Article pubs.acs.org/jced
Solubility Measurement and Modeling for Betaine in Different Pure Solvents Shui Wang, Yingying Zhang, and Jidong Wang* College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: By utilizing a laser monitoring observation technique, solubilities of betaine in various solvents including acetic acid, DMSO, ethylene glycol, 1-pentanol, and isoamyl alcohol were determined at varying temperatures. The experimental solubilities in solo solvents were regressed by λh (Buchowski) equation, van’t Hoff equation, Wilson model, and NRTL model, and the results show that the van’t Hoff equation was the best for fitting betaine’s solubilities. The change of dissolution Gibbs free energy of betaine in different solvents was predicted via the van’t Hoff equation.
1. INTRODUCTION Betaine (CAS registry no. 107-43-7) was first found in molasses with a concentration of 8% and took its name from sugar beets. As an important nutrient, betaine is of great significance in biological systems. For example, the presence of betaine is essential to the maintenance of normal bowel function and cell update for humans.1 Meanwhile, betaine itself was not only taken as a kind of commonly used feed additive, acting as methyl transfer agents to complex lipids, but also could be used to treat fatty liver and hypertension.2 The derivatives of betaine are also generally used in many industries such as husbandry, food service, and cosmetics industry.3,4 The solubilities of betaine in solvents is extremely significant for the optimization of the operating conditions and crystallization processes.5 Solubilities of the material have a great impact on crystal properties, such as crystal structure and crystal size distribution (CSD). In addition, for many biological and pharmaceutical products, the solubility also affects their bioavailability, biological isolation, drug efficacy, and drug delivery.6,7 To our best knowledge, there is little precedent research on the crystallization and isolation of betaine, and the solubilities of betaine in organic solvents are scarcely reported, except Wang et al.8 reported their solubility measurements of betaine in water, five kinds of alcohol, and two kinds of the mixed solutions. However, in order to enhance the effective separation and purification of betaine from a solution, the precise solubilities data of betaine in organic solvents should be determined. Herein, we would like to investigate the solubility of betaine in various solutions including acetic acid, dimethyl sulfoxide (DMSO), ethylene glycol, 1-pentanol, and isoamyl alcohol through a laser monitoring observation technique to choose the most favorable crystallization solvent and gain systematic crystallization thermodynamic information. The λh (Buchowski) equation, van’t Hoff, Wilson model, and NRTL model were employed to examine correlation of the measured digitals. © 2014 American Chemical Society
Furthermore, the dissolution Gibbs free energy of betaine in different solvents were predicted via the van’t Hoff equation.
2. EXPERIMENTAL SECTION 2.1. Materials. Betaine provided by Aladdin Reagent Co. Ltd. of China was purified by recrystallizing from water several times. The solvents were analytic pure and purchased from Beijing Chemical Reagent Co. with a mass fraction of 0.995. Deionized water was utilizing high-performance liquid chromatography (HPLC) level. 2.2. Apparatus and Procedure. 2.2.1. Melting Properties Measurements. The enthalpy of fusion ΔfusH and melting temperature Tm1 of betaine were measured using TGA/DSC simultaneous thermal analyzer (model TGA/DSC 1/1100SF, Mettler-Toledo, Switzerland) under a nitrogen atmosphere. The size of the sample was about 5 mg, with a heating rate of 10 K·min−1. The temperature accuracy of this instrument is ± 0.15 K, and the sensitivity of balance of the instrument is 0.1 μg. 2.2.2. Solubility Measurements. Solubilities of betaine in solo solvents was tested by a laser monitoring observation technique. As shown in Figure 1, a 150 mL jacketed glass containers containing an excess of betaine powder and one kind of the proposed organic solvents was stirred using a magnetic stirrer for 5 h at varying temperatures in a thermostatical bath (type 501A, Shanghai Laboratory Instrument Works Co., Ltd., China) with an uncertainty of ± 0.05 K. Preliminary experiments indicated equilibrium could be achieved after 5 h of contacts. A laser monitoring system consist of a laser generator and a laser receiver connected to the computer, this laser monitoring system was used to detect the solute’s dissolution the certain the dissolved of the solute in the solvent Received: March 27, 2014 Accepted: July 7, 2014 Published: July 24, 2014 2511
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Figure 1. Experimental apparatus for the solubility measurement: A, thermostatical bath; B, laser generator; C, magnetic stirrer; D, jacketed glass vessel; E, mercury-in-glass thermometer; F, condenser; G, laser receiver; H, computer.
