Solubilities of Benzoic Acid in Binary Methylbenzene + Benzyl Alcohol

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Solubilities of Benzoic Acid in Binary Methylbenzene + Benzyl Alcohol and Methylbenzene + Benzaldehyde Solvent Mixtures Hui Wang,† Qinbo Wang,*,† Zhenhua Xiong,‡ Chuxiong Chen,‡ and Binwei Shen‡ †

Department of Chemical Engineering, Hunan University, Changsha, 410082 Hunan, P. R. China Zhejiang Shuyang Chemical Co. Ltd., Quzhou, 324002 Zhejiang, P. R. China

‡

ABSTRACT: By using the synthetic method, the solubilities of benzoic acid in binary methylbenzene + benzyl alcohol solvent mixtures at (301.05 to 355.65) K and in binary methylbenzene + benzaldehyde solvent mixtures at (301.05 to 354.45) K were determined at atmospheric pressure. The studied mass fractions of benzyl alcohol and benzaldehyde in the corresponding binary solvent mixtures range from 0.0 to 1.0. It was found that the measured solubilities increase with the increase of temperature at constant solvent composition. For the ternary system benzoic acid + methylbenzene + benzyl alcohol, the results show that the binary methylbenzene + benzyl alcohol solvent mixture with the mass fraction of benzyl alcohol at 0.80 has the best dissolving capacity for benzoic acid at constant temperature. However, for the ternary system benzoic acid + methylbenzene + benzaldehyde, the results show that the binary methylbenzene + benzaldehyde solvent mixture with the mass fraction of benzaldehyde of 0.20 has the best dissolving capacity for benzoic acid at constant temperature. The experimental data were correlated by both the nonrandom two-liquid (NRTL) and the Apelblat equations, and the correlated solubilities agree satisfactorily with the experimental observations. By coupling the Apelblat equation with the Clark and Glew equation, the thermodynamic functions for the two studied solid−liquid equilibrium systems, including dissolution enthalpy, entropy, Gibbs energy, and isobaric heat capacity, were calculated and discussed.

1. INTRODUCTION Benzoic acid, benzyl alcohol, and benzaldehyde are all important fine chemicals. They are widely used in the field of pharmaceutical, perfumery, dyestuff, and agrichemicals, etc. Commercially, they are manufactured by the air oxidation of methylbenzene.1,2 The oxidized mixtures include the products benzoic acid, benzyl alcohol, and benzaldehyde, and the unreacted methylbenzene. Sequentially, the method of distillation would be used to separate the reacted mixture. Because of the higher boiling temperature of benzyl alcohol and benzaldehyde, the distillation temperature is usually higher than 400 K. At this operation condition, the product benzoic acid is prone to esterification with benzyl alcohol, which might result in another byproduct benzyl benzoate that makes the separation process difficult and complex. Alternatively, one may expect to separate most of the benzoic acid from the reaction mixtures first, and then use the method of distillation to separate the remaining mixtures. Usually crystallization is the preferred method to separate benzoic acid from the reaction mixtures.3 In this sense, the solubility data of benzoic acid in benzyl alcohol + methylbenzene and benzaldehyde + methylbenzene solvent mixtures are essential for the proper separation process design. Unfortunately, besides some reports on the solubility of benzoic acid in pure water4−8 and in pure methylbenzene,9,10 no reports on the solubility of benzoic in benzyl alcohol or benzaldehyde could be found, let alone that in the above-mentioned solvent mixtures. Thus, it is © XXXX American Chemical Society

essential to obtain the solubility data of benzoic acid in methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde. In this work, by using the synthetic method, the solubilities of benzoic acid in binary methylbenzene + benzyl alcohol mixtures and methylbenzene + benzaldehyde mixtures at different temperatures were measured. The effects of mass fraction of benzyl alcohol and benzaldehyde in the corresponding solvent mixtures at (0.0 to 1.00) on the solubilities were studied. The experimental data were correlated by both the NRTL model11 and the Apelblat equation. The model parameters were regressed, and the correlated solubilities agree satisfactorily with the experimental observations. By coupling the Apelblat equation with the Clark and Glew equation, the thermodynamic functions for the two studied solid−liquid equilibrium systems, including dissolution enthalpy, entropy, Gibbs energy, and isobaric heat capacity, were calculated and discussed.

2. EXPERIMENTAL SECTION 2.1. Materials. Benzoic acid, methylbenzene, benzyl alcohol, and benzaldehyde were obtained from Aladdin Chemistry Co., and had a declared purity of >0.990 in mass Received: August 20, 2014 Accepted: December 22, 2014

A

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Table 1. Suppliers and Mass Fraction Purity of the Materials

a

chemical name

suppliers

benzoic acid methylbenzene benzyl alcohol benzaldehyde water

Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Hangzhou Wahaha Group Co. b

mass fraction > > > >

electrical resistivity/MΩ·cm

analysis method HPLCa GCb GCb GCb

0.995 0.990 0.990 0.985 18.2c

c

High-performance liquid chromatography. Gas chromatograph. Pure water resistivity measuring instrument.

To verify the repeatability of the experimental data, each data point of the experimental solubility was measured at least two times, and the uncertainty of each saturated temperature was within ± 0.05 K.

