Phase Equilibria in the Ternary System Hexacosane + Dibenzofuran +

Jun 3, 2014 - Solid–liquid equilibria for ternary mixtures consisting of hexacosane + dibenzofuran + biphenyl were determined using microdifferentia...
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Phase Equilibria in the Ternary System Hexacosane + Dibenzofuran + Biphenyl: Experimental Data and Prediction with DISQUAC Model Abdelaziz Chikh Baelhadj,*,† Omar Dahmani,† Rachid Mahmoud,‡ Fabrice Mutelet,§ Mohammed Bouroukba,§ and Michel Dirand§ †

Laboratoire de thermodynamique et de modélisation moléculaire, Faculté de chimie, USTHB, BP 32 El-Alia, 16111 Bab-Ezzouar, Alger Algérie ‡ Ecole Militaire Polytechnique EMP, BP 17 Bordj-el-Bahri, Alger Algérie § Laboratoire Réactions et génie des procédés (LRGP), Ecole Nationale Supérieure des Industries Chimiques (ENSIC), Université de Lorraine, 1, rue Grandville BP 20451, 54001 Nancy, France ABSTRACT: Solid−liquid equilibria for ternary mixtures consisting of hexacosane + dibenzofuran + biphenyl were determined using microdifferential scanning calorimetry. The phase diagrams were established according to the experimental results. A polynomial equation was used to correlate the experimental data. The experimental results were examined in terms of the predictive group contribution model DISQUAC and then compared with the ideal model.

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INTRODUCTION Solid compounds solubility in liquids is an important practical interest in developing methods of preparation, separation, and purification of substances. Crystallization is an operation where the performance depends essentially on good comprehension of compounds behavior in a mixture. It is known that long-chain alkanes play a crucial role in paraffin waxes deposition from crude oil.1−3 Experimental data on phase equilibria related to these compounds are important, both to understand the crystallization mechanisms and the development of thermodynamic models.4 Several works on solubility of long-chain alkanes in aromatics concern mainly binary systems.5−21 Yet, to our knowledge, the study of their ternary systems is limited.22−24 In this work, solid−liquid equilibria (SLE) of the (hexacosane + dibenzofuran + biphenyl) ternary system and SLE of their related binary systems, namely, (hexacosane + dibenzofuran), (hexacosane + biphenyl), and (dibenzofuran + biphenyl), were investigated using the microdifferential scanning calorimeter (micro DSC). The experimental results were modeled with DISQUAC group contribution model.

Table 1. Characteristics of the Studied Substances molecular weight/g·mol−1

purity (%)

origin

hexacosane biphenyl dibenzofuran

366.706 154.211 168.194

> 99 98 99

Fluka Acros Avocado

Figure 1. Chemical structure of the aromatic compounds.

The solubility measurements were carried out using a micro DSC III SETARAM under a 0.4 °C·min−1 heating rate. After preparing the molar fractions of the solid mixtures, 10 mg (on average) was taken for each measurement and placed in a stainless steel cell. This later was tightly sealed and put into the calorimetric block. The reference consists of an empty identical cell.

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EXPERIMENTAL SECTION The chemicals were used without further purification. Origin and purity of the studied substances are listed in Table 1. Figure 1 shows the molecular structure of the aromatic compounds. The mixture solubility was determined for temperatures ranging from 25 °C to the highest melting point of its components. © XXXX American Chemical Society

compound

Received: February 10, 2014 Accepted: May 19, 2014

A

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• (a,e) in (hexacosane + dibenzofuran) system • (b,e) in (biphenyl + dibenzofuran) system quac Dispersive, Cdisp st,l , and quasichemical, Cst,l , interchange parameters, where l = 1 for Gibbs energy and l = 2 for enthalpy are given in Table 4. The subscript st stands for the three contact types (a,b; a,e; or b,e).

Table 2. Thermodynamic Properties of Phase Change of the Studied Pure Substances at Pressure p = 0.1 M Paa compound hexacosane

dibenzofuran

biphenyl

Tm/K b

329.55 329.25c 329.21f 330.10g 355.20h 355.10i 353.87 f 355.31k 341.99l 340.69 f 342.098m

ΔHm/J·mol−1

ΔHtr/J·mol−1

Ttr/K

b

59540 59790d 68345 f 63600 g 18600h 19405j 22297 f 19293.65k 18600l 18608 f 18576.0m

32240b 32820d 36718 f 37500 g

e

326.55 326.40 f 327.00g

292.5k

Table 4. Interchange Parameters contact (s,t)

