J. Phys. Chem. C 2007, 111, 15487-15492
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ARTICLES tPC-PSAFT Modeling of Gas Solubility in Imidazolium-Based Ionic Liquids† Eirini K. Karakatsani,‡ Ioannis G. Economou,*,‡,§ Maaike C. Kroon,|,⊥ Cor J. Peters,| and Geert-Jan Witkamp⊥ Molecular Thermodynamics and Modeling of Materials Laboratory, Institute of Physical Chemistry, National Center for Scientific Research “Demokritos”, GR-15310 Aghia ParaskeVi Attikis, Greece, Center for Phase Equilibria and Separation Processes (IVC-SEP), Department of Chemical Engineering, Technical UniVersity of Denmark, DK-2800 Lyngby, Denmark, Physical Chemistry and Molecular Thermodynamics, Department of Chemical Technology, Faculty of Applied Sciences, Delft UniVersity of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands, and Laboratory for Process Equipment, Department of Process & Energy, Faculty of Mechanical, Maritime, and Materials Engineering, Delft UniVersity of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands ReceiVed: January 22, 2007; In Final Form: June 11, 2007
The truncated perturbed chain-polar statistical associating fluid theory (tPC-PSAFT) is re-parametrized for imidazolium-based ionic liquids (ILs) by fitting IL density data over a wide temperature range and restricting the model to predict very low vapor pressure values, in agreement with recent experimental evidence. The new set of parameters is used for the correlation of carbon dioxide solubility in various ILs using a binary interaction parameter, kij. The correlated kij values are much lower than the values used previously for the same mixtures (Kroon et al., J. Phys. Chem. B 2006, 110, 9262). Furthermore, the solubilities of carbon monoxide, oxygen, and trifluoromethane in 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim+][PF6-]) are correlated. In all cases, the agreement between tPC-PSAFT correlation and experimental data for mixtures is very good.
Introduction Ionic liquids (ILs) are increasingly used today for chemical reactions and separations.1 In fact, it is expected that ILs may revolutionize the chemical process industry in the years to come.2 An absolute prerequisite for the use of an IL mixture in a chemical process is the accurate knowledge of its physical properties. A growing number of experimental investigations have been reported in the literature3-12 while various activity coefficient models and equations of state (EoS) have been proposed for the calculation of thermodynamic properties and phase equilibria of IL mixtures.13-15 Recently, we proposed an equation of state for the calculation of carbon dioxide solubility in various imidazolium-based ILs based on the truncated perturbed chain-polar statistical associating fluid theory (tPC-PSAFT).16 tPC-PSAFT accounts explicitly for weak dispersion and highly oriented polar and short-range strong hydrogen bonding interactions, and so it is an appropriate model for such mixtures. In tPC-PSAFT, ILs were modeled as highly polar neutral ion pairs. The IL model parameters, that is, the segment energy parameter, u/k, the segment volume, V00, and the segment effective polar diameter, σP, were estimated on the basis of the thermodynamic and physicochemical data †
Part of the “Keith E. Gubbins Festschrift”. * Corresponding author. E-mail:
[email protected]. Institute of Physical Chemistry, NCSR Demokritos. § Technical University of Denmark. | Department of Chemical Technology, Delft University of Technology. ⊥ Department of Process & Energy, Delft University of Technology. ‡
