Solid–Liquid Equilibria of Nine Binary Systems with Dicarboxylic Acids

Article pubs.acs.org/jced

Solid−Liquid Equilibria of Nine Binary Systems with Dicarboxylic Acids Tzu-Chi Wang* and Wun-Han Hu Department of Chemical and Materials Engineering and Master Program of Nanomaterials, Chinese Culture University, Taipei, Taiwan 11114, ROC ABSTRACT: In this study, solid−liquid equilibria of dicarboxylic acids for binary mixtures, hexanedioic acid (1) + octanedioic acid (2) (eutectic temperature TE = 390.54 K, eutectic composition x1E = 0.419); hexanedioic acid (1) + nonanedioic acid (2) (TE = 372.52 K, x1E = 0.269); hexanedioic acid (1) + decanedioic acid (2) (TE = 387.43 K, x1E = 0.514); heptanedioic acid (1) + octanedioic acid (2) (TE = 365.81 K, x1E = 0.782); heptanedioic acid (1) + nonanedioic acid (2) (TE = 352.50 K, x1E = 0.558); heptanedioic acid (1) + decanedioic acid (2) (TE = 367.07 K, x1E = 0.753); octanedioic acid (1) + decanedioic acid (2) (TE = 387.97 K, x1E = 0.465); nonanedioic acid (1) + octanedioic acid (2) (TE = 367.62 K, x1E = 0.712); and nonanedioic acid (1) + decanedioic acid (2) (TE = 370.49 K, x1E = 0.687), are measured using differential scanning calorimetry and correlated using Clarke-Glew equation. An observation here is simple eutectic phase diagrams for these systems. It can be noted that experiment results, correlated with Wilson and nonrandom two-liquid activity coefficient models, are highly satisfactory.

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INTRODUCTION Various combinations of compounds and conditions exist in the world of unit operation, and in industries operators are striving to apply suitable methods to get viable solutions and prevent ensuing problems from occurring. For crystallization operations occurring at relatively low temperatures, such as the separation of isomeric or thermolabile compounds, traditional distillation approach is not adequate for industrial applications. In order to address the problem, solid−liquid equilibrium (SLE) measurement is therefore widely adopted here. However, before efficient separation processes can be developed, SLE data of various systems should be well-prepared. Having wide application in industry, dicarboxylic acids are essential constituents in adhesives, plasticizers, lubricants, and greases, as well as in pharmaceuticals, cosmetics, and food. This study centers on measuring SLE data of various binary mixtures of dicarboxylic acids, including hexanedioic acid, heptanedioic acid, octanedioic acid, nonanedioic acid, and decanedioic acid, aiming to further complete the results established in previous literature. Most notably, this experiment involves the use of differential scanning calorimetry (DSC), which records the heat effect that occurs in the phase transformation, thereby aiding researchers in obtaining more accurate results and saving time. This is unlike the traditional method used to obtain SLE data, which involves either the cooling curve or visual measurement.1 Determination of phase boundaries of SLE is based on the measurements of both the peak temperatures and the heat of phase transformation.2 Results reported in literature include experimental SLE data on metal, polymer, and organic compound systems, all of which are obtained by using the DSC method.3−6 Additionally, mathematical models used for © 2017 American Chemical Society

correlating SLE results of dicarboxylic acids with binary mixtures from DSC experiments are also present in existing literature.7−11 This study focuses on the measurement of novel SLE data of nine binary organic mixtures: hexanedioic acid (C6H10O4) + octanedioic acid (C8H14O4); hexanedioic acid + nonanedioic acid (C 9 H 16 O 4 ); hexanedioic acid + decanedioic acid (C10H18O4); heptanedioic acid (C7H12O4) + octanedioic acid; heptanedioic acid + nonanedioic acid; heptanedioic acid + decanedioic acid; octanedioic acid + decanedioic acid; nonanedioic acid + octanedioic acid; and nonanedioic acid + decanedioic acid. As noted before, both the Wilson12 and nonrandom two-liquid (NRTL)13 activity coefficient models are used to correlate experimental data. Finally, it is demonstrated that the eutectic temperatures and compositions obtained from model correlation for all nine binary mixtures correspond to the results from existing experimental observations.

