Ind. Eng. Chem. Res. 2002, 41, 3253-3259
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Thermodynamics of Binary Mixtures Containing Organic Carbonates. 12. SLE and LLE Measurements for Systems of Dimethyl Carbonate with Long n-Alkanes. Comparison with DISQUAC and Modified UNIFAC Predictions†,‡ U. Doman ´ ska* and M. Szurgocin ´ ska Physical Chemistry Division, Faculty of Chemistry, Warsaw University of Technology, 00-664 Warsaw, Poland
J. A. Gonza´ lez Departamento de Termodina´ mica y Fı´sica Aplicada II, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain
Using the available interaction parameters for organic carbonate + alkane mixtures, the ability of the DISQUAC and modified UNIFAC group contribution model to predict solid-liquid equilibria (SLE) and liquid-liquid equilibria (LLE) is investigated. Six sets of the SLE and LLE temperatures for dimethyl carbonate + n-alkane (octadecane, eicosane, docosane, tetracosane, hexacosane, and octacosane) systems have been measured by a dynamic method from 278.65 K to the melting point of the long-chain n-alkane and to the upper critical temperature of two coexisting phases. The SLE data have been correlated by three equations: Wilson, UNIQUAC, and NRTL. The existence of a solid-solid first-order phase transition in n-alkanes has been taken into consideration in the solubility calculations. The relative standard deviations of the solubility temperature correlation for all measured data vary from 0.2 to 1.3 K and depend on the particular equation used. The LLE coexistence curves are very asymmetrical with respect to mole fraction, with the asymmetry increasing with the size of the n-alkane. The critical solution points vary almost linearly with the number of carbon atoms of the n-alkane. The SLE curves are usually well predicted by DISQUAC and modified UNIFAC models with an average standard deviation of less than 1.6 K. Introduction The thermodynamic study of carbonic acid’s esters is of considerable interest because of their uses in the pharmaceutical industry, in agricultural and chemical products, as solvents of synthetic and natural resins and polymers, as solvents in Li battery technology, and many others. As a part of our systematic program of research on mixtures containing linear organic carbonates with different solvents (alkanes, benzene, toluene, or CCl4 ), experimental data on vapor-liquid equilibria (VLE),1-4 liquid-liquid equilibria (LLE),5 HE,6,7 and VE 8,9 have been previously reported. These systems have been treated10-12 in the framework of the DISQUAC model.13,14 In mixtures with alkanes, the corresponding interaction parameters show that the n-alkyl groups attached to the carbonate group, O-CO-O, exert a relatively weak steric effect on the quasichemical parameters and have practically no inductive effect on the dispersive parameters.10-12 In exchange, steric effects are found for these parameters in the case of systems including benzene, toluene, or CCl4.11,12 A deep understanding of the interactions present in the solutions mentioned is needed to treat mixtures including cyclic, ethylene, and propylene carbonates, which are widely used as extractive solvents †
Part XI: Fluid Phase Equilib. 2001, 190, 15-31. Presented at ESAT 2000, Kutna´ Hora, Czech Republic. * Corresponding author. E-mail:
[email protected]. Phone: 00-48-22-6213115. Fax: 00-48-22-6282741. ‡
in the chemical industry. Previous comparative studies on linear and cyclic molecules, secondary and tertiary amines,15 oxaalkanes,16-19 and ketones20 show that the position of the functional group in a ring or in an open chain may change the properties considerably and hence the values of the interaction parameters. On the other hand, the good prediction of enthalpies of mixing and VLE of organic linear carbonates + n-alkanes mixtures was achieved by the modified UNIFAC model (MUNIFAC).21 Here, we continue our experimental work by extending the available database on systems with dialkyl carbonates with solid-liquid equilibria (SLE) and LLE measurements for mixtures containing long-chain nalkanes and dimethyl carbonate (DMC). Previously, we also reported solubilities of some normal paraffins in diethyl carbonate (DEC)22 and in various solvents (e.g., alkanes and alkanols), which can be found in the discussion on literature given in ref 22 and in references quoted therein. The new data are useful to test the quality of the DISQUAC and MUNIFAC predictions when the difference in size of the mixture components is large. Experimental Section 1. Materials. The origins of the chemicals (in parentheses Chemical Abstracts registry numbers) are as follows: octadecane (593-45-3), Koch-Light Lab.; eicosane (112-95-8), Fluka AG; docosane (629-97-0), Fluka AG; tetracosane (646-31-1), Fluka AG; hexacosane (630-01-
