chemical Society

Received: September 15, 2012 Accepted: November 29, 2012 Published: December 6, 2012 143

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Table 1. Properties of Pure Components vm/10−4 m3·mol−1 ri qi

L-lactide

ethanol

ethyl acetate

acetone

isopropanol

methanol

methylbenzene

1.1122 4.7000 3.9120

1.6800 2.1055 1.9720

2.8600 3.4786 3.1160

2.1300 2.5735 2.3360

2.2200 3.2491 3.1140

1.1700 1.4311 1.4320

3.1600 3.9228 2.9680

Table 2. Description of Materials Used in This Paper chemical name L-lactide D-lactide

ethanol ethyl acetate acetone isopropanol methanol methylbenzene a

source

initial mass fraction purity

purification method

analysis method

National Medicines Corporation of China National Medicines Corporation of China Tianjin Chemical Reagent Co. of China Tianjin Chemical Reagent Co. of China Tianjin Chemical Reagent Co. of China Tianjin Chemical Reagent Co. of China Tianjin Chemical Reagent Co. of China TianjinChemical Reagent Co. of China

0.980 0.980 0.995 0.995 0.995 0.995 0.995 0.995

none none none none none none none none

HPLCa HPLCa GCb GCb GCb GCb GCb GCb

High-performance liquid chromatography. bGas−liquid chromatography.

know the thermodynamic data such as the solubility and dissolving enthalpy. Since L-lactide is not soluble in water and it will hydrolyze in aqueous solution, organic solvents are widely used in the solution crystallization of L-lactide.11 From literature review, no accurate solubility data of L-lactide in organic solvents can be found. In this paper, the solubility of L-lactide in ethanol, ethyl acetate, acetone, isopropanol, methanol, and methylbenzene from (278.15 to 338.15) K was experimentally determined by using a laser monitoring technique. Since experimental determination can only give several points of the solubility curve, to get a full picture of L-lactide solubility data from (278.15 to 338.15) K, modified Apelblat, Wilson, nonrandom two-liquid (NRTL), and universal quasichemical (UNIQUAC) models were chosen to correlate the experimental data based on the pure component thermophysical properties (including the mole volume vm, parameters of pure substance ri and qi which are calculated by van der Waals volume and surface area of molecule) which are shown in Table 1.12 The standard dissolution enthalpy, entropy, and the free Gibbs energy changes of L-lactide in these solvents were calculated from the measured solubility data using the modified version of the van’t Hoff equation.

Figure 2. Schematic diagram of solubility measurement apparatus. (1) transistor laser generator; (2) jacketed glass vessel; (3) thermometer; (4) condenser; (5) control and digital monitor; (6) water bath; (7) photoelectric transformer; (8) electric magnetic stirrer; (9) rotor.

8.000·10−5 m3 jacked crystallizer was used to determine the solubility. The temperature was controlled by a thermostatted bath (type 501A, Shanghai Laboratory Instrument Works Co., Ltd. of China). The solution was kept under agitation by a magnetic stirring bar. The dissolution of the solute was examined by the laser beam penetrating the vessel. To prevent the evaporation of the solvent, a condenser was introduced. The mass of the samples and solvents was weighed using an analytical balance (Mettler Toledo AB204-N of Switzerland) with a standard uncertainty of 1.000·10−7 kg. This method is based on transferring predetermined amounts of solute (m1) and solvent (m2) into the jacketed vessel. After stirring at a fixed temperature for 7.200·103 s, the solution was heated at a speed of 8.330·10−4 K·s−1. When the solute dissolved completely, the solution was clear, and the laser intensity penetrated through the solution reached its maximum. All determinations were repeated three times, and the average value was used to calculate the mole fraction solubility x1 based on the following equation

