Ind. Eng. Chem. Res. 2006, 45, 3207-3219
3207
Prediction of Binary VLE for Imidazolium Based Ionic Liquid Systems Using COSMO-RS Tamal Banerjee, Manish K. Singh, and Ashok Khanna* Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India
A novel method based on unimolecular quantum mechanical calculation has been used to predict the binary vapor-liquid equilibria (VLE) of ionic liquids (ILs).The recently developed conductor-like screening model (COSMO), along with the most common quantum chemical package of GAUSSIAN 03, has been used in this work. These conductor-like screening model calculations combined with exact statistical thermodynamics provide the information necessary for the evaluation of molecular interactions in liquids. An effective parametrization has been done using 10 associated and 22 binary nonassociated systems; these 32 systems are all non-ILs. The effective contact surface area aeff and the hydrogen-bonding coefficient chb have been estimated using a sequential scheme. The root-mean-square error obtained for excess Gibb’s free energy is ∼0.1 for aeff and chb. Values for R′ (misfit constant), σhb (cutoff surface charge density for hydrogen bonding), and cavity radii (ri) as given in the literature have been used as default. COSMO-RS has then been used to predict the vapor-liquid equilibria for 116 non-IL binary sets out of which 33 are azeotropic systems. COSMORS predicts a better pressure a priori with a relative error of ∼4%, as compared to a 7-8% error for the Wilson/NRTL/UNIQUAC models. Being an a priori model, it does fall short with respect to absolute average deviation in mole fraction for the vapor phase: 0.025 as compared to ∼0.0075 for the Wilson, NRTL, and UNIQUAC models. Having thus benchmarked extensively, the COSMO-RS model has then been used to predict the VLE for 13 systems based on five imidazolium ILs: (a) 1-methyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [MMIM] [(CF3SO2)2N] with (1) benzene and (2) cyclohexane; (b) 1-ethyl-3methylimidazolium bis(trifluoromethanesulfonyl)imide [EMIM][(CF3SO2)2N] with (3) acetone, (4) 2-propanol, and (5) water; (c) 1-butyl-3-methyl-imidazolium bis(trifluoromethanesulfonyl) imide [BMIM][(CF3SO2)2N] with (6) acetone, (7) 2-propanol, and (8) water; (d)1-methyl-3-methylimidazolium dimethylphosphate [MMIM][(CH3)2PO4] with (9) acetone, (10) tetrahydrofuran, and (11) water; and (e) 1-ethyl-3-methylimidazolium ethoxysulfate [EMIM][C2H5OSO3] with (12) benzene and (13) cyclohexane. The root-mean-square deviation for pressure prediction is 6% as compared to 4%, 1.45%, and 3.13% for the Wilson, NRTL, and UNIQUAC models, respectively. The mole fraction in the vapor phase has also been predicted, confirming the negligible presence of ionic liquids in the vapor phase even at very low pressures. 1. Introduction Recently, a tremendous amount of work has been carried out in the prediction of phase equilibria properties of ionic liquids (ILs). These liquids, owing to their negligible vapor pressure and limitless combinations of cations and anions, have been used as a replacement1,2 for volatile organic solvents (VOC). However, the experimental data associated with these novel solvents are scarce and do not cover a wide range of application. Data available include those of infinite dilution activity coefficients, liquid-liquid equilibria, and solid-liquid equilibria measurements. An excellent review of the phase equilibria properties of ionic liquids is given by Heintz.3 The purecomponent thermodynamic properties of imidazolium-based ionic liquids have been studied using molecular dynamics4 and Monte Carlo5 simulation techniques. The properties include molar volumes, cohesive energy density, liquid structure, volumetric compressiblities, and isothermal expansivities. These techniques require an efficient description of force field along with the reliable force field parameters, thus making them computationally expensive. Recently, Klamt and Eckert6 proposed a completely new perspective in liquid-phase thermodynamics. In contrast to the excess Gibb’s free energy (Gex) models, Klamt started from the * Corresponding author. E-mail:
[email protected]. Tel.: +91512-2597117. Fax: +91-512-2590104.
