Solid–Liquid Equilibria for Six Binary Mixtures of Nonanedioic Acids

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Solid−Liquid Equilibria for Six Binary Mixtures of Nonanedioic Acids, Decanedioic Acid, 3‑Methylheptanedioic Acid, 2,2-Dimethylbutanedioic Acid, and 2,3-Dimethylbutanedioic Acid Tzu-Chi Wang* and Chi-Yang Chan Department of Chemical and Materials Engineering and Master Program of Nanomaterials, Chinese Culture University, Taipei, 11114, Taiwan ROC ABSTRACT: Solid−liquid equilibria of dicarboxylic acids for binary mixtures nonanedioic acid (1) + 3-methylheptanedioic acid (2) (eutectic temperature TE = 342.25 K, eutectic composition x1E = 0.364); nonanedioic acid (1) + 2,2-dimethylbutanedioic acid (2) (TE = 367.51 K, x1E = 0.653); nonanedioic acid (1) + 2,3-dimethylbutanedioic acid (2) (TE = 354.27 K, x1E = 0.463); decanedioic acid (1) + 3-methylheptanedioic acid (2) (TE = 352.47 K, x1E = 0.134); decanedioic acid (1) + 2,2-dimethylbutanedioic acid (2) (TE = 384.38 K, x1E = 0.483); and decanedioic acid (1) + 2,3-dimethylbutanedioic acid (2) (TE = 365.38 K, x1E = 0.192)are measured using differential scanning calorimetry (DSC) and correlated using the Clarke−Glew equation in this study. Simple eutectic phase diagrams for these systems are observed. The experimental results are correlated using the Wilson and nonrandom two-liquid (NRTL) activity coefficient models, and satisfactory results are presented.

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INTRODUCTION In the world of unit operation, there are various kinds of combinations of compounds and conditions. To tackle the ensuing problems, suitable methods must be applied to obtain viable solutions. When industrial applications in which the crystallization operation at relatively low temperatures occurs, such as the separation of isomeric or thermolabile compounds, the traditional distillation approach has its limits. This is where solid−liquid equilibrium (SLE) measurements prevail. The SLE data of various systems therefore are required for the development of separation processes. This study centers on measuring the SLE data of various binary mixtures of dicarboxylic acids including nonanedioic acid; decanedioic acid; 3-methylheptanedioic acid; 2,2-dimethylbutanedioic acid; and 2,3-dimethylbutanedioic acid. Dicarboxylic acids have a wide application in industry: they are essential constituents in adhesives, plasticizers, lubricants, and greases, as well as in pharmaceuticals, cosmetics, and foods. This study is motivated to fill the gap of experimental data for dicarboxylic acids that are not available in previous literature. Other than the traditional methods used to obtain SLE data by either the cooling curve or visual measurement,1 an alternative approach has been developed. The differential scanning calorimetry (DSC), a device that records the heat effect occurring in the phase transformation, provides researchers a time-saving tool with more accurate results. With the measurement of peak temperatures and heats of phase transformation, the phase boundaries of the SLE are determined.2 Experimental SLE data obtained by the DSC method on metal, polymer, and organic compound systems have been reported in the literature.3−6 Furthermore, mathematical models for correlating © XXXX American Chemical Society

the SLE results of dicarboxylic acids for binary mixtures from DSC experiments have also been presented in the literature.7−10 This study is dedicated to using the DSC method to measure the novel SLE data of six binary organic mixtures: nonanedioic acid (C9H16O4) + 3-methylheptanedioic acid (C6H10O4); nonanedioic acid + 2,2-dimethylbutanedioic acid (C6H10O4); nonanedioic acid + 2,3-dimethylbutanedioic acid (C6H10O4); decanedioic acid (C10H18O4) + 3-methylheptanedioic acid; decanedioic acid + 2,2-dimethylbutanedioic acid; and decanedioic acid + 2,3-dimethylbutanedioic acid. The Wilson11 and nonrandom two-liquid (NRTL)12 activity coefficient models are employed in correlating the experimental data. The eutectic temperatures and compositions from model correlation for all six binary mixtures are finally demonstrated to be in good agreement with the ones obtained from experimental observations.