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EXPERIMENTAL SECTION The authors have paid considerable caution in preparing the following mixtures: from Alfa Aesar comes the nonanedioic acid with purity greater than mass fraction w = 0.98; from SigmaAldrich, all other chemicals have purity greater than mass fraction w = 0.99. These chemicals are applied in their original states without going through any purification process for the Received: July 13, 2016 Accepted: February 10, 2017 Published: February 24, 2017 931

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Table 1. Comparison of the Measured Melting Temperatures and Heats of Fusion with Literature Data for Pure Compounds at Pressure p = 0.1 MPaa ΔfusHom/kJ·mol−1

Tm/K

a

compound

source

purity (mass fraction)

this study

literature

this study

literature

hexanedioic acid heptanedioic acid octanedioic acid nonanedioic acid decanedioic acid

Aldrich Aldrich Aldrich Alfa Aesar Aldrich

0.99 0.99 0.99 0.98 0.99

425.28 378.57 415.07 379.89 406.76

425.5020 379.1521 416.1518 379.6520 407.6518

39.03 30.76 30.70 35.92 46.74

34.8520 27.6218 29.1619 32.6819 40.8119

Combined expanded uncertainties Uc are Uc (Tm) = 0.86 K, Uc (ΔfusHom) = 0.87 kJ·mol−1 (0.95 level of confidence).

sake of consistency. DSC (PerkinElmer DSC 4000) is used to capture both the melting temperatures and the enthalpies of fusion of these compounds. Comparison is made between the properties of these pure components and the existing data from literature data (see Table 1). It is obvious that the first two pure fluids’ properties show considerable agreement in cases where literature data exist for comparison. As stated, extreme caution is exercised to achieve desired results. For each binary mixture, a 4 ± 0.4 mg sample of a specific weight composition is kept airtight in a high-pressure aluminum container (from PerkinElmer). The balance (Shimadzu C9AS-AUW220D) used in this experiment has an accuracy of ±0.01 mg. For cleanup purposes, the DSC is first infused with nitrogen gas, then heated to 673.15 K. Before experiment, the DSC is calibrated using high-purity indium and zinc. Each mixture undergoes the first-stage heating, most notably to homogenize the sample mixture and to prevent thermal histories from interfering the accuracy of the experiment. The mixture is heated to a temperature above the melting point of the heavier component in the binary mixture (distinguished by molecular weight) at a heating rate of 10 K·min−1. Then the sample is kept at this temperature for 1 min before being allowed to cool down to 303.15 K, specifically at a rate of 10 K·min−1. Last in the pretreatment process is to keep the sample at this temperature for 30 min. Samples for nine binary mixtures are all heated at the rate of 1 K·min−1. The eutectic temperatures were determined from the onset temperatures from the DSC measurement. In most research, the determination of eutectic temperature is through the onset temperature, and the liquidus temperature is determined through the peak temperature. However, sometimes the liquidus temperature cannot be unequivocally determined because interference such as phase change occurs. In such a situation, the liquidus temperature is determined using the modified peak temperature proposed by researchers.6 Any further attempt to use a slower heating rate (say, 0.5 K·min−1) does not influence the final liquidus temperature. To ensure the results are reproducible, the experiment is repeated multiple times. The uncertainty of temperature measurement is about ±1 K. The maximum uncertainty range for some experimental liquidus and solidus temperatures is 3−5 K. Justification of the reproducibility of our results is based on repeating the experiment for every sample mixture.

ln(γixi) = −

o ⎛T ⎞ ΔfusHmi m, i − 1⎟ ⎜ ⎠ RTm, i ⎝ T

(1)

where the constant γ denotes the activity coefficient; ΔfusHom is the molar enthalpy of fusion; Tm is the melting temperature; and x is the equilibrium liquid composition in mole fraction. The value of γ in eq 1 represents the nonideal solution behavior and is obtained by using the Wilson and NRTL models. The Wilson model can be represented as ⎞ ⎛ Λ12 Λ 21 ln γ1 = −ln(x1 + Λ12x 2) + x 2⎜ − ⎟ Λ 21x1 + x 2 ⎠ ⎝ x1 + Λ12x 2 (2)

⎞ ⎛ Λ12 Λ 21 ln γ2 = −ln(x 2 + Λ 21x1) − x1⎜ − ⎟ Λ 21x1 + x 2 ⎠ ⎝ x1 + Λ12x 2 (3)