solvation of molecules in a conductor and developed a “conductor-like screening model for real solvent” (COSMO-RS) that, in principle, can be used to determine the chemical potential of any species in any mixture from quantum mechanical calculations. An interesting and unique feature of the COSMO-RS method is that it does not presuppose a specific concentration dependence of the Gex function, as is the case with UNIFAC, for example, which is based on the UNIQUAC approach. This provides greater flexibility in treating systems of very different chemical functionality. In COSMO-RS, molecules are treated as a collection of surface segments. An expression for the chemical potential of segments in the condensed phase is derived in which needed interaction energies between segments are calculated from COSMO.7 The chemical potential of each molecule is then obtained by summing the contributions of the segments. This model has been originally applied to the prediction of vapor pressures and partition coefficients, with an average deviation within 200%. Variants of COSMO-RS have also evolved thereon, which include the COSMO-SAC8 and COSMO-RS (Ol).9 Till now, COSMO-RS has been used to predict the infinite dilution activity coefficients of ionic liquids in organic compounds.10 Vapor-liquid equilibria (VLE) has been previously predicted by Klamt and Eckert11,12 for nonionicliquid-based binary mixtures. Recently, Gmehling and coworkers13-15 measured the vapor-liquid equilibria of imidazolium-based ionic liquids based on the bis(trifluoromethylsulfonyl)imide, ethylsulfate, and dimethyl phosphate anions.
10.1021/ie051116c CCC: $33.50 © 2006 American Chemical Society Published on Web 03/30/2006
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Table 1. Equations Used in COSMO-RS6,8,23
The generation of the COSMO files, although time consuming, has to be done once for each compound. The COSMO file implementation is available on quantum mechanical packages such as TURBOMOLE,16 DMOL3,17 GAMESS,18 and GAUSSIAN 03.19 In the next few sections, we will discuss our parametrization scheme, which uses the GAUSSIAN 03 package for generating the COSMO files.
Table 2. Cavity Radii Values Considered for Our Work element
radius in A°
element
radius in A°
H C N O F
1.30 2.00 1.83 1.72 1.72
S Cl Br I P
2.16 2.05 1.85 1.98 1.80a
a
2. COSMO-RS In COSMO-RS, a liquid is considered to be an ensemble of almost closely packed, ideally screened molecules. Each surface contact now has a direct partner. In reality, there is no conducting medium between them, and the energy difference between the real situation of such contact and the ideally screened situation is defined as a local electrostatic interaction energy. Considering a contact on a region of molecular surface of area aeff (effective contact area), and considering that the two neighboring contacting surfaces have average ideal screening charge densities σ and σ′, the interaction energy is the energy which is necessary to remove the residual screening charge density σ + σ′ from the contact. In the special situation of σ ) -σ′, there is nothing to remove and, hence, the interaction energy is zero. Such a contact here is called ‘‘ideal electrostatic contact”. The various interaction energy terms are as follows: misfit (eq 1), hydrogen bonding (eq 2), and van der Waals (eq 3); these are used in this work as given in Table 1. The misfit of the partners arises when σ + σ′ does not vanish. The hydrogenbonding term (Ehb) needs to be parametrized. This comes into play only if two sufficiently polar pieces of surface of opposite polarity are in contact and becomes important with increasing
Default radii of Bondi.30