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EXPERIMENTAL SECTION In the preparation of these mixtures, considerable caution is exercised. Nonanedioic acid, decanedioic acid, 3-methylheptanedioic acid, 2,2-dimethylbutanedioic acid, and 2,3-dimethylbutanedioic acid are bought from Aldrich. These chemicals are applied in the state of their purchase with no further purification for the purpose of consistencyusually having a purity greater than mass fraction w = 0.99. The melting temperatures and the enthalpies of fusion of these compounds are taken in this study employing the DSC (PerkinElmer DSC 4000). These measured pure component properties are compared with literature data Received: July 21, 2014 Accepted: October 24, 2014

A

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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

nonanedioic acid 3-methylheptanedioic acid 2,2-dimethylbutanedioic acid 2,3-dimethylbutanedioic acid decanedioic acid

Alfa Aesar Aldrich Aldrich Aldrich Aldrich

0.98 0.99 0.99 0.99 0.99

380.30 358.61 412.95 390.52 407.17

379.6520 358.6110 412.9510 392.4810 407.6518

36.9 31.0 38.1 16.9 44.9

32.719 31.010 38.110 16.910 40.8119

Combined expanded uncertainties Uc are Uc (Tm) = 0.14 K, Uc (ΔfusHom) = 0.78 kJ·mol−1 (0.95 level of confidence).

Table 2. Experimental SLE Data (Eutectic Temperatures TE and Liquidus Temperatures TL) for Six Binary Systems at Mole Fraction x and Pressure p = 0.1 MPaa,b 100x1 0.00 4.99 10.12 15.35 19.98 24.76 39.96 44.86 50.04 54.71 0.00 4.74 10.16 15.12 19.91 24.85 29.90 34.73 40.30 45.18 0.00 5.25 9.85 15.12 19.76 24.76 30.20 35.05 60.47 65.31 0.00 4.96

TE/K

TL/K

100x1

TE/K

TL/K

100x1

Nonanedioic Acid (1) + 3-Methylheptanedioic Acid (2) N/A 358.61 59.88 340.49 361.60 340.39 355.29 64.91 344.53 365.69 341.93 355.14 69.96 339.44 363.91 342.03 349.77 74.88 343.67 370.63 343.27 350.06 79.65 340.19 372.56 343.25 347.53 84.71 344.00 374.64 342.73 347.45 89.90 343.38 375.76 343.11 350.49 94.91 340.11 377.36 341.40 358.35 100.00 N/A 380.30 341.83 359.56 Nonanedioic Acid (1) + 2,2-Dimethylbutanedioic Acid (2) N/A 412.95 49.85 364.09 379.66 365.10 407.56 65.27 361.79 367.30 365.31 404.62 69.96 362.28 368.07 367.10 402.21 75.26 363.30 369.46 363.56 399.17 79.84 363.65 371.33 364.78 395.74 84.71 362.32 374.85 367.05 391.68 89.93 362.65 376.94 367.00 387.56 95.31 362.59 378.77 362.29 386.21 100.00 N/A 380.30 362.57 382.17 Nonanedioic Acid (1) + 2,3-Dimethylbutanedioic Acid (2) N/A 390.52 69.96 352.94 368.98 350.88 384.81 74.50 354.37 371.08 354.93 381.40 80.30 355.64 372.58 351.77 374.02 85.06 352.36 373.75 354.36 372.00 89.96 351.34 375.25 353.85 370.66 94.13 353.67 378.72 354.73 366.24 100.00 N/A 380.30 355.35 361.33 354.63 363.97 353.01 364.28 Decanedioic Acid (1) + 3-Methylheptanedioic Acid (2) N/A 358.61 54.73 351.35 388.04 350.26 357.08 59.83 351.72 390.09

9.77 14.94 20.29 25.16 29.93 35.05 39.89 44.91 49.80 0.00 5.13 9.94 15.30 19.88 25.01 30.24 34.91 54.97 60.10 0.00 4.97 6.86 9.97 11.96 14.90 50.05 54.80 59.92 65.09 69.81