fraction. The mass fraction purity of benzoic acid was checked by high-performance liquid chromatography (HPLC). The mass fraction purities of methylbenzene, benzyl alcohol, and benzaldehyde were checked by gas chromatography (GC). Purified water was obtained from Hangzhou Wahaha Group Co., and had the reported electrical resistivity of 18.2 MΩ·cm, which falls into the category of ultrapure water. All the chemicals were used without further purification. The suppliers and the mass fraction of the used chemical reagents are shown in Table 1. 2.2. Apparatus and Procedures. The solubilities of benzoic acid in methylbenzene + benzyl alcohol mixtures and methylbenzene + benzaldehyde mixtures were measured by a synthetic method. The laser technique was used, and the experimental principle and technique have been introduced in detail by Chen and Jiang et al.12,13 Briefly, the main apparatus include a solid−liquid equilibrium cell, a laser-detecting system, a temperature-controlling and measurement system, and a magnetic stirring system. The equilibrium cell is approximately 150 mL. The cell was heated in a thermostatic water bath and the equilibrium temperature was determined by a mercury thermometer with an uncertainty of ± 0.05 K. The mixture was stirred by a magnetic agitator to accelerate the dissolution of benzoic acid.14,15 In each experiment, carefully preweighed amounts of the solute and solvent were placed in the equilibrium cell. All the chemicals were weighted by an electronic analytical balance (type AL204, Mettler Toledo instrument Co. Ltd., uncertainty of ± 0.0001 g). The cell was then put into a thermostatic water bath, and the mixture was continuously stirred. The temperature of the mixture was then increased in a continuous fashion (2.5 K/h) until the benzoic acid was dissolved. Near the dissolution temperature, the temperature increase was typically kept at 0.2 K/h or slower. The laser monitoring equipment was used to monitor the dissolution condition of the solution. A steady laser beam was passed through the solvent−solute mixture and received by a laser power meter. If there were solids in the path of the beam, it would be scattered and the transmitted intensity would be reduced. The intensity of the transmitted laser light is recorded by a computer in terms of the photovoltage. The corresponding temperature at a given composition is determined as the one at which the solid phase just disappears. The method of calculating the solubility data was the ratio method. The solubility is defined as the mass of solute in 100 g of solvent. In this paper, the solubility was calculated by the following equation:

S=

m1 100 m2

3. RESULTS AND DISCUSSION 3.1. Validation of the Experimental Technique. To check the reliability of the experimental technique, the solubilities of benzoic acid in pure water were measured, and the experimental solubility data are listed in Table 2 along with Table 2. Solubilities of Benzoic Acid (cr,1) in Water at Different Temperatures and p = 101.3 kPaa T/K

S/(g(100g)−1)

RD1 %

RD2 %

RD3 %

RD4 %

298.85 305.95 312.85 319.35 323.25 329.55 335.25 340.25

0.337 0.431 0.540 0.679 0.826 1.026 1.271 1.560

1.157 1.671 3.129 4.348 1.586 4.150 1.196 1.384

0.564 0.975 0.352 0.516 0.012 −0.721 0.645 0.487

1.157 −0.418 1.648 0.516 1.102 −0.721 −0.220 −0.474

1.454 −0.418 1.092 0.516 0.618 0.253 0.803 1.192

a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(S) = 0.04. S is the measured solubility of benzoic acid in water; RD1 %, RD2 %, RD3 %, and RD4 % are the relative deviations of our determined solubility with the literature data from Apelblat,6 Lee,4 Oliveria,5 and Liu,7 respectively. The solubility is defined as the mass of solute (g) in 100 g of solvent.

the relative deviations between experimental data and literature data.4−7 Figure 1 is also provided to show the result. From Table 2 and Figure 1, a fairly good agreement was obtained between the experimentally determined and literature reported

(1)

Figure 1. Comparisons between experimental solubility of benzoic acid in water with that reported in literature: □, literature data from Lee;4 ○, literature data from Liu;7 △, literature data from Oliveria;5 ▽, literature data from Apelblat;6 ●, experimental data.

where S is the solubility of the solute; m1 and m2 are the mass of solute and solvent in the saturated solution, respectively. B

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that the measured solubility data increases with increasing temperature. To illustrated the effect of solvent composition on the solubilites more apparently, the solubility data of benzoic acid in methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde binary mixtures at (303.15 to 353.15) K were predicted by the NRTL model using the regressed model parameters listed in Table 6. The results are shown in Figures 5 and 6. From Figure 5 it can also be seen that at each measured temperature, binary methylbenzene + benzyl alcohol solvent mixtures with a mass fraction of benzyl alcohol at 0.80 usually has the best dissolving capacity for benzoic acid. It indicates that the higher or the lower the mass fraction of benzyl alcohol is, the less is the solubility. In other words, within this mass fraction of benzyl alcohol range, there is a slope presenting the change of solubility influenced by solvent concentrations at each measured temperature. This maximum-solubility effect has also been noticed by Chen and Ma for the solubility of terephthalic acid in the mixture of acetic acid and water,12 and Wang et al. for the solubility of phthalic acid in the mixture of acetic acid + wate,16 and the solubility of adipic acid and succinic acid in the mixture of acetic acid + water.26,27 Similar maximum-solubility effects also could be found for the solubility of benzoic acid in binary methylbenzene + benzaldehyde mixtures. From Figure 6, it can be seen that at each measured temperature, binary methylbenzene + benzaldehyde solvent mixtures with a mass fraction of benzaldehyde at 0.20 usually has the best dissolving capacity for benzoic acid. 3.3. Correlation of Experimental Data. Generally, solid− liquid equilibrium without solid−solid phase transition can be approximated by eq 1:

data. The agreement with published data suggests that the technique is reliable. To further verify the reliability of the experimental results, the solubility data of benzoic acid in pure methylbenzene was measured. The determined experimental data are listed in Table 3 and plotted in Figure 2, along with the relative deviations Table 3. Solubilities of Benzoic Acid (cr,1) in Methylbenzene at Different Temperatures and p = 101.3 kPaa T/K

S/(g(100g)−1)

RD1 %

RD2 %

301.05 306.05 311.75 316.95 323.35 330.25 336.55 340.75 344.65 348.25 351.35 354.05

11.33 13.17 16.16 19.81 24.46 30.14 37.91 47.65 58.82 71.53 86.16 102.6

−3.24 −0.36 −1.49 −0.75 −0.62 −0.25 −0.76 −1.23 −1.04 −0.61 −0.16 −0.62

−3.24 −3.63 −5.58 1.27 2.32 0.51 −3.90 0.01 1.96 0.74 0.73 0.40

a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(S) = 0.04. S is the measured solubility of benzoic acid in methylbenzene; RD1 % and RD2 % are the relative deviations of our determined solubility with the literature data from Thati9 and Chipman,10 respectively. The solubility is defined as the mass of solute (g) in 100 g of solvent.

ln(γ1x1) = −

ΔfusH ⎛ 1 1 ⎞ ⎟ ⎜ − R ⎝T Tfus ⎠

(2)

where ΔfusH is the molar fusion enthalpy of solute, Tfus is the fusion temperature, T is the absolute temperature, R is the universal gas constant, γ1 is the activity coefficient of solute, and x1 is the real mole fraction of solute in solution. In this equation, the enthalpy of melting is assumed to be independent of temperature. Because the activity coefficient γ1 depends on the solution composition and temperature, eq 1 must be solved iteratively. For the calculation of the activity coefficient, the NRTL activity coefficient model was used in this work as Figure 2. Comparisons between experimental solubility of benzoic acid in methylbenzene with that reported in literature: □, literature data from Thati;9 ○, literature data from Chipman;10 ●, experimental data.