Cdisp st,l

Cdisp st,2

Cquac st,l

Cquac st,2

(a,b)a (a,e)b (b,e)c

0.170 15.500 16.140

0.465 24.900 24.410

0.000 6.400 6.000

0.000 9.240 12.000

0.00k a

Gonzalez.24 bKehiaian.34 cMarongiu.35

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a

Uncertainties u are u(T) = 0.5 K, u(p) = 0.1 kPa, and ur(ΔH) = 0.05 for this work. bDomanska.16 cAndon.25 dClaudy.26 eSchaerer.27 fThis work. gBriard.28 hHafsaoui.8 iMahmoud.7 jAoulmi.6 kChirico.29 l Yokoyama.30 mChirico.31

RESULTS AND DISCUSSION The binary system consisting of (biphenyl + dibenzofuran) has already been studied.36 In Figure 2, our experimental data are shown with those of literature. The liquidus are comparable

The properties of phase change of the studied pure compounds are presented in Table 2. These properties are close to literature data.

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DISQUAC MODEL In the framework of DISQUAC, the excess thermodynamic properties GE and HE are given as the sum of a combinatorial (comb), a dispersive (dis), and a quasichemical (quac) contribution. They are independently calculated and simply added: GE = GE,comb + GE,dis + GE,quac

(1)

HE = HE,dis + HE,quac

(2) 32

E,comb

where G is the Flory−Huggins combinatorial term. Details about calculation of dispersive and quasichemical contribution are reported elsewhere.32 Assessment of Geometrical Parameters. According to the DISQUAC model, the geometrical parameters are estimated using the method described by Bondi.33 The investigated systems are regarded as possessing three types of surface: • an aliphatic surface type “a” (CH3, CH2 or H groups) in hexacosane. • an aromatic surface type “b” (C6H5 or C6H4 groups) in biphenyl or dibenzofuran. • an ether surface type “e” (O in cyclic ether) in dibenzofuran. The geometrical parameters, namely, relative volumes ri, relative total surfaces qi, and molecular surface fractions αs (s = a, b, or e), for the present compounds in the mixture are listed in Table 3.

Figure 2. Solid−liquid equilibria for dibenzofuran (1) + biphenyl (2) system compared with the literature data. ■, experimental points; ▲, literature results.36

Table 5. Experimental Soild−Liquid Equilibria Temperatures for the System Hexacosane (1) + (2) Dibenzofuran at Pressure p = 0.1 MPaa

Table 3. Geometrical Parameters compounds

ri

qi

αa

αb

αe

hexacosane dibenzofuran biphenyl

15.9381 5.0569 5.2465

12.6345 3.2640 3.5928

1.0000 0.0000 0.0000

0.0000 0.9345 1.0000

0.0000 0.0655 0.0000

x1

Te/K

Tm/K

solid phaseb

0.0000 0.0998 0.2009 0.3001 0.4000 0.5000 0.5986 0.7000 0.8101 0.8902 1.0000

323.25 323.35 323.25 322.55 323.32 323.33 323.45 323.14 323.27 326.40c

353.87 348.44 338.90 334.15 329.35 323.32 324.37 325.47 326.15 326.25 329.21

dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, I)

a Uncertainties u are u(T) = 0.5 K, u(x) ≤ 0.0005 and u(p) = 0.1 kPa for all solid−liquid measurements. b(cr) stands for a single solid phase and hexacosane(cr, I) and hexacosane(cr, II) correspond to the solid phase I and solid phase II, respectively. cTemperature of solid−solid transition.

Estimation of Interchange Parameters. The three types of surface previously identified generate three contact types: • (a,b) in (hexacosane + biphenyl) or (hexacosane + dibenzofuran) systems B

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Table 6. Experimental Solid−Liquid Equilibria Temperatures for the System Hexacosane (1) + (2) Biphenyl at Pressure p = 0.1 MPaa x1 0.0000 0.1098 0.2004 0.2970 0.4001 0.4607 0.5023 0.6008 0.7002 0.8062 0.9112 1.0000

Te/K

Tm/K

solid phaseb

321.89 322.19 322.27 321.54 321.93 321.78 321.87 321.95 322.02 322.11 326.40c

340.69 336.94 333.37 329.54 321.54 323.46 323.78 324.82 325.07 326.22 328.25 329.21

biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr,I) hexacosane(cr, I)

Table 9. Experimental Solid−Liquid Equilibria Temperatures for the System (Hexacosane + Dibenzofuran + Biphenyl), with xbiphenyl/xhexacosane =3 at Pressure p = 0.1 MPaa

a Uncertainties u are u(T) = 0.5 K, u(x) ≤ 0.0005, and u(p) = 0.1 kPa for all solid−liquid measurements. b(cr) stands for a single solid phase and hexacosane(cr, I) and hexacosane(cr, II) correspond to the solid phase I and solid phase II, respectively. cTemperature of solid−solid transition.

