Cross-Association Model for the Phase Equilibria and Surface

Feb 9, 2011 - ... contribution of CO2 on the vapor–liquid equilibria and surface tensions of CO2–hydrocarbon binary mixtures. Dong Fu , Fang Gu , ...
0 downloads 0 Views 1MB Size
Download PDF
ARTICLE pubs.acs.org/JPCC

Cross-Association Model for the Phase Equilibria and Surface Tensions of CO2-Methanol and CO2-Ethanol Mixtures Dong Fu,* XueYin Hua, and YiFei Xu School of Environmental Science and Engineering, North China Electric Power University, Baoding 071003, China ABSTRACT: A cross-association PC-SAFT is proposed for the phase behavior of CO2-methanol and CO2-ethanol mixtures by treating CO2 as a pseudoassociating molecule. Both the vapor-liquid equilibria and vapor-liquid surface tensions from low temperature-pressure to high temperature-pressure are satisfactorily calculated using this model. The results illustrate the temperature and pressure dependence of the cross-association between CO2 and alcohol hydroxyls in the bulk phases and the vapor-liquid surface, and the influence of the cross-association on the calculation of the bulk and interfacial properties.

1. INTRODUCTION Supercritical carbon dioxide (SC-CO2) is the most widely used fluid for supercritical fluid extraction due to its easy separation and nonresidual properties. However, because of its nonpolar characteristic, CO2 fails to efficiently extract large and dipolar molecules. Methanol and ethanol are typically added to SC-CO2 as cosolvents to increase the polarity and the solvency of the resulting extraction fluid. Study on the thermodynamic properties such as phase equilibria and surface tensions of CO2methanol and CO2-ethanol mixtures is significant in the field of SC-CO2 extraction. Many experimental and theoretical studies have focused on the phase equilibria of CO2-methanol and CO2-ethanol mixtures.1-10 In most of the theoretical studies, semiempirical EOS such as Peng-Robinson EOS and Patel-Teja EOS were used to model the p-x diagrams.2-4,8-10 Very recently, following the work of Button and Gubbins,11 Li and Firoozabadi,12 Valtz et al.,13 Ji et al.,14 and Fu et al.15 introduced the crossassociation contribution into the formulation of the Helmholtz free energy of CO2-methanol and CO2-ethanol mixtures, and modeled the bulk properties satisfactorily using SAFT.16-22 However, when applied to the interface, SAFT model fails to correctly predict the surface tensions with the influence parameters of pure CO2 and ethanol as input. Surface tension is an important parameter affecting the heat transfer and mass transfer, for example, in the extraction column, it is closely related to the droplet size, mass transfer area and retention, hence significantly affects the extraction efficiency. In SC-CO2 extraction, as the pressure is very high and the surface tension is of small value, a full study on the temperature and pressure dependence of surface tensions of CO2-methanol and CO2-ethanol mixtures is very important for the intensification of mass transfer and heat transfer, as well as the simulation and design of the extraction process. However, only Oei et al.,23 Dittmar et al.,24,25 and Sun and Shekunov26 have measured the r 2011 American Chemical Society

surface tensions of CO2-ethanol mixtures thus far, and the concerned theoretical models have been rarely reported. In this work, a cross-association model is proposed for the bulk and interfacial properties of CO2-alcohol mixtures based on PC-SAFT.27,28 The temperature and pressure dependence of the cross-association between CO2 and alcohol hydroxyls across the vapor-liquid surface is analyzed, and the influence of the crossassociation on the calculation of the phase equilibria and surface tensions of binary mixtures is illustrated.

2. THEORY For binary mixtures composed of associating molecules i and j, the fraction of molecule i not bonded at site A is expressed as: XX F jX Bj ΔAi Bj -1 ð1Þ X Ai ¼ ½1þ j

Bj

where F stands for the number density, ΔAiBj is related to the association strength between atom A in molecule i and atom B in molecule j: ΔAi Bj ¼ gijhs ½expðεAi Bj =kTÞ-1ðdij 3 kAi Bj Þ

