Thermodynamics of mixtures containing organic carbonates

Fluid Phase Equilibria 200 (2002) 349–374

Thermodynamics of mixtures containing organic carbonates Part XIII. Solid–liquid equilibria of long-chain 1-alkanol + dimethyl or diethyl carbonate systems: DISQUAC and ERAS analysis of the hydroxyl/carbonate interactions J.A. Gonzalez a,∗ , M. Szurgocinska a , U. Domanska b a

b

G.E.T.E.F., Departamento de Termodinámica y F´ısica Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain Physical Chemistry Division, Faculty of Chemistry, Warsaw University of Technology, 00-664 Warsaw, Poland Received 5 October 2001; accepted 11 January 2002

Abstract Solid–liquid equilibrium temperatures for systems of 1-tetradecanol, 1-hexadecanol, 1-octadecanol, or 1-icosanol with dimethyl or diethyl carbonate have been measured using a dynamic method. The alcohols present two first order transitions. 1-Alkanols + linear organic carbonates mixtures are studied using DISQUAC and ERAS models. The corresponding interaction parameters are reported. They behave similarly in both models. In DISQUAC, the QUAC parameters are independent of the mixture compounds, as in many other alcoholic solutions previously analyzed. The DIS parameters increase with the size of the alcohol. They remain constant for the longer alcohols. In ERAS, ∗ is independent of the mixture components, while h∗ depends only on the carbonate. vAB AB DISQUAC yields a consistent description of the thermodynamic properties examined: vapor–liquid equilibria molar excess Gibbs energies, Solid–liquid equilibria and molar excess enthalpies. DISQUAC improves ERAS results on excess molar enthalpies, as the calculated curves using ERAS are shifted to the region of low concentration in alcohol. This means that, in terms of ERAS, the contribution to the excess molar enthalpy from the self-association of the alcohol is overestimated. Molar excess volumes are well represented by ERAS. From the analysis of the excess molar enthalpy curves, it is concluded that they are determined mainly by dipolar interactions between carbonate molecules. Excess molar volumes are relatively low indicating strong structural effects. © 2002 Elsevier Science B.V. All rights reserved. Keywords: SLE; Long-chain 1-alkanols; Organic carbonates; Models; Interactions

∗

Corresponding author. Fax: +34-983-423136. E-mail address: [email protected] (J.A. Gonzalez). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 2 ) 0 0 0 4 5 - 6

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1. Introduction Organic carbonates, linear or cyclic, are widely employed in the industry. They are used in the synthesis of organic compounds [1], e.g. pharmaceuticals [2] and agricultural chemicals, and as solvents for many synthetic and natural resins [3]. They are also important in the Li battery technology [4–6]. Dimethyl carbonate (DMC) is used in the replacement of hazardous chemicals [7–9], as fuel additive [10] or in the design of new refrigerants [11]. From a theoretical point of view, the study of linear organic carbonates is a previous step to the analysis of cyclic carbonates, ethylene or propylene carbonates. It is well known that the position of a given functional group in a ring or in an open chain may change considerably the molecular properties, and hence, the interaction parameters when mixtures of these compounds are studied theoretically. This is the case in solutions of linear or cyclic secondary and tertiary amines [12], oxaalkanes [13–16] or ketones [17]. On the other hand, propylene carbonate is an aprotic solvent of high dipole moment which is interesting to be studied in view of its local structure [18,19]. In the framework of the TOM Project (Thermodynamics of Organic Mixtures) [20,21], the OCO program is developed to get a better understanding of the interactions between the O (oxygen) and CO (carbonyl) groups in the same or in different molecules. Particularly, we are engaged in a systematic study of mixtures involving organic carbonates (OCOO group). Up to now, we have reported data on vapor–liquid equilibria (VLE) [22–25], liquid–liquid equilibria (LLE) [26,27], excess molar enthalpy (HmE ) [28,29], excess molar volume (VmE ) [30,31] and Solid–liquid equilibria (SLE) [27,32] of systems formed by DMC or diethyl carbonate (DEC) and alkanes, benzene, toluene, or CCl4 . We have also presented the characterization of the OCOO/aliphatic, OCOO/cyclic; OCOO/aromatic and OCOO/CCl4 contacts [33–35] in terms of the DISQUAC model [20,21]. In previous articles of this series [27,32], we have examined the ability of DISQUAC to describe SLE measurements of systems formed by DMC or DEC and long chain alkanes. Now, we report SLE for DMC or DEC and 1-tetradecanol, 1-hexadecanol, 1-octadecanol or 1-icosanol. These data, together with those available in the literature on VLE [8,36] and HmE [36–40] for linear organic carbonates + 1-alkanols mixtures, are used for the characterization of the OCOO/OH contacts in terms of DISQUAC. At this end, we have previously measured VLE of the 1-hexanol + DMC or + DEC mixtures [41]. The systems are also analyzed using the ERAS model [42].

2. Experimental 2.1. Materials The origin of the chemicals (in parentheses Chemical Abstracts registry numbers) are: 1-tetradecanol (112-72-1, Merck AG); 1-hexadecanol (36653-82-4, Fluka AG), 1-octadecanol (112-92-5. POCh), 1-eicosanol (629-96-9, Merck AG). DMC (616-38-6) and DEC (105-58-8) (anhydrous, mole fraction >99%) were supplied by Aldrich and stored over freshly activated molecular sieves of type 4 Å (Union Carbide). All compounds were checked by GLC analysis and no significant impurities were found. The purity of 1-alkanols was 98 or 99%. Physical properties of pure compounds are collected in Table 1.