polarity. Taking the screening charge density σ as a local measure of polarity, Ehb is not zero when either σdon is less than or σacc is greater than the threshold value σhb. The hydrogenbonding energy is proportional to the product of the excess screening charge densities, i.e., (σdon + σhb)(σacc - σhb). The van der Waals (vdW) energy contribution is expressed by element-specific dispersion coefficient parameters τ(e), which have to be fitted to experimental data. The vdW energy gained by a molecule X during the transfer from the gas phase to any liquid phase is given in eq 3. This contribution is not an interaction term but is a state of the molecule embedded with vdW interacting surface species. This so-called “reference state” does not contribute to the prediction of liquid-phase activity coefficients and is important only for liquid-gas transfer processes, e.g., vapor-pressure data. The interactions of molecular surfaces in COSMO-RS are given by an interaction energy functional e(σ,σ′) ) emisfit(σ,σ′) + ehb(σ,σ′) (eq 4), which depends only on the screening charge densities. The vdW contribution is subsumed in the reference state energy. The generic interaction functional e(σ,σ′) has three adjustable parameters, R′, σhb, and chb, while the vdW term has the dispersion coefficient τ(e) as an adjustable parameter per element. In addition to these explicit parameters, the screening
Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3209 Table 3. Vapor-Liquid Equilibria Calculations property
equations used
total pressure prediction (P)
P)
mole fraction in vapor phase (y)
y1 )
γ1x1Psat 1 + x1γ1Psat 1
γ2x2Psat 2
(11) (12)
P
nonideality of vapor phase
φ1 Py1 ) x1Psat 1 γ1 φ10
fugacity coefficient (φi/φ0)
φ1 -(V1 - B11)(Py1 - Psat 1 ) ) exp φ10 RT
absolute average deviation in mole fraction in vapor phase (AADy)
AADy )
relative absolute average deviation in total pressure (RAADp)
(13)
(
1 M
)
(14)
M
∑|y
exp j
- ycalc j |
(15)
- Pcalc Pexp j j | | exp Pj
(16)
j
1
RAADp ) 100 M
M
∑ j
charge densities also depend on the element-specific radii which are used in the cavity construction and roughly fixed by the rule 1.2RBondi. Thus, there are three general parameters plus two element-specific parameters per element. For the nine elements H, C, N, O, F, S, Cl, Br, and I, we have altogether 21 parameters. Details of COSMO-RS can be found in Klamt and Eckert.6,7 If the liquid system under consideration is a pure liquid X, then the σ-profile pS(σ) (eq 5) of the system is identical with the σ-profile pX(σ) of the pure compound. In general, a system may be a mixture consisting of several compounds X with molar concentrations xi. The screening charge densities σ* from the COSMO output are averaged to give the “apparent” charge density σm on a surface segment using eq 6. The σ-profile of
the system is given by the weighted sum of the σ-profiles of the components. An exact expression for the sigma potential of these segments based on a rigorous statistical mechanical argument is given by eq 7. The activity coefficients of the segment in the mixture and in the pure liquid, ΓS(σ) and Γi(σ), are determined from eq 8. Then the activity coefficient of each component is computed using eq 9a. Molecular volumes and areas from the COSMO calculation are normalized by a standard volume (66.69 Å3) and surface area (79.53 Å2) to yield the r and q parameters which are used for computing the StavermanGuggenheim term (eq 9b). It is interesting to note that the activity coefficient of a species in a mixture is obtained as a function of composition without specifying a priori the form of this composition dependence.
Figure 1. (a) Representative sigma profiles of compounds used for benchmarking. (b) Reported sigma profiles of benchmarking compounds.6
Figure 2. (a) Representative sigma potentials of compounds used for benchmarking. (b) Reported sigma potentials of benchmarking compounds.6
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Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006
4. Parameter Estimation
Table 4. Associated and Nonassociated Systems for COSMO Parameter Estimation25 associated systems (data points ) 141)
temp (°C)
ethanol-water ethanol-acetonitrile hexanes-ethanol hexanes-ethanol hexanes-ethanol heptane-ethanol ethanol-heptane methanol-water water-hexanol
40 40 25 40 50 40 60 40 40
nonassociated systems (data points ) 274)
temp (°C)