10.1021/ie010662c CCC: $22.00 © 2002 American Chemical Society Published on Web 05/31/2002
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Table 1. Physical Constants of Pure Compounds: Tm, Melting Point (This Work); ∆Hm, Molar Heat of Fusion; Ttr, Transition Temperature; ∆Htr, Molar Heat of Transition (r f β); ∆Cpm, Heat Capacity Change at the Melting Temperature and V298.15 Molar Volume
e
n-alkane
Tm (K)
∆Hm (kJ‚mol-1)
Ttr (K)a
∆Htr (kJ‚mol-1)
∆Cpm (J‚K-1‚mol-1)
V298.15 (cm3‚mol-1)b
octadecane eicosane docosane tetracosane hexacosane octacosane
301.61 309.28 318.19 324.67 330.13 336.95
61.71c 66.93e 48.95f 57.31g 63.92g 66.52g
308.65 315.95 320.55 326.15 331.35
18.39e 28.20f 27.68g 30.36g 33.60g
50.0d 54.0d 58.5g 66.6g 78.3g 118.9g
326.5 359.4 392.0 424.6 457.2 489.8
a Reference 23. b Reference 24. c Reference 25. Reference 27. f Reference 28. g Reference 29.
d
From linear extrapolation of data for even-numbered n-alkanes C22-C28 from ref 26.
3), INC Pharm; octacosane (630-02-4), Fluka AG. DMC (616-38-6; 99+%) was supplied by Aldrich and was stored over freshly activated molecular sieves of type 4A (Union Carbide). All compounds were checked by gas-liquid chromatographic analysis, and no significant impurities were found. Commercially available n-alkanes were directly used without purification. The purity of octadecane was chromatographically determined to be 0.99. The purity of higher n-alkanes was 0.98 or 0.99. The physical properties of pure n-alkanes are collected in Table 1. The molar volume of DMC is equal to 84.72 cm3‚mol-1, calculated from densities at 298.15 K.29 2. Apparatus and Procedure. SLE temperatures were determined using a dynamic method described in detail previously.22 Mixtures were heated very slowly (at less than 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 electronic thermometer totally immersed in the thermostating liquid. The thermometer was calibrated on the basis of the ITS-90 scale of temperature. The accuracy of the temperature measurements was (0.01 K, and the reproducibility was (0.1 K. The error in the mole fraction did not exceed ∆x1 ) 0.0005. The solid-solid-phase transition temperatures Ttr presented in Table 1 were taken for the calculations from our previous work.23 In many solvents it is possible to observe the changing of the structure of crystals during the crystallization accompanied by the characteristic inflection on the liquidus curve for the very close experimental points. The LLE coexistence curves at the binary mixtures were determined visually for the increasing temperatures. Every experimental point of LLE was observed at the upper temperature for the same mole fraction, for which the SLE point was previously observed. Results and Discussion Table 2 lists the direct experimental results of the SLE TSLE and LLE TLLE temperatures, vs x2, the mole fraction of n-alkane. The solubility of a solid 2 in a liquid may be expressed in a very general manner by the equation
-ln x2 )
(
)
(
)
∆Hm2 1 ∆Cpm2 Tm2 T 1 ln + -1 + R T Tm2 R Tm2 T ln γ2 (1)
where x2, γ2, ∆Hm2, ∆Cpm2, Tm2, and T stand for the mole fraction, the activity coefficient, the enthalpy of fusion, the difference in the solute heat capacity between the
solid and the liquid at the melting point, the melting point of the solute, and the equilibrium temperature, respectively. If the solid-solid transition occurs before fusion, an additional term must be added to the right-hand side of eq 1.30,31 The solubility equation for temperatures below that of the phase transition must include the effect of the transition. The result for the first-order transition is
-ln x2 )
(
)
( (
)