TE/K

TL/K

100x1

TE/K

Decanedioic Acid (1) + 3-Methylheptanedioic Acid (2) 350.96 353.67 64.93 350.98 351.97 355.67 69.88 350.84 351.13 360.73 75.19 351.04 351.63 365.40 79.80 348.28 352.08 371.52 85.08 349.59 351.65 376.71 90.19 348.66 352.31 376.42 94.88 346.41 351.73 382.58 100.00 N/A 351.59 385.38 Decanedioic Acid (1) + 2,2-Dimethylbutanedioic Acid (2) N/A 412.95 64.93 383.63 383.86 408.20 69.81 383.22 380.26 404.67 75.13 383.06 384.19 400.62 79.75 383.79 382.26 398.61 84.79 382.44 382.50 397.25 89.63 382.46 382.82 393.33 94.87 380.87 383.44 390.90 100.00 N/A 383.75 387.87 383.78 389.32 Decanedioic Acid (1) + 2,3-Dimethylbutanedioic Acid (2) N/A 390.52 75.13 370.03 368.01 386.97 80.06 369.50 367.32 385.99 85.04 368.63 369.37 382.44 90.21 367.33 369.99 380.44 95.20 367.46 370.15 377.02 100.00 N/A 371.65 385.14 369.77 387.18 370.95 388.73 370.83 392.53 370.60 394.51

TL/K 391.97 392.90 395.59 398.77 400.99 403.08 404.65 407.17

391.89 394.02 395.89 398.99 400.42 402.43 404.39 407.17

396.84 397.78 400.44 402.00 404.71 407.17

a

NA: not available. bStandard uncertainties u is u(x) = 0.002 and combined expanded uncertainties Uc are Uc(TE) = 0.91 K, Uc(TL) = 1.48 K (0.95 level of confidence).

accuracy of ± 0.01 mg. To clean up the devices, the DSC is infused with nitrogen gas first and then heated to 673.2 K. Before its application in the SLE measurements, the DSC is calibrated with highpurity indium and zinc. To prevent the thermal histories of the previous use interfering with the accuracy of the experiment and to homogenize the sample mixture, each mixture undergoes the firststage heating. With a heating rate of 10 K·min−1, the mixture is heated to a temperature above the melting temperature of the heavier

and the results are listed in Table 1. Satisfactory agreement on the properties of the first two pure fluids are observed where literature data are available. To achieve the final goal without any miss, every step of the experiment is taken with meticulous care. For each binary mixture, a 4-mg sample of a specific weight composition is kept in an airtight high-pressure aluminum container purchased from PerkinElmer. The balance (Shimadzu C9AS-AUW220D) used in this experiment has an B

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Table 3. Optimally Fitted Binary Parameters and the Deviations of Regression from the Wilson and NRTL Models Wilson parametersa

NRTL parameter (α12 is 0.3 in this study)

AADTb/%

mixture

[(λ12 − λ11)/R]/K, [(λ21 − λ22)/R]/K

[(g12 − g22)/R]/K, [(g21 − g11)/R]/K

Wilson

NRTL

nonanedioic acid (1) + 3-methylheptanedioic acid (2) nonanedioic acid (1) + 2,2-dimethylbutanedioic acid (2) nonanedioic acid (1) + 2,3-dimethylbutanedioic acid (2) decanedioic acid (1) + 3-methylheptanedioic acid (2) decanedioic acid (1) + 2,2-dimethylbutanedioic acid (2) decanedioic acid (1) + 2,3-dimethylbutanedioic acid (2)

−184.95, 49.586 371.97, −399.04 223.73, −90.364 −435.45, 394.23 −160.53, −242.36 −548.94, 518.72

−561.01, 757.21 1569.6, −905.00 −392.90, 590.89 −589.40, 1133.3 −864.26, 957.58 −806.50, 1187.7

0.21 0.35 0.30 0.27 0.35 0.20

0.20 0.62 0.29 0.28 0.37 0.23

a

Liquid molar volumes: V/(m3/kmol), T/K, where V = 0.12438 + 0.00015166·T for nonanedioic acid; V = 0.1369 + 0.0001646·T for decanedioic acid, V = 0.087037 + 0.00011062·T for 3-methylheptanedioic acid, V = 0.088476 + 0.00010552·T for 2,2-dimethylbutanedioic acid, V = 0.087254 + 0.0001084·T for 2,3-dimethylbutanedioic acid. bThe AADT is calculated as AADT =