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Table 1 Physical constants of long-chain 1-alkanols: Tfus , melting point; Hfus , molar heat of fusion and Htrs , molar heat of transition Compound

Tfus (K)

Hfus a (J mol−1 )

Htrs a (J mol−1 )

17500 (β 2130 (γ 19970 (β 3310 (γ

→ α)g → β)g → α)g → β)g

22400 (β 4500 (γ 25000 (β 5700 (γ

→ α)g → β)g → α)g → β)g

This work

Literature

1-Tetradecanol

312.36

20140

1-Hexadecanol

323.02

1-Octadecanol

331.70

310.79b 311.15c 322.50d 322.65c 322.85e 331.65c

1-Icosanol

336.44

336.50f 338.15c

68600

34080

47200

a

[101,102]. [103]. c [45]. d [104]. e [105]. f [46]. g Type of transition. b

2.2. Apparatus and procedure Solid–liquid equilibrium temperatures were determined using a dynamic method described in detail earlier [43,44]. Mixtures were heated very slowly (at <2 K h−1 near the equilibrium temperature) with continuous stirring inside a Pyrex glass cell, placed in a thermostat. The crystal disappearance temperatures, detected visually, were measured with a DOSTMANN GmbH (Germany) electronic thermometer, which was totally immersed in the thermostating liquid. The thermometer was calibrated on the basis of the ITS-90 temperature scale. The precision of temperature measurements was ±0.01 K and the reproducibility was ±0.1 K. The error in the mole fraction did not exceed δx1 = 0.0005. In many solvents it is possible to observe the change of structure of the crystals during the crystallization [45] accompanied by the characteristic inflection on the liquidus curve. 2.3. Results and data analysis Tables 2–9 list the direct experimental results of the solid–liquid equilibrium temperatures, T, versus x1 , the mole fraction of the 1-alkanols, for the investigated mixtures (see Fig. 1). The 1-alkanols studied show two first order transitions in the solid phase (Table 10). The same trend has been observed in other alcoholic mixtures previously investigated, namely those formed by long-chain 1-alcohols + n-alkanes [46,47]; + benzene or + toluene [48]; + cyclohexane or + tetrachloromethane [49], or shorter 1-alkanols [50]. It seems that the solid–solid transitions may be changed by the presence of the solvent [46–51]. The same behaviour is also observed, e.g. in the case of long n-alkanes [52,53] or cholesterol [54].

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Table 2 Experimental solid–liquid equilibrium temperatures for the 1-tetradecanol (1) + DMC (2) mixturea x1

Tα 1 (K)

0.9546 0.9300 0.8953 0.8717 0.8400 0.8148 0.7900 0.7597 0.7324 0.6874 0.6504 0.6121 0.5788 0.5294 0.4802 0.4398 0.3934 0.3500 0.3063 0.2710 0.2266 0.1900 0.1572

311.47 310.93 310.42 310.03 309.43 308.88

a

Tβ 1 (K)

Tγ 1 (K)

308.65 308.42 308.11 307.64 307.21 306.65 306.25

x1

Tγ 1 (K)

0.1208 0.1194 0.0913 0.0744 0.0599 0.0503 0.0412 0.0248 0.0123 0.0037

302.07 302.00 301.43 300.64 299.52 298.51 297.26 294.03 287.56 281.58

305.73 305.35 305.04 304.69 304.35 303.96 303.66 303.31 302.94 302.57

The Greek subscripts mean the type of the solid phase of the alcohol.

3. Theory 3.1. DISQUAC In the framework of DISQUAC, mixtures of 1-alkanols with linear organic carbonates are regarded as possessing three types of surfaces: (i) type a, (aliphatic: CH3 , CH2 in 1-alkanols or carbonates; (ii) type d (OCOO in linear organic carbonates); (iii) type h (hydroxyl, OH in 1-alkanols). 3.1.1. Assessment of geometrical parameters When DISQUAC is applied, the total relative molecular volumes, ri , surfaces, qi , and the molecular surface fractions, α si , of the compounds present in the mixture are usually calculated additively on the basis of the group volumes VG and surfaces AG , recommended by Bondi [55]. As volume and surface units, the volume VCH4 and surface ACH4 of methane are taken arbitrarily [56]. The geometrical parameters referred to in this work are given elsewhere [35,57]. 3.1.2. Equations The equations used to calculate GEm and HmE are the same as in other applications [57]. The interaction terms in the excess thermodynamic properties GEm and HmE contain a DIS and a QUAC contribution which are calculated independently by the classical formulas and then simply added.

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Table 3 Experimental solid–liquid equilibrium temperatures for the 1-hexadecanol (1) + DMC (2) mixturea x1

Tα 1 (K)

0.9667 0.9133 0.8788 0.8491 0.8226 0.8068 0.7778 0.7511 0.7201 0.6897 0.6593 0.6269 0.6047 0.5782 0.5496 0.5100 0.4785 0.4402 0.3996 0.3585 0.3141 0.2667 0.2283

322.46 321.99

a

Tβ 1 (K)

Tγ 1 (K)

321.56 321.17 320.67 320.39 319.98 319.51 318.94 318.43 317.97 317.49 317.18 316.77 316.40

x1

Tγ 1 (K)

0.1749 0.1320 0.0882 0.0635 0.0487 0.0468 0.0380 0.0217 0.0094

313.18 312.30 311.11 309.57 308.26 307.75 306.09 302.43 298.31

316.05 315.80 315.48 315.18 314.83 314.51 314.18 313.80

The Greek subscripts mean the type of the solid phase of the alcohol.