Λ12 =

⎛ λ − λ11 ⎞ V2 ⎟ exp⎜ − 12 ⎝ V1 RT ⎠

(4)

Λ 21 =

V1 ⎛ λ 21 − λ 22 ⎞ ⎟ exp⎜ − V2 ⎝ RT ⎠

(5)

where R is the gas constant, V1 and V2 are the liquid molar volumes determined by DIPPR.15 The two adjustable parameters are (λ12 − λ11)/R and (λ21 − λ22)/R. The NRTL equations are ⎤ ⎞2 ⎛ G21 τ12G12 ⎥ ln γ1 = x 2 τ21⎜ ⎟ + ⎢⎣ ⎝ x1 + x 2G21 ⎠ (x 2+x1G12)2 ⎥⎦

(6)

⎤ ⎞2 ⎛ G12 τ21G21 ⎥ ln γ2 = x1 τ12⎜ ⎟ + ⎢⎣ ⎝ x 2 + x1G12 ⎠ (x1+x 2G21)2 ⎥⎦

(7)

ln G12 = −α12τ12

(8)

⎡

2⎢

⎡

2⎢

τ12 =

g12 − g22 RT

ln G21 = −α12τ21 τ21 =

g21 − g11 RT

(9)

where (g12 − g22)/R and (g21 − g11)/R are adjustable parameters, independent of composition and temperature. On the one hand, α12, the nonrandomness factor of the NRTL model is designated as 0.3. Furthermore, for every binary mixture, note that the adjustable parameters (in both the Wilson and the NRTL models) are calculated with the minimization of the following objective function (obj), which is the mean sum of the ratio of the difference between the calculated and experimentally determined liquidus temperatures TL

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MODEL AND CORRELATION Equal fugacity criterion helps in determining the thermodynamic relationship for SLE.14 Assuming that the difference between the heat capacities of liquid and those of solid is negligible, we have 932

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Table 2. Experimental SLE Data (Eutectic Temperatures TE and Liquidus Temperatures TL) for Nine Binary Systems at Mole Fraction x and Pressure p = 0.1 MPaa,b TE/K

100x1

TL/K

100x1

TE/K

Hexanedioic Acid (1) + Octanedioic Acid (2) N/A 415.07 75.070 391.97 387.51 412.69 79.509 390.70 392.06 409.92 84.670 391.81 391.94 406.55 89.952 392.46 390.93 405.99 94.917 392.11 390.99 405.51 100.000 N/A 391.36 402.86 391.58 405.58 390.99 406.50 392.28 408.13 Hexanedioic Acid (1) + Nonanedioic Acid (2) N/A 379.89 79.801 372.26 372.15 379.73 84.823 372.15 370.71 378.05 89.675 372.75 372.67 377.25 95.262 372.36 372.79 375.97 100.000 N/A 372.83 400.70 370.94 402.36 372.81 407.72 372.46 409.98 370.75 412.54 Hexanedioic Acid (1) + Decanedioic acid (2) N/A 406.76 79.908 391.71 388.89 405.84 84.862 391.89 390.64 404.00 89.751 392.03 391.12 402.15 95.217 391.49 391.10 400.15 100.000 N/A 391.69 398.78 391.87 401.82 391.92 406.83 391.92 410.06 Heptanedioic acid (1) + Octanedioic Acid (2) N/A 415.07 54.835 366.09 366.08 413.19 85.096 366.58 367.07 411.07 90.263 366.47 363.70 407.38 95.140 366.86 363.20 406.02 100.000 N/A 364.58 402.73 366.24 401.22 365.19 396.13 367.25 393.21 366.07 389.60 366.59 389.01 Heptanedioic acid (1) + Nonanedioic Acid (2) N/A 379.89 77.674 354.92 349.76 378.08 80.542 353.60 349.29 378.17 82.458 353.65 350.64 374.02 84.962 353.75 351.26 372.61 89.672 354.28 354.34 370.08 95.137 354.52

0.000 5.037 9.680 15.402 17.097 19.718 22.404 62.689 64.994 69.978 0.000 5.110 7.985 10.039 14.891 54.645 60.042 65.520 70.124 74.825 0.000 5.091 10.365 14.713 19.675 24.750 59.748 65.019 70.207 0.000 5.132 10.221 14.582 20.127 24.781 30.000 34.793 39.741 45.211 50.107 0.000 5.050 9.652 14.658 20.269 25.055