at a fixed temperature. A mercury-inglass thermometer was plugged into the inner chamber of the container with an uncertainty of ± 0.05 K. The quality of the betaine and organic solvents were weighted employing an analytical balance (Sartorius CP224S) with an uncertainty of ± 0.0001 g. A condenser was connected to the vessel to avoid the evaporation of the solvent at high temperature. In the first place, we put excess solvent and a certain amount of solute into the jacked container in one portion, set the thermostatical bath to a fixed temperature, and opened the circulating pump and magnetic stirring. By the time the thermometer reached the set temperature, the measuring of betaine solubility was started. When the betaine dissolved fully (at this moment the laser intensity was supposed to reach the maximum value), 5 mg of betaine was added into the container per time until the last addition can not dissolve totally (a indicator from the laser is its lower intensity than the maximum). Then the previous measurement point was taken as the balance point, and the corresponding total amount of consumed solute was recorded. Each solubility-measuring experiment was conducted three times separately. The uncertainty of the measured solubilities is approximately 3% and is attributed to uncertainties in the temperature values, weighing course and uncertainty of the water bath. The following formula was used to determine the mole fraction solubility: x1 =
m1/M1 m1/M1 + m2 /M 2
Figure 2. Thermal analysis (TGA/DSC) of betaine.
566.15 K, and this value was consistent with literature values.9 However, decomposition of the compound began at almost the same time as melting. Viertorinne et al. have reported that the total energy of the melting and decomposition was 74.00kJ· mol−1.9 Then the conventional calorimetric test could not be used in the measurement of betaine’s fusion enthalpy considering its thermal instability. 3.1.1. Evaluation of Fusion Enthalpy. The fusion enthalpy ΔfusH1 and the melting point Tm1 of specific substances offer information on molecular packing in crystal lattices and are essential thermodynamic parameters for predicting solid−liquid equilibria (SLE).10 In the current case, calorimetric measurement revealed that betaine start to decompose prior to reach a clear melting peak (Figure 2), indicating it was thermally unstable. To circumvent this problems, we tried the group contribution method.11 The fusion enthalpy ΔfusH1 of betaine finally estimated to be 17.980 kJ·mol−1, which consistent with the experimental result, but it should be noted that these estimated figures could not be regarded as the real physical properties of betaine. The entropy of fusion ΔfusS1 of betaine was calculated with the following equation:12
(1)
where m1 and m2 accounts for the weight of the betaine and solvent. M1 and M2 are the molecular weights of the betaine and solvent, respectively. Finally, x1 represents the mole fraction solubility of betaine. Based on the above approach, the solubilities of betaine in five solvents (acetic acid, DMSO, ethylene glycol, 1-pentanol, and isoamyl alcohol) was determinated.