The degree of non-randomness is thus expressed by the relative amounts of dispersive and quasichemical terms: + GE,DIS GEm = GE,COMB + GE,QUAC m m m

(1)

HmE = HmE,DIS + HmE,QUAC

(2)

where GE,COMB is the Flory-Huggins combinatorial term [56,58]. m For the QUAC part, as coordination number the reference value was chosen, that is z = 4. The temperature dependence of the interaction parameters has been expressed in terms of the DIS and QUAC DIS QUAC interchange coefficients Cst,l and Cst,l [57], where s, t = a, d, h and l = 1, Gibbs energy; l = 2, enthalpy; and l = 3, heat capacity. T0 = 298.15 K is the scaling temperature. The equation of the solid–liquid equilibrium curve of a pure solid component 1 including two first order transitions is, for temperatures below that of the phase transitions [59,60]:



      Htrs1 Htrs1 Hfus1 1 1 1 1 1 1 −ln x1 = − + + −  −  + ln γ1 R T Tfus1 R T Ttrs1 R T Ttrs1 (3)

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Table 4 Experimental solid–liquid equilibrium temperatures for the 1-octadecanol (1) + DMC (2) mixturea x1

Tα 1 (K)

0.9788 0.9572 0.9480 0.9159 0.8752 0.8122 0.7746 0.7171 0.6779 0.6256 0.5912 0.5448 0.5179 0.4829 0.4510 0.4219 0.3964 0.3546 0.3308 0.2872 0.2638 0.2522 0.2174

330.83 330.11 329.95

a

Tβ 1 (K)

Tγ 1 (K)

329.28 328.71 328.09 327.64 327.07 326.67 326.14 325.83 325.38 325.11 324.78 324.53 324.25 323.98 323.56

x1

Tγ 1 (K)

0.1749 0.1370 0.1135 0.0924 0.0782 0.0651 0.0500 0.0254 0.0137 0.0088

321.32 320.57 320.03 319.23 318.31 317.33 315.84 312.03 307.93 304.31

323.30 322.84 322.54 322.38 321.91

The Greek subscripts mean the type of the solid phase of the alcohol.

Conditions at which Eq. (3) is valid have been specified elsewhere [48]. In Eq. (3), x1 is the mole fraction and γ 1 the activity coefficient of component 1 in the solvent mixture, at temperature T. In this work, DISQUAC is used to calculate γ 1 Hfus1 , Tfus1 are, respectively, the molar enthalpy of fusion and the the     melting temperature of component 1, while Htrs1 , Htrs1 , Ttrs1 , Ttrs1 , stand for the molar enthalpies of transition and transition temperatures, respectively. The terms, in Eq. (3), related to the molar heat capacity change during the melting/transition process of component 1 have been neglected because of the lack of reliable data and of negligible influence of those terms on solubility calculations for the investigated mixtures. 3.2. The ERAS model This model combines the real association solution model [61–64] with Flory’s equation of state [65]. E E E The excess functions are written as Xm = Xm,phys +Xm,chem where X is G (Gibbs energy), H (enthalpy), V E E represents (volume). Xm,chem is the chemical contribution, mainly due to association reactions, and Xm,phys the physical contribution, a consequence of the physical interactions between molecules. Expressions for these terms when cross-association between compounds exist are given elsewhere [66–68] for X = H , and V and will not repeated here.

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Table 5 Experimental solid–liquid equilibrium temperatures for the 1-icosanol (1) + DMC (2) mixturea x1

Tα 1 (K)

0.9215 0.8649 0.8111 0.7698 0.7344 0.7094 0.6779 0.6382 0.5993 0.5518 0.4986 0.4600 0.4093 0.3664 0.3246 0.2845 0.2297 0.1712 0.1198 0.0828 0.0456 0.0192 0.0100 0.0079

335.76 335.07

a

Tβ 1 (K)

Tγ 1 (K)

334.28 333.60 332.87 332.35 331.69 330.85 330.07 329.16 328.13 327.45 326.55 325.90 325.20 324.59 323.90 323.16 322.25 321.39 319.83 316.62 312.97 311.74

The Greek subscripts mean the type of the solid phase of the alcohol.

The chemical contribution to the excess properties arises from chemical interactions between the molecules, in particular hydrogen bonding. It is assumed that there is an equilibrium of linear chain association of the component A (alcohol) KA

Am + A↔Am+1

(4)

with m being the degree of self association, ranging from 1 to ∞. Linear organic carbonates (B) are considered to be not self-associated. The cross-association between A and B molecules is represented by KAB

Am + B ↔ Am B

(5)

The association constants Ki are assumed to be independent of the chain length. Their temperature dependence is given by  
∗
hi 1 1 Ki = K0 exp − (6) − R T T0 where K0 is the equilibrium constant at the standard temperature T0 (298.15 K) and h∗i is the enthalpy variation for reactions 4–5, which corresponds to the hydrogen bond energy. Reactions 4–5 are also characterized by the volume change vi∗ , related to the formation of the linear chains.

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Table 6 Experimental solid–liquid equilibrium temperatures for the 1-tetradecanol (1) + DEC (2) mixturea x1

Tα 1 (K)

0.9125 0.8915 0.8750 0.8598 0.8498 0.8244 0.7981 0.7758 0.7485 0.7221 0.6889 0.6518 0.6099 0.5671 0.5264 0.5001 0.4630 0.4302 0.4027 0.3691 0.3378 0.3097 0.2814

311.00 310.40 309.85 309.35 309.00

a

Tβ 1 (K)

Tγ 1 (K)

308.72 308.36 307.96 307.57 307.03 306.39 306.07 305.60 305.16 304.73 304.40 303.94 303.50 303.09 302.54 302.05 301.65 301.26

x1

Tγ 1 (K)

0.2481 0.2112 0.1673 0.1324 0.1100 0.0938 0.0733 0.0627 0.0516 0.0389 0.0281 0.0233 0.0136 0.0088

300.63 299.90 298.34 297.11 295.81 294.38 292.79 291.61 290.24 288.18 285.26 283.23 278.42 274.36

The Greek subscripts mean the type of the solid phase of the alcohol.