of the constituent ions and on parameters values for hydrocarbons chemically similar to IL cations, while IL density experimental data were used to adjust the segment number, m, of the IL. Finally, the strong association between carbon dioxide and the anion of IL was calculated explicitly using Wertheim’s approach. The model provided excellent correlation of the experimental data over a wide pressure range using a temperature-dependent binary interaction parameter (kij) that assumed significantly high values.16 In this work, tPC-PSAFT parameters for ILs are re-estimated by fitting very recently available experimental liquid density data over a wider range of temperature. Furthermore, we restrict the model to predict very low vapor pressure values for ILs, in agreement with experimental evidence. Until recently, ILs were considered to have almost zero vapor pressure. Very recently, experimental measurements were made available showing that some ILs have very low but still probably measurable vapor pressures.17-20 Accordingly, the model is tuned here in order to be in agreement with experimental evidence. The pure component parameters are used subsequently for the correlation of solubility of carbon dioxide, carbon monoxide, oxygen, and trifluoromethane in imidazolium-based ILs. In all cases, the agreement between experimental data and model correlation is very good. Model Description tPC-PSAFT EoS has been discussed in detail previously.16,21 Here, only the major concepts are provided with emphasis to
10.1021/jp070556+ CCC: $37.00 © 2007 American Chemical Society Published on Web 08/07/2007
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TABLE 1: tPC-PSAFT Pure-Component Parameters for Imidazolium-Based Ionic Liquids IL
MW (g/mol)
m (-)
V00 (mL/mol)
u/k (K)
µ (D)
σP (Å)
T (K)
% AAD in F
refa
[emim+][PF6-] [bmim+][PF6-] [hmim+][PF6-] [omim+][PF6-] [emim+][BF4-] [bmim+][BF4-] [hmim+][BF4-] [omim+][BF4-]
256.13 284.18 312.24 340.29 197.97 226.02 254.08 282.13
8.936 10.748 12.268 13.750 8.375 9.600 11.460 12.620
11.34 11.55 11.85 12.19 10.14 11.19 11.05 11.40
251.47 251.47 251.47 251.47 214.53 214.53 214.53 214.53
1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70
5.625 5.660 5.709 5.767 5.418 5.485 5.559 5.636
333-500 273-363 293-393 293-393 293-333 278-353 298.15 293-393
1.72 0.71 0.79 1.54 2.21 1.32 0.63 1.40
1 2-14 5, 15 5, 15 16, 17 3, 15, 18-26 26 15
a (1) Alavi and Thompson. J. Chem. Phys. 2005, 122, 154704; (2) Magee et al. J. Chem. Eng. Data 2004, 49, 453; (3) Rogers et al. Green Chem. 2001, 3, 156; (4) Brennecke et al. J. Phys. Chem. B 2001, 105, 2437; (5) Bartsch et al. Anal. Chem. 2001, 73, 3737; (6) Gu and Brennecke. J. Chem. Eng. Data 2002, 47, 339; (7) Zhuo et al. J. Solution Chem. 2005, 34, 585; (8) Maurer et al. Fluid Phase Equilib. 2005, 228-229, 207; (9) Kanakubo et al. J. Chem. Eng. Data 2005, 50, 1777; (10) Zafarani-Moattar and Shekaari. J. Chem. Eng. Data 2005, 50, 1694; (11) Costa Gomes et al. Fluid Phase Equilib. 2006, 240, 87; (12) Rebelo et al. Int. J. Thermophys. 2006, 27, 39; (13) Yokohama et al. Int. J. Thermophys. 2006, 27, 39; (14) Zafarani-Moattar and Shekaari. J. Chem. Thermodyn. 2006, 38, 624; (15) Coutinho et al. J. Chem. Eng. Data 2006, ASAP Article; (16) Luo et al. Phys. Chem. Liq. 2003, 41, 487; (17) Watanabe et al. J. Phys. Chem. B 2001, 105, 4603; (18) Brennecke et al. J. Phys. Chem. B 2004, 108, 20355; (19) Yamamoto et al. J. Fluorine Chem. 2003, 120, 135; (20) From ref 7; (21) Brennecke et al. J. Chem. Eng. Data 2004, 49, 954; (22) Wilkes et al. Thermochim. Acta 2005, 425, 181; (23) Rebelo et al. J. Chem. Eng. Data 2005, 50, 997; (24) Chen et al. J. Chem. Eng. Data 2006, 51, 905; (25) Yokoyama et al. Int. J. Thermophys. 2006, 27, 39; (26) Wasserscheid and Welton Ionic Liquids in Synthesis; Wiley-VCH Verlag: Weinheim, Germany, 2003.