ð2Þ

where εAiBj and κAiBj are respectively the association energy and association volume between atom A in molecule i and atom B in molecule j. ghs and d are respectively the radial pair distribution function and hard sphere diameter. For CO2(1)-alcohol(2) mixture, when CO2 is treated as a pseudoassociating molecule, there is no self-association between CO2 molecules, and the formulation of XAi is different from that of binary mixtures composed of two associating molecules. According to the work of Huang and Radosz,17 the ‘2B’ bonding type is adopted for both alcohol and CO2 molecules in this work, Received: September 2, 2010 Revised: December 13, 2010 Published: February 09, 2011 3340

dx.doi.org/10.1021/jp108400z | J. Phys. Chem. C 2011, 115, 3340–3345

The Journal of Physical Chemistry C

ARTICLE

that is, one site on the O atom and one site on the H atom in alcohol molecules and two O atoms in CO2 molecules should be taken into account in the formulation of association energy. Each O atom can associate with only one H atom, and vice versa: 1 1 , X O2 ¼ , 1þF2 X H2 ΔO1 H2 1þF2 X H2 ΔO2 H2 1 ¼ O2 H2 O 2 1þF2 X Δ þF1 X O1 ΔO1 H2

Table 1. Molecular Parameters and Influence Parameters of Pure Fluids

CO2 2.073 methanol 1.526 ethanol 2.383

X O1 ¼ X H2

2.785 3.230 3.177

κa

169.21 188.90 0.0351 198.24 0.0323

εa.k-1/K

κi i/10-19 J 3 m5 3 mol-2

2899.5 2653.4

0.14 0.00224T - 0.3829 0.00372T - 0.6718

ð3Þ as:

where the association energy and association volume between atoms O and H in alcohol hydroxyl could be obtained by fitting the experimental data of pure fluids. However, determination of the cross-association between atom O in CO2 molecules and atom H in alcohol molecules is problematic because CO2 itself is not an associating molecule, and the cross-association cannot be obtained by mathematical or geometric average on the selfassociation of pure fluids. In this work, according to the previous work of Segura et al.,29 Yu and Wu,30 and Fu and Li,31 ΔO1H2 is expressed as follows: ΔO1 H2 ¼ 4πKgijhs ½expðεO1 H2 =kTÞ-1

σ/10-10m ε.k-1/K

m

ð4Þ

where K = 1.4849  10-4σ312 and σ is the soft sphere diameter of molecules. εO1H2/k is an adjustable parameter, which could be determined by fitting to the experimental data of phase equilibria. When XO1, XO2, and XH2 are correctly expressed, the Helmholtz free energy for the bulk phase of CO2-alcohol binary mixtures may be formulated using PC-SAFT.27,28 In the vaporliquid surface, the Helmholtz free energy density f can be expressed under the framework of density gradient theory (DGT):32,33 XX1 kij rFi ðrÞrFj ðrÞþ:::::: f ¼ f0 þ ð5Þ 2 i j where Fi(r) is the local number density of molecule i at position r and r[Fi(r)] is the corresponding local density gradient. f0[F1(r),F2(r)] is the free energy density for the bulk phase. κ11, κ22 are respectively the influence parameters for components 1 and 2, (κ12 = κ11κ22)1/2 is the cross-influence parameter. Keeping the lowest order term in eq 5, the Helmholtz free energy for the interface of CO2-alcohol binary mixtures can be expressed as: 2 3 Z XX1 kij rFi ðrÞrFj ðrÞ5dr ð6Þ A ¼ 4f0 þ 2 i j Because the density varies only in the direction perpendicular to the interface (z direction), F(r) can be replaced by F(z). To calculate the surface tensions, one should first select a reference fluid of which the density profile is a monotonic function of z over the whole interface, and then numerically determine the density profiles of each component, F1(z) and F2(z).34-40 Dividing the vapor-liquid surface into N0 thin layers, the number density in the kth layer can be expressed as: F2 ðzk Þ ¼ F2 ðzk-1 Þ þ ΔF2 ,ΔF2 ¼ ðFL2 -FV2 Þ=N0 , N0 > 10 000 ð7Þ

where F2(z0) and F2(zN0þ1) respectively equal to the equilibrium vapor density FV2 and the equilibrium liquid density FL2 . The number density of component 1 in the kth layer can be expressed