E Xm,phys is derived from Flory’s equation of state [65], which is assumed to be valid not only for pure components but also for the mixture: 1/3 V¯ P¯i V¯i 1 − = 1/3i T¯i V¯i − 1 (V¯i T¯i )

(7)

where i = A, B, M (mixture). In Eq. (7), V¯i = Vi /Vi∗ ; P¯i = P /Pi∗ and T¯i = T /Ti∗ are the reduced parameters, volume, pressure and temperature, respectively. The reduction parameters for pure components Vi∗ , Pi∗ , and Ti∗ are calculated previous determination of density, thermal expansion coefficient and isothermal compressibility. They also depend on Ki , h∗i , vi∗ . The method is clearly explained elsewhere [66,67]. The reduction parameters for the mixture PM∗ and TM∗ are calculated via the certain mixing rules [66,67] where XAB , the energetic interaction parameter characterizing the difference of dispersive intermolecular interactions between molecules A and B in the solution and in the pure components is introduced. It is the only adjustable parameter of the physical part of HmE and VmE . It must be mentioned that the total relative molecular volumes and surfaces of the components present in the analyzed mixtures were calculated additively on the basis of the Bondi’s method [55].

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Table 7 Experimental solid–liquid equilibrium temperatures for the 1-hexadecanol (1) + DEC (2) mixturea x1

Tα 1 (K)

0.8875 0.8860 0.8591 0.8271 0.7969 0.7692 0.7481 0.7159 0.6807 0.6447 0.6131 0.5792 0.5433 0.4972 0.4434 0.4104 0.3747 0.3377 0.3077 0.2816 0.2610 0.2034 0.1731 0.1400

321.98 321.94

a

Tβ 1 (K)

Tγ 1 (K)

321.45 320.91 320.40 319.90 319.56 319.07 319.07 317.88 317.30 316.73

x1

Tγ 1 (K)

0.1063 0.0764 0.0612 0.0452 0.0213 0.0134 0.0086

307.97 306.58 304.06 300.78 295.01 290.07 286.21

316.30 315.68 314.92 314.34 313.75 313.17 312.68 312.22 311.83 310.83 310.10 309.16

The Greek subscripts mean the type of the solid phase of the alcohol.

4. Estimation of the adjustable parameters 4.1. DISQUAC interaction parameters The three types of surface generate three pairs of contacts: (a, d), (a, h) and (d, h). The aliphatic/carbonate (a, d) and the aliphatic/hydroxyl (a, h) interactions are represented by DIS and QUAC coefficients calculated on the basis of experimental data for linear organic carbonates [35] or 1-alkanols + n-alkanes [57,69,70] systems, respectively. So, because the (a, d) and (a, h) parameters are known, only those for the (d, h) contacts must be obtained. The general procedure applied has been explained in detail elsewhere [57,68]. Final interaction parameters are listed in Table 11. 4.2. ERAS parameters Reduction parameters for pure compounds are listed in Table 12. The parameters adjustable to excess ∗ properties are KA , KAB , h∗A , h∗AB , vA∗ , vAB , XAB . KA and h∗A are known for all alcohols from HmE of alcohol + alkane mixtures (Table 12). vA∗ is also known, as it is fitted to VmE of alcohol + alkane

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Table 8 Experimental solid–liquid equilibrium temperatures for the 1-octadecanol (1) + DEC (2) mixturea x1

Tα 1 (K)

0.9550 0.9369 0.9239 0.8931 0.8661 0.8161 0.7813 0.7332 0.6955 0.6502 0.5978 0.5579 0.5244 0.4920 0.4639 0.4296 0.3996 0.3785 0.3560 0.3315 0.2934 0.2413 0.2084

330.05

a

Tβ 1 (K)

Tγ 1 (K)

329.70 329.52 329.23 328.87 328.41 327.93 327.38 326.91 326.36 325.76 325.33 324.97 324.52 324.16 323.67 323.23 322.88 322.54 322.04 321.33 320.39 319.72

x1

Tγ 1 (K)

0.1728 0.1410 0.1078 0.0849 0.0726 0.0640 0.0550 0.0498 0.0409 0.0334 0.0269 0.0202 0.0151 0.0118 0.0079

318.56 317.31 315.89 314.69 313.62 312.65 311.15 310.43 308.54 306.97 305.42 303.37 301.31 299.08 295.79

The Greek subscripts mean the type of the solid phase of the alcohol

∗ systems (Table 12). The remaining parameters KAB , h∗AB , vAB and XAB are adjusted to HmE and VmE data for 1-alkanols + linear organic carbonates. More details are given in literature [66,67]. When HmE data at 298.15 K were not available, DISQUAC values were used to determine the ERAS parameters [71]. They are listed in Table 13.

5. Comparison with experiment 5.1. DISQUAC results The DISQUAC results are listed in Tables 14–17 for VLE, GEm , SLE and HmE . Figs. 1–7 show graphically DISQUAC calculations for some selected systems. For the sake of clarity, Tables 14 and 16 include standard relative deviations for pressure (P) or SLE temperatures defined as: 
  1/2  1  (Mexp − Mcalc ) 2 σr (M) = (8) N Mexp

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Table 9 Experimental solid–liquid equilibrium temperatures for the 1-icosanol (1) + DEC (2) mixturea x1

Tα 1 (K)

0.9482 0.9247 0.8853 0.8649 0.8401 0.8088 0.7861 0.7608 0.7376 0.7092 0.6684 0.6293 0.6049 0.5778 0.5369 0.5141 0.4769 0.4393 0.4202 0.3881 0.3688 0.3468 0.3249 0.3190

335.66 335.31 334.70 334.30

a

Tβ 1 (K)

334.07 333.62 333.30 332.86 332.45 331.88 331.08 330.32 329.86 329.40 328.53 328.10 327.11 326.18 325.65 324.93 324.48 323.97 323.47 323.24

x1

Tγ 1 (K)

0.2988 0.2674 0.2346 0.2176 0.1927 0.1591 0.1254 0.0838 0.0687 0.0500 0.0309 0.0132 0.0053

322.79 322.12 321.41 320.96 320.32 319.53 318.23 316.33 315.10 313.14 310.41 305.33 299.76

The Greek subscripts mean the type of the solid phase of the alcohol.