methyl acetate-butyraldehyde methyl acetate-butyraldehyde butyraldehyde-heptane acetone-nitromethane acetone-methyl acetate acetone-methyl acetate diethyl ether-acetone acetone-hexane acetone-hexane acetone-heptane 2-butanone-acetonitrile 2-butanone-acetonitrile dimethyl ether-methyl tert-butylether 1-hexene-hexane 1-butene-butane 1-butene-butane 1-hexene-octane 1-heptene-heptane 1-heptene-octane acetonitrile-heptane nitroethane-octane octane-butyronitrile
40 50 45 45 35 55 0 10 35 40 60 55 25 55 35 52 55 55 55 45 35 90
The parametrization scheme adopted in this work has been on the same lines as that done in the COSMO-SAC model of Lin and Sandler.8 However, Lin and Sandler have used a different term for calculating the combinatorial term. The parameter estimation has been done by various workers in different manners. Lin and Sandler,8 in their parameter estimation, have used 70 nonassociating binary mixtures and 102 associating binary mixtures. Klamt and Eckert6 used the data sets of 890 room-temperature values of infinite dilution activity coefficients, vapor pressures, and partition coefficients of water, hexane, benzene and diethyl ether covering around 310 compounds. Grensemann and Gmehling,9 in their formulation of COSMO-RS(Ol), have used 112 datasets of vapor-liquid equilibrium along with the data related to excess enthalpy and solid-liquid equilibrium. In addition, there are several other empirical parameters such as λ, β, and rav.9 It should be noted that the sigma profile for any component will depend on the quantum mechanical package used, which results in a different model parametrization. The COSMO-RS model currently uses a total of 21 parameters: the radii for the nine elements, vdW parameters for each of these nine elements, one cutoff surface charge density σhb for distinguishing hydrogen-bond donors and acceptors, and two segment interaction-related variables (the surface area of a standard segment aeff and the hydrogen-bonding coefficient chb). These parameters are specific to the program and basis sets used for doing a COSMO calculation. A COSMO implementation is available in Gaussian 03 which can generate these files. Since parameters for processing COSMO files are not available for Gaussian 03, these had to be estimated. Only aeff and chb are considered as adjustable parameters in this work. The other parameters have been taken from the previous work of Klamt and Eckert,6 as stated earlier. These parameters were optimized using a large data set. The other two adjustable parameters were sequentially determined by minimizing the root-mean-square (rms) deviation of the calculated excess Gibbs free energy from that obtained from VLE data
3. Computational Details The Quantum Chemistry package of Gaussian 03 has been used to compute the COSMO files. The first step for COSMORS calculation is to estimate the sigma profile of each species. The equilibrium geometry of the molecules in the ideal gas phase are first obtained using the density functional theory of P BV86.20 The triple zeta valence potential (TZVP)21 basis set has been used in combination with the density fitting basis set of DGA1.22 The ideal screening charges on the molecular surface are then computed using the same level of theory (P BV86). The radii of the elements are used to define the cavity for the molecule. The radii of the nine components are taken from Klamt and Eckert6 and are reported in Table 2. For phosphorus, a default value of 1.2RBondi has been used.
rms )
[ ∑(
)]
1
M
ex ex Gcalc - Gexpt j j
M
j
RT
2 1/2
(10)
ex expt expt )/ with Gex calc/RT ) Σxi ln γi/S and Gexpt/RT ) Σxi ln((yi P vap (xiPi )). Here, M is the total number of data points, Gex is the
Table 5. COSMO Parameters Used by Different Workers COSMO-RS7
parameter
a
Å2
COSMO-SAC8 Å2
aeff r′ chb
6.25 5 950 kJ/mol/Å2 36 700 kJ/mol/Å4/e2
7.50 5 950 kJ/mol/Å2 35 772 kJ/mol/Å4/e2
σhb
0.085 e/Å2
0.0084 e/Å2
COSMO-RS (Ol)9
this work
6.31 Å2 30.74 kJ/mol a36.52 kJ/mol @ 298 K 33.82 kJ/mol @ 313 K 31.35 kJ/mol @328 K 0.0082 e/Å2
7.55 Å2 5 950 kJ/mol/Å2 34 984 kJ/mol/Å4/e2 0.0082 e/Å2
cThb ) 1.552; chb(T) ) chb max(0,1 - cThb + cThb((298.15 K)/T )).