0.0000 0.1002 0.2001 0.3001 0.4000 0.5000 0.6000 0.7000 0.8002 0.9001 1.0000

Te/K

321.30 321.85 322.28 321.99 322.11 322.35 321.97 321.65

Tm/K

solid phaseb

340.69 335.96 330.89 329.02 326.57 321.99 330.47 338.11 341.45 346.90 353.87

biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr)

316.89 316.83 316.97 316.81 316.89 316.50 317.07 316.99 316.52 316.48

322.19 321.69 320.45 319.00 317.30

334.34 330.30 326.85 322.66 318.92 319.61 322.13 326.51 333.24 337.23 342.91 348.11 353.87

biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr)

318.47 318.84 318.23

Tbe/K

Tm/K

solid phase

337.02 335.86 333.04 325.91 318.92 321.97 323.20 324.62 326.85 331.26 336.39 340.69

dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr) biphenyl(cr)

xhexacosane

Tte/K

Tbe/K

Tm/K

solid phaseb

0.0000 0.0570 0.1006 0.2006 0.3105 0.3999 0.4999 0.6000 0.7004 0.8109 0.8999 1.0000

316.87 316.86 316.86 316.94 316.91 316.85 316.89 316.92 316.92 316.86

322.69 321.15 320.11 318.14 320.96 321.10 321.32 322.21 322.40 322.87 322.65 326.40c

339.23 337.08 335.70 331.28 326.21 321.10 322.66 323.46 324.10 325.57 326.09 329.21

dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) dibenzofuran(cr) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, II) hexacosane(cr, I)

Uncertainties u are u(T) = 0.5 K, u(x) ≤ 0.0005, and u(p) = 0.1 kPa for all solid−liquid measurements. b(cr) stands for a single solid phase and hexacosane(cr, I) and hexacosane(cr, II) correspond to the solid phase I and solid phase II, respectively. cTemperature of solid−solid transition.

although those of literature are slightly higher. This is consistent with the relatively higher melting temperatures of pure substances used by the authors. Table 5 to 10 present solid−liquid equilibria experimental results for binary and ternary mixtures. These results are compared with DISQUAC calculation as shown on Figures 3 to 8. A polynomial fitting of the experimental results was carried out according the following equation:

b

323.35 322.10 321.31 317.87

318.37 318.28 318.55 318.89 319.59

solid phaseb

a

Table 8. Experimental Solid−Liquid Equilibria Temperatures for the System (Hexacosane + Dibenzofuran + Biphenyl), with xdibenzofuran/xhexacosane = 3 at Pressure p = 0.1 MPaa Tte/K

316.61 316.89 316.93 316.87 316.71 316.80 316.85 316.89 316.93 316.96 316.71

Tm/K

Table 10. Experimental Solid−Liquid Equilibria Temperatures for the System (Hexacosane + Dibenzofuran + Biphenyl), with xdibenzofuran/xbiphenyl =3 at Pressure p = 0.1 MPaa

Uncertainties u are u(T) = 0.5 K, u(x) ≤ 0.0005, and u(p) = 0.1 kPa for all solid−liquid measurements. b(cr) stands for a single solid phase.

0.0000 0.0490 0.1002 0.2001 0.2901 0.4106 0.5000 0.6008 0.6902 0.8000 0.9057 1.0000

0.0000 0.0490 0.1103 0.2100 0.2908 0.3500 0.4000 0.4948 0.6069 0.6999 0.7998 0.9001 1.0000

Tbe/K

Uncertainties u are u(T) = 0.5 K, u(x) ≤ 0.0005, and u(p) = 0.1 kPa for all solid−liquid measurements. b(cr) stands for a single solid phase.

a

xbiphenyl

Tte/K

a

Table 7. Experimental Solid−Liquid Equilibria Temperatures for the System Dibenzofuran (1) + (2) Biphenyl at Pressure p = 0.1 MPaa x1

xdibenzofuran

2 T = P0 + Px 1 i + P2xi

(3)

Tables 11 and 12 report the values of the parameters P0, P1, and P2, standard deviations SD, and coefficients of determination R2 corresponding to the two liquidus branches and the binary eutectic curves, respectively. Concerning the ternary mixtures, tree isopleth cuts (vertical sections) were performed as follows: xbiphenyl/xhexacosane = 3, xdibenzofuran/xhexacosane = 3, and xdibenzofuran/xbiphenyl = 3.