Table 10 Transition points in 1-alkanols (1) + linear organic carbonates (2) mixtures System

1-Tetradecanol(1) + DMC(2) 1-Hexadecanol(1) + DMC(2) 1-Octadecanol(1) + DMC(2) 1-Icosanol(1) + DMC(2) 1-Tetradecanol(1) + DEC(2) 1-Hexadecanol(1) + DEC(2) 1-Octadecanol(1) + DEC(2) 1-Icosanol(1) + DEC(2)

Transition (β → α)

Transition (γ → β)

Ttrs (K)

x1trs

Ttrs (K)

x1trs

308.88 321.99 329.95 335.07 309.00 321.94 330.05 334.30

0.8148 0.9133 0.9480 0.8649 0.8498 0.8860 0.9550 0.8649

305.93 316.15 323.56 325.20 306.39 316.73 325.95 323.24

0.5550 0.5298 0.3546 0.6889 0.3246 0.5792 0.6240 0.3190

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Fig. 1. SLE curves for 1-alkanol (1) + DEC (2) mixtures. Points, experimental results (this work): (䊉), 1-hexadecanol; (䊏), 1-octadecanol. Solid lines, DISQUAC calculations. Dashed lines, ideal solubility curves.

Table 11 QUAC DIS Interchange coefficients, dispersive Cdh,1 and Cdh,1 (l = 1, Gibbs energy; l = 2, enthalpy; l = 3, heat capacity for contacts (d, h) (type d, OCOO in linear organic carbonates; type h, OH in 1-alkanols)a,b 1-Alkanol

Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol 1-Decanol ≥1-Tetradecanol

DIS Cdh,1

DIS Cdh,2

DMC

MECc

≥DEC

DMC

MECc

≥DEC

1.25 1.80 2.55 3.45 4.35 5.40 10.0 15.0 27.0

1.15 1.75 2.3d 3.0d 3.6d 4.3d 7.5d 11.5d 27d

1.10 1.70 2.10 2.50 2.90 3.20 5.00 8.00 27.0

−8.0d −7.4d −6.7d −5.65 −5.65 −5.65 −5.65 −5.65 −5.65

−7.6d −7.0d −6.3d −5.65d −5.65d −5.65d −5.65 −5.65d −5.65c

−7.3 −6.6 −5.9 −5.65 −5.65 −5.65 −5.65 −5.65 −5.65

QUAC QUAC QUAC Cdh,1 = 3.5; Cdh,2 = 12.0; Cdh,3 = 10.0. The coordination number used for the QUAC part is z = 4. c Ethyl methylcarbonate. d Estimated value. a

b

DIS Cdh,3

5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0

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Table 12 ERAS parameters of pure compounds at temperature 298.15 K Compound

K

P∗ (J cm−3 )

Vm (cm3 mol−1 )

V∗ (cm3 mol−1 )

h∗i (J mol−1 )

vi∗ (cm3 mol−1 )

Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol 1-Decanol DMC DEC

986a 317a 197a 175b 153c 120d 89e 88f 0 0

443.6g 426.4g 433.9g 422.7g 411.0c 431.1h 436.5i 445.6i 695.00l 582.00l

40.73i 58.67i 75.16i 91.97g 108.69c 125.19h 158.33f 191.58f 84.71l 121.9l

32.13g 47.11g 61.22g 75.70g 89.76c 103.52h 131.77j 160.10j 65.41l 95.3l

−25.10k −25.10k −25.10k −25.10k −25.10k −25.10k −25.10k −25.10k 0.0 0.0

−5.6k −5.6k −5.6k −5.6k −5.6k −5.6k −5.6k −5.6k 0.0 0.0

a

[66,67,74,95,106]. [42,66,95,106]. c [67]. d [42,106,107]. e [67,106]. f [42,67,106]. g [66]. h [107]. i [106]. j [42]. k Values widely used: [66,67,95,106,108]. l From P–V–T data given in [109,110]. b

Table 13 ERAS parameters for 1-alkanols + linear organic carbonates mixtures at 298.15 K System

K

h∗AB (kJ mol−1 )

∗ vAB (cm3 mol−1 )

XAB (J cm−3 )

Methanol + DMC Ethanol + DMC 1-Propanol + DMC 1-Butanol + DMC Methanol + DEC Ethanol + DEC 1-Propanol + DEC 1-Butanol + DEC 1-Pentanol + DEC 1-Hexanol + DEC 1-Octanol + DEC 1-Decanol + DEC

20.0 11.0 11.0 11.0 20.0 10.5 10.5 10.5 10.5 8.0 6.0 5.8

−3.0 −3.0 −3.0 −3.0 −4.0 −4.0 −4.0 −4.0 −4.0 −4.0 −4.0 −4.0

−7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5 −7.5

2.0 15.0 23.0 29.0 8.5 15.0 17.7 17.7 17.7 21.0 25 29.0

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Table 14 Molar excess Gibbs energies, GEm , at temperature T and equimolar composition for 1-alkanol + linear organic carbonate mixtures System

Methanol + DMC Ethanol + DMC 1-Propanol + DMC 1-Hexanol + DMC Ethanol + DEC 1-Hexanol + DEC

T (K)

313.15 338.88a 313.15 348.32b 313.15 353.15 363.15 356.85c 353.15 363.15

N

27 28 20 10 9 12 13

GEm (J mol−1 )

σ r (P)

Reference

Experimental

DQ

Experimental

DQ

939 833 953 787 966 741 665 759 440 400

950 877 967 819 988 735 659 705 453 382

0.006

0.007

0.007

0.009

0.006 0.008 0.006

0.013 0.050 0.023

0.008 0.004

0.016 0.010

[36] [8] [36] [8] [36] [41] [41] [8] [41] [41]

Comparison between experimental results (experimental) and values obtained using DISQUAC (DQ) with the coefficients from Table 11. It has also included a comparison between the respective standard relative deviations, σ r (P) (Eq. (8)). N is the number of data points for each system. a x1 = 0.4987. b x1 = 0.5312. c x1 = 0.5229.