Figure 1. Close-packed molar volumes mVoo for imidazolium-based ILs with [PF6-] and [BF4-] anions against molecular weight.
the polar interactions that differentiate tPC-PSAFT from PCSAFT EoS. In terms of the residual Helmholtz free energy, the model is given as the sum of the hard-sphere term (hs), the hard-chain term (chain), the association term (assoc), and the dispersive term (disp). In order to account for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions in polar systems such as CO2 + IL mixtures, an explicit polar contribution, apolar, is added:16
ares(T,F) ahs(T,F) ) + RT RT achain(T,F) aassoc(T,F) adisp(T,F) apolar(T,F) + + + (1) RT RT RT RT The hs, chain, assoc, and disp terms are identical to the corresponding terms proposed for PC-SAFT and are given by Gross and Sadowski.22,23 The polar term is based on a simple Pade´ approximant proposed by Stell and co-workers:24
apolar 2 apolar )m polar polar RT 1 - a /a 3
(2)
2
Subscripts 2 and 3 in eq 2 denote the second and third-order term in the perturbation expansion for polar interactions, whereas
Figure 2. Experimental data5,7,27-29 and tPC-PSAFT correlation for the bubble-point pressure of (top) [emim+][PF6-] + CO2, [bmim+][PF6-] + CO2, and [hmim+][PF6-] + CO2 mixtures at 333.15 K and (bottom) [bmim+][BF4-] + CO2, [hmim+][BF4-] + CO2, and [omim+][BF4-] + CO2 mixtures at 333.15 K.
the third-order term consists of a two-body and a three-body term so that
apolar apolar apolar 3 3,2 3,3 ) + RT RT RT
(3)
In the tPC-PSAFT model, the higher order terms of the polynomials introduced by Stell and co-workers are truncated,
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µ˜ ij ) xµ˜ iµ˜ j
(11)
Q ˜ ij ) xQ ˜ iQ ˜j
(12)
Finally, for the three-body polar term (apolar 3,3 ), the following mixing rules are proposed:
µ˜ )
∑i ∑j ∑k xixjxkmimjmkµ˜ ijk
(∑ ) ximi
(13)
3
i
Q ˜ )
Figure 3. Temperature dependence of the binary interaction parameter for various IL + CO2 mixtures.
RT
()[ () [
)-
]
˜ 12 µ˜ Q 12 Q u 4 µ˜ ˜ η + + kT 3 (σ /σ)3 5 (σ /σ)5 5 (σ /σ)7 p p p 4
2
2
2
4
apolar 3,2 u 3 2 6 µ˜ 4 ) ηQ ˜ + RT kT 5 (σ /σ)8
ximi
p
]
p
apolar 3,3 u 3 2 10 µ˜ 6 η + ) RT kT 9 (σ /σ)3 p
]
˜6 ˜2 ˜4 159 µ˜ 4Q 689 µ˜ 2Q 243 Q + + (6) 125 (σ /σ)5 1000 (σ /σ)7 800 (σ /σ)9 p
p
p
where:
µ/m
µ˜ ) 85.12
x(u/k)σ3
Q ˜ ) 85.12
Q/m
x(u/k)σ5
(7)
(8)
and µ is the dipole moment of the fluid in D, and Q is its quadrupole moment in DÅ. For mixture calculations, the mixing rules for the two-body polar terms (apolar and apolar 2 3,2 ) are
∑i ∑j xixjmimjµ˜ ij
(∑ ) ximi
2
(9)
i
Q ˜ )
∑i ∑j xixjmimjQ˜ ij
(∑ ) ximi
i
with:
1/3
)
2
(10)
∑i ∑j ∑k xixjxkmimjmkΛ˜ ijk
(∑ )
3
ximi
(4)
Q ˜4 ˜2 144 µ˜ 2Q 72 + (5) 175 (σ /σ)10 245 (σ /σ)12
µ˜ )
˜) Λ ˜ ) (µ˜ Q 2
(15)
i
Γ ˜ ) (µ˜ Q ˜ 2)1/3 )
p
()[
(∑ )
(14)
3
i
whereas a new pure component parameter is introduced that accounts for the spatial extent of polar interactions compared with hard core repulsive interactions. As a result, the following expressions are used for the polar interactions:
apolar 2
∑i ∑j ∑k xixjxkmimjmkQ˜ ijk
∑i ∑j ∑k xixjxkmimjmkΓ˜ ijk
(∑ ) ximi
3
(16)
i
with:
µ˜ ijk ) (µ˜ iµ˜ jµ˜ k)1/3
(17)
˜ iQ ˜ jQ ˜ k)1/3 Q ˜ ijk ) (Q
(18)
Λ ˜ ijk ) (µ˜ iµ˜ jQ ˜ k)1/3
(19)