TL/K 30.000 35.496 40.268 75.000

411.86 415.33 418.64 421.01 423.70 425.28

0.000 4.986 10.147 15.209 19.922 24.847 29.830 35.222 39.943 44.984 84.937

415.69 418.71 421.18 424.23 425.28

0.000 4.889 10.018 15.026 20.085 25.000 29.776 64.878 69.978 75.013

416.89 419.10 422.14 423.84 425.28

0.000 4.956 9.951 15.200 20.245 24.775 29.692 34.562 40.265 45.097

385.25 370.98 373.67 376.84 378.57

0.000 5.339 10.313 15.189 20.131 25.072 29.963 35.063 39.708 45.253 84.728

366.90 367.89 369.49 371.06 373.63 376.05

Heptanedioic acid (1) + Nonanedioic Acid (2) 352.31 367.75 100.000 N/A 352.27 364.45 352.89 362.58 353.84 365.40 Heptanedioic acid (1) + Decanedioic acid (2) N/A 406.76 89.888 366.00 362.27 404.92 94.782 365.53 363.97 403.18 100.000 N/A 364.85 401.28 365.18 399.42 365.57 397.20 365.83 394.58 365.91 392.33 366.01 389.43 366.05 388.20 366.04 370.75 Octanedioic Acid (1) + Decanedioic acid (2) N/A 406.76 80.000 380.27 385.59 405.25 84.818 381.43 381.35 402.11 89.935 381.15 384.30 400.05 95.239 377.84 383.42 398.51 100.000 N/A 384.16 396.69 383.55 394.39 382.19 396.83 382.02 398.72 382.79 401.38 Nonanedioic Acid (1) + Octanedioic Acid (2) N/A 415.07 50.079 367.65 364.94 410.74 79.912 366.15 368.17 409.14 85.042 367.89 366.96 406.75 90.024 368.17 367.05 404.57 94.637 368.23 366.90 401.17 100.000 N/A 368.68 399.04 367.25 394.67 367.88 392.32 368.49 387.90 Nonanedioic Acid (1) + Decanedioic acid (2) N/A 406.76 86.799 368.33 367.78 406.07 90.314 370.83 368.84 404.57 92.200 370.70 368.99 401.00 95.315 369.62 368.80 399.35 100.000 N/A 369.82 396.95 369.43 394.18 369.70 394.96 370.41 389.62 370.39 387.61 370.78 376.07

378.57

373.32 374.96 378.57

402.99 406.35 409.57 412.30 415.07

386.14 374.05 375.82 377.57 378.71 379.89

377.14 377.86 378.16 380.03 379.89

a NA: not available. bStandard uncertainties u is u(x) = 0.002 and combined expanded uncertainties Uc are Uc (TE) = 0.67 K, Uc (TL) = 0.92 K (0.95 level of confidence). N

obj =

⎛ 1 ⎞⎧ TL(calc) − TL(expt) ⎫ ⎟⎨ ⎬ N ⎠⎩ TL(expt) ⎭

∑ ⎜⎝

k=1

k

between experimental and calculated results are presented in what follows.

(10)

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RESULTS AND DISCUSSION Table 2 shows the measured eutectic temperatures (TE) and the liquidus temperatures (TL) of all combinations of nine

Subscript k denotes the kth data point. The SLE phase boundaries can be determined using these models after assigning optimal parameters. Both the data and the corresponding comparisons 933

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Table 3. Optimally Fitted Binary Parameters and the Deviations of Regression from the Wilson and NRTL Models Clarke-Glew equationa

Wilson parametersb

NRTL parameter (α12 is 0.3 in this study)

A12, B12, C12 A21, B21, C21

[(λ12 − λ11)/R]/K, [(λ21 − λ22)/R]/K

[(g12 − λ22)/R]/K, [(g21 − λ11)/R]/K

19.70/−22.12/−9.20 48.44/−51.96/−32.07 385.02/−390.19/−327.39 8.57/−11.23/0.48 80.14/−84.45/−55.65 −117.78/118.09/103.07 74.47/−78.05/−54.19 −103.97/103.68/98.98 11.31/−12.89/−0.93 9.69/−10.85/−1.63 52.81/−56.21/−34.47 288.36/−291.60/−248.86 240.77/−247.21/−192.28 208.44/−214.52/−165.23 39.14/−41.96/−25.12 −518.59/520.78/470.25 18.03/−20.84/−5.48 9.52/−11.58/3.61 a