3

ln γi =

∑ j = 1 τjiGjixj 3 ∑k = 1 Gkixk

3

+

xjGij 3 j = 1 ∑k = 1 Gkjxk

∑

3 ⎛ ∑ xτ G ⎞ ⎜τ − k = 1 k kj kj ⎟ 3 ⎜ ij ∑k = 1 Gkjxk ⎟⎠ ⎝

between experimental data and literature data.9,10 It can be found that the obtained experimental data have no important deviations with the literature data. The agreement with published data further suggests that the technique is reliable. 3.2. Experimental Solubility Data. The measured solubilities of benzoic acid in methylbenzene + benzyl alcohol mixtures are shown in Table 4 and Figure 3, and the measured solubilities of benzoic acid in methylbenzene + benzaldehyde mixtures are summarized in Table 5 and Figure4. In these tables and figures, w3 is defined as the mass fraction of benzyl alcohol in binary methylbenzene + benzyl alcohol and benzoic acid in binary methylbenzene + benzaldehyde solvent mixtures, and T and S represent the absolute temperature and the measured solubility data, respectively. The results clearly show

τij = aij +

(3)

bij (4)

T

Gij = exp( −αijτij)

αij = αji ,

·

τij ≠ τji ,

(5)

τii = 0

(6)

where T is the absolute temperature; γi is the activity coefficient of component i; aij and bij are the NRTL binary interaction parameters. To calculate the solubility, fusion temperature (Tfus) and molar enthalpy of fusion of solute (ΔfusH) are required. Tfus and C

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Table 4. Solubilities and Thermodynamic Functions of Benzoic Acid (cr,1) in Methylbenzene (2) + Benzyl Alcohol (3) Solvent Mixtures at Different Temperatures and p = 101.3 kPaa T K

S g(100g)

Sc,1 −1

g(100g)

RD1 −1

%

Sc,2 g(100g)

ΔHT0

RD2 −1

%

301.05 306.05 311.75 316.95 322.65 328.25 334.55 339.85 344.65 348.25 351.35 354.05

11.33 13.33 16.32 19.97 24.62 30.30 38.07 47.81 58.99 71.69 86.33 102.78

11.09 13.06 16.18 20.13 25.35 30.85 37.89 47.54 59.20 73.67 86.21 101.5

−2.07 −2.01 −0.88 0.78 2.95 1.82 −0.47 −0.56 0.36 2.76 −0.14 −1.24

11.01 13.09 15.92 19.86 23.91 31.09 37.06 48.02 59.03 70.08 86.13 102.2

2.79 1.80 2.47 0.55 2.90 −2.61 2.65 −0.44 −0.07 2.25 0.23 0.61

303.35 307.45 312.75 317.35 321.75 327.85 333.05 338.55 343.35 348.75

19.70 21.92 25.35 29.77 34.81 41.79 50.25 60.26 72.11 85.75

19.64 21.80 25.25 29.62 34.56 41.77 49.96 59.84 70.69 84.36

−0.30 −0.57 −0.39 −0.50 −0.73 −0.07 −0.58 −0.70 −1.97 −1.63

19.58 21.69 24.96 29.39 34.09 41.22 51.06 59.63 71.08 86.03

0.62 1.05 1.52 1.27 2.07 1.38 −1.61 1.04 1.43 −0.33

301.55 304.85 310.05 316.65 323.05 330.95 337.55 343.45 348.25 353.45

22.60 25.06 28.55 34.43 42.42 52.72 64.89 79.09 95.21 113.47

22.82 24.98 28.25 33.83 41.19 51.49 63.15 76.34 92.93 112.97

0.96 −0.30 −1.05 −1.74 −2.90 −2.32 −2.68 −3.48 −2.39 −0.44

22.91 25.19 28.03 34.01 41.58 51.29 64.31 79.19 96.01 114.9

−1.35 −0.53 1.82 1.22 1.98 2.70 0.90 −0.13 −0.84 −1.22

303.35 307.35 311.55 317.45 323.45 329.15 334.55 339.65 344.25 348.95

25.99 28.44 32.00 37.69 44.67 52.66 61.89 72.73 84.73 97.73

26.39 28.63 31.86 37.18 43.87 51.64 60.66 71.10 82.49 95.96

1.55 0.64 −0.45 −1.33 −1.79 −1.93 −1.99 −2.24 −2.64 −1.82

25.68 28.01 31.88 37.06 44.06 52.13 61.02 72.38 85.19 99.01

1.18 1.53 0.38 1.66 1.36 1.01 1.41 0.48 −0.54 −1.31

307.85 310.45 314.25 318.85 323.85 328.55 333.25 338.35 343.55 349.75

26.77 29.07 33.56 39.98 47.04 55.22 64.45 74.73 87.02 101.28

27.07 30.10 34.11 39.68 45.99 53.12 63.29 72.24 84.59 101.17

1.11 3.53 1.65 −0.75 −2.24 −3.80 −1.81 −3.34 −2.79 −0.11

26.86 29.39 34.21 39.86 46.68 54.62 63.88 74.01 88.19 103.1

−0.32 −1.10 −1.94 0.31 0.76 1.08 0.89 0.97 −1.35 −1.78

−1b

kJ·mol

w3 = 0.0 36.77 38.10 39.61 40.96 42.46 43.93 45.61 47.06 48.45 49.58 50.66 51.70 w3 = 0.2 36.87 38.01 39.50 40.80 42.07 43.87 45.46 47.20 48.82 50.68 w3 = 0.4 36.48 37.47 39.04 41.08 43.12 45.71 47.99 50.13 52.00 54.06 w3 = 0.6 37.72 39.03 40.43 42.43 44.51 46.53 48.50 50.42 52.21 54.07 w3 = 0.8 40.58 41.53 42.94 44.67 46.57 48.37 50.21 52.20 54.27 56.73