˜ jQ ˜ k)1/3 Γ ˜ ijk ) (µ˜ iQ
(20)
Parameter Estimation Experimental data reported in the literature very recently17,18 indicate that ILs exhibit some marginal volatility, unlike earlier conclusions that ILs were not volatile at all. The volatility is very low, and especially at low temperatures, only estimated values can be provided. Magee and co-workers19 reported an order-of-magnitude estimate of the vapor pressure of 1-butyl3-methylimidazolium hexafluorophosphate ([bmim+][PF6-]), while Heintz and co-workers20 measured the vapor pressures for a series of 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ILs by the integral effusion Knudsen method. These new findings should be taken into account in the development of accurate thermodynamic models for ILs in solution. In this work, tPC-PSAFT parameters for the same ILs are re-estimated by fitting the model to recently available IL density data over a broad temperature range, not used in our earlier work,16 and by imposing the model to predict very low vapor pressure values over a wide temperature range examined. Since the exact vapor pressures of ILs are not accurately known, we only impose an order-of-magnitude match of these experimental values. IL molecules are considered as neutral ion pairs with a permanent dipole moment, consistent with the earlier work.16
15490 J. Phys. Chem. C, Vol. 111, No. 43, 2007
Figure 4. Experimental data31 and tPC-PSAFT correlation for the bubble-point pressure of [bmim+][PF6-] + CO at 293.15 K (top) and 373.15 K (bottom).
Karakatsani et al.
Figure 5. Experimental data31 and tPC-PSAFT correlation for the bubble-point pressure of [bmim+][PF6-] + O2 at 293.15 K (top) and 373.1 K (bottom).
More specifically, the descriptor used for the estimation of tPCPSAFT parameters for ILs is
% AAD )
1 Ndens
∑ | i)1
Ndens
Fcalc - Fexp i i Fexp i 0.1 Npsat
∑ | i)1
Npsat
|
× 100 +
P s,calc - P s,exp i i P s,exp i
|
× 100 (21)
where Ndens and Npsat are the number of data points used for liquid density and vapor pressure. A weight factor of 0.1 was used for the vapor pressure data. The inclusion of vapor pressure data in the parameter regression did not reduce the accuracy of the fit of the liquid density data, as can be seen in Table 1. To the best of our knowledge, the only experimental vapor pressure data available for ILs are the ones reported by Heintz et al.20 for the 1-n-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and the estimates of Magee et al.19 for the case of [bmim+][PF6-]. On the other hand, the enthalpy of vaporization for many ILs is known and so an Antoine-type of expression, lnPsat ) A - ∆Hvap/RT, can be implemented. The constant of integration A is obtained from a generalized plot of A versus ∆Hvap/R for very many different compounds for which accurate vapor pressure values exist.19,20 In this way, one may get estimates for the vapor pressures of these additional ILs. Results and Discussion In Table 1, tPC-PSAFT parameters are presented for the eight imidazolium-based ILs studied previously.16 If one compares
Figure 6. Binary interaction parameter for [bmim+][PF6-] + CO mixture (top) and [bmim+][PF6-] + O2 mixture (bottom) at different temperatures.