F1 ðzk Þ ¼ F1 ðzk-1 Þ þ

dF1 ðzk-1 Þ ΔF , dF2 ðzk-1 Þ 2

F1 ðz0 Þ ¼ FV1 ,F1 ðzN0 þ1 Þ ¼ FL1

ð8Þ

where the differentiation dF1/dF2 in (k - 1)th layer is expressed as: pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi k22 ½Dμ1 =DF2 T , p,F1 - k11 ½Dμ2 =DF2 T , p,F1 dF1 ðzÞ ¼ pffiffiffiffiffiffiffi ð9Þ pffiffiffiffiffiffiffi dF2 ðzÞ k11 ½Dμ2 =DF1 T , p,F2 - k22 ½Dμ1 =DF1 T , p,F2 where μ1 and μ2 are the chemical potentials for components 1 and 2, respectively. Suppose FV2 corresponds to z = 0, the value of z in each layer can be calculated from: Z FL2 rffiffiffiffiffiffiffiffiffiffi k dF2 ðzÞ with z¼ V 2ΔΩ F2   dF1 ðzÞ 2 dF ðzÞ k ¼ k11 þ 2k12 1 þ k22 ð10Þ dF2 ðzÞ dF2 ðzÞ P where Ω[F1(r), F2(r)] = f[F1(r), F2(r)] - iFi(r)μi0 is the grand potential density and μi0 = ((∂{f0[F1(r), F2(r)]})/ (∂Fi(r)))1/2|T,V,Fj(r) is the chemical potential of component i in bulk phase. By evaluating the integral numerically, a distance z may be determined for any F2 lying between the bulk densities, hence F1(z) and F2(z) can be determined. Once the equilibrium density profiles are obtained, the surface tension can be calculated from: Z FL2 pffiffiffiffiffiffiffiffiffiffiffiffiffi 2ΔΩkdF2 ðzÞ ð11Þ γ¼ FV2

3. RESULTS AND DISCUSSION At given temperature T, the vapor-liquid equilibria of CO2-alcohol mixtures can be determined according to the requirement that the total pressure and the chemical potential of component i in each phase should be equal. The molecular parameters of CO2, methanol and ethanol are taken from the work of Gross and Sadowski,27 as shown in Table 1. During the calculation of the phase equilibria of binary mixtures, the molecular parameters of pure fluids are used as input, and εO1H2/k and kij are regressed by fitting to the experimental data of p-x diagram. Once εO1H2/k and kij are available, the p-x diagrams and the nonbonded fraction of CO2 can be predicted in a wide temperature and pressure range. Figures 1 and 2 show the correlated p-x diagrams for CO2-methanol and CO2-ethanol mixtures, and the comparison with experimental data. One finds that the PC-SAFT well captures the p-x relationship of CO2-alcohol mixtures in the 3341

dx.doi.org/10.1021/jp108400z |J. Phys. Chem. C 2011, 115, 3340–3345

The Journal of Physical Chemistry C

3

Figure 1. p-x diagrams for CO2-methanol mixtures. Symbols: experimental data.1,2 Lines: calculated results, ----: εO1H2/k = 2801.29, kij = 0.07; —: εO1H2/k = 0, kij = 0.01. Main plot: 298.15K (O), 308.15K (0), 320.15K ()), 335.00K (3); Insert plot: 291.15K (O), 303.15K (0), 313.15K (43), 30.00K ( ), 342.80K ()).

Figure 2. p-x diagrams for CO2-ethanol mixtures. Symbols: experimental data.2,7 Lines: calculated results, ----: εO1H2/k = 3.0899T þ 2067.10, kij = 0.14; —: εO1H2/k = 0, kij = 0.05. Main plot: 303.15K (O), 322.15K (3), 338.15 K (0), 373.15K ()); Insert plot: 293.15K (O), 313.15K (0), 333.15K (4), 353.15 K ()), 391.15K (3).

case of low pressure; however, in the case of high pressure, the calculations significantly overestimate the experiments. Moreover, PC-SAFT predicts a phase transition from vapor-liquid