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EXPERIMENTAL SECTION Materials. Table 2 shows the description of materials used in this paper, including L-lactide (molecular weight 0.144 kg·mol−1, CAS No. 4511-42-6), D-lactide (CAS No. 13076-170), ethanol, ethyl acetate, acetone, isopropanol, methanol, and methylbenzene. The melting point of L-lactide and D-lactide is (370.50 ± 0.5) K, and the fusion enthalpy is 1.620·104 J·mol−1 which is analyzed by differential scanning calorimetry (DSC) and consistent with the literature data.13 Melting Properties Measurement. The melting temperature Tm and enthalpy of fusion ΔfusH of L-lactide and D-lactide were determined by differential scanning calorimetry (DSC 1/ 500, Mettler Toledo of Switzerland) under a nitrogen atmosphere. Precalibration of the temperature and heat flow of the instrument was performed with a high-purity indium standard before measuring. Approximately 5.000·10−6 kg of lactide was added into DSC pan and heated from (298.15 to 398.15) K at a heating rate of 0.033 K·s−1. Solubility Measurement. The solubility of L-lactide was measured by a dynamic method. As shown in Figure 2, a

x1 =

m1/M1 m1/M1 + m2 /M 2

(1)

where m1 and m2 represent the mass of the solute and solvent, respectively; M1 and M2 are the molecular weights of the solute and the solvent, respectively. To testify the confidence of the dynamic method, solubility data of L-lactide in binary solvents 144

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⎛ ⎞ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2

at different temperature were also measured using the gravimetrical method. The experimental process and method are the same as in the literature.14,15 The solution with an excess of solute was allowed to reach equilibrium isothermally under agitation. Samples of the clear solution with the mass determined (m0) were evaporated in a vacuum oven at 318.15 K for about 4.320·104 s, and then the dry powder was weighed (m1). Each determination was also repeated three times. The mole fraction solubility can be calculated as m1/M1 x1 = m1/M1 + (m0 − m1)/M 2

(7)

where

(2)

G21 = exp( −α12τ21)

(10)

τ21 = (g21 − g11)/RT

(11)

where Δg12 (= g12 − g22) and Δg21 (= g21 − g11) are the cross interaction energy parameters; and parameter α12 is a measurement of the nonrandomness of the mixture, which generally varies between 0.20 and 0.47.22 In the current study, the α12 = 3.0 was obtained and used for the correlation of Llactide solubility data in pure solvents. UNIQUAC Model. In the binary system, the activity coefficient of UNIQUAC model23,24 is calculated by

(4)

⎛ r ⎞ θ1 ⎛Z⎞ ⎜ ⎟q ln + ϕ2⎜l1 − 1 l 2⎟ 1 ⎝2⎠ x1 r2 ⎠ ϕ1 ⎝ ⎞ ⎛ τ21 τ12 − q1 ln(θ1 + θ2τ21) + θ2q1⎜ − ⎟ θ2 + θ1τ12 ⎠ ⎝ θ1 + θ2τ21

ln γ1 = ln

where f1 is the fugacity of the solute 1 in the liquid phase and f1s is the fugacity of the solute 1 in the pure solid phase, respectively. The fugacity of solute in the liquid phase f11 can be expressed with the help of the activity coefficient

li =

(5)

ϕ1

+

Z (ri − qi) − (ri − 1) 2

Z = 10 (12)

where γ1 is the activity coefficient of solute in the liquid phase. Further assumptions lead to the following simplified equation depending only on the melting point data of the solute ΔfusH1 ⎛ 1 1⎞ − ⎟ − ln γ1 ⎜ R ⎝ Tm1 T⎠

(9)

τ12 = (g12 − g22)/RT (3)

1

ln x1 =

(8)

G12 = exp( −α12τ12)

where A, B, and C are empirical constants. The values of A and B represent the variation in the solution activity coefficient, while the C value reflects the effect of temperature on the fusion enthalpy.17 Local Composition Models. At phase equilibrium, the fugacity of the solute 1 in the liquid phase and the fugacity of the solute 1 in the pure solid phase should be the same under constant temperature T and pressure P.

x1γ1(T , P , x1)f11 (T , P) = f1s (T , P)