3. RESULTS AND DISCUSSION 3.1. TGA/DSC. The thermal analysis (TGA/DSC) of betaine was shown in Figure 2. According to the DSC analysis, the calorimetric measurement of betaine exhibited a clear melting peak, indicating the melting temperature Tm1 was
ΔfusS1 = 2512
ΔfusH1 Tm1
(2)
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Table 1. Experimental Solubility of Betaine in Different Pure Solvents (p = 0.1 MPa)a 102 RD
T K
x1
292.83 297.84 302.28 308.31 312.79 317.76 322.58 328.87 333.12
0.2296 0.2394 0.2524 0.2677 0.2792 0.2977 0.3065 0.3272 0.3441 102 ARD 102 AAD
283.42 288.53 292.46 298.03 303.87 308.52 314.59 318.19 323.98 328.33
0.1015 0.1087 0.1167 0.1247 0.1372 0.1452 0.1605 0.1668 0.1827 0.1923 102 ARD 102 AAD
288.51 292.73 298.34 305.16 308.53 313.20 318.16
0.001001 0.001157 0.001386 0.001724 0.001902 0.002195 0.002529
λh
van’t Hoff
Acetic Acid 1.26 0.96 −0.29 −0.46 0.08 0.00 −0.49 −0.45 −0.86 −0.79 0.64 0.74 −1.04 −0.95 −0.28 −0.18 1.02 1.05 0.00 −0.01 0.66 0.62 Ethylene Glycol 1.48 1.18 −0.09 −0.28 0.69 0.60 −1.28 −1.28 −0.36 −0.36 −1.38 −1.31 0.25 0.37 −0.72 −0.60 0.88 0.99 0.52 0.62 0.00 −0.01 0.76 0.76 DMSO 0.70 0.80 −0.52 −0.44 0.14 0.07 0.23 0.12 −0.37 −0.47 −0.14 −0.23 −0.43 −0.55
102 RD
T
Wilson 0.65 −0.92 −0.52 −0.93 −1.18 0.50 −0.98 0.09 1.60 −0.19 0.82
−9.23 −8.60 −6.30 −4.41 −3.08 0.20 0.10 2.81 5.23 −2.59 4.44
3.25 −0.28 0.43 −1.68 −0.87 −1.86 −0.12 −1.02 0.77 0.57 −0.08 1.09
5.62 5.70 7.71 7.70 10.28 10.88 14.21 14.57 −8.98 −6.71 6.10 9.23
2.10 0.79 −5.12 0.93 −6.05 0.09 −0.59
7.69 5.42 4.56 2.90 1.52 0.64 −0.87
a
λh
x1
K
NRTL
322.88 327.87 333.58
0.002908 0.003338 0.003909 102 ARD 102 AAD
285.88 289.50 294.44 299.59 304.38 309.45 313.80 318.18 323.02
0.0002162 0.0002495 0.0003010 0.0003677 0.0004363 0.0005233 0.0006091 0.0007053 0.0008225 102 ARD 102 AAD
286.47 289.13 293.93 298.25 302.72 307.37 314.06 318.23 322.60
0.0001661 0.0001853 0.0002253 0.0002688 0.0003164 0.0003784 0.0004772 0.0005562 0.0006461 102 ARD 102 AAD
van’t Hoff
DMSO 0.03 0.00 −0.03 0.09 0.41 0.67 0.00 0.01 0.30 0.34 1-Pentanol 0.28 0.32 0.08 0.08 −0.43 −0.47 0.16 0.11 −0.23 −0.30 0.00 −0.04 0.25 0.23 0.24 0.27 −0.15 −0.05 0.02 0.02 0.20 0.21 Isoamyl Alcohol 0.36 0.12 0.05 −0.05 −0.13 −0.09 0.30 0.45 −0.70 −0.41 −0.29 0.16 −1.40 −0.69 −0.72 0.16 −0.68 0.37 −0.36 0.00 0.52 0.28
NRTL
−0.41 −0.84 −0.90 −1.00 1.78
−1.44 −2.58 −3.38 1.45 3.10
0.93 0.64 0.03 0.49 −0.07 −0.02 0.03 −0.17 −0.80 0.12 0.35
1.99 1.56 0.73 0.95 0.23 0.11 0.03 −0.27 −0.98 0.48 0.76
−0.36 −0.38 −0.18 0.60 −0.13 0.55 −0.17 0.68 0.88 0.17 0.44
3.79 3.18 2.40 2.31 0.79 2.35 −1.15 −0.90 −1.28 1.28 2.02
Standard uncertainty ur(T) = 0.05 K, ur(x) = 0.03.