these parameters to the previously reported parameters in Table 2 of ref 16, one concludes that the re-estimated m values are higher than before while V00 values are lower than before. In other words, the model assumes chain-like or polymer-like
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TABLE 2: Binary Interaction Parameters for Various Imidazolium-Based IL + CO2 Mixtures T (K)
[emim+][PF6-]
[bmim+][PF6-]
[hmim+][PF6-]
[bmim+][BF4-]
[hmim+][BF4-]
[omim+][BF4-]
313.15 323.15 333.15 343.15 353.15
0.0312 0.0345 0.0357 0.0391 0.0414
0.0198 0.0219 0.0247 0.0273 0.0296
0.0107 0.0129 0.0150 0.0177 0.0205
0.0596 0.0626 0.0658 0.0693 0.0730
0.0381 0.0401 0.0431 0.0464 0.0501
0.0288 0.0325 0.0349 0.0382 0.0415
TABLE 3: tPC-PSAFT Parameters for CO and CHF3 Fitted to Experimental Vapor Pressure and Liquid Density Data compd
MW (g/mol)
m (-)
V00 (mL/mol)
u/k (K)
µ (D)
Q (DÅ)
σp (Å)
T (K)
% AAD in Psat
% AAD in Fliq
CO CHF3
28.010 70.014
1.188 2.641
16.35 9.82
95.94 147.79
1.65
2.5 4.87
5.174 4.839
82-132 141-296
0.92 1.89
0.94 1.74
characteristics for the IL molecules. Indeed, it has been found experimentally that there are analogies between the phase diagrams of IL solutions and those of polymer solutions;24 for example, the ionic solutions exhibit an Ising-type phase behavior similar to that of polymer systems.25 Moreover, the Tait equation, most frequently used in the correlation of polymer melt densities, was found recently to adequately describe the isothermal experimental densities of several imidazolium-based ILs.26 The suitability of the new sets of parameters toward the prediction of very low vapor pressure values can be assessed from the following example: Paulechka et al. provided an experimental estimated value for the Psat of [bmim+][PF6-] at 400 K equal to 2 × 10-10 MPa.19 tPC-PSAFT, using the parameters of Table 1, predicts Psat ) 1.8 × 10-6 MPa, while the use of the parameters of Table 2 in ref 16 predicts Psat ) 4.6 × 10-2 MPa. As more experimental data for the vapor pressure of ILs will hopefully become available in the near future, the model parameters can be tuned further in order to provide better agreement with these data. New parameter values reported here vary systematically with the IL molecular structure, as was also the case in our previous work.16 An example is shown in Figure 1, where the molar volume mV00 of the ILs varies linearly with the molecular weight. This behavior allows reliable extrapolation to other ILs of similar chemical structure. The molar volume mV00 values are very close to the molar volume values reported in our previous work21 since the segment number m is now higher and the segment volume V00 lower, corresponding to a more physically acceptable molecular picture. Even more important is the fact that the new IL parameters provide an accurate correlation of the carbon dioxide solubility in various ILs using very low kij values. In macroscopic
thermodynamic models as the one presented here, kij parameters are empirical parameters used to account for model deficiencies. As a result, kij ) 0 corresponds to pure predictions while a small nonzero value fitted to experimental data is an indication of the model’s accuracy. In Figure 2, experimental data and model correlations are shown for three [PF6-] + CO2 and three [BF4-] + CO2 mixtures at 333.15 K. In all calculations, the Lewis acid-base interactions between CO2 molecules and IL anions are modeled using the association parameters reported in ref 16. In Table 2, the optimum kij values are shown for the various IL + carbon dioxide mixtures examined. It should be mentioned that these new kij values follow the same trends with respect to temperature and molecular weight as in the previous case; that is, they increase linearly with temperature, as shown in Figure 3, and decrease