Hexanedioic Acid (1) + Octanedioic Acid (2) −197.04/42.75 −748.85/1121.90

0.11

0.12

Hexanedioic Acid (1) + Nonanedioic Acid (2) −220.13/209.53 −599.21/1212.03

0.16

0.11

Hexanedioic Acid (1) + Decanedioic acid (2) −131.34/33.55 −732.49/1233.86

0.12

0.11

Heptanedioic acid (1) + Octanedioic Acid (2) 35.45/130.39 270.70/−83.77

0.21

0.21

Heptanedioic acid (1) + Nonanedioic Acid (2) −282.85/277.70 410.51/−498.87

0.10

0.13

Heptanedioic acid (1) + Decanedioic acid (2) −194.61/−103.59 807.71/−731.04

0.11

0.11

Octanedioic Acid (1) + Decanedioic acid (2) 517.30/−522.31 −494.22/414.57

0.16

0.18

Nonanedioic Acid (1) + Octanedioic Acid (2) 5.72/−5.75 877.56/−398.31

0.20

0.14

Nonanedioic Acid (1) + Decanedioic Acid (2) 362.85/−376.23 1405.91/−620.38

0.24

0.16

Tr

Clarke-Glew equation. ln x1 = A12 + B12 T + C12 ln m3

volumes: V / kmol , T/K. V = octanedioic acid. V =

1 + (1 − T /809)0.282

0.25915

0.6479

1 + (1 − T /811)0.28571

0.2316

0.37965

T Tr

Tr

ln x 2 = A 21 + B21 T + C21 ln

for hexanedioic acid. V =

for nonanedioic acid. V =

x1

Hexanedioic Acid (1) + Octanedioic Acid (2) Wilson model 0.422 NRTL model 0.421 Clarke-Glew equation 0.419 Hexanedioic Acid (1) + Nonanedioic Acid (2) Wilson model 0.246 NRTL model 0.253 Clarke-Glew equation 0.269 Hexanedioic Acid (1) + Decanedioic acid (2) Wilson model 0.427 NRTL model 0.441 Clarke-Glew equation 0.514 Heptanedioic acid (1) + Octanedioic Acid (2) Wilson model 0.739 NRTL model 0.740 Clarke-Glew equation 0.782 Heptanedioic acid (1) + Nonanedioic Acid (2) Wilson model 0.553 NRTL model 0.550 Clarke-Glew equation 0.558

0.22

0.22835

0.3468

T Tr Tr

1 + (1 − T /805)0.28571

0.46914

1 + (1 − T /815)0.28571

Table 4. Comparison of the Eutectic Point Results (Eutectic Composition x1 and Eutectic Temperature TE) from Different Methods for Nine Binary Mixtures method

AADTc/%

= 330 K is a reference temperature. bliquid molar 0.28571

for heptanedioic acid. V =

for decanedioic acid. cAADT =

100 N

0.2191 + (1 − T /809) 0.41925 N

∑k = 1

for

TL(calc) − TL(expt) TL(expt)

k

Table 4. continued method

x1

Heptanedioic acid (1) + Decanedioic acid (2) Wilson model 0.715 NRTL model 0.711 Clarke-Glew equation 0.753 Octanedioic Acid (1) + Decanedioic acid (2) Wilson model 0.505 NRTL model 0.511 Clarke-Glew equation 0.465 Nonanedioic Acid (1) + Octanedioic Acid (2) Wilson model 0.681 NRTL model 0.677 Clarke-Glew equation 0.712 Nonanedioic Acid (1) + Decanedioic acid (2) Wilson model 0.706 NRTL model 0.699 Clarke-Glew equation 0.687

TE/K 388.24 385.68 390.54 370.24 372.69 372.52 389.52 388.05 387.43 368.44 368.62 365.81

TE/K 361.21 360.63 367.07 381.81 381.44 387.97 367.37 370.88 367.62 367.88 370.37 370.49

binary mixtures, each at various compositions (determined by differences in mole fractions). The uncertainties in measurement, for experimentally determined temperatures and compositions, are (estimated) ± 1 K (with the maximum uncertainty of 3−5 K) and ±0.002 mole fraction, respectively.