D

ΔGT0 kJ·mol

−1c

ΔST0 −1

J·mol ·K

−1d

ΔCp0

ζH

ζTS

J·mol−1·K−1e

%

%

22.21 22.51 22.99 23.57 24.25 24.99 25.84 26.71 27.41 27.96 28.29 28.39

48.35 50.94 53.31 54.87 56.42 57.68 59.09 59.90 61.05 62.10 63.66 65.83

280.1

71.64 70.96 70.44 70.20 69.99 69.88 69.76 69.81 69.72 69.63 69.37 68.92

28.36 29.04 29.56 29.80 30.01 30.12 30.24 30.19 30.28 30.37 30.63 31.08

28.77 28.86 28.99 29.17 29.31 29.39 29.42 30.01 31.16 31.66

26.71 29.75 33.58 36.67 39.66 44.16 48.16 52.83 57.44 63.14

286.3

81.98 80.60 79.00 77.81 76.73 75.19 73.92 72.52 71.23 69.01

18.02 19.40 21.00 22.19 23.27 24.81 26.08 27.48 28.77 30.29

25.70 26.80 27.73 28.58 29.29 29.89 30.26 30.51 30.65 30.71

19.15 22.40 27.53 34.18 40.97 49.60 57.50 65.24 72.38 80.25

304.9

86.34 84.59 82.06 79.15 76.52 73.58 71.20 69.11 67.35 65.59

13.66 15.41 17.94 20.85 23.48 26.42 28.80 30.89 32.65 34.41

22.01 23.05 24.02 24.94 25.83 26.63 27.35 27.99 28.52 28.84

28.50 33.17 38.25 45.48 53.04 60.46 67.77 75.01 81.88 88.89

329.5

81.35 79.29 77.24 74.61 72.18 70.04 68.15 66.43 64.94 63.54

18.65 20.71 22.76 25.39 27.82 29.96 31.85 33.57 35.06 36.46

23.74 23.47 23.02 22.41 21.72 20.99 20.21 19.35 18.39 17.26

54.72 58.17 63.40 69.83 76.71 83.34 90.00 97.11 104.43 112.87

361.0

70.67 69.70 68.31 66.74 65.21 63.86 62.60 61.37 60.20 58.97

29.33 30.30 31.69 33.26 34.79 36.14 37.40 38.63 39.80 41.03

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Table 4. continued T

S

Sc,1

RD1

Sc,2

ΔHT0

RD2

K

g(100g)−1

g(100g)−1

%

g(100g)−1

%

306.35 309.05 312.75 316.25 321.75 327.45 332.85 338.55 343.05 347.25 351.75 355.65

29.78 31.57 34.00 37.38 42.32 48.48 55.29 64.28 73.26 82.91 94.14 106.42

28.61 30.52 33.17 36.47 41.53 47.69 54.46 63.22 71.87 81.65 94.78 107.45

−3.93 −3.32 −2.43 −2.45 −1.87 −1.63 −1.49 −1.64 −1.90 −1.52 0.68 0.97

29.26 31.82 33.86 37.02 43.52 49.06 54.68 63.88 71.16 81.09 95.18 107.3

1.74 −0.80 0.42 0.97 −2.83 −1.19 1.10 0.62 2.87 2.19 −1.10 −0.86

ΔGT0

−1b

kJ·mol

w3 = 1.0 42.12 43.21 44.71 46.12 48.34 50.64 52.82 55.12 56.94 58.63 60.45 62.03

kJ·mol

−1c

14.63 14.39 14.03 13.68 13.10 12.45 11.80 11.08 10.49 9.91 9.26 8.69

ΔST0 J·mol−1·K

−1d

89.73 93.27 98.08 102.57 109.53 116.62 123.23 130.08 135.41 140.33 145.52 149.98

ΔCp0

ζH

ζTS

J·mol−1·K−1e

%

%

403.7

60.51 59.98 59.31 58.71 57.83 57.01 56.29 55.59 55.07 54.61 54.15 53.76

39.49 40.02 40.69 41.29 42.17 42.99 43.71 44.41 44.93 45.39 45.85 46.24

a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(S) = 0.04. The solubility is defined as the mass of solute (g) in 100 g of solvent. w3 is the mass fraction of benzyl alcohol in binary methylbenzene + benzyl alcohol solvent mixtures. Sc,1 and RD1 represent the NRTL model correlated solubility data and the relative deviation between the correlated and experimental determined solubilities, respectively. Sc,2 and RD2 represent the Apelblat equation correlated solubility data and the relative deviation between the correlated and experimental determined solubilities, respectively. b Calculated by eq 13. cCalculated by eq 15. dCalculated by eq 14. eCalculated by eq 12.

where n is the total number of experimental points, Sci and Si are the ith calculated and experimental solubility. The correlated results and the corresponding RD are given in Table 4 and Table 5. The optimized model parameters and the averaged relative deviation (ARD) defined are given in Table 6. Generally satisfactorily agreement between the experimental and correlated data were obtained. This indicates that the NRTL model equation could be used to correlate the solubility of benzoic acid in methylbenzene + benzyl alcohol mixtures and methylbenzene + benzaldehyde mixtures. The thermodynamic functions are important for the solid− liquid equilibrium for ternary benzoic acid + methylbenzene + benzyl alcohol and benzoic acid + methylbenzene + benzaldehyde system. The obtained NRTL model parameters could moderately supplement the NRTL databank of basic binary interaction parameters. However, it is difficult to derive the thermodynamic functions directly from the NRTL model. Further, a very convenient operational model of engineering interest to calculate the solubility of benzoic acid without bothering with the NRTL model is desired. Thus, the modified Apelblat equation was also used to correlate the experimental solubilities of benzoic acid in methylbenzene + benzyl alcohol binary mixtures and methylbenzene + benzaldehyde binary mixtures,18,19 which was previously proposed by Apelblat to describe the relationship between the mole fraction of solute and temperature for saturated solution, and the expression is

Figure 3. Solubility data of benzoic acid (cr,1) in methylbenzene (2) + benzyl alcohol (3) solvent mixtures: ■, w3 = 0.0; ●, w3 = 0.2; ▲, w3 = 0.4; ▼, w3 = 0.6; ◀, w3 = 0.8; ▶, w3 = 1.0. w3 is the mass fraction of benzyl alcohol in binary methylbenzene + benzyl alcohol solvent mixtures.