Uncertainties u are u(T) = 0.5 K, u(x) ≤ 0.0005, and u(p) = 0.1 kPa for all solid−liquid measurements. b(cr) stands for a single solid phase. a

C

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Table 13. Eutectic Points for Studied Binary Systems x1 system

Te/K

ideal model

DISQUAC model

ideal model

DISQUAC model

0.463

0.490

321.74

324.38

0.350

0.414

319.58

320.87

0.400

0.384

315.75

319.57

hexacosane (1) + dibenzofuran (2) hexacosane (1) + biphenyl (2) dibenzofuran (1) + biphenyl (2)

Figure 3. Solid−liquid phase diagram for hexacosane (1) + (2) dibenzofuran system. -+-, DISQUAC model; -·-, UNIFAC model; dashed line, ideal model; solid line, polynomial fitting; ■, experimental points.

All binary diagrams are simple eutectic systems. The ternary mixtures possess a ternary eutectic point and present binary eutectic temperatures (Tbe). For a comparison with the experimental results, the binary and the ternary eutectic points, Te and Tte, calculated with DISQUAC and ideal models are summarized in Tables 13 and 14. The following equation allows the solubility calculation of component i in a liquid:8 ΔHm, i ⎛ 1 1 ⎞ ΔHtr , i ⎛ 1 1 ⎞ ⎜⎜ − ⎟⎟ − ⎜⎜ − ⎟⎟ R ⎝T Tm, i ⎠ R ⎝T Ttr , i ⎠ ΔC P, i ⎡ (Tm, i − T ) T ⎤ ⎢ ⎥ − ln γi + + ln R ⎢⎣ T Tm, i ⎥⎦

Figure 4. Solid−liquid phase diagram for hexacosane (1) + biphenyl (2) system. -+-, DISQUAC model; -·-, UNIFAC model; dashed line, ideal model; solid line, polynomial fitting; ■, experimental points.

ln xi = −

where ΔHm,i, Tm,i, ΔCP,i, ΔHtr,i, and Ttr,i are respectively the molar enthalpy of melting, the melting temperature, the molar heat capacity change (assumed to be independent of operating temperature T during the melting process), the enthalpy

(4)

Table 11. Parameters, Standard Deviations, and Coefficients of Determination of Polynomial Fitting binary or pseudobinary system hexacosane (1) + dibenzofuran (2) hexacosane (1) + biphenyl (2) dibenzofuran (1) + biphenyl (2) (dibenzofuran + hexacosane) (1) + biphenyl (2) (biphenyl + hexacosane) (1) + dibenzofuran (2) (dibenzofuran + biphenyl) (1) + hexacosane (2)

liquidus branch

p0

P1

P2

SD

R2

1 2 1 2 1 2 1 2 1 2 1 2

324.015 354.294 318.483 340.432 277.830 340.346 337.349 320.180 331.880 302.714 339.168 320.860

−6.455 −75.437 8.772 20.779 104.267 −45.323 −34.307 −10.906 −41.881 46.661 −32.385 −2.382

11.198 28.125 1.838 −63.758 −29.125 20.053 −102.941 31.349 −9.580 4.395 −31.608 10.156

0.671 1.242 0.593 0.817 1.502 1.091 0.536 0.743 0.439 0.351 0.156 0.631

0.933 0.993 0.960 0.993 0.989 0.983 0.997 0.993 0.996 0.999 0.999 0.962

Table 12. Parameters, Standard Deviations, and Coefficients of Determination of Polynomial Fitting for the Binary Eutectic Temperatures pseudobinary system (dibenzofuran + hexacosane) (1) + biphenyl (2) (biphenyl + hexacosane) (1) + dibenzofuran (2) (dibenzofuran + biphenyl) (1) + hexacosane (2)

binary eutectic curve a

1 1a 1 2

P0

P1

P2

SD

R2

323.253 322.229 322.620 307.402

−15.709 −13.260 −13.520 74.534

−55.256 −12.327 −137.940 −100.506

0.327 0.173 0.364 0.230

0.993 0.996 0.992 0.996

a

Just one curve representing binary eutectic temperature was drawn, because there are no experimental points between the ternary invariant (the lower horizontal solid line) and pseudobinary invariant (the higher horizontal solid line). D