∆Hm2 1 ∆Cpm2 Tm2 1 T -1 + ln + R T Tm2 R Tm2 T
)
∆Htr2 1 1 + ln γ2 (2) R T Ttr2 where ∆Htr2 and Ttr2 stand for the enthalpy of transition and the transition temperature of the solute, respectively. In this study three methods are used to derive the solute activity coefficients γ2 from the so-called correlation equations that describe the Gibbs excess energy of mixing (GE): Wilson,32 UNIQUAC,33 and NRTL.34 The exact mathematical forms of the equations have been presented in our previous paper.35 The parameter R12, a constant of proportionality similar to the nonrandomness constant of the NRTL equation, was R12 ) R21 ) 0.45, which was observed as the best result of correlation in the systems under study. The parameters of the equations were found by an optimization technique: n
Ω)
[Ti exp - Ticalc(x2i,P1,P2)]2 ∑ i)1
(3)
where Ω is the objective function, Ti exp denotes an experimental value of the temperature for a given concentration x2i, and Ticalc is the temperature calculated for a given concentration x2i and parameters P1 and P2, obtained by solving the nonlinear equation (eq 1 or 2), depending upon the value of temperature and the expression for the logarithm of the activity coefficient according to the assumed model. The nonlinear equations were solved using the secant method. The rootmean-square deviation of temperature (σT defined by eq 4) was used as a measure of the goodness of the solubility correlation
σT )
(∑
)
n
(Ticalc - Ti)2
i)1
n - nad
1/2
(4)
where Ti exp and Ticalc are respectively the experimental and calculated temperatures of the ith point, n is the number of experimental points (including the melting
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3255 Table 2. Experimental SLE and LLE Temperatures (T; Phases r and β, Respectively) for DMC (1) + n-Alkane (2) Mixturesa x2
Tβ1SLE TR1SLE
TLLE
x2
Octadecane 0.5432 0.5681 0.5684 0.5889 318.17 0.5899 325.25 0.6232 325.98 0.6597 325.65 0.6967 324.84 0.7440 323.45 0.8088 319.08 0.8831 310.65 0.9667 306.65 1.0000 303.21
Tβ1SLE
TR1SLE
0.0071 0.0152 0.0231 0.0279 0.0448 0.0991 0.1633 0.1951 0.2280 0.2601 0.3304 0.4360 0.4760 0.5070 0.5292
293.73 296.31 298.02 298.32 298.35 298.69 298.71 298.81 298.70 298.71 298.71 298.69 298.71 298.71 298.72
0.0521 0.0648 0.1013 0.1252 0.1579 0.2038 0.2471 0.2777 0.3290 0.3692 0.4251
305.75 305.84 305.85 305.85 305.85 305.90 305.93 305.92 305.87 305.88 305.85
Eicosane 327.06 0.4588 328.65 0.5096 330.95 0.5612 331.37 0.6062 331.44 0.6311 331.18 0.6930 330.12 0.7144 328.77 0.7693 325.62 0.8400 323.03 0.9041 318.35 1.0000
0.0221 0.0352 0.0668 0.0993 0.1180 0.1707 0.1983 0.2451 0.3142
314.49 314.35 314.36 314.35 314.33 314.29 314.32 314.32 314.37
Docosane 319.40 0.4031 328.71 0.4490 336.42 0.5019 338.12 0.5578 338.20 0.6559 338.47 0.7810 337.90 0.8540 336.19 0.9412 331.38 1.0000
0.0151 0.0289 0.0500 0.0691 0.0872 0.0911 0.1138 0.1811 0.2240 0.2962 0.3706 0.3814
317.91 318.06 317.91 318.00 318.06 318.02 318.00 318.00 318.02 318.06 318.15 318.20
Tetracosane 324.12 0.4191 333.77 0.4744 340.87 0.5132 343.27 0.5824 344.93 0.6232 344.35 0.6790 344.64 0.7659 344.07 0.7878 341.99 0.8311 337.01 0.9233 328.86 0.9426 327.74 1.0000
0.0231 0.0334 0.0520 0.0862 0.1209 0.1601 0.2167 0.2782
323.33 324.51 324.47 324.41 324.44 324.45 324.55 325.04
Hexacosane 336.67 0.3490 342.74 0.4108 347.97 0.5266 350.03 0.6109 350.23 0.6852 349.74 0.8134 346.99 0.9351 341.41 1.0000
0.0390 0.0734 0.1256 0.1679 0.2042 0.2381 0.2814 0.3283 0.3952 0.4458
328.70 328.73 328.60 328.61 328.65 328.65 328.60 328.62 328.78 329.31
Octacosane 351.71 0.4924 329.83 354.97 0.5723 330.80 355.14 0.6158 331.50 354.08 0.6749 332.25 351.85 0.7210 333.18 348.61 0.7971 334.32 344.41 0.8642 335.27 339.79 0.9043 336.02 332.42 0.9530 336.80 1.0000 337.34
TLLE
298.66 299.45 299.66 298.74 298.93 299.10 299.30 299.35 299.50 299.92 301.00 301.82 303.11
305.88 305.79 305.88 306.14 306.23 306.81 307.21 308.18
314.85 309.55
308.87 309.34 309.46 314.46 314.30 314.36 314.57 314.66 315.92
322.94 318.73
316.73 318.15 318.43 318.63 318.68 318.89 319.50 320.18
323.11
Figure 1. SLE of binary mixtures [DMC (1) + n-alkane (2) (C18, C22, C26)]. Solid lines: NRTL equation calculations. Dotted lines: ideal solubility. Points: experimental values.