ν1 ⎛ λ 21 − λ 22 ⎞ ⎟ exp⎜ − RT ⎠ ν2 ⎝

Here,

THERMODYNAMIC MODELS Modified Apelblat Equation. The modified Apelblat equation can be used to correlate the solubility and the temperature as16

f11 (T , P , x1) = f1s (T , P)

Λ 21 =

2 ⎡ ⎤ τ21G21 τ12G12 ⎥ ln γ1 = x 22⎢ + (x 2 + x1G12)2 ⎦ ⎣ (x1 + x 2G21)2

■

B + C ln(T /K) T /K

ν2 ⎛ λ12 − λ11 ⎞ ⎟ exp⎜ − RT ⎠ ν1 ⎝

in which Δλ12 (= λ12 − λ11) and Δλ21 (= λ21 − λ22) are the cross interaction energy parameters; ν1 and ν2 are the mole volumes of solute and solvent, respectively.21 NRTL Model. In the binary system, the activity coefficient of NRTL model is calculated by

where m0 and m1 represent the mass of the sampled solution and the residue after drying, respectively; M1 and M2 are the same as in eq 1. The relative standard uncertainty of the solubility measurement is estimated to ur (x) = 0.02. To testify the solubility consistency of D-lactide and L-lactide, the solubility of D-lactide in ethanol was also measured and compared with the solubility of L-lactide.

ln x1 = A +

Λ12 =

θi =

qixi ∑j qjxj

⎛ uji ⎞ ⎟ τji = exp⎜ − ⎝ RT ⎠

(6)

ϕi =

rx i i ∑j rjxj

i = 1, 2; j = 1, 2

(13)

where ri and qi are calculated by van der Waals volume and surface area of molecule; θi and ϕi are the mean surface area and volume fraction; uji is the interaction energy of molecule j− i.

Therefore, the thermodynamic equation for the calculation of solubility requires knowledge of the melting temperature, the enthalpy of fusion, and the activity coefficient in the liquid. A more detailed derivation of eq 6 can be found in the literature.18 In this paper, three well-established activity coefficient models were employed to calculate the activity coefficient of solute: the Wilson, NRTL, and UNIQUAC models.19,20 Wilson Model. In the binary system, the activity coefficient of the Wilson model can be expressed as

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RESULTS AND DISCUSSION Thermodynamic Properties of Pure Components. The DSC analysis data of L-lactide and D-lactide are presented in Figure 3. From this figure, it can be seen that L-lactide and Dlactide have the same melting point Tm and fusion enthalpy 145

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Figure 3. DSC curves of L-lactide and D-lactide. Solid line: L-lactide; dashed line: D-lactide; HF stands for heat flow.

Figure 4. Fractional deviations Δx = {x(gravimetric) − x(dynamic)}/ x(gravimetric) of the experimental mole fraction solubility x of Llactide obtained by the gravimetric method and dynamic method, respectively.

ΔfusH. The corresponding data are listed in Table 3 with their uncertainties. The fusion entropy ΔfusS was calculated by using the equation as

ΔfusS =

ΔfusH Tm

(14)

The densities ρ of solid state L-lactide and D-lactide were also measured by a 5.000·10−6 m3 pycnometer with the water displacement method three times. During the experiments, solid state lactide was added into pycnometer with full water at room temperature (298.15 ± 1.00 K). Their molar volumes vm were calculated by using the experimental density data.25,26 The results with their uncertainties are also listed in Table 3. From Table 3, it can be found the melting point, the fusion enthalpy, and the density data of D-lactide are nearly the same with those data of L -lactide. This confirmed the consistency of thermodynamic properties of D-lactide and L-lactide. Solubility Data of L-Lactide. The mole fraction solubility data of L-lactide in ethanol−acetate mixture solvent were measured by the dynamic method and gravimetric method, respectively. The fractional deviations of the experimental mole fraction solubility of L-lactide obtained by these two methods were shown in Figure 4. From this figure, it can be seen that the deviations of the solubility data from two methods are less than 0.050. It indicates that the dynamic method used to measure the solubility in this paper is reliable and accurate. Since it is more time-saving and convenient than the gravimetric method, the dynamic method was used to measure the rest of the solubility data of L-lactide in this paper. To further test the consistency of L-lactide and D-lactide, the solubility of both D-lactide and L-lactide in ethanol was measured using the same method and compared. The fractional deviations of the mole fraction solubility of L-lactide and Dlactide are shown in Figure 5. From this figure, it can be found