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Table 14. Eutectic Coordinates of the Ternary System Hexacosane (1) + Dibenzofuran (2) + Biphenyl (3) ideal model

DISQUAC model

x1

x2

x3

Tte/K

x1

x2

x3

Tte/K

0.177

0.322

0.500

307.89

0.209

0.294

0.495

312.69

DISQUAC model was then applied to predict ternary data. For the isopleth cut xbiphenyl/xhexacosane = 3 of (hexacosane + dibenzofuran + biphenyl) system (Figure 7), calculation and

Figure 5. Solid−liquid phase diagram for dibenzofuran (1) + biphenyl (2) system. -+-, DISQUAC model; -·-, UNIFAC model; dashed line, ideal model; solid line, polynomial fitting; ■, experimental points. Figure 7. Solid−liquid phase diagram for (hexacosane + dibenzofuran + biphenyl) system, xbiphenyl/xhexacosane = 3. -+-, DISQUAC model; dashed line, ideal model; solid line, polynomial fitting; ■, experimental points.

experiment agree generally well. Nevertheless the eutectic region is poorly represented. Unsatisfactory results were obtained by DISQUAC prediction in the isopleth cuts xdibenzofuran/xhexacosane = 3 and xdibenzofuran/xbiphenyl = 3 (Figures 6 and 8). It seems that the

Figure 6. Solid−liquid phase diagram for (hexacosane + dibenzofuran + biphenyl) system, xdibenzofuran/xhexacosane =3. -+-, DISQUAC model; dashed line, ideal model; solid line, polynomial fitting; ■, experimental points.

change corresponding to the transition, and the transition temperature of the pure component i. R is the universal gas constant, γi is the activity coefficient and xi is the mole fraction of component i in the liquid phase. The value of ΔCP,i is rather weak so that it can be neglected.37 In Figures 3 to 5, it can be seen that DISQUAC fairly represents the experimental results in binary systems, except for the middle area of (dibenzofuran + biphenyl) phase diagram where calculated values are smaller than the experimental ones. For comparison, the UNIFAC model38−40 was tested for the three binary systems (Figures 3 to 5). The prediction with DISQUAC provides generally better results than UNIFAC calculation for these binary systems. Consequently, it is expected that DISQUAC ternary results are better than those from UNIFAC.

Figure 8. Solid−liquid phase diagram for (hexacosane + dibenzofuran + biphenyl) system, xdibenzofuran/xbiphenyl = 3. -+-, DISQUAC model; dashed line, ideal model; solid line, polynomial fitting; ■, experimental points.

model overestimates or underestimates the experimental values concerning the first and the second depositions of compounds, notably in the left region of phase diagrams. E

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ACKNOWLEDGMENTS One of the authors (Abdelaziz Chikh Baelhadj) would like to thank the Thermodynamique et Energie team of LRGP for their assistance and welcome in the laboratory.

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Figure 9. DISQUAC results for solid−liquid ternary system hexacosane (1) + dibenzofuran (2) biphenyl (3). Dashed line, isothermal lines; solid line, eutectic lines.

The solid−liquid diagram of the ternary system is shown in Figure 9. In this figure, the isotherms (dashed lines) and eutectic (solid lines) were plotted using DISQUAC calculations. Furthermore, it can be observed, through the figures, that the polynomial fitting reproduce correctly the experimental data. Coefficients of determination R2 summarized in Tables 11 and 12 are superior than 0.93.

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CONCLUSION Micro DSC was used to determine solid−liquid phase diagrams for ternary mixtures containing long-chain alkanes and aromatics. (Hexacosane + dibenzofuran + biphenyl) mixtures and their related binary systems were investigated and behavior of these components in mixtures was described. It was found that the behavior of binary and ternary mixtures is relatively simple. In fact, liquid mixtures are miscible in the whole range of composition; there is no solid solution and no association phenomena too. DISQUAC calculation presents some deviations from experimental data in the middle of (dibenzofuran + biphenyl) phase diagram. Except for the isopleth cut xbiphenyl/xhexacosane = 3, the calculation in the case of the (hexacosane + dibenzofuran + biphenyl) system was unsatisfactory. This is may be due to the fact that DISQUAC interchange parameters for (b,e) contact are not suitable. In fact, the interchange parameters for (b,e) contact were evaluated from binary experimental data concerning aromatic ether with alkane (n-heptane).33 It seems that (b,e) contact in dibenzofuran + hexacosane is not exactly the same as in aromatic ether + n-heptanes. In this case, suitable experimental data (GE and HE) are needed to evaluate the specific interchange parameters (b,e).

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