ΔfusH used in the calculation are 395.6 K and 17316 J·mol−1, which are obtained from the literature.17 Using model eqs 1 to 5, the measured solubilities were correlated, and the model parameters were optimized. As Renon and Prausnitz proposed, in the optimization, αij was chosen as 0.3.11 The optimum algorithm applied in the parameter estimation program was the Nelder−Mead Simplex approach.17 Function f minsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder−Mead Simplex approach and can be employed for the minimization of the objective function, which is the averaged relative deviation (ARD) between the experimental and calculated solubility defined by ARD =

1 n

ln x1 = A +

B + C ln T T

(9)

where x1 is the mole fraction of benzoic acid, T is the absolute temperature, and A, B, and C are the empirical model parameters. To use eq 9 correlating the solubility of benzoic acid at different solvent compositions, the following empirical correlations were adopted:20

n

∑ abs(RDi) i=1

S − Si RDi = ci 100 Si

A = A 0 + A1x 2 + A 2 x 2 2

(7)

B = B0 + B1x 2 + B2 x 2 2 C = C0 + C1x 2 + C2x 2 2

(8) E

(10) DOI: 10.1021/je500775r J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Solubilities and Thermodynamic Functions of Benzoic Acid (cr,1) in Methylbenzene (2) + Benzaldehyde (3) Solvent Mixtures at Different Temperatures and p = 101.3 kPaa T K

S g(100g)

Sc,1 −1

g(100g)

RD1 −1

%

Sc,2 g(100g)

ΔHd

RD2 −1

%

301.05 306.05 311.75 316.95 323.35 330.25 336.55 340.75 344.65 348.25 351.35 354.05

11.33 13.33 16.32 19.97 24.62 30.30 38.07 47.81 58.99 71.69 86.33 102.78

11.09 13.06 16.18 20.13 25.35 30.85 37.89 47.54 59.20 73.67 86.21 101.50

−2.07 −2.01 −0.88 0.78 2.95 1.82 −0.47 −0.56 0.36 2.76 −0.14 −1.24

10.98 13.05 15.87 19.80 23.84 31.00 36.95 47.88 58.85 69.86 85.87 101.8

3.09 2.10 2.77 0.85 3.20 −2.31 2.95 −0.14 0.23 2.55 0.53 0.91

307.95 312.85 317.25 321.85 326.75 332.25 337.25 342.35 346.95 351.65

13.46 15.94 19.87 24.92 31.76 40.14 50.78 63.55 78.64 95.88

13.56 15.88 19.72 24.63 31.18 39.27 49.27 61.43 75.51 92.29

0.69 −0.38 −0.74 −1.15 −1.81 −2.18 −2.98 −3.34 −3.99 −3.75

13.34 15.73 19.50 24.53 31.00 39.47 51.45 62.70 77.28 96.54

0.92 1.35 1.82 1.57 2.37 1.68 −1.31 1.34 1.73 −0.68

307.75 312.65 317.45 323.85 329.65 335.25 340.45 345.55 349.75 352.95

10.47 12.87 17.20 23.39 31.83 42.19 54.23 67.59 82.43 98.85

10.43 12.74 17.06 23.27 31.66 41.75 53.33 66.59 80.96 95.42

−0.42 −0.96 −0.81 −0.48 −0.55 −1.04 −1.66 −1.48 −1.79 −3.47

10.58 12.99 16.84 23.03 31.11 40.92 53.58 67.48 82.88 99.76

−1.05 −0.96 2.12 1.52 2.28 3.00 1.20 0.17 −0.54 −0.92

307.35 312.35 317.95 324.25 329.25 337.45 342.25 346.65 350.75 354.45

9.70 12.14 16.27 22.36 29.95 39.46 50.60 62.79 75.84 90.35

9.63 12.00 16.12 22.29 29.84 40.14 51.41 63.77 77.31 92.40

−0.66 −1.15 −0.91 −0.32 −0.36 1.71 1.62 1.56 1.93 2.27

9.55 11.92 16.16 21.92 29.46 38.94 49.73 62.30 76.03 91.26

1.48 1.83 0.68 1.96 1.66 1.31 1.71 0.78 −0.24 −1.01

305.35 310.65 316.75 322.35 327.95 333.35 338.35 343.35 348.25 352.75

6.51 9.15 13.31 18.63 24.99 33.07 42.57 52.66 64.69 78.83

6.54 9.04 13.15 18.54 25.06 33.28 42.81 53.25 65.94 80.94

0.55 −1.19 −1.18 −0.46 0.27 0.63 0.56 1.13 1.94 2.68

6.52 9.22 13.52 18.52 24.73 32.61 42.07 51.99 65.36 80.00

−0.21 −0.80 −1.64 0.61 1.06 1.38 1.19 1.27 −1.05 −1.48

−1b

kJ·mol

w3 = 0.0 18.92 20.29 21.88 23.35 25.00 26.67 28.62 30.38 32.07 33.49 34.83 36.10 w3 = 0.2 21.20 22.64 23.98 25.42 27.02 28.86 30.65 32.57 34.42 36.38 w3 = 0.4 21.60 23.15 24.72 26.86 28.91 30.97 32.99 35.04 36.84 38.33 w3 = 0.6 22.08 23.82 25.82 28.12 30.02 33.14 35.12 36.99 38.77 40.44 w3 = 0.8 22.03 24.11 26.52 28.77 31.05 33.29 35.41 37.55 39.68 41.69