where M = P or T. Similarly, Table 17 lists the standard deviation for HmE 1/2 
   1 −1 E E E 2 σ Hm J mol = (Hm,exp − Hm,calc ) N

(9)

In Eqs. (8) and (9), N is the number of data points of each system. The model represents, rather accurately, the thermodynamic properties examined, including the temperature dependence of GEm and HmE . So, DISQUAC reproduces the decreasing of GEm for the higher temperatures, a behavior also encountered in, e.g. 1-alkanols + n-alkanes [57], + aromatic compounds [72] or + n-alkanones [73]. Table 15 Comparison of experimental (experimental) coordinates of azeotropes: pressure (Paz ), temperature (Taz ) and mole fraction (x1az ) for 1-alkanol (1) + linear organic carbonate (2) mixtures with DISQUAC (DQ) results using the interchange coefficients from Table 11a System Methanol + DMC Ethanol + DMC 1-Propanol + DMC Ethanol + MEC a

Ethyl methylcarbonate.

Taz (K)

313.15 337.10 313.15 348.10 313.15 351.05

Paz (kPa)

x1az

Reference

Experimental

DQ

Experimental

DQ

38.71 101.32 23.91 101.32 16.64 101.32

38.78 103.9 24.03 102.3 16.52 102.0

0.809 0.855 0.585 0.655 0.219 0.906

0.805 0.849 0.579 0.697 0.233 0.919

[36] [8] [36] [8] [36] [8]

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Table 16 Values of the relative standard deviations, σ r (Eq. (8)), and of absolute mean deviations a , of the solid–liquid equilibrium temperatures using DISQUAC with the coefficients from Table 11b System

N

σr

 (K)

1-Tetradecanol + DMC 1-Hexadecanol + DMC 1-Octadecanol + DMC 1-Icosanol + DMC 1-Tetradecanol + DEC 1-Hexadecanol + DEC 1-Octadecanol + DEC 1-Icosanol + DEC

33 32 33 24 37 31 38 37

0.009 0.008 0.007 0.003 0.007 0.006 0.003 0.008

2.5 2.3 1.8 0.8 2.1 1.7 0.9 2.1

(T )/K = (1/N) |Texp − Tcalc |. b N is the number of data points. a

Table 17 Molar excess enthalpies, HmE , at temperature T and equimolar composition for 1-alkanol + linear organic carbonate mixtures. Comparison between experimental results (experimental) and values obtained using DISQUAC (DQ) with the coefficients from Table 11and ERAS using parameters from Tables 12–13a System

T (K)

N

HmE (J mol−1 ) Experimental

Methanol + DMC Ethanol + DMC 1-Propanol + DMC 1-Butanol + DMC Methanol + DEC Ethanol + DEC 1-Propanol + DEC 1-Butanol + DEC

1-Pentanol + DEC 1-Hexanol + DEC 1-Octanol + DEC 1-Decanol + DEC

298.15 313.15 298.15 313.15 298.15 313.15 288.15 298.15 313.15 298.15 298.15 298.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 298.15 298.15 298.15 298.15

15 16 17 16 16 16 16 15 15 17 17 16 17 17 17 17 17 16 17 16

1543 1972 2321 2126 2356 2570 1258 1523 1794 1785 1858 1944 2076 2100 2206 2223 1984 2016 2160 2248

␴(HmE ) (J mol−1 )

DQ

ERAS

1144 1513 1583 1928 1981 2311 2096 2308 2614 1233 1496 1754 1689 1790 1891 1993 2095 2197 2297 1980 2050 2117 2148

1198

Experimental

Reference DQ

ERAS

7

62

[36]

6

65

[36]

10.0 9 8 9 6 6 4 6 10 7 10 9 7 9 7 6 5 10

43 56 74 38 29 28 37 61 44 40 54 33 40 74 27 27 40 73

[36] [38] [38] [38] [37] [37] [37] [39] [39] [37] [39] [39] [39] [39] [40] [37] [37] [37]

1566 1958

2154 1258 1557 1857

1931

2009 2043 2130 2265

159 61 62 122

110

131 139 146 133

It has also included a comparison between the respective standard deviations, σ (HmE ) (Eq. (9)). N is the number of data points for each system. a

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Fig. 2. VLE phase diagrams for 1-alkanol (1) + DMC (2) mixtures at 313.15 K. Points, experimental results [36]: (䊉), ethanol; (䊏), 1-propanol. Solid lines, DISQUAC calculations.

Fig. 3. HmE at 313.15 K for 1-alkanol (1) + DMC (2) systems. Points, experimental results [36]: (䊉), methanol, (䊏), ethanol; (䉱), 1-propanol. Solid lines, DISQUAC calculations.

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365

Fig. 4. HmE at 298.15 K the for 1-butanol (1) + DMC (2) system. Points, experimental results [38]. Solid line, DISQUAC calculations. Dashed line, ERAS results.

Fig. 5. HmE at 298.15 K the for methanol (1) + DEC (2) system. Points, experimental results [37]. Solid line, DISQUAC calculations. Dashed line, ERAS results.

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Fig. 6. HmE at 298.15 K for 1-alkanol (1) + DEC (2) systems. Points, experimental results [37]: (䊉), ethanol, (䊏), 1-butanol. Solid lines, DISQUAC calculations. Dashed lines, ERAS results.

Fig. 7. HmE at 298.15 K for 1-alkanol (1) + DEC (2) systems. Points, experimental results [37]: (䊉), 1-octanol, (䊏), 1-decanol. Solid lines, DISQUAC calculations. Dashed lines, ERAS results.