point), and nad is the number of adjustable parameters (nad ) 2). Table 3 lists the results of fitting the solubility curves by the three equations used: Wilson, UNIQUAC, and NRTL. The structural parameters for the pure components were obtained in accordance with the methods suggested by Vera et al.36 and the relationship from Hofman and Nagata37
ri ) 0.029281Vm 320.89 321.79 321.64 322.58 324.07 324.04 325.14
324.98 324.97 325.96 325.80
qi )
333.03
327.48 329.52 329.95 331.53
a The Greek subscripts indicate the type of solid phase of the n-alkane.
(z - 2)ri 2(1 - li) + z z
(5) (6)
where Vm is the molar volume of pure component i at 298.15 K, z is the coordination number, assumed to be equal to 10, and li is the bulk factor; it was assumed that li ) 0. For the six systems presented in this work, the best description of SLE was given by the two-parameter NRTL equation with the average standard deviation σT ) 0.57 K. For the two other equations, the standard deviations were slightly worse, σT ) 0.76 K (Wilson equation) and σT ) 0.78 K (UNIQUAC equation). SLE of mixtures investigated in this work are characterized mainly by the following: (i) the solubility of n-alkanes in DMC decreases with increasing number of the carbon atoms; (ii) the solubility is lower than the ideal solubility (positive deviations from Raoult’s law γ2 > 1), especially for the β crystallographic form (low-temperature form), which is presented in Figures 1 and 2. The solubility of n-alkanes in DMC is lower than that in DEC, in heptane, in ethyl 1,1-dimethylpropyl ether, and in cyclohexane but is better than that in n-alcohols and tert-butyl alcohol. For example, the equilibrium temperature of a saturated solution of hexacosane in
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Table 3. Correlation of the Solubility Data, SLE of DMC (1) + n-Alkane (2) by Means of the Wilson, UNIQUAC, and NRTL Equations: Values of Parameters and Measurements of Deviations parameters
deviations
n-alkane
Wilson g21 - g11 and g12 - g22 (J‚mol-1)
UNIQUAC ∆u21 and ∆u12 (J‚mol-1)
NRTLa ∆g21 and ∆g12 (J‚mol-1)
Wilson σTb (K)
UNIQUAC σTb (K)
NRTL σTb (K)
octadecane eicosane docosane tetracosane hexacosane octacosane
5844.28, 7348.48 5881.88, 8370.81 6839.00, 46 530.63 5452.07, 1 840 710.4 5635.23, 3 159 805.1 4934.38, 6 523 149.4
305.61, 1986.53 -201.44, 2603.39 -82.22, 2617.33 197.23, 1911.56 -71.69, 2348.40 -85.19, 2237.55
8390.15, 2983.29 7235.03, 2251.80 8534.35, 3083.10 9430.50, 1182.34 8846.11, 1168.58 8966.75, 401.10
0.70 1.44 0.31 0.58 0.72 0.79
1.22 0.48 1.24 0.95 0.55 0.25
0.88 0.39 0.67 0.69 0.49 0.32
a
Calculated with the third nonrandomness parameter, R ) 0.45. b According to eq 4 in the text. Table 5. Relative Group Increments for Molecular Volumes, rG ) VG/VCH4, and Areas, qG ) AG/ACH4 (VCH4 ) 17.12 × 10-6 m3‚mol-1; ACH4 ) 2.90 × 10-5 m2‚mol-1) group
rG
qG
group
rG
qG
CH3a CH2a
0.798 48 0.597 55
0.731 03 0.465 52
O-CO-Ob
1.092 29
0.965 52
a
Reference 15. b Reference 12.