Table 6. Relative Comparison of Deviations8 COSMO-SAC8
COSMO-RS (this work)
COSMO-SAC8
COSMO-RS (this work)
binary systems with
no of binary systems
no of points
number of binary systems
no of points
%AAD in P
%AAD in y
%AAD in P
%AAD in y
1-octene cyclohexane benzene phenol
1 38 62 1
23 584 865 12
1 6 20 1
9 102 284 16
2.24 6.11 6.89 6.75
2.24 1.93 2.69 1.20
2.50 8.08 5.19 3.48
3.03 1.30 1.52 1.05
Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3211 Table 7. Comparison of Deviations for Different VLE Models RAADp% in P system
no of pts
this work
Wilson
NRTL
AADy in y (mole fraction) UNIQUAC
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
ethanol-water methanol-ch3cooha methanol-ethanola acetone-methanolb methyl acetate-methanolb methanol-1-propanol butane-methanol methanol-1-butanol methanol-2-methyl propanol methanol-benzeneb methanol-cyclohexaneb methanol-butyl acetate methanol-hexaneb ethanol-ch3cooh ethanol-2-butanoneb diethylamine-ethanol pentane-ethanola ethanol-benzeneb ethanol-cyclohexaneb 1-hexene-ethanolb hexane-ethanolb ethanol-tolueneb ethanol-heptaneb ethanol-octaneb ccl4-1-propanolb 2-propanol-1-propanol benzene-1-propanola cyclohexane-1-propanolb hexane-1-propanol 1-propanol-heptaneb ch3cooh-hexanolb
13 11 10 14 22 26 11 21 14 9 9 10 7 15 7 11 21 9 9 8 9 19 15 17 20 16 9 12 9 33 11
32 33 34 35 36 37 38 39 40 41 42 43 44 45
acetaldehyde-acetonea acetaldehyde-1-penteneb propionaldehyde-methyl acetate propionic acid-ethyl acetate pentane-propionaldehydeb propionaldehyde-benzene propionaldehyde-toluene methyl acetate-butyraldehyde butyraldehyde-propyl acetate butyraldehyde-benzene butyraldehyde-toluene butyraldehyde-heptaneb butane-furfurala butene-furfural
8 5 15 18 26 15 9 17 14 17 13 19 9 11
alcohol-based systems24b,c,d 8.60 0.92 4.50 3.94 23.20 0.77 0.88 0.92 4.20 21.98 22.61 21.96 1.19 6.08 5.97 5.97 4.28 1.12 0.77 0.82 2.09 1.76 1.88 1.77 4.53 156.27 170.58 219.88 3.42 1.18 1.14 1.18 4.20 0.18 0.15 0.17 9.13 1.06 0.35 1.86 1.87 4.59 4.25 4.95 6.80 1.38 1.35 1.41 3.28 1.14 1.73 12.37 9.40 0.46 0.45 0.46 7.78 8.41 8.49 8.54 6.75 5.29 4.57 6.24 10.20 19.35 14.29 14.22 8.22 0.53 0.35 1.18 4.13 0.43 0.91 1.87 8.87 10.15 11.79 15.65 3.68 0.74 3.37 3.58 6.46 0.83 0.91 2.95 1.99 1.18 1.28 7.26 2.15 0.96 1.20 7.98 2.27 1.05 1.96 2.20 1.28 0.34 0.34 0.34 10.32 0.70 0.37 1.39 4.53 0.98 0.87 2.73 8.51 1.58 1.70 4.59 4.07 2.11 1.54 4.92 5.20 0.79 0.81 0.81 aldehyde-based systems24e 15.00 19.53 23.99 19.80 7.86 51.28 47.72 52.80 0.97 1.37 1.44 1.43 7.10 2.66 2.68 2.66 14.43 8.59 7.05 6.89 4.28 2.44 2.46 2.40 3.64 5.87 5.89 5.79 0.52 1.90 1.90 1.91 1.13 1.25 1.41 1.49 1.94 0.19 0.22 0.51 1.85 2.60 2.70 3.12 1.10 1.41 1.63 1.66 49.32 143.44 44.92 46.00 2.30 148.48 58.79 42.71