Figure 5. Fractional deviations Δx = {x(D-lactide) − x(L-lactide)}/ x(D-lactide) of the mole fraction solubility x of L-lactide and D-lactide in ethanol at different temperatures.

that the solubility data of L-lactide in ethanol are consistent with the solubility data of D-lactide in ethanol. This confirms again that the thermodynamic properties of D-lactide are consistent with L-lactide. Due to this reason, only solubility data of Llactide was measured in other solvents. The experimentally measured mole fraction solubility data of L-lactide in ethanol, ethyl acetate, acetone, isopropanol, methanol, and methylbenzene at different temperatures with their uncertainties are shown in Table 4. The modified Apelblat, Wilson, NRTL, and UNIQUAC models were used to correlate these solubility data. The Matlab software was used to calculate the parameters in every model and the calculated solubility of L-lactide at specified temperature. To minimize the

Table 3. Thermodynamic Properties of L-Lactide and D-Lactide (0.1 MPa)a,b Tm K L-lactide D-lactide

370.97 370.38

ΔfusH

ΔfusS

−1

J·mol

J·(mol·K) 4

1.620·10 1.621·104

43.675 43.763

ρ −1

vm −3

m ·mol−1 3

kg·m

3

1.2959·10 1.2873·103

1.1122·10−4 1.1196·10−4

a The standard uncertainty u is u(Tm) = 0.5 K; relative standard uncertainties u are ur(ΔfusH) = 0.05, ur(ρ) = 0.05; the combined expanded uncertainties U are Uc(ΔfusS) = 0.05ΔfusS, Uc(vm) = 0.10 vm (0.95 level of confidence). bDensities were determined for the crystalline phase at T = (298.15 ± 1) K.

146

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Table 4. Experimental and Calculated (Using Modified Apelblat, Wilson, NRTL, and UNIQUAC Models) Mole Fraction Solubility x of L-Lactide in Six Pure Solvents at Different Temperatures (0.1 MPa)a T/K

10xexptl

10xcalcd,Apel

283.95 288.65 295.35 299.95 303.45 310.15 314.65 319.95 325.15 329.25 333.25 336.45

0.02805 0.04226 0.08778 0.1345 0.3098 0.4397 0.5691 0.8101 1.147 1.611 2.578 3.370

0.02707 0.04282 0.08149 0.1259 0.1747 0.3242 0.4882 0.7857 1.245 1.783 2.522 3.320

277.05 282.35 287.65 296.15 301.65 305.15 308.35 313.15 318.25 324.95 331.35 336.35

1.150 1.308 1.469 1.784 1.993 2.211 2.420 2.718 3.107 3.693 4.359 4.914

1.219 1.342 1.489 1.784 2.021 2.196 2.373 2.675 3.050 3.645 4.346 5.003

278.95 286.95 290.65 294.65 299.35 304.95 309.15 314.35 319.05 323.35 328.25

2.170 2.473 2.645 2.830 3.071 3.346 3.602 3.939 4.227 4.552 4.897

2.163 2.483 2.645 2.830 3.063 3.362 3.604 3.924 4.235 4.538 4.907

279.65 290.95 295.65 299.95 304.15 309.35 314.15 318.65 323.65 329.15 333.15

0.08222 0.1308 0.1698 0.2078 0.2558 0.3382 0.4549 0.6048 0.8540 1.269 1.775

0.03318 0.08225 0.1184 0.1643 0.2249 0.3294 0.4652 0.6392 0.9040 1.314 1.716

278.25 282.15 284.15 290.25 294.25 298.85 302.25 308.15 311.45

0.1526 0.2208 0.2309 0.3018 0.3730 0.4741 0.6140 0.8950 1.164

0.1745 0.2176 0.2435 0.3416 0.4253 0.5455 0.6544 0.8940 1.062

10xcalcd,Wilson

10xcalcd,NRTL

10xcalcd,UNIQUAC

0.07200 0.09300 0.1370 0.1800 0.2700 0.4020 0.5350 0.7810 1.149 1.647 2.591 3.354