100 N

N

∑ k=1

TL(calc) − TL(expt) TL(expt)

k

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

x1

TE/K

Nonanedioic Acid (1) + 3-Methylheptanedioic Acid (1) Wilson model 0.334 342.67 NRTL model 0.342 341.88 Clarke−Glew equation 0.364 342.25 Nonanedioic Acid (1) + 2,2-Dimethylbutanedioic Acid (2) Wilson model 0.639 364.44 NRTL model 0.635 359.66 Clarke−Glew equation 0.653 367.51 Nonanedioic Acid (1) + 2,3-Dimethylbutanedioic acid (2) Wilson model 0.421 354.17 NRTL model 0.426 353.33 Clarke−Glew equation 0.463 354.27 Decanedioic Acid (1) + 3-Methylheptanedioic Acid (2) Wilson model 0.146 352.70 NRTL model 0.140 354.42 Clarke−Glew equation 0.134 352.61 Decanedioic Acid (1) + 2,2-Dimethylbutanedioic Acid (2) Wilson model 0.463 378.66 NRTL model 0.460 378.04 Clarke-Glew equation 0.483 384.38 Decanedioic Acid (1) + 2,3-Dimethylbutanedioic Acid (2) Wilson model 0.276 365.73 NRTL model 0.286 359.45 Clarke-Glew equation 0.192 365.38

Figure 1. Comparison of the experimental and calculated liquidus temperature for the binary mixture of nonanedioic acid (1) + 3-dethylheptanedioic acid (2): ●, liquidus temperature; ▲, eutectic temperature; ---, Wilson model; , Clarke−Glew equation.

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MODEL AND CORRELATION In this study, the thermodynamic relationship for SLE is obtained by using the equal fugacity criterion.13 Assuming that the difference between the heat capacities of the liquid and that of the solid is negligible, we have ln(γix i) = −

(molecular weight) component in the binary mixture. The sample is then kept at this temperature for 1 min before cooling down, at a rate of 10 K·min−1, to 303.15 K. The sample stays in this temperature for 30 min to finish the pretreatment procedure. Samples for six binary mixtures are all heated at the rate of 1 K·min−1. The eutectic temperatures were determined from the onset temperatures or peak temperatures from the DSC measurement. The liquidus temperatures are taken as the modified peak temperatures in the DSC results.6 Any further attempt to use a slower heating rate (say, 0.5 K·min−1) did not influence the final liquidus or eutectic temperatures. Repeated runs are conducted to confirm the reproducibility of experimental results. The uncertainty for the temperature measurement is about ±1.5 K. The maximum uncertainties for some experimental liquidus and solidus temperatures are 3 K to 5 K. The reproducibility of our experimental results was justified by repeated experiments for each sample mixture.

o ⎛T ⎞ ΔfusHmi m,i − 1⎟ ⎜ ⎠ RTm,i ⎝ T

(1)

ΔfusHom

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

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

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Figure 2. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Nonanedioic Acid (1) + 2,2dimethylbutanedioic Acid (2): ●, liquidus temperature; ▲, eutectic temperature; ---, Wilson model; , Clarke−Glew equation.

Figure 4. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Decanedioic acid (1) + 3-methylheptanedioic Acid (2): ●, liquidus temperature; ▲, eutectic temperature; ---, Wilson model; , Clarke−Glew equation.

Figure 3. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Nonanedioic Acid (1) + 2,3dimethylbutanedioic acid (2): ●, liquidus temperature; ▲, eutectic temperature; ---, Wilson model; , Clarke−Glew equation.

Figure 5. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Decanedioic acid (1) + 2,2dimethylbutanedioic Acid (2): ●, liquidus temperature; ▲, eutectic temperature; ---, Wilson model; , Clarke−Glew equation.

Λ12 =

Λ 21 =

⎛ λ − λ11 ⎞ V2 ⎟ exp⎜ − 12 ⎝ V1 RT ⎠ ⎛ λ − λ 22 ⎞ V1 ⎟ exp⎜ − 21 ⎝ V2 RT ⎠

ln G12 = −α12τ12 (4)

τ12 = (5)

⎡

2⎢

⎤ ⎡ ⎛ ⎞2 G12 τ21G21 ⎥ ln γ2 = x12⎢τ12⎜ ⎟ + ⎢⎣ ⎝ x 2 + x1G12 ⎠ (x1+x 2G21)2 ⎥⎦

RT

τ21 =

(8)

g21 − g11 (9)

RT

where (g12 − g22)/R and (g21 − g11)/R are adjustable parameters which are independent of composition and temperature. On the one hand, α12, the nonrandomness factor of the NRTL model is set to be 0.3. On the other hand, the adjustable parameters for each binary mixture, whether in the Wilson model or the NRTL model, 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:

where R is the gas constant, V1 and V2 are the liquid molar volumes, which are determined by DIPPR14 or Elbro’s group contribution method.15 The two adjustable parameters are (λ12−λ11)/R and (λ21−λ22)/R. The NRTL equations are presented as ⎤ ⎞2 ⎛ G21 τ12G12 ⎥ ln γ1 = x 2 τ21⎜ ⎟ + ⎢⎣ ⎝ x1 + x 2G21 ⎠ (x 2+x1G12)2 ⎥⎦

g12 − g22

ln G21 = −α12τ21

(6)