ARTICLE

equilibrium to liquid-liquid equilibrium for methanol-CO2 mixtures at 308.15 (7.58 MPa) and 313.15K(8.40 MPa), and for ethanol-CO2 mixtures at 293.15K (5.54 MPa), 303.15 (7.10 MPa), and 313.15K(8.35 MPa). Because the liquid-liquid equilibria have not been observed in experiments, only the p-x diagrams corresponding to vapor-liquid equilibria are shown in Figures 1 and 2. When CO2 is treated as a pseudoassociating molecule and the cross-association between CO2 and alcohol hydroxyls is taken into account, the predicted p-x diagrams are significantly improved, thus suggesting that the sensitivity of the cross-association contribution may overcome the lack of the fit of the original model for correlating bulk properties of CO2-alcohol mixtures. It is worth noting that besides the cross-association PC-SAFT used in this work, the quadrupole versions of PC-SAFT (PCPSAFT) proposed by Gross41 can also improve the prediction of the bulk properties for binary mixtures containing quadrupolar molecules. For example, when applied to the mixtures of CO2 and alkanes,41 PCP-SAFT significantly improves the vaporliquid equilibria; when applied to the vapor-liquid surface,42 PCP-SAFT also yields quantitatively better surface tensions than PC-SAFT. However, when applied to the mixtures of CO2 and alcohols, PCP-SAFT still unsatisfactorily estimates the experimental data in the region of high pressure and high temperature, in particular, for CO2-ethanol mixtures, the predicted critical pressures corresponding to 293.15, 338.15, and 391.15K are respectively 5.704, 17.449, and 22.072 MPa (with kij = -0.04 and the quadrupolar moment Q = 4.4DA). Although the cross-association PC-SAFT yields better phase equilibria than PC-SAFT and PCP-SAFT, one may find that the optimized cross-association energies between CO2 and alcohol, εO1H2/k, are very similar to the self-association energies of the pure alcohols. To reduce the debatable magnitude of εO1H2/k effect, the p-x diagrams of CO2-ethanol mixtures are calculated by taking both quadrupolar and cross-association interactions into account. It is found that when kij values are around -0.04, there exists small εO1H2/k that can yield quantitatively good p-x diagrams, for example, at 391.15K, when εO1H2/k is no greater than 2000, the calculated p-x diagrams are very close to those from PCP-SAFT. At other kij values, the calculated results become worse and the adjustment of εO1H2/k has little effect on the phase equilibria, indicating simultaneously taking quadrupolar and cross-association interactions into account is not an appropriate approach. Figure 3 shows the nonbonded fractions of CO2 in vapor and liquid phases and the corresponding equilibrium densities for CO2-methanol mixture. In the vapor phase, because the number densities of methanol are of very small values (as shown in the insert plot), only small amount of CO2 molecules can be associated with methanol molecules; hence the mole fraction of bonded CO2 are of very small values and XO1 is very close to 1.0. However, in the liquid phase, when the pressure is low, the densities of CO2 and methanol are respectively very low and very high, and much more CO2 molecules can be associated with methanol molecules, hence the fractions of bonded CO2 are of large values. With the increase of pressure, the densities of CO2 and methanol respectively increase and decrease, and the fraction of bonded CO2 decreases consequently. When the equilibrium bulk properties and the influence parameters (as also shown in Table 1) of pure fluids34,36 are available, the surface tensions of CO2-methanol and CO2ethanol mixtures can be determined using DGT. Under the framework of DGT, the accuracy of both correlation and prediction of the 3342

dx.doi.org/10.1021/jp108400z |J. Phys. Chem. C 2011, 115, 3340–3345

The Journal of Physical Chemistry C

ARTICLE

Figure 3. Nonbonded fractions of CO2 (—, T = 330.15K; - - -, T = 335.15K; ----, T = 342.15K) in vapor and liquid phases, and the equilibrium densities of CO2 (—) and methanol (----) at 330.15K (insert plot).

Figure 4. Comparison of the experimental23-25 (symbols) and predicted (lines, from PC-SAFT combined with DGT) surface tensions of CO2-ethanol mixtures. Main plot: b, 292.65K; O, 313.15K; 9, 334.15K; 0, 354.65K; ----, 292.65K; —, 313.15K; - -, 334.15K; - - -, 354.65K. Insert plot: b, 303.65K; O, 323.65K; 9, 344.65K; 0, 363.15K; ----, 303.65K; —, 323.65K; - -, 344.65K; - - -, 363.15K.