Table 6. Interchange Coefficients,a Dispersive Cad,1DIS, and Quasichemical Cad,1QUAC for Contacts (a, d): Type a, CH3 or CH2 in n-Alkane and DMC; Type d, O-CO-O in DMC (l ) 1, Gibbs Energy; l ) 2, Enthalpy; l ) 3, Heat Capacity) Cad,1DIS
Cad,2DIS
Cad,3DIS
Cad,1QUAC
Cad,2QUAC
Cad,3QUAC
1.20
3.00
0
3.15
4.10
0
a
Figure 2. SLE of binary mixtures [DMC (1) + n-alkane (2) (C20, C24, C28)]. Solid lines: NRTL equation calculations. Dotted lines: ideal solubility. Points: experimental values. Table 4. Upper Critical Solution Temperature Tc and Composition x2c for DMC (1) + n-Alkane (2) Systems n-alkane
Tc
x2c
n-alkane
Tc
x2c
octadecane eicosane docosane
325.8 331.5 338.3
0.16 0.15 0.15
tetradecane hexacosane octacosane
344.3 350.3 355.1
0.12 0.11 0.10
DMC is 325.00 K for x1 ) 0.42, while that in DEC is 323.43 K,22 that in heptane is 319.35 K,38 that in ethyl 1,1-dimethylpropyl ether is 320.20 K,23 that in cyclohexane is 324.15 K,38 that in heptanol is 326.45 K,35 and that in tert-butyl alcohol is 328.20 K.39 The LLE coexistence curves are shifted toward a high mole fraction of DMC (see the experimental points in Figures 1 and 2), as was observed for n-alkanes from decane to hexadecane.5 The critical temperatures and compositions, listed in Table 4, vary almost linearly with the number of carbon atoms of the n-alkanes and agree very well with the data published previously.5 DISQUAC Treatment The molecules under study, i.e., DMC and n-alkanes, are regarded as possessing two types of surfaces: (1)
Reference 12.
type a (CH3 and CH2 in DMC or n-alkanes) and (2) type d (O-CO-O group in DMC). The geometrical parameters, relative volumes rG, total relative surfaces qG, and surface fraction Rdi for the compounds considered in this work were calculated on the basis of the group volumes and surfaces recommended by Bondi,40 taking arbitrarily the volume and surface of methane as unity. Values of the needed geometrical parameters are given in Table 5. These systems are characterized by a single type of contact (a or d). The interaction parameters were estimated with the GE, HE, and LLE data available in the literature and were published previously by Kehiaian et al.10 and after correction by Gonza´lez et al.12 In the DISQUAC model
ln γi ) ln γiCOMB + ln γiDIS + ln γiQUAC
(7)
Here, ln γiCOMB is the combinatorial term represented by the Flory-Huggins equation, while ln γiDIS and ln γiQUAC are the dispersive and quasichemical contributions, respectively. Expressions for each of the three terms are given elsewhere.41 The temperature dependence of the interaction parameters has been expressed in terms of DIS and QUAC interchange coefficients Cad,lDIS and Cad,lQUAC where l ) 1 [Gibbs energy; Cad,1 ) gad (To/RTo)], l ) 2 [enthalpy; Cad,2 ) had (To/RTo)], l ) 3 [heat capacity; Cad,3 ) Cpad (To/R)], and l ) 4 [the linear dependence with the temperature of the heat capacity (To is the scaling temperature, 298.15 K)]. For the QUAC part, the coordination number used was z ) 4. The Cad,lDIS and Cad,lQUAC (l ) 1-3) coefficients used are listed in Table 6. The interaction parameters,12 presented in Table 7, were developed from (i) VLE for systems involving DMC + hydrocarbons (C6-C10), (ii) molar excess en-
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3257
Figure 3. SLE of binary mixtures [DMC (1) + n-alkane (2) (C18, C22, C26)]. Solid lines: MUNIFAC predictions. Dotted lines: DISQUAC predictions. Points: experimental values. Table 7. Geometrical Parameters rG and qG and Interaction Parameters anm,i for Organic Carbonate + n-Alkane for the MUNIFAC Model21 rG
qG
subgroup
0.6325 1.0608 CH3
main group
CH2
O-CO-O
CH2
0 5788.95 0 -35.11 0.6325 0.7081 CH2 CH2 0 0.0581 1488.85 0 2.0069 1.3890 O-CO-O O-CO-O -2.7981 0 -0.0050 0
thalpies (HE) for systems containing DMC + hydrocarbons (C6-C10), and (iii) LLE for DMC + n-alkane (C10C16). For longer-chain n-alkanes, which were not included in the development of parameters, the description was expected to be slightly worse. Graphical comparisons between experimental and calculated solubility curves are shown in Figures 3 and 4. We note that, for the treated mixtures at x2 , 0.2, γ2exp < γ2calc and, as a consequence, Texp < Tcalc. Larger differences are encountered for lower temperatures, where the positive deviations from Raoult’s law become very strong. DISQUAC predictions of SLE for mixtures of longchain n-alkanes and DMC differ slightly from the normal trend observed for the isothermal vapor-liquidphase equilibria diagrams or for the molar excess enthalpy of DMC (1) + n-alkane (2),12 where the predictive values represent very well the experimental points. For the SLE the prediction follows a trend similar to that observed before.39 We remark that measured mixtures show strong positive deviations from Raoult’s law, in such way that the ideal solubility curve does not represent a SLE phase diagram (see Figures 1 and 2). It was discussed before39 that in view of eq 7 the combinatorial term used