⎛1 ⎛ 1 − x1 ⎞ 1 ⎞ ln⎜1 + λ ⎟ ⎟ = λh⎜ − x1 ⎠ Tm ⎠ ⎝T ⎝
The ΔfusS1 value was finally determined to be 31.76 J·(mol· K)−1. 3.2. Soubility of Betaine in Solo Solvent. Solubilities of betaine in various solo solvents were listed in Table 1 and plotted in Figure 3 (a and b). Thus, it can be known that the solubilities of betaine increased in a temperature-dependent manner in all of the investigated solvents. And at a sustaining temperature, the sequence of solubilities in the mentioned five solvents ranks as acetic acid > ethylene glycol > DMSO > 1pentanol > isoamyl alcohol. This phenomenon was mainly attributed to the dissimilarity amid the physicochemical qualities of the solvents, for instance, intermolecular interplay, polarity, ideality and the capacity between solute and solvent molecules form hydrogen bonds. The solubility behavior of the betaine was complied with the empirical rule “like dissolves like”. 3.3. Correlation of Solubility Data. In order to quantitative description solid−liquid equilibrium, the connection between the solubility of betaine in pure solvent and temperature was associated with the below thermodynamic equations. 3.3.1. λh Equation. The solubility data was associated by the λh equation, which was initially raised by Buchowski et al.,13 is shown as following equation:
Wilson
(3)
where λ (representing the nonideality of solution system) and h (representing the enthalpy of solution) are model parameters.14 3.3.2. van’t Hoff Equation. The relationship between the solute’s mole fraction solubility and the temperature in a real solution could be reflected by the van’t Hoff equation,15,16 which is formulated as: ln x1 = −
ΔHd ΔSd + RT R
(4)
where ΔHd and ΔSd account for dissolution enthalpy and entropy, respectively, and R for gas constant. The dissolution enthalpy and entropy were assumed to be independent of temperature within a limited temperature range, and thus a nearly linear solubility curve of ln x versus 1/T would be afforded. 3.3.3. Local Composition Model. Based on the activity coefficient model, the solubilities of a certain solute could be reflected by the simplified equation below: ln x1 = 2513
ΔfusH1 ⎛ 1 1⎞ − ⎟ − ln γ1 ⎜ R ⎝ Tm1 T⎠
(5)
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Here, Δλ12 and Δλ21 are the cross interaction energy parameters which could be fitted by measured solubility. v1 and v2 are the mole volumes of betaine and solvent, respectively.18 3.3.3.2. NRTL Model. NRTL model is shown in the formula below:19 2 ⎞ ⎛ τ21G21 τ12G12 ⎟ ln γ1 = x 22⎜ + 2 (x 2 + G12x1)2 ⎠ ⎝ (x1 + G21x 2)
(8)
where G12 = exp( −α12τ12) τ12 =
g12 − g22 RT
G21 = exp( −α12τ21) Δg12
=
τ21 =
RT
g21 − g22 RT
(9)
=
Δg21 RT (10)
Here, Δg12 and Δg21 are the cross interaction energy parameters. In addition, α12 is a constant and it reflects the nonrandomness of the admixture. The parameters of the mentioned models were shown in Table 2. The relative deviation (RD), the average relative deviation (ARD), and the average absolute deviation percentage (AAD) were determined as the difference between the experimental and predicted values and are respectively represented by the following formulas: RD = Figure 3. (a and b) Experimental solubility of betaine in different pure solvents: (◆) acetic acid; (●) ethylene glycol; (□) DMSO; (▲) 1pentanol; (○) isoamyl alcohol. The corresponding lines are calculated values based on the van’t Hoff equation.
x1 − x1cal x1
∑
1 N
∑
AAD =
In order to determine the solute’s solubility via eq 5, the activity coefficient γ1, enthalpy of fusion ΔfusH1 and melting temperature Tm1 must be provided. In the current case, Wilson model and the NRTL model were employed. 3.3.3.1. Wilson Model. Wilson model could be represented as follows:17
(6)
Λ 21 =
v1 ⎛ Δλ 21 ⎞ ⎟ exp⎜ − v2 ⎝ RT ⎠
N
x1, i
(12)
x1, i − x1,cali
i=1
x1, i
(13)
where x1 and represent the values of solubilities measured and calculated, respectively. N account for the amount of measured dots. x1,iand xcal 1,i stand for the datas of measured and predicted solubilities, respectively. The RD, ARD and AAD of those four conjunction models were listed in Table 1. The all AADs of the above models were 0.49 % (λh), 0.44 % (van’t Hoff), 0.90 % (Wilson), and 3.91 % (NRTL), respectively. Therefore, the van’t Hoff equation was the best for regressing betaine’s solubilities in different pure solvents. 3.4. Prediction of Dissolution Gibbs Free Energy Change. The van’t Hoff equation, shown in eq 4, involves the logarithm of the mole fraction of a solute as a linear function of the reciprocal of the absolute temperature. Based on the solubility data obtained from the experiment, the values of