0.03600 0.04300 0.06300 0.08700 0.2020 0.3220 0.4600 0.7540 1.196 1.782 2.704 3.156

1.145 1.291 1.464 1.790 2.046 2.221 2.401 2.708 3.087 3.677 4.352 4.945

1.387 1.570 1.734 2.028 2.186 2.361 2.505 2.669 2.846 3.040 3.184 3.261

2.159 2.499 2.651 2.835 3.057 3.365 3.594 3.905 4.228 4.534 4.927

2.900 2.966 3.003 3.035 3.072 3.102 3.129 3.156 3.172 3.189 3.200

0.06700 0.1280 0.1670 0.2100 0.2630 0.3490 0.4610 0.6050 0.8430 1.260 1.782

0.1110 0.1430 0.1700 0.1970 0.2340 0.3020 0.4080 0.5590 0.8330 1.304 1.836

0.1720 0.2180 0.2350 0.3100 0.3790 0.4810 0.6050 0.8760 1.120

0.1270 0.1780 0.1880 0.2550 0.3270 0.4390 0.6040 0.9640 1.305

Ethanol 0.06900 0.08600 0.1250 0.1640 0.2680 0.3920 0.5180 0.7550 1.104 1.580 2.512 3.293 Ethyl Acetate 0.9740 1.147 1.343 1.717 1.996 2.211 2.422 2.759 3.169 3.785 4.465 5.048 Acetone 2.018 2.382 2.565 2.776 3.041 3.385 3.660 4.025 4.380 4.723 5.140 Isopropanol 0.08300 0.1360 0.1710 0.2090 0.2560 0.3340 0.4410 0.5810 0.8180 1.229 1.734 Methanol 0.1040 0.1450 0.1580 0.2220 0.2850 0.3810 0.5040 0.7780 1.034 147

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Table 4. continued T/K

10xexptl

10xcalcd,Apel

10xcalcd,Wilson

10xcalcd,NRTL

10xcalcd,UNIQUAC

Methanol

a

315.75 322.25 332.55 333.15

1.261 2.042 2.818 3.367

1.327 1.849 3.093 3.185

278.55 283.65 286.95 291.15 298.35 303.15 308.15 315.95 321.65 324.25 326.95

0.1276 0.2108 0.2305 0.2897 0.3706 0.4362 0.6663 0.8545 1.076 1.346 1.570

0.01467 0.01859 0.02170 0.02646 0.03734 0.04710 0.06008 0.08812 0.1168 0.1329 0.1520

1.205 2.014 3.099 3.543 Methylbenzene 0.1520 0.2030 0.2310 0.2810 0.3750 0.4540 0.6250 0.8550 1.104 1.341 1.567

1.287 2.008 2.940 3.285

1.429 2.214 2.697 2.902

0.1550 0.2050 0.2300 0.2800 0.3700 0.4460 0.6240 0.8510 1.102 1.345 1.569

0.1490 0.2160 0.2310 0.2820 0.3520 0.4110 0.6570 0.8480 1.077 1.363 1.577

The standard uncertainty u is u(T) = 0.01 K; the relative standard uncertainty u is ur(x) = 0.07.