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
acetone-methyl acetateb acetone-aceticacid acetone-benzene acetone-cyclohexaneb acetone-hexaneb acetone-triethylamine acetone-toluene acetone-heptaneb acetone-ethylbenzene acetone-xylene acetone-octane acetone-2,2,4-trimethyl pentanea,b acetone-decane 2-butanone-ch3cooh 2-butanone-benzeneb 2-butanone-cyclohexaneb 2-butanone-triethylamineb 2-butanone-toluene 2-butanone-heptaneb 2-butanone-octane 2-butanone-2,2,4-trimethyl pentaneb 2-butanone-decane benzene-nmpa cyclohexane-nmpa benzene-3-pentanone hexane-3-pentanonea heptane-3-pentanonea
10 9 21 27 10 25 14 16 17 16 21 24 19 14 12 32 11 15 18 12 34 10 14 13 25 9 9
9.06 7.55 4.88 2.24 3.25 2.29 3.41 1.81 2.62 2.72 2.38 11.61 9.87 4.57 4.57 2.39 2.71 1.29 1.53 2.40 0.60 2.92 13.57 33.32 4.03 14.70 13.36
ketone-based systems24e 0.63 0.62 1.66 3.02 0.25 0.35 1.61 1.79 13.53 13.65 3.38 3.64 1.00 1.10 0.60 3.36 2.35 2.40 2.73 2.78 2.09 1.88 2.64 2.78 10.69 11.23 1.62 1.70 0.98 0.98 0.50 0.70 1.03 0.98 0.77 0.77 0.70 0.84 1.85 1.53 0.49 0.90 14.83 15.64 0.36 0.34 1.55 0.64 0.67 0.70 9.11 8.96 1.33 1.23
0.64 1.77 0.23 3.44 13.69 3.73 0.88 3.82 2.34 2.72 4.12 2.83 10.74 1.73 0.97 0.81 0.97 0.72 0.92 1.53 0.99 15.76 0.36 2.01 0.85 8.89 1.21
this work
Wilson
NRTL
UNIQUAC
temp
0.0434 0.0511 0.2257 0.0218 0.0204 0.0086 0.0028 0.0107 0.0040 0.0337 0.0145 0.0303 0.0199 0.0318 0.0548 0.1049 0.0142 0.0344 0.0184 0.0275 0.0123 0.0336 0.0140 0.0072 0.0102 0.0079 0.0374 0.0159 0.0178 0.0241 0.1272
0.0020 0.0115 0.0045 0.0089 0.0019 0.0042 0.0035 0.0094 0.0104 0.0078 0.0145 0.0045 0.0038 0.0039 0.0159 0.0127 0.0041 0.0056 0.0030 0.0032 0.0024 0.0046 0.0120 0.0040 0.0072 0.0081 0.0046 0.0044 0.0032 0.0055 0.0282
0.0360 0.0124 0.0039 0.0091 0.0019 0.0042 0.0045 0.0095 0.0105 0.0030 0.0096 0.0043 0.0056 0.0043 0.0160 0.0119 0.0035 0.0030 0.0051 0.0036 0.0109 0.0052 0.0071 0.0037 0.0099 0.0082 0.0032 0.0054 0.0027 0.0038 0.0286
0.0116 0.0112 0.0045 0.0091 0.0019 0.0042 0.0052 0.0094 0.0104 0.0135 0.0200 0.0041 0.0377 0.0041 0.0160 0.0110 0.0035 0.0111 0.0138 0.0100 0.0116 0.0113 0.0361 0.0213 0.0087 0.0082 0.0066 0.0134 0.0072 0.0156 0.0290
40 35 100 25 25 26 50 25 25 25 25 24 25 35 55 40 20 25 25 60 25 45 40 45 35 25 25 25 25 60 35
0.0790 0.0450 0.0910 0.1150 0.0570 0.0200 0.0020 0.0030 0.0120 0.0070 0.0110 0.0060 0.0010 0.0010
0.0420 0.0210 0.0090 0.0050 0.0050 0.0080 0.0010 0.0040 0.0070 0.0070 0.0060 0.0090 0.0010 0.0010
0.0420 0.0190 0.0090 0.0050 0.0090 0.0080 0.0010 0.0040 0.0080 0.0020 0.0060 0.0090 0.0010 0.0010