asymptotically with molecular weight. In order to establish the accuracy of the new IL parameters for mixtures with other compounds besides CO2, three more binary mixtures were examined, namely, [bmim+][PF6-] + CO, [bmim+][PF6-] + O2, and [bmim+][PF6-] + CHF3. tPC-PSAFT parameters for oxygen were taken from ref 21, while carbon monoxide and trifluoromethane parameters were estimated here fitting vapor pressure and saturated liquid density data and are shown in Table 3. In Figures 4 and 5, experimental data and tPC-PSAFT correlation of the CO and O2 solubility in [bmim+][PF6-] are shown. There is a negligible temperature effect on these data. The model correlates the experimental data accurately using a temperature-dependent kij value. In Figure 6, the temperature dependence of kij is shown for the two mixtures. Finally, experimental data and tPC-PSAFT correlation are shown for the [bmim+][PF6-] + CHF3 mixture in Figure 7. For this mixture, a temperature-independent kij value of -0.031 was used. In all cases (with the exception of high CHF3 mole fraction), tPC-PSAFT provides an accurate correlation of the experimental data. Conclusions tPC-PSAFT parameters for imidazolium-based ILs were fitted to liquid density and order-of-magnitude vapor pressure data and used subsequently for the correlation of IL + CO2, IL + CO, IL + O2, and IL + CHF3 phase equilibria at low and high pressure. tPC-PSAFT is shown to model accurately different types of phase behavior. In all cases, with the exception of the latter mixture, a temperature-dependent binary interaction parameter was used. The values of the binary parameter used here are significantly lower than the values used before.16
data28
Figure 7. Experimental and tPC-PSAFT correlation for the bubble-point pressure of [bmim+][PF6-] + CHF3 at various temperatures.
Acknowledgment. Financial support provided by INTAS through Research Project No. 05-1000008-8020 on DeVelopment of Sustainable Industrial Processes: Experimental, Theoretical and Computational InVestigation of Thermodynamic Properties
15492 J. Phys. Chem. C, Vol. 111, No. 43, 2007 and Phase Equilibria of Ionic Liquid Mixtures is gratefully acknowledged. I.G.E. is thankful to the Technical University of Denmark, Department of Chemical Engineering, IVC-SEP for a visiting professorship funded by the Danish Research Council for Technology and Production Sciences (project: DeVelopment and Validation of Computational Tools for Soft Material Structure and Properties, project coordinator: Associate Professor Georgios Kontogeorgis). References and Notes (1) Wasserscheid, P., Welton, T., Eds. Ionic Liquids in Synthesis; Wiley-VHC Verlag, Weinheim, 2003. (2) Seddon, K. R. J. Chem. Tech. Biotechnol. 1997, 68, 351. (3) Anthony, J. L.; Anderson, J. L.; Maginn, E. J.; Brennecke, J. F. J. Phys. Chem. B 2005, 109, 6366. (4) Husson-Borg, P.; Majer, V.; Costa Gomes, M. F. J. Chem. Eng. Data 2003, 48, 480. (5) Shariati, A.; Peters, C. J. J. Supercrit. Fluids 2004, 29, 43. (6) Kroon, M. C.; Shariati, A.; Costantini, M.; Van Spronsen, J.; Witkamp, G. J.; Sheldon, R. A.; Peters, C. J. J. Chem. Eng. Data 2005, 50, 173. (7) Shariati, A.; Peters, C. J. J. Supercrit. Fluids 2005, 34, 171. (8) Seddon, K. R.; Stark, A.; Torres, M.-J. Pure Appl. Chem. 2000, 72, 2275. (9) Zhang, S.; Li, X.; Chen, H.; Wang, J.; Zhang, J.; Zhang, M. J. Chem. Eng. Data 2004, 49, 760. (10) Lo´pez-Pastor, M.; Ayora-Can˜ada, M. J.; Valca´rcel, M.; Lendl, B. J. Phys. Chem. B 2006, 110, 10896. (11) Katayanagi, H.; Nishikawa, K.; Shimozaki, H.; Miki, K.; Westh, P.; Koga, Y. J. Phys. Chem. B 2004, 108, 19451. (12) Jork, C.; Seiler, M.; Beste, Y.-A.; Arlt, W. J. Chem. Eng. Data 2004, 49, 852. (13) Belve`ze, L. S.; Brennecke, J. F.; Stadtherr, M. A. Ind. Eng. Chem. Res. 2004, 43, 815.
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