Figure 5. (a) Density profiles of CO2 and ethanol across the vaporliquid surfaces. Lines: predicted by the cross-association PC-SAFT combined with DGT: —, ethanol; ----, CO2. Main plot: p = 5 MPa. The mole fractions of CO2 in vapor and liquid phases are respectively 0.9882 and 0.3061 at 313.15K, and respectively 0.9579 and 0.2110 at 353.15K; Insert plot: T = 353.15K. The mole fractions of CO2 in vapor and liquid phases are respectively 0.9387 and 0.1110 at 2.5 MPa, and respectively 0. 9590 and 0.3115 at 7.5 MPa. (b) Density profiles for CO2-methanol mixtures and the accumulation of CO2 (insert plot) at 353.15K. In the main plot, the mole fraction of CO2 in liquid phases, x1L = 0.2. ----, predicted by PC-SAFT combined with DGT; —, predicted by the cross-association PC-SAFT combined with DGT.

surface tensions significantly depends on the accuracy of the calculation of bulk properties. When treating CO2 as nonpolar molecule and calculating the phase equilibria of CO2-alcohol binary mixtures with PC-SAFT, the calculated surface tensions in

the high pressure region deviate obviously from the experimental data due to the inaccuracy of the calculation of bulk properties. Moreover, the higher is the temperature, the larger is the deviation, as shown in Figure 4. 3343

dx.doi.org/10.1021/jp108400z |J. Phys. Chem. C 2011, 115, 3340–3345

The Journal of Physical Chemistry C

ARTICLE

Figure 6. Nonbonded fractions XO1 across the vapor-liquid surfaces: main plot, T = 353.15K; insert plot, p = 2.5 MPa.

Figure 7. Same as in Figure 4, except that the surface tensions are predicted by the cross-association PC-SAFT combined with DGT.

Part a of Figure 5 shows the density distributions of CO2 and ethanol across the vapor-liquid surfaces predicted by the crossassociation PC-SAFT combined with DGT. One finds from this figure that the density profile of CO2 displays a nonmonotonic trend due to the accumulation in the surface but that of ethanol is of monotonic function of z over the vapor-liquid surface. Because the density profile of the reference fluid must be a monotonic function of z over the whole surface, in all of the calculations in this work, alcohol is selected as the reference fluid. Part b of Figure 5 shows the density distributions of CO2 and methanol predicted by the cross-association PC-SAFT and PCSAFT, and the relationship between the accumulation of CO2 and x1L, the mole fraction of CO2 in liquid phases. It seems the densities in the liquid phases predicted from PC-SAFT are higher than those from cross-association PC-SAFT; hence the surface tensions predicted from PC-SAFT should be higher than those from cross-association PC-SAFT because higher liquid density tends to yield higher surface tension.43,44 Besides the density difference in the liquid phases, the geometric difference may also significantly affect the calculation of surface tensions.45 To numerically compare the geometric difference, the accumulation of CO2 in the vapor-liquid surface, Γ, is defined as: Z ð12Þ Γ ¼ fFCO2 ðzÞ-Fbulk CO2 gdz=z10 000 where z10 000 is the whole distance from vapor side to liquid side, which can be determined by DGT. Because the vapor-liquid surface corresponds to two bulk densities, eq 12 may be expressed as: ( n0 X ½FCO2 ðzi Þ-FVCO2  Γ¼ i¼0

 zi þ

10 000 X i¼n0 þ1

), ½FCO2 ðzi Þ-FLCO2   zi

z10 000

ð13Þ

Figure 8. Predicted surface tensions of CO2-methanol mixtures. Lines: predicted by cross-association PC-SAFT combined with DGT. Main plot: ----, 293.15K; —, 313.15K; - -, 333.15K; - - -, 353.15K. Insert plot: ----, 303.15K; —, 323.15K; - -, 343.15K; - - -, 363.15K.