Table 5. Parameters of the Four Correlation Models Apelblat model

Wilson model NRTL model UNIQUAC model

A B C Δλ12/(J·mol−1) Δλ21/(J·mol−1) Δg12/(J·mol−1) Δg21/(J·mol−1) u12/(J·mol−1) u21/(J·mol−1)

ethanol

ethyl acetate

acetone

isopropanol

methanol

methylbenzene

−107.836 −2785.01 20.1620 8468.40 −88.0000 1761.70 1127.30 −1282.70 4827.30

−114.666 3263.41 18.3147 3803.60 −2035.00 2151.00 −30303.0 −2035.00 12654.0

−110.334 3756.82 17.3447 3663.10 −3323.60 11436.0 −22097.0 −1846.70 6230.00

−113.244 −689.956 19.9454 8457.00 −400.000 7028.90 −7690.10 −2000.00 5470.00

−113.600 953.129 19.2641 8178.50 −6.70000 3369.30 5043.50 −542.000 3457.70

−228.694 6495.94 36.1402 7835.50 −1500.00 7967.10 5278.70 −1961.40 5305.00

Table 6. APD% of Different Correlation Models in Six Pure Solvents models

ethanol

ethyl acetate

acetone

isopropanol

methanol

methylbenzene

modified Apelblat Wilson NRTL UNIQUAC

5.3200 11.410 13.620 14.801

1.7500 2.5010 0.70100 15.080

0.24000 2.7470 0.46600 14.802

7.0300 2.1400 1.6400 5.9340

5.7900 13.417 2.2990 11.626

5.4600 2.1300 1.7800 2.1750

objective function f = (xcal − xexp), a nonlinear least-squares method is adopted in the program. The calculated solubility data were also shown in Table 4. The model parameters obtained during the optimization procedure are given in Table 5. From Table 4, it can be found that the solubility of L-lactide increases with temperature in all solvents tested in this paper. At a given temperature, the solubility order is isopropanol ≈ ethanol < methylbenzene ≈ methanol < ethyl acetate < acetone when the temperature is below 305 K, while the solubility order is isopropanol < ethanol < methylbenzene < methanol < ethyl acetate < acetone when temperature is above 305 K. These sequences are not consistent with the polarity order of these solvents (polarity: methanol > ethanol > acetone > isopropanol > ethyl acetate > methylbenzene).27 It was conjectured that the hydrogen bond in solution might play an important role in making this difference. There are four oxygen atoms in lactide, two of which are in the carbonyl group. These oxygen atoms can form different hydrogen bonds in different solvents. To evaluate the applicability and accuracy of the models used in this paper, the average percent deviation (APD %) was used

to evaluate the correlation results. The average percent deviation (APD %) is defined as APD% =

100 N

N

∑ i=1

x1, i − x1,cali x1, i

(15)

where N refers to the number of experimental points; x1,i and xcal 1,i represent the experimental and calculated solubility data, respectively. The APD% of different correlation models are shown in Table 6. From this table, it can be seen that almost all models give correlation results with APD% less than 15. The modified Apelblat equation gives best correlation results for ethanol with an APD% less than 5.4. The NRTL equation gives best correlation results for other solvents. Except for ethanol, the APD% of NRTL equation for L-lactide solubility correlation is less than 2.3. The comparison between the experimental data and the calculated data by NRTL model is shown in Figure 6. From this figure, it can also be seen that the calculated data by NRTL model is very consistent with experimental data. It can be concluded from the data in Table 6 and Figure 6 that the 148

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Table 7. Dissolution Enthalpy ΔHd, Entropy ΔSd, and Gibbs Free Energy Change ΔGd of L-Lactide in Six Pure Solventsa ΔHd

ΔSd

ΔGd

solvent

J·mol−1

J·mol−1·K−1

J·mol−1

ethanol ethyl acetate acetone isopropanol methanol methylbenzene

71835.271 20023.581 12851.357 53442.744 43502.440 34620.229

203.715 53.3030 33.1380 145.065 121.115 89.4390

11097.526 4131.3370 2971.3550 10191.517 7391.9800 7954.0680

a

Combined expanded uncertainties U are Uc(ΔHd) = 0.040ΔHd, Uc(ΔSd) = 0.060ΔSd, Uc(ΔGd) = 0.065ΔGd (0.95 level of confidence). Figure 6. Mole fraction solubility data of L-lactide in six solvent: ■, ethanol; ○, ethyl acetate; ●, acetone; □, isopropanol; ▲, methanol; △, methylbenzene; , calculated data by the NRTL model.