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Table 18 Excess molar volumes, VmE , at equimolar composition, 298.15 K and atmospheric pressure, for 1-alkanol + linear organic carbonatea System

Methanol + DMC Ethanol + DMC 1-Propanol + DMC 1-Butanol + DMC Methanol + DEC Ethanol + DEC 1-Propanol + DEC 1-Butanol + DEC 1-Pentanol + DEC 1-Hexanol + DEC 1-Octanol + DEC 1-Decanol + DEC

VmE (cm3 mol−1 )

Reference

Experimental

ERAS

−0.044b 0.151 0.369 0.477 0.523 −0.048 0.014 0.114 0.115 0.222 0.236 0.281 0.292 0.335 0.394 0.520 0.639

−0.061 0.183 0.349 0.585 −0.056 0.112 0.188 0.282 0.362 0.397 0.538 0.630

[36] [111] [111] [38] [111] [37] [112] [37] [112] [37] [112] [37] [112] [112] [37] [37] [37]

a Comparison of experimental (experimental) results with values calculated from the ERAS model with the coefficients listed in Tables 12 and 13. b Value at 313.15 K.

DISQUAC results on SLE are similar to those obtained for other solutions including the same long-chain 1-alkanols, (between parenthesis, we give the mean R.S.D.s, σ¯ r , (calculated as #σ r /number of systems) such as 1-alkanols+cyclohexane (0.005) [49], + benzene (0.008) [48], + toluene (0.006) [48], or +CCl4 (0.008) [49]. For 1-alkanols + DMC, or + DEC, σ¯ r = 0.007 and 0.006, respectively. In previous works, the observed deviations have been attributed, at least in part, to the inadequacy of the Flory-Huggins term to represent GE,COMB in mixtures with compounds very different in size [50]. m 5.2. ERAS results and comparison with DISQUAC Results on HmE and VmE using ERAS are listed in Tables 17 and 18, respectively. Figs. 4–9 show these results in a graphical way for some systems. ERAS calculations for HmE are improved by DISQUAC because the symmetry of the HmE curves is better represented by this model (Figs. 4,6,7). VmE is usually well reproduced by ERAS (Table 18, Figs. 8 and 9). Results are similar to those obtained for other systems such as 1-alkanols + branched ethers [74]. Of course, the main advantage of ERAS is its ability to represent VmE . However, one should keep in mind that physical theories (as DISQUAC) can be applied to any type of binary mixture (see, e.g. [15,16,68,75]), while ERAS (or any association model) can be only used for those systems where association is expected.

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Fig. 8. VmE at 298.15 K for the 1-propanol (1) + DEC (2) system. Points, experimental results [37]. Solid line, ERAS results. Dashed lines, chemical and physical contributions to VmE in ERAS.

Fig. 9. VmE at 298.15 K for the 1-hexanol (1) + DEC (2) system. Points, experimental results [37]. Solid line, ERAS results. Dashed lines, chemical and physical contributions to VmE in ERAS.

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6. Discussion Thermodynamic properties of mixtures can be examined taking differences in molecular size and shape, anisotropy, dispersion forces and so forth into account. To investigate the impact of polarity on bulk properties, the effective dipole moment, µ, ¯ can be used [15,16,68,76,77]. Moreover, µ¯ gives an indication of the ratio between dipolar and non-polar interactions [78], e.g. we note that µ¯ of 1-alkanols decreases in the sequence: methanol (µ= ¯ 1.023) > ethanol (µ= ¯ 0.852) > · · · > 1-decanol (µ= ¯ 0.443) (see Table 8 in [68]), what indicates that the alcohol–alcohol interactions in the condensed phase also decreases in the same order, and that the contribution from dipolar interactions to thermodynamic properties are more important for the lower alcohols. The same effect is seen in carbonates, µ¯ (DMC) = 0.362 (µ/D = 0.87 [79]) > µ¯ (DEC) = 0.312 (µ = 0.9 [79]). Dipolar interactions are stronger in solutions with DMC, non miscible, at room temperature, with the longer n-alkanes [26,28]. 6.1. Excess functions 1-Alkanols + linear organic carbonates mixtures are characterized by large HmE s (Table 17). For a given carbonate, at equimolar composition, HmE increases with the length of the alcohol; the variation is parallel to that in linear organic carbonates + n-alkanes systems when the size of the alkane increases [28,29]. Moreover, the HmE curves are symmetrical (Figs. 3–7), and GEm < HmE being TSEm positive. These features reveal that polar interactions between carbonate molecules are more important than the self-association of the alkanol. A similar situation is encountered in 1-alkanols + polyoxaalkanes [80–83], or alkoxyethanols [84] + n-alkanes mixtures. In contrast, 1-alkanols + linear monoethers systems behave in opposite way [83,85]. Here, HmE increases from methanol to 1-propanol and then slightly decreases with the chain length of the alkanol. The HmE curves are skewed towards low mole fractions of the alkanol. In addition, GEm ≈ HmE and TSEm is s-shaped or slightly positive. All this shows that the self-association of the alcohol plays a role of the major importance. On the other hand, the increase of HmE with the decrease of µ¯ of the alkanol when mixed with a given carbonate must be, at least in part, attributed to a decrease of the interactions between unlike molecules. In contrast, µ(DMC) ¯ > µ(DEC) ¯ and, for a given alkanol, HmE (DMC) ≈ HmE (DEC) (Table 17), as dipole–dipole interactions are more important between DMC molecules. Only for mixtures with methanol or ethanol, HmE (DMC) ≈ HmE (DEC) (Table 17), probably because the more important polar interactions between DMC molecules are balanced by stronger interactions between unlike molecules, as the OCOO group is less sterically hindered in DMC. Another interesting feature of the analyzed systems is their relative low VmE values (Table 18), which contrast with the large HmE s (Table 17). It underlines  3 structural the existence of Estrong effects. So, at −1 −1 E 298.15 K and equimolar composition, Hm J mol = 1328 [29] and Vm cm mol = 0.736 [31] for   DEC + n-heptane; and HmE J mol−1 = 2016 [37]; VmE cm3 mol−1 = 0.394 [37] for DEC + 1-hexanol. Other systems behave similarly, e.g. alkoxyethanols + di-n-butylether [86,87]. 6.2. The interaction parameters QUAC The Cdh,1 (1 = 1, 2, 3) coefficients are independent of the mixture compounds. The same trend is observed in 1-alkanol + n-alkanone systems [73] and in other many alcoholic solutions [72,75,88–92].