F

ΔGd kJ·mol

−1c

ΔSd −1

J·mol ·K

−1d

ΔCp0

ζH

ζTS

J·mol−1·K−1e

%

%

11.65 11.89 12.24 12.68 13.19 13.76 14.46 15.24 15.98 16.69 17.34 17.90

24.14 27.46 30.90 33.68 36.61 39.33 42.33 44.55 46.69 48.24 49.77 51.41

284.4

72.25 70.71 69.43 68.63 67.91 67.38 66.89 66.74 66.59 66.59 66.57 66.48

27.75 29.29 30.57 31.37 32.09 32.62 33.11 33.26 33.41 33.41 33.43 33.52

16.02 16.20 16.52 16.89 17.33 17.76 18.22 18.62 18.97 19.21

16.84 20.59 23.53 26.52 29.66 33.41 36.87 40.72 44.51 48.82

305.3

80.35 77.86 76.26 74.86 73.60 72.22 71.14 70.02 69.03 67.94

19.65 22.14 23.74 25.14 26.40 27.78 28.86 29.98 30.97 32.06

20.06 20.07 20.05 19.99 19.86 19.67 19.45 19.26 19.07 18.97

8.54 13.04 17.22 22.89 28.02 33.16 38.18 43.39 47.96 51.76

327.0

89.15 85.02 81.89 78.37 75.78 73.59 71.74 70.04 68.71 67.72

10.85 14.98 18.11 21.63 24.22 26.41 28.26 29.96 31.29 32.28

21.03 21.05 21.07 21.05 21.03 20.86 20.75 20.60 20.42 20.22

3.41 8.87 14.94 21.79 27.31 36.39 41.99 47.28 52.34 57.06

357.7

95.46 89.58 84.46 79.92 76.95 72.97 70.96 69.30 67.87 66.66

4.54 10.42 15.54 20.08 23.05 27.03 29.04 30.70 32.13 33.34

21.68 21.65 21.57 21.45 21.28 21.08 20.84 20.57 20.26 19.94

1.17 7.92 15.63 22.71 29.78 36.64 43.05 49.45 55.76 61.65

396.8

98.41 90.74 84.27 79.72 76.07 73.16 70.85 68.86 67.14 65.72

1.59 9.26 15.73 20.28 23.93 26.84 29.15 31.14 32.86 34.28

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Table 5. continued T

S

Sc,1

RD1

Sc,2

ΔHd

RD2

K

g(100g)−1

g(100g)−1

%

g(100g)−1

%

307.45 310.95 315.05 319.35 322.95 327.05 331.65 334.95 339.55 343.35 347.35 350.55

5.64 7.39 9.99 13.21 17.09 21.95 27.63 33.97 41.27 49.16 57.91 67.41

5.72 7.38 9.88 13.21 17.25 22.64 27.64 34.33 41.05 50.37 58.30 69.14

1.48 −0.22 −1.02 0.00 0.95 3.16 0.07 1.07 −0.54 2.46 0.67 2.57

5.53 7.43 9.91 13.04 17.52 22.14 27.24 33.65 39.96 47.93 58.38 67.78

2.04 −0.50 0.72 1.27 −2.53 −0.89 1.40 0.92 3.17 2.49 −0.80 −0.56

−1b

kJ·mol

w3 = 1.0 23.78 25.36 27.20 29.13 30.75 32.59 34.66 36.14 38.21 39.92 41.71 43.15

ΔGd kJ·mol

−1c

20.57 20.53 20.45 20.35 20.24 20.10 19.91 19.75 19.51 19.29 19.04 18.83

ΔSd J·mol−1·K 10.44 15.52 21.41 27.50 32.54 38.21 44.48 48.93 55.06 60.06 65.27 69.39

−1d

ΔCp0

ζH

ζTS

J·mol−1·K−1e

%

%

449.37

88.11 84.01 80.13 76.84 74.53 72.29 70.14 68.80 67.14 65.93 64.79 63.95

11.89 15.99 19.87 23.16 25.47 27.71 29.86 31.20 32.86 34.07 35.21 36.05

a Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(S) = 0.04. The solubility is defined as the mass of solute (g) in 100 g of solvent. w3 is the mass fraction of benzyl alcohol in binary methylbenzene + benzyl alcohol solvent mixtures. Sc,1 and RD1 represent the NRTL model correlated solubility data and the relative deviation between the correlated and experimental determined solubilities, respectively. Sc,2 and RD2 represent the Apelblat equation correlated solubility data and the relative deviation between the correlated and experimental determined solubilities, respectively. b Calculated by eq 13. cCalculated by eq 15. dCalculated by eq 14. eCalculated by eq 12.

Figure 5. Solubility data of benzoic acid (cr,1) in methylbenzene (2) + benzyl alcohol (3) solvent mixtures: ■, 303.15 K; ●, 313.15 K; ▲, 323.15 K; ▼, 333.15K; ◀, 343.15K; ▶, 353.15 K. w3 is the mass fraction of benzyl alcohol in binary methylbenzene + benzyl alcohol solvent mixtures.

Figure 4. Solubility data of benzoic acid (cr,1) in methylbenzene (2) + benzaldehyde (3) solvent mixtures: ■, w3 = 0.0; ●, w3 = 0.2; ▲, w3 = 0.4; ▼, w3 = 0.6; ◀, w3 = 0.8; ▶, w3 = 1.0. w3 is the mass fraction of benzaldehyde in binary methylbenzene + benzaldehyde solvent mixtures.

Table 6. Optimized Temperature-Independent Binary Interaction Parameters for the NRTL Model for Benzoic Acid (1) + Methylbenzene(2) + Benzyl Alcohol (3) + Benzaldehyde (4) i−j

aij

aji

bij/K

bji/K

ARD/%

1−2 1−3 1−4 2−3 2−4 3−4

0.948 4.820 5.007 −0.868 −3.058 4.668

6.232 −0.162 −7.858 1.417 −5.348 −2.619

−239.9 −1889 −1933 128.7 4557 −889.2

−203.9 1540 3983 370.3 1814 505.7

3.68

Figure 6. Solubility data of benzoic acid (cr,1) in methylbenzene (2) + benzaldehyde (3) solvent mixtures: ■, 303.15 K; ●, 313.15 K; ▲, 323.15 K; ▼, 333.15 K; ◀, 343.15 K; ▶, 353.15 K. w3 is the mass fraction of benzaldehyde in binary methylbenzene + benzaldehyde solvent mixtures.

where x 2 is the mole fraction of methylbenzene in methylbenzene + benzyl alcohol mixtures or in methylbenzene + benzaldehyde mixtures; Ai, Bi, and Ci are model parameters. Using model eqs 9 to 10, the measured solubilities were correlated, and the model parameters were optimized. The optimum algorithm applied in the parameter estimation program was the same as that used in the NRTL correlation. G

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Similarly for the dissolution entropy ΔS0T at the measured temperature, the relationship for ΔS0θ with temperature could be given by

The correlated results and the corresponding RD are given in Table 4 and Table 5. The optimized model parameters and the averaged relative deviation (ARD) defined are given in Table 7 Table 7. Apelblat Model Parameters for Ternary Benzoic Acid (1) + Methylbenzene (2) + Benzyl Alcohol (3) System i=0 i=1 i=2