N

obj = (7)

k=1

D

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

∑ ⎜⎝

k

(10)

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The eutectic composition and temperature calculated by using the Clarke−Glew equation for nonanedioic acid (1) + 3-methylheptanedioic acid (2) are determined as x1E = 0.364 and TE = 342.25 K; for nonanedioic acid (1) + 2,2-dimethylbutanedioic acid (2), x1E = 0.653 and TE = 367.51 K; for nonanedioic acid (1) + 2,3-dimethylbutanedioic acid (2), x1E = 0.463 and TE = 354.27 K; for decanedioic acid (1) + 3-methylheptanedioic acid (2), x1E = 0.134 and TE = 352.47 K; for decanedioic acid (1) + 2,2-dimethylbutanedioic acid (2), x1E = 0.483 and TE = 384.38 K; and for decanedioic acid (1) + 2,3-dimethylbutanedioic acid (2), x1E = 0.192 and TE = 365.38 K.

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CONCLUSION The solid−liquid equilibrium (SLE) measurements of various mixtures are indispensable in theoretical research and practical applications alike when these mixtures occur in the process. This study measures the solid−liquid equilibrium for six binary mixtures of organic dicarboxylic acids by using DSC. All these binary systems show simple eutectic behavior. The measured liquidus temperatures are applied to the calculation of data correlation in both the Wilson and the NRTL activity coefficient models. Satisfactory correlation results are obtained for both models, and their optimally fitted binary parameters are reported. The measured liquidus results are also applied to find the fitting curve of the Clarke−Glew equation. It is also observed that the smoothing data and the eutectic results derived from both models are in satisfactory agreement. Novel eutectic compositions and temperatures data are finally presented for six binary systems. The differences in their eutectic temperatures and compositions are discussed consistently with the trend of the melting temperatures of pure components.

Figure 6. Comparison of the experimental and calculated liquidus temperature for the binary mixture of Decanedioic acid (1) + 2,3dimethylbutanedioic acid (2): ●, liquidus temperature; ▲, eutectic temperature; ---, Wilson model; , Clarke−Glew equation.

The subscript k denotes the kth data point. After the assignment of these optimal parameters the SLE phase boundaries in turn can be determined with these models. The data and corresponding comparison between the experimentally measured and calculated results are presented in the next sections.

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RESULTS AND DISCUSSION Table 2 shows the measured temperaturesthe eutectic temperatures (TE), and the liquidus temperatures (TL)of all combinations of the six binary mixtures at various compositions (mole fractions). The uncertainties of the measurment for both the experimentally determined temperatures and compositions are estimated as ± 1.5 K (with a maximum uncertainty of 3 K to 5 K) and ± 0.002 mole fraction, respectively. The best-fitted parameters of the Wilson and NRTL models are then evaluated from liquidus data points. It is demonstrated that the satisfactory experimental data can be obtained under the assignment of optimal binary parameters (shown in Table 3) to either the Wilson or the NRTL model. Also shown in Table 3 are the absolute average deviations (AADT) in the calculated liquidus temperatures. The AADT values fall within the ranges of experimental uncertainty for all six binary mixtures. The absolute average deviations of both the activity coefficient models are nearly the same, all less than 0.62 % of liquidus temperatures. For the six binary mixtures of this research, Table 4 displays the eutectic compositions and temperatures. From the table it can be observed that the data calculated and the data measured are in satisfactory agreement. The numbers listed in this table are the results gleaned by using the Clarke−Glew equation,16,17 or the Wilson model or the NRTL model. The Clarke−Glew equation is a general-purpose regression equation widely used in the field of thermodynamics to find an appropriate fitting curve for measured data. The calculated phase boundaries for the six binary systems nonanedioic acid + 3-methylheptanedioic acid; nonanedioic acid + 2,2-dimethylbutanedioic acid; nonanedioic acid + 2,3dimethylbutanedioic acid; decanedioic acid + 3-methylheptanedioic acid; decanedioic acid + 2,2-dimethylbutanedioic acid; and decanedioic acid + 2,3-dimethylbutanedioic acidare illustrated in Figures 1 to 6 with their graphical presentations, respectively.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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REFERENCES

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