351.09 349.85 352.50 934

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Figure 1. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Hexanedioic Acid (1) + Octanedioic Acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

Figure 4. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Heptanedioic acid (1) + Octanedioic Acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

Figure 2. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Hexanedioic Acid (1) + Nonanedioic Acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

Figure 5. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Heptanedioic acid (1) + Nonanedioic Acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

Figure 3. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Hexanedioic Acid (1) + Decanedioic acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

Figure 6. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Heptanedioic acid (1) + Decanedioic acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

From liquidus data points, the best-fitted parameters of the Wilson and the NRTL models are then determined. The main demonstration is that desirable experimental data can be acquired from assigning optimal binary parameters (shown in Table 3) to either the Wilson or the NRTL model. The absolute average deviations (AADTs) in the calculated liquidus

temperatures are also presented in Table 3. For all nine binary mixtures, the AADTs fall within the ranges of experimental uncertainty. The AADTs of both activity coefficient models are nearly identical, which is about 0.24% of liquidus temperatures. The eutectic compositions and temperatures of all nine binary mixtures adopted in this study are presented in Table 4, which shows satisfactory agreements between the calculated 935

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Figure 9. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Nonanedioic Acid (1) + Decanedioic acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

Figure 7. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Octanedioic Acid (1) + Decanedioic acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

nonanedioic acid (1) + decanedioic acid (2), x1E = 0.687 and TE = 370.49 K.

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CONCLUSION When mixtures (presented in this study) occur in theoretical research and/or practical applications, solid−liquid equilibrium (SLE) measurements of various mixtures become indispensable in this situations. Notably, this study uses DSC to measure the SLE for nine binary mixtures of organic dicarboxylic acids. All binary systems here show simple eutectic behavior. Furthermore, to calculate correlations in both the Wilson and the NRTL activity coefficient models, the measured liquidus temperatures are applied. The same results are also helpful in finding the fitting curve of the Clarke-Glew equation. As stated, satisfactory correlation results, and the optimally fitted binary parameters, are obtained for both models. Also, both the smoothing data and the eutectic results (derived from both models) are in satisfactory agreement. Novel eutectic compositions and temperature data are presented in these nine binary systems. Finally, consistent with the trend of the melting temperatures of pure components, a discussion of differences in their eutectic temperatures and compositions is presented here.

Figure 8. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Nonanedioic Acid (1) + Octanedioic Acid (2) (•, liquidus temperature; ▲, eutectic temperature; ---, NRTL model; −, Wilson model).

data and the measured data. The figures are obtained by using Clarke-Glew equation,16,17 the Wilson model, or the NRTL model. In the field of thermodynamics, application of ClarkeGlew equation, a general-purpose regression equation, is so one can find an appropriate fitting curve for measured data. The graphical representations of the calculated phase boundaries for all nine binary systems, hexanedioic acid + octanedioic acid; hexanedioic acid + nonanedioic acid; hexanedioic acid + decanedioic acid; heptanedioic acid + octanedioic acid; heptanedioic acid + nonanedioic acid; heptanedioic acid + decanedioic acid; octanedioic acid + decanedioic acid; nonanedioic acid + octanedioic acid; and nonanedioic acid + decanedioic acid, are presented in Figures 1 to 9, respectively. The eutectic composition and temperature calculated by using Clarke-Glew equation for hexanedioic acid (1) + octanedioic acid (2) are x1E = 0.419 and TE = 390.54 K; for hexanedioic acid (1) + nonanedioic acid (2), x1E = 0.269 and TE = 372.52 K; for hexanedioic acid (1) + decanedioic acid (2), x1E = 0.514 and TE = 387.43 K; for heptanedioic acid (1) + octanedioic acid (2), x1E = 0.782 and TE = 365.81 K; for heptanedioic acid (1) + nonanedioic acid (2), x1E = 0.558 and TE = 352.50 K; for heptanedioic acid (1) + decanedioic acid (2), x1E = 0.753 and TE = 367.07 K; for octanedioic acid (1) + decanedioic acid (2), x1E = 0.465 and TE = 387.97 K; for nonanedioic acid (1) + octanedioic acid (2), x1E = 0.712 and TE = 367.62 K; and for

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +886-2-2861-4011. ORCID

Tzu-Chi Wang: 0000-0001-9365-9194 Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jced.6b00628 J. Chem. Eng. Data 2017, 62, 931−937