where v2 ⎛ Δλ12 ⎞ ⎟ exp⎜ − v1 ⎝ RT ⎠
i=1
x1, i − x1,cali
xcal 1
⎞ ⎛ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ x 2 + Λ 21x1 ⎠ ⎝ x1 + Λ12x 2
Λ12 =
N
1 ARD = N
(11)
(7)
Table 2. Parameters of the λh, van’t Hoff, Wilson, and NRTL Models for the Solubility of Betaine in Different Pure Solvents solvent λh van’t Hoff Wilson NRTL
acetic acid λ h ΔHd ΔSd Δλ12 Δλ21 Δg12 Δg21 α12
1.44 748.28 8130.88 15.45 −8407.99 3615.40 −109310.65 55297.94 0.10
ethylene glycol 1.12 1219.76 11109.49 20.08 −7290.67 3612.82 −6467.79 40915.22 0.19 2514
DMSO 0.13 21973.06 24210.20 26.42 5186.00 5388.00 5357.11 2888.61 0.11
1-pentanol 0.07 49787.27 27698.57 26.70 9297.21 9615.82 9935.09 2572.23 0.04
isoamyl alcohol 0.07 51890.00 28835.68 28.29 9959.61 9960.83 7758.15 4445.34 0.06
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temperature is positive (ΔHd > 0) that illustrates the process of dissolution is endothermic and declares the solubilities of betaine increases with gradually increasing temperature. Moreover, according to the consequence it can be observed that the enthalpy and entropy of dissolution of betaine in isoamyl alcohol is far higher than that in other solvents, it could be settled that it is harder for the organization to overcome the energy barrier dissolution. Dissolution process is endothermic, since the interplay among the molecules of betaine and solvent are more formidable than those among the solvent molecules. The ΔSd in acetic acid, ethylene glycol, DMSO, 1-pentanol, and isoamyl alcohol are all positive, which denotes that the procedures included in dissolving betaine in these five solvents were all entropically favorable.21 The lower ΔHd corresponded to larger solubility, which implied more favorable dissolving. This conclusion has guidance significance to the optimized and design crystallization processes of betaine.
dissolution enthalpy (ΔH d ) and entropy (ΔS d ) were determined from the slope and the intercept of the plot of ln x1 versus 1/T. As shown in figure 4 (a and b), the van’t Hoff plot of the logarithm of mole fraction solubilities versus reciprocal of the
4. CONCLUSION Measured values on the solubilities of betaine were obtained in a variety of absolute solvents including acetic acid, ethylene glycol, DMSO, 1-pentanol, and isoamyl alcohol in the range of temperature from (283.19 to 328.38) K. The solubilities values of betaine in pure solvents at any given temperature ranked as acetic acid > ethylene glycol > DMSO > 1-pentanol > isoamyl alcohol, partially due to the polarity of the solvent. The λh equation, van’t Hoff equation, Wilson model, and NRTL model have readily correlated the solubilities value. The van’t Hoff equation was much more appropriate in correlating the solubilities of betaine in comparsion with the rest. The change of Gibbs free energy for dissolution of betaine in different solvents was predicted via the van’t Hoff equation. The results indicated that the solution procedure of betaine in the five solvents was all endothermic and entropically favorable.
Figure 4. (a and b). The van’t Hoff plot of logarithm mole fraction solubility of betaine in different solvents: (◆) acetic acid; (●) ethylene glycol; (□) DMSO; (▲) 1-pentanol; (○) isoamyl alcohol.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] absolute temperature. The change of dissolution Gibbs free energy could be counted by the next formula:20 ΔGd = ΔHd − T ΔSd
Notes
The authors declare no competing financial interest.
■
(14)
The values ΔGd of betaine in organic solvents were listed in Table 3. Results show that the Gibbs free energy of solution were all positive, moreover, those values were reduced with the growing temperature. In addition, Table 2 shows that the ΔHd of betaine in every solvent in the range of experimental
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Table 3. Predicted Values for the Gibbs Free Energy of Betaine in Different Pure Solvents acetic acid
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1-pentanol
isoamyl alcohol
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