Figure 4. SLE of binary mixtures [DMC (1) + n-alkane (2) (C20, C24, C28)]. Solid lines: MUNIFAC predictions. Dotted lines: DISQUAC predictions. Points: experimental values.
(the Flory-Huggins equation41) plays an important role with an important negative contribution to ln γ2 at low x2. The results obtained for SLE are not perfect (the average standard deviation is σT ) 1.57 K) because the interaction parameters were determined for hydrocarbons not longer than C16. There is no doubt that from the wider thermodynamic description (VLE, LLE, HE, and SLE) including longer-chain components the interaction parameters for the linear organic carbonatealkane mixtures will be more representative. Parts a-c of Figure 5 show a comparison between experimental and predicted LLE lines. The upper critical compositions are not predictable; the shape of the calculated LLE curve is not adequate. The differences between the calculated and experimental upper critical solution temperatures were 12 and 25 K for alkanes and cycloalkane, respectively. For the DMC + n-hexadecane mixture, the difference is about 10 K.12 The predictions fail completely for the LLE of the DMC + docosane, tetracosane, or octacosane mixture (see Figure 5b,c). Large discrepancies, especially for longer-chain n-alkanes, are encountered for the LLE probably because of the strong dependence of the quasichemical interaction coefficient on the size of the molecule. The influence of Cad,3DIS and Cad,3QUAC parameters (which are zero in our discussion; no experimental data) and their dependence on the temperature should be examined using CpE data because, for the mixtures under study, this quantity changes strongly with the temperature. Otherwise, within its inherent limits of applicability, the model may be used safely for the prediction of other thermodynamic data. UNIFAC Treatment The MUNIFAC model (Dortmund version)42 improved by the combinatorial term and the temperature depen-
3258
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 Table 8. Values of the Standard Deviations, σT (Eq 4), of the SLE Temperatures Obtained Using DISQUAC and MUNIFAC for the DMC (1) + n-Alkane (2) Binary Mixtures (N ) Number of Data Points) n-alkane
n
σTDISQ (K)
σTMUNIF (K)
n-C18 n-C20 n-C22 n-C24 n-C26 n-C28
40 25 18 24 16 20
1.29 2.59 2.34 0.91 1.37 0.91
1.25 2.47 1.81 1.31 1.34 1.07
Gibbs excess energies GE and excess molar enthalpies HE of the organic carbonates (1) + n-alkanes (2) and presented in Table 7. The geometrical parameters rG and qG for methyl and methylene groups were calculated using the Bondi method for the original UNIFAC, presented by Gmehling et al.,42 and for the carbonate group these parameters were fited to data together with interaction parameters.21 The parameters rG and qG used in the calculations are also presented in Table 7. The number of interaction parameters in DISQUAC calculated by Kehiaian et al.10 and Gonza´lez et al.12 varies with the carbonate length. The number of interaction parameters in MUNIFAC for linear carbonate + n-alkane is constant and equal to 6. Furthermore, the parameters are independent of the carbonate length. The parameters are less complicated, but the description is similar; the average standard deviation is σT ) 1.54 K. The results of the SLE calculations and comparisons with DISQUAC theory are shown in Table 8. The second anm parameter for the O-CO-O group has a high value, which indicates a very strong dependence of temperature on the CH2/O-CO-O parameter. That parameter was developed from GE and HE data at 298.15 K and for hydrocarbons C6-C10. The extension of the same set of parameters for the longer-chain n-alkanes is responsible for the deviations of the predictions. Conclusions
Figure 5. SLE and LLE of binary mixtures [DMC (1) + n-alkane (2)]: (a) for C20; (b) for C24; (c) for C26. Solid lines: MUNIFAC model predictions. Dotted lines: DISQUAC model predictions. Points: experimental values.