where zn0 corresponds to the position in the surface at which the peak of the density profile of CO2 occurs. Using eq 13, Γ of CO2-methanol mixtures is calculated, as also shown in part b of Figure 5. One finds that Γ values from PC-SAFT are lower than those from cross-association PCSAFT, which may partially explain the factor that the surface tensions calculated from PC-SAFT are larger than those from 3344

dx.doi.org/10.1021/jp108400z |J. Phys. Chem. C 2011, 115, 3340–3345

The Journal of Physical Chemistry C cross-association PC-SAFT at given temperatures. For a binary mixture, molecules with lower surface tension have a tendency to accumulate in the vapor-liquid surface, in this regard, the surface tensions may decrease with the increase of Γ at a given temperature. Figure 6 shows the nonbonded fractions XO1 across the vapor-liquid surfaces. One finds from this figure that although the bonded fractions of CO2 in vapor phases are of very small values, those in the liquid phases are of large values. Across the vapor-liquid surface, XO1 decreases distinguishably with the increase of z, which significantly affects the calculation of Helmholtz free energy and the surface tensions. Figures 7 and 8 respectively show the surface tensions of CO2-ethanol and CO2-methanol binary mixtures predicted from the cross-association PC-SAFT combined with DGT. In a wide temperature and pressure range, the surface tensions of CO2ethanol mixtures are satisfactorily predicted compared with the experimental data. Compared with the PC-SAFT, the cross-association PC-SAFT yields much more accurate phase equilibria for CO2-ethanol mixtures and hence provides more accurate bulk properties as the input of the calculation of interfacial properties and yields more accurate surface tensions. Also presented in these figures is that, at a given temperature, the surface tensions decrease with the increase of pressure, and the lower is the temperature, the more rapidly the surface tensions decrease.

4. CONCLUSIONS In conclusion, a cross-association model is established based on PC-SAFT by treating CO2 as a pseudoassociating molecule and considering both the self-association between alcohol hydroxyls and the cross-association between CO2 and alcohol hydroxyls. The phase equilibria and surface tensions of CO2-methanol and CO2-ethanol mixtures in a wide temperature and pressure range are investigated. The results show that when the crossassociation is correctly taken into account for the Helmholtz free energy, the calculated bulk and interfacial properties of CO2methanol and CO2-ethanol mixtures can be significantly improved. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel. 86-312-7522037.

’ ACKNOWLEDGMENT The authors appreciate the financial support from the National Natural Science Foundation of China (No. 21076070), and the Fundamental Research Funds for the Central Universities (No. 09MG13). ’ REFERENCES (1) Joung, S. N.; Yoo, C. W.; Shin, H. Y.; Kim, S. Y.; Yoo, K. P.; Lee, C. S.; Huh, W. S. Fluid Phase Equilib. 2001, 185, 219–230. (2) Chang, C. M J.; Chiu, K. L.; Day, C. Y. J. Supercrit. Fluids 1998, 12, 223–237. (3) Zhu, H. G.; Tian, Y. L.; Chen, L.; Feng, J. J.; Fu, G. F. Chem. Res. Chin. Univ. 2002, 23, 1588–1591. (4) Tian, Y. L.; Han, M.; Feng, J. J.; Qin, Y. Acta. Phys. Chim. Sinica 2001, 17, 155–160. (5) Secuianu, C.; Feroiu, V.; Geana, D. J. Supercrit. Fluids 2008, 47, 109–116.