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Nevertheless, some different values of such coefficients have been obtained for methanol or ethanol, what may be explained by their different character when compared to the longer ones (higher dielectric constant, stronger self-association). This is the case of 1-alkanols + CCl4 [88], or + aromatic compounds [72]. A similar trend has been obtained when treating such mixtures is terms of the Barker’s theory [93,94]. DIS The increase of Cdh,2 when passing from DMC to DEC (for a given alkanol) may be attributed to an increase of inductive effects, as in linear organic carbonate + n-alkane systems [33,35]. On the other DIS hand, Cdh,1 is large and constant for the longer 1-alkanols. 1-Alkanols + n-alkanes [70], + cyclohexane [49], + benzene or toluene [48] or + CCl4 [49] mixtures behave similarly. ∗ In terms of the ERAS model, h∗AB and vAB are also independent of the alcohol (Table 13). The h∗AB values are high when are compared to those of other mixtures, e.g. 1-alkanols + primary amines ([−46.3, −38.6] kJ mol−1 ) [66,67], + secondary amines ([−45.5, −34.5]) [68,71], + triethyl amine ([−35.5, −33.2]) [92], + oxaalkanes ([−24.5, −18.4]) [74,95] or + 1-alkynes (−15.7, −10.) [96,97]. This reveals that cross-association between unlike molecules are here much less important from an energetic point of view. It is supported by the low KAB and large XAB values (Table 13). The latter remark the importance of the physical interactions in the present mixtures, as the XAB values usually vary from 2–12 [66,67]. However, the calculated HmE curves are slightly skewed to the region of low mole fraction in alkanol (Figs. 4,6,7), which means that the model overestimates the contribution to the HmE from the self-association of the alcohol. ∗ The vAB parameter is also independent of the carbonate and relatively low, what may be attributed to quite strong structural effects. Note, the values for the following mixtures: 1-alkanols + primary amines ([−12.3, −10.1] cm3 mol−1 ) [66,67], + secondary amines ([−13.3, −11.2]) [68,71], + triethyl amine (−13.8) [92], + oxaalkanes ([−14.7, −8.4]) [74,95] or + 1-alkynes (−8.5, −6) [96,97]. Finally, it should be mentioned that quick reference values of interaction parameters for the OH/COO (ester) contacts can be obtained as the mean values of the interaction parameters of the OH/CO [73] and OH/OCOO contacts. At equimolar composition, DISQUAC provides 5.2% as mean deviation for HmE , while the Nitta-Chao [98] and Dortmund UNIFAC [99] models give, respectively, 5.6 and 8.7% [100]. The poorer results from DISQUAC are obtained when the contribution to the HmE from the self-association of the alkanol is more relevant.

7. Conclusions 1-Alkanol + linear organic carbonate mixtures were studied in the frameworks of the DISQUAC and ERAS models. The corresponding interaction parameters are reported. They behave similarly in both models. In DISQUAC, the QUAC parameters are independent of the mixture compounds, as in other many alcoholic solutions previously analyzed. The DIS parameters remain constant for the longer ∗ alcohols. In ERAS, vAB is also independent of the mixture components, while h∗AB depends only on the carbonate. DISQUAC improves ERAS results on HmE , as the calculated curves using ERAS are shifted to the region of low concentration in alcohol. This means that, in terms of ERAS, the contribution to HmE from the self-association of the alcohol is overestimated. VmE is well represented by ERAS. From the analysis of the HmE curves, it is concluded that they are determined mainly by dipolar interactions between carbonate molecules. VmE s are relatively low indicating strong structural effects.

J.A. Gonzalez et al. / Fluid Phase Equilibria 200 (2002) 349–374

List of symbols C interchange coefficient in DISQUAC G Gibbs energy H enthalpy h∗A self-association enthalpy of component A h∗AB association enthalpy of component A with component B Hfus molar enthalpy of fusion of pure compound Htrs molar enthalpy of transition of pure compound KA self-association constant of component A KAB association constant of component A with component B P pressure P¯ reduced pressure P∗ reduction parameter for pressure q relative molecular area of component in DISQUAC r relative molecular volume of component in DISQUAC R gas constant (8.314 J mol−1 K−1 ) T absolute temperature Tfus melting temperature Ttrs Transition temperature T¯ reduced temperature T∗ reduction parameter for temperature ∗ vA self-association volume of component A ∗ vAB association volume of component A with component B V molar volume V¯ reduced volume ∗ V reduction parameter for volume x mole fraction in the liquid phase XAB physical adjustable parameter in ERAS model y mole fraction in the vapor phase z coordination number Greek letters α molecular surface fraction, or solid phase of the alcohol β solid phase of the alcohol  absolute mean deviation γ solid phase of the alcohol, or activity coefficient µ dipole moment µ¯ effective dipole moment σ standard deviation σr standard relative deviation Superscripts COMB combinatorial part DIS dispersive term

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E QUAC

excess property quasichemical term

Subscripts a, h, d chem i l m M phys s, t

type of contact surface: a, CH3 , CH2 ; h, OH in DISQUAC; d, OCOO chemical contribution to excess functions in ERAS model type of molecule; in ERAS model i = A (alcohol); B (carbonate); M (mixture) order of interchange coefficient: l = 1, Gibbs energy; l = 2, enthalpy; l = 3, heat capacity molar property mixture physical contribution to excess functions in ERAS model type of contact surface in DISQUAC (s = t)

Acknowledgements J.A.G. acknowledges the financial support from the Programa Sectorial de Promoción General del Conocimiento de la S.E.U.I. y D. del M.E.C. (Spain), Project no PPQ2001-1664 and from the Consejer´ıa de Educación y Cultura de la Junta de Castilla y León (Spain) y de la Unión Europea (Fondo Social Europeo), under the Project VA039/01. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

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