The results and the uncertainty are also listed in Table 7. From the data in Table 7, it can be seen that the ΔHd, ΔSd, and ΔGd values are positive in all solvents. It indicates that the dissolution process of L-lactide in these solvents is endothermic, entropically driven, and not spontaneous. The order of ΔGd values is all opposite to the order of the solubility in these solvents. These phenomena are consistent with the classical thermodynamics theory.

NRTL model and the modified Apelblat model can be combined to give accurate solubility data correlation for design and control of solution crystallization process of L-lactide. Dissolution Properties. The van’t Hoff equation expresses the relationship between the mole fraction solubility of a solute and the temperature by taking the solvent effect into account

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CONCLUSIONS The solubility of L-lactide in six pure solvents from (278.15 to 338.15) K was experimentally determined by the dynamic method with the laser monitoring technique. It was found that the solubility of L-lactide increases with increasing temperature in all solvents tested in this paper. At given temperature, the solubility order is isopropanol ≈ ethanol < methylbenzene ≈ methanol < ethyl acetate < acetone when temperature is below 305 K, while the solubility order is isopropanol < ethanol < methylbenzene < methanol < ethyl acetate < acetone when temperature is above 305 K. Five models were used to correlate the solubility data of L-lactide in different solvents. It was found that the NRTL model gives the best correlation results with APD% less than 2.3 for the solvents except for ethanol, while the modified Apelblat model gives satisfactory correlation results for ethanol with APD% less than 5.5. The data and models can be used to calculate the solubility data of L-lactide in these solvents and are helpful and necessary to the understanding and design of the solution crystallization of L-lactide. The dissolution enthalpy, entropy, and the free Gibbs free energy change of L-lactide in these solvents were also determined. Furthermore, from the thermodynamic data (including solubility data, fusion enthalpy, fusion entropy, and melting point) of L-lactide and D-lactide, it was proven that Dlactide has the same thermodynamic data as L-lactide. Therefore, the solubility data and the models obtained for Llactide in this paper can also be applied to D-lactide.

ΔHd ΔSd + (16) RT R where x1 is the mole fraction solubility of solute in the solvent; T is the corresponding absolute temperature; ΔHd and ΔSd denote the standard enthalpy and entropy of dissolution, respectively. Using eq 16, the plot illustrating the relationship between natural logarithm of saturated mole fraction solubility of Llactide and reciprocal of absolute temperature is presented in Figure 7. Using the data in Figure 7, the dissolution enthalpy ln x1 = −

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Figure 7. Relationship between natural logarithm of saturated mole fraction solubility of L-lactide and reciprocal temperature: ■, ethanol; ●, ethyl acetate; ○, acetone; □, isopropanol; △, methanol; ▲, methylbenzene.

Corresponding Author

*Tel.: +86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected].

and entropy of L-lactide in these solvents were determined. The results with their uncertainties are shown in Table 7. The changes of Gibbs free energy ΔGd for the dissolution of Llactide in different solvents were also calculated by using the Gibbs−Helmholtz equation28 ΔGd = ΔHd − T ΔSd

AUTHOR INFORMATION

Funding

The work was financially supported by National Technology R&D Program from China Ministry of Science and Technology (No. 2011BAD23B02). Notes

The authors declare no competing financial interest.

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dx.doi.org/10.1021/je301014d | J. Chem. Eng. Data 2013, 58, 143−150

Journal of Chemical & Engineering Data

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Article

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ACKNOWLEDGMENTS The authors gratefully acknowledge the assistance of Kaiser Optical Co. Ltd. This material is based upon works supported by the National Engineering Research Center of Industrial Crystallization Technology.

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