Ai

Bi/K

Ci

ARD/%

−315.8 215.1 −118.6

9810 −9545 5446

48.56 −36.25 21.51

2.94

ΔST0

Bi/K

Ci

ARD/%

−362.4 254.4 −101.5

13757 −11315 4871

54.05 −38.65 16.40

3.28

ζH% =

ζTS% =

|ΔHT0| |ΔHT0| + |T ΔST0|

100

|T ΔST0| |ΔHT0| + |T ΔST0|

(16)

100 (17)

The calculated values of ζH % and ζTS % are also listed in Table 4 and Table 5. The results show that in all cases the main contributor to standard Gibbs energy of the dissolving process of benzoic acid in methylbenzene + benzyl alcohol solvent mixtures and methylbenzene + benzaldehyde solvent mixtures is the enthalpy. With the increase of temperature or the increasing mass fraction of benzyl alcohol or benzaldehyde in solvent mixtures, the contribution of enthalpy to standard Gibbs energy gradually decreases. The thermodynamic parameters of solution, ΔG0T, ΔH0T, and ΔS0T for benzoic acid in methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde binary mixtures are listed in Tables 4 and 5. It can be found that the values of ΔH0T and ΔG0T are positive and the value of ΔH0T increases with increasing temperature gradually, which indicates that the two dissolving processes are endothermic and not spontaneous. From Table 4, one can see that ΔG0T shows a gradual increase, while ΔH0T and ΔS0T show a gradual decrease with the increasing mass fraction of benzyl alcohol in methylbenzene + benzyl alcohol solvent mixtures at constant temperature when the mass fraction of benzyl alcohol is less than 0.8. When the mass fraction of benzyl alcohol is more than 0.8, the value of ΔG0T shows a gradual decrease, while ΔH0T and ΔS0T show a gradual increase with the increasing mass fraction of benzyl alcohol. This indicates that when benzyl alcohol is added into the solvent system (w3 is less than 0.8), less energy is required to overcome the cohesive force between the solute benzoic acid and the solvent in the dissolving process. It causes a marked increase of solubility of benzoic acid with the increasing mass fraction of benzyl alcohol in methylbenzene + benzyl alcohol solvent mixtures. On the contrary, when the mass fraction of benzyl alcohol is more than 0.8, the cohesive force between benzoic acid and the solvent increases and the solubility of benzoic acid in the solvent mixture decreases. From Table 5, similar conclusions could also be obtained for the ternary system benzoic acid + methylbenzene + benzaldehyde. The value of ΔG0T increases with the increasing mass fraction of benzaldehyde when the mass fraction of benzaldehyde is less than 0.2. However, when the mass fraction of benzaldehyde is more than 0.2, ΔG0T shows a gradual decrease with the increment of benzaldehyde.

(11)

where R is the gas constant, T is the absolute temperature of the solution, and θ is the reference temperature which is chosen to be 273.15 K. ΔG0θ, ΔH0θ, and ΔC0pθ are the Gibbs free energy change, dissolution enthalpy, the isobaric heat capacity at reference temperature, respectively. A comparison of eqs 9 and 11 shows that the following equations can be derived: ΔGθ0 = (Cθ − B)R − (A + C(1 + ln θ ))Rθ ΔHθ0 = (Cθ − B)R ΔC p0 = CR (12)

The dissolution enthalpy at the experiment temperature ΔH0T is a well-behaved function of T, so it can be calculated by the following equation: ΔHT0 = ΔHθ0 + ΔC p0(T − θ ) = CRT − BR

(15)

To compare the relative contribution to the standard Gibbs energy by enthalpy (ζH %) and entropy (ζTS %) in the dissolving process, eq 16 and eq 17 were employed.23−25

ln x1 = −

ΔHθ0 − ΔGθ0 = (A + C(1 + ln θ ))R T

dT = R(A + C + C ln T )

T

The values of Gibbs free energy can be calculated by the equation:

and Table 8. Generally satisfactorily agreement between the experimental and correlated data were also obtained. It indicates that the Apelblat equation could also be used to correlate the solubility of benzoic acid in methylbenzene + benzyl alcohol mixtures and methylbenzene + benzaldehyde mixtures. 3.4. Thermodynamic Functions of the Solution. To evaluate standard thermodynamic functions from solubility data, here the approach originally proposed by Clark and Glew21,22 was used. Assuming the temperature-independent heat capacity change for the temperature range studied and using the mole fraction unitary scale, one can write

ΔSθ0 =

∫θ

ΔC p0

ΔGT0 = ΔHT0 − T ΔST0

Ai

ΔGθ0 ΔHθ0 ⎡ 1 1⎤ + ⎢⎣ − ⎥⎦ Rθ R θ T ΔC p0 ⎡ θ ⎛ T ⎞⎤ + ⎢⎣ − 1 + ln⎝⎜ ⎠⎟⎥⎦ θ R T

+

T

(14)

Table 8. Apelblat Model Parameters for Ternary Benzoic Acid (1) + Methylbenzene (2) + Benzaldehyde System i=0 i=1 i=2