dence of the group interaction parameters (anm, bnm, and cnm) is discussed. This dependence is as follows:
Ψnm ) exp[-(anm + bnmT + cnmT 2)/T]
(8)
The equation used to calculate activity coefficient γi of component i is
ln γi ) ln γiCOMB + ln γiRES
(9)
where ln γiCOMB is the combinatorial term and ln γiRES is the residual term. In MUNIFAC DMC is characterized by two main groups: the methyl CH3 and the carbonate group O-CO-O, developed earlier21 on the basis of molar
The best results for the SLE correlation of experimental points in binary systems of long-chain n-alkanes in DMC were obtained by means of the two-parameter NRTL equation, for which the average standard deviation is σT ) 0.57 K. Finally, the ability of the models to predict curves in a temperature range fairly close to the experimental, using the same interaction parameters as those for VLE and HE, is an obvious success. Deviations observed are similar to those found in other n-alkane solutions. Poorer but acceptable results are obtained because of the size effects for the systems with the longer nalkanes. The shape of the SLE vs composition curves is well predicted. Unfortunately, for the LLE, the calculated curves differ considerably from the experimental ones. This is true not only in the critical region, where no classical behavior may be involved in order to explain the flattening of the coexistence curves, but also at lower than VLE temperatures. List of Symbols a, b, c ) UNIFAC group interaction parameters C ) interchange energy coefficient in DISQUAC Cp ) interchange heat capacity parameter in DISQUAC ∆Cpm ) molar heat capacity change during the melting process
Ind. Eng. Chem. Res., Vol. 41, No. 13, 2002 3259 ∆Cptr ) molar heat capacity change during transition g ) interchange Gibbs energy parameter in DISQUAC h ) interchange enthalpy parameter in DISQUAC ∆Hm ) molar enthalpy of fusion of a pure compound ∆Htr ) molar enthalpy of transition of a pure compound n ) number of carbon atoms in the n-alkane q ) relative molecular area r ) relative molecular volume R ) gas constant (8.314 J‚mol-1‚K-1) T ) temperature Tm ) melting temperature Ttr ) solid-solid-phase transition temperature x ) mole fraction z ) coordination number Greek Letters R ) molecular surface fraction or solid phase of the alkane β ) solid phase of the alkane ∆ ) absolute mean deviation γ ) activity coefficient σT ) standard deviation σ j T ) average standard deviation ω ) ratio between the relative molecular volumes of compounds in the mixture (r1/r2) Ψ ) temperature dependence function in UNIFAC Superscripts c ) liquid-liquid critical property calc ) calculated value DIS ) dispersive term in DISQUAC DISQ ) calculated by DISQUAC COMB ) combinatorial part in UNIFAC E ) excess property exp ) experimental value QUAC ) quasichemical term in DISQUAC RES ) residual part in UNIFAC UNIF ) calculated by UNIFAC Subscripts a, d ) type of contact (a, CH3, CH2; d, O-CO-O in DISQUAC) i ) type of molecule (component) l ) order of the interchange coefficient (l ) 1, Gibbs energy; l ) 2, enthalpy; l ) 3, heat capacity; l ) 4, linear dependence with the temperature of heat capacity) s, t ) contact surfaces n, m ) type of contact in UNIFAC
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Received for review August 1, 2001 Accepted April 9, 2002 IE010662C