ARTICLE

(6) Galicia-Luna, L. A.; Ortega-Rodriguez, A.; Richon, D. J. Chem. Eng. Data 2000, 45, 265–271. (7) MendozadelaCruz, J. L.; Galicia-Luna, L. A. Int. Electron J. Phys. Chem. Data 1999, 5, 157–164. (8) Lopez, J. A.; Trejos, V. M.; Cardona, C. A. Fluid Phase Equilib. 2008, 275, 1–7. (9) Polishuk, I.; Wisniak, J.; Segura, H. Chem. Eng. Sci. 2001, 56, 6485–6510. (10) Wang, W. L.; Zhang, X. D.; Liu, X. W.; Xia, Y. J.; Li, Z. Y. J. Chem. Ind. Eng. 2003, 24, 1–4. (11) Button, J. K.; Gubbins, K. E. Fluid Phase Equilib. 1999, 158-160, 175–181. (12) Li, Z. D.; Firoozabadi, A. AIChE J. 2009, 55, 1803–1813. (13) Valtz, A.; Chapoy, A.; Coquelet, C.; Paricaud, P.; Richon, D. Fluid Phase Equilib. 2004, 226, 333–344. (14) Ji, X. Y.; Tan, S. P.; Adidharma, H.; Radosz, M. Ind. Eng. Chem. Res. 2005, 44, 8419–8427. (15) Fu, D.; Yang, Z.; Lu, J. Y.; Liu, J. M. Sci. China Ser. B 2010, 53, 1438–1444. (16) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. Fluid Phase Equilib. 1989, 52, 31–38. (17) Huang, S. H.; Radosz, M. E. Ind. Eng. Chem. Res. 1990, 2, 2284– 2294. (18) Mi, J. G.; Tang, Y. P.; Zhong, C. L. J. Phys. Chem. B 2005, 109, 20546–20553. (19) Mi, J. G.; Zhong, C. L.; Li, Y. G. J. Chem. Phys. 2004, 121, 5372– 5380. (20) Li, X. S.; Wu, H. J.; Li, Y. G. J. Chem. Thermo. 2007, 39, 417–425. (21) Li, X. S.; Wu, H. J.; Englezos, P. Ind. Eng. Chem. Res. 2006, 45, 2131–2137. (22) Fu, D. J. Phys. Chem. B 2006, 110, 19575–19581. (23) Oei, S. B.; Dittmar, D.; Eggers, R. Chem. Ing. Tech. 2001, 73, 830–834. (24) Dittmar, D.; Oei, S. B.; Eggers, R. Chem. Eng. Technol. 2002, 5, 23–27. (25) Dittmar, D.; Fredenhagen, A.; Oei, S. B.; Eggers, R. Chem. Eng. Sci. 2003, 58, 1223–1233. (26) Sun, Y.; Shekunov, B. Y. J. Supercrit. Fluids 2003, 27, 73–83. (27) Gross, J.; Sadowski, G. Ind. Eng. Chem. Res. 2001, 40, 1244– 1260. (28) Gross, J.; Sadowski, G. Ind. Eng. Chem. Res. 2002, 41, 5510– 5515. (29) Segura, C. J.; Chapman, W. G.; Shukla, K. P. Mol. Phys. 1997, 90, 759–771. (30) Yu, Y. X.; Wu, J. Z. J. Chem. Phys. 2002, 116, 7094–7103. (31) Fu, D.; Li, X. S. J. Chem. Phys. 2006, 125, 084716. (32) Cahn, J. W.; Hilliard, J. E. J. Chem. Phys. 1958, 28, 258–267. (33) Dee, G. T.; Sauer, B. B. Adv. Phys. 1998, 47, 161–205. (34) Fu, D.; Wei, Y. Z. Ind. Eng. Chem. Res. 2008, 47, 4490–4495. (35) Liu, S. T.; Fu, D.; Lu, J. Y. Ind. Eng. Chem. Res. 2009, 48, 10734– 10739. (36) Fu, D. Ind. Eng. Chem. Res. 2007, 46, 7378–7383. (37) Miqueu, C.; Mendiboure, B.; Graciaa, A.; Lachaise, J. Fluid Phase Equilib. 2003, 207, 225–246. (38) Miqueu, C.; Mendiboure, B.; Graciaa, A.; Lachaise, J. Fluid Phase Equilib. 2004, 218, 189–203. (39) Queimada, A. J.; Miqueu, C.; Marrucho, I. M.; Kontogeorgis, G. M.; Coutinho, J. A. P. Fluid Phase Equilib. 2005, 228, 479–485. (40) Miqueu, C.; Mendiboure, B.; Graciaa, A.; Lachaise, J. Ind. Eng. Chem. Res. 2005, 44, 3321–3329. (41) Gross, J. AIChE J. 2005, 51, 2556–2568. (42) Nino-Amezquita, O. G.; Enders, S. Comput.-Aided Chem. Eng. 2010, 28, 85–90. (43) Macleod, D. B. Trans. Faraday Soc. 1923, 19, 38–41. (44) Sugden, S. J. Chem. Soc. 1924, 125, 1177–1189. (45) Mejia, A.; Segura, H.; Vega, L. F.; Wisniak J. Fluid Phase Equilib. 2005, 227, 225–238. 3345

dx.doi.org/10.1021/jp108400z |J. Phys. Chem. C 2011, 115, 3340–3345