=

ΔSθ0

(13) H

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(6) Apelblat, A.; Manzurola, E. The Solubility of Benzene Polycarboxylic Acids in Water. J. Chem. Thermodyn. 2006, 38, 565− 571. (7) Liu, J. C.; Chen, Z. M.; Tian, H. H.; Li, Q. D. Measurement and Correlation of Solubilities of Benzoic Acid in Different Solvents. J. Zhengzhou Univ. Technol. 2001, 22, 97−99. (8) Strong, L. E.; Neff, R. M.; Whitesel, I. Thermodynamics of Dissolving and Solvation Processes for Benzoic Acid and the Toluic Acids in Aqueous Solution. J. Solution Chem. 1989, 18, 101−114. (9) Thati, J.; Nordstrom, F. L.; Rasmuson, A. C. Solubility of Benzoic Acid in Pure Solvents and Binary Mixtures. J. Chem. Eng. Data 2010, 55, 5124−5127. (10) Chipman, J. The Solubility of Benzoic Acid in Benzene and in Toluene. J. Am. Chem Soc. 1924, 46, 2445−2448. (11) Renon, H.; Prausnitz, J. M. Estimation of Parameters for NRTL Equation for Excess Gibbs Energy of Strongly Non-ideal Liquid Mixtures. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 413−419. (12) Chen, M. M.; Ma, P. S. Solid−Liquid Equilibria of Several Systems Containing Acetic Acid. J. Chem. Eng. Data 2004, 49, 756− 759. (13) Jang, Q.; Gao, G. H.; Yu, Y. X.; Qin, Y. Solubility of Sodium Dimethyl Isophthalate-5-sulfonate in Water + Methanol Containing Sodium Sulfate. J. Chem. Eng. Data 2000, 45, 292−294. (14) Song, W. W.; Ma, P. S.; Xiang, Z. L. Determination and Correlation of the Solubility for Succinic Acid in Five Different Organic Solvent. J. Chem. Eng. Chin. Univ. 2007, 21, 341−344. (15) Huo, Y.; Xia, S. Q.; Ma, P. S. Solubility of Alcohols and Aromatic Compounds in Imidazolium-Based Ionic Liquids. J. Chem. Eng. Data 2008, 53, 2535−2539. (16) Wang, Q. B.; Hou, L. X.; Cheng, Y. W.; Li, X. Solubilities of Benzoic Acid and Phthalic Acid in Acetic Acid + Water Solvent Mixtures. J. Chem. Eng. Data 2007, 52, 936−940. (17) Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308−313. (18) Apelblat, A.; Manzurola, E. Solubilities of o-Acetylsalicylic, 4Aminosalicylic, 3,5-Dinitrosalicylic, and p-Toluic Acid, and Magnesium-DL-aspartate in Water from T = (278 to 348) K. J. Chem. Thermodyn. 1999, 31, 85−91. (19) Manzurola, E.; Apelblat, A. Solubilities of L-Glutamic Acid, 3Nitrobenzoic Acid, p-Toluic Acid, Calcium-L-lactate, Calcium Gluconate, Magnesium-DL-aspartate, and Magnesium-L-lactate in Water. J. Chem. Thermodyn. 2002, 34, 1127−1136. (20) Li, L.; Feng, L.; Wang, Q. B.; Li, X. Solubility of 1,2,4Benzenetricarboxylic Acid in Acetic Acid + Water Solvent Mixtures. J. Chem. Eng. Data 2008, 35, 298−300. (21) Kustov, A. V.; Berezin, M. B. Thermodynamics of Solution of Hemato- and Deuteroporphyrins in N,N-Dimethylformamide. J. Chem. Eng. Data 2013, 58, 2502−2505. (22) Takebayashi, Y.; Sue, K.; Yoda, S.; Hakuta, Y.; Furuya, T. Solubility of Terephthalic Acid in Subcritical Water. J. Chem. Eng. Data 2012, 57, 1810−1816. (23) Liu, J. Q.; Cao, X. X.; Ji, B. M.; Zhao, B. T. Determination and Correlation of Solubilities of (S)-Indoline-2-carboxylic Acid in Six Different Solvents from (283.15 to 358.15) K. J. Chem. Eng. Data 2013, 58, 2414−2419. (24) Perlovich, G. L.; Kurkov, S. V.; Bauer-Brandl, A. Thermodynamics of Solutions: II. Flurbiprofen and Diflunisal as Models for Studying Solvation of Drug Substances. Eur. J. Pharm. Sci. 2003, 19, 423−432. (25) Liu, M. J.; Fu, H. L.; Yin, D. P.; Zhang, Y. L.; Lu, C. C.; Cao, H.; Zhou, J. Y. Measurement and Correlation of the Solubility of Enrofloxacin in Different Solvents from (303.15 to 321.05) K. J. Chem. Eng. Data 2014, 59, 2070−2074. (26) Shen, B. W.; Wang, Q. B.; Wang, Y. F.; Ye, X.; Lei, F. Q.; Gong, X. Solubilities of Adipic Acid in Acetic Acid + Water Mixtures and Acetic Acid + Cyclohexane Mixtures. J. Chem. Eng. Data 2013, 58, 938−942. (27) Lei, F. Q.; Wang, Q. B.; Gong, X.; Shen, B. W.; Zhang, W. M.; Han, Q. Solubilities of Succinic Acid in Acetic Acid + Water Mixtures

4. CONCLUSIONS By using the synthetic method, the solubilities of benzoic acid in binary methylbenzene + benzyl alcohol solvent mixtures at (301.05 to 355.65) K and in binary methylbenzene + benzaldehyde solvent mixtures at (301.05 to 353.35) K were determined at atmospheric pressure. The studied mass fractions of benzyl alcohol and benzaldehyde in the corresponding binary solvent mixtures range from 0.0 to 1.0. It was found that the measured solubilities increase with the increase of temperature at constant solvent composition. For the ternary system benzoic acid + methylbenzene + benzyl alcohol, the results show that the binary methylbenzene + benzyl alcohol solvent mixture with the mass fraction of benzyl alcohol at 0.80 has the best dissolving capacity for benzoic acid at constant temperature. However, for the ternary system benzoic acid + methylbenzene + benzaldehyde, the results show that the binary methylbenzene + benzaldehyde solvent mixture with a mass fraction of benzaldehyde of 0.20 has the best dissolving capacity for benzoic acid at constant temperature. The experimental data were correlated by the nonrandom two-liquid (NRTL) equations, and the correlated solubilities agree satisfactorily with the experimental observations. To get the thermodynamic functions, the modified Apelblat equation was also used to correlate the experimental solubilities. The thermodynamic functions for the solid−liquid equilibria system of benzoic acid in methylbenzene + benzyl alcohol solvent mixtures and methylbenzene + benzaldehyde solvent mixtures, including ΔG0T, ΔH0T, ΔS0T, and ΔC0p were calculated by the Clark and Glew equation. It shows that the dissolution process is endothermic and not spontaneous. The obtained interaction parameters might be used in the calculation of the solubility of benzoic acid in methylbenzene + benzyl alcohol and methylbenzene + benzaldehyde mixtures as well as for the design and optimization of the related purification process.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: 86-731-88664151. E-mail: [email protected]. Funding

The project is supported by Key S&T Special Project of Zhejiang Province (2012C13007-2), the Fundamental Research Funds for the Central Universities, and the National Nature Science Fund (21302049). Notes

The authors declare no competing financial interest.

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REFERENCES

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J

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