0.0420 0.0220 0.0090 0.0050 0.0060 0.0080 0.0070 0.0040 0.0080 0.0040 0.0070 0.0090 0.0010 0.0010
25 40 30 18 40 40 40 40 50 40 55 45 38 38
0.0010 0.0076 0.0640 0.0090 0.0200 0.0090 0.0070 0.0040 0.0020 0.0020 0.0020 0.0240 0.0011 0.0115 0.0115 0.0078 0.0061 0.0042 0.0033 0.0151 0.0070 0.0063 0.0076 0.0136 0.0101 0.0159 0.0073
0.0040 0.0100 0.0010 0.0050 0.0160 0.0070 0.0020 0.0030 0.0020 0.0020 0.0020 0.0080 0.0013 0.0144 0.0023 0.0027 0.0066 0.0026 0.0028 0.0127 0.0031 0.0080 0.0002 0.0005 0.0036 0.0268 0.0063
0.0040 0.0100 0.0020 0.0050 0.0110 0.0080 0.0020 0.0040 0.0020 0.0020 0.0020 0.0080 0.0012 0.0156 0.0025 0.0013 0.0067 0.0026 0.0043 0.0124 0.0045 0.0081 0.0003 0.0002 0.0036 0.0271 0.0077
0.0040 0.0100 0.0010 0.0060 0.0110 0.0080 0.0020 0.0040 0.0020 0.0020 0.0020 0.0080 0.0012 0.0160 0.0021 0.0046 0.0067 0.0025 0.0048 0.0124 0.0049 0.0081 0.0002 0.0005 0.0037 0.0272 0.0080
35 30 25 50 35 45 40 40 40 40 40 48 30 9 25 50 30 57 45 40 40 70 20 20 50 52 26
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Table 7 (Continued) RAADp% in P system
no of pts
this work
Wilson
NRTL
AADy in y (mole fraction) UNIQUAC
73 74 75 76 77 78 79 80
1-butene-butane butane-pentane diethylamine-1-hexene 1-hexene-benzene 1-hexene-hexane octene-benzene benzene-octane cyclopentane-benzene
11 11 7 21 11 9 9 6
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
tetrachloromethane-benzene benzene-nmf benzene-dmf a diethylamine-benzene benzene-pyridine benzene-chlorobenzene benzene-aniline benzene-triethylamine benzene-toluene diethylamine-toluene toluene-chlorobenzene toluene-aniline diethylamine-ethylbenzene ethylbenzene-aniline phenol-styrene
14 30 12 15 7 9 11 20 14 10 11 11 8 16 16
96 97 98 99 100 101 102 103 104 105
water-hcoohb methanol-water acetaldehyde-watera water-acetic acida ethanol-water water-dmso acetone-watera 2-butanone-waterb water-furfural a,b water-pyridinea,b
9 10 5 10 12 9 21 11 7 9
1.19 1.50 0.45 1.10 8.60 3.20 2.10 0.56 7.44 3.00
106 107 108 109 110
triethylamine-waterb nitroethane-octane 2-methylpentane-nitroethane diethyl ether-nitromethane benzene-benzonitrile
9 13 13 6 11
nitrogen-based systems24j 5.30 0.49 0.45 1.50 1.61 0.50 6.40 7.16 0.39 7.83 3.95 5.24 1.95 25.57 25.71
111 112 113
diethyl ether-acetonitrile diethyl ether-ethyl acetate dimethyl ether-propane
6 11 9
6.47 3.49 4.81
114 ethyl mercaptan-butane 115 ethyl mercaptan-butane 116 tert-butyl mercaptan-propanea relative errors (without deviant compounds) a
18 15 19 1602
this work
Wilson
NRTL
UNIQUAC
temp
0.0056 0.0497 0.0157 0.0092 0.0042 0.0040 0.0090 0.0020
0.0047 0.0258 0.0171 0.0029 0.0026 NAc NAc NAc
0.0048 0.0246 0.0173 0.0029 0.0027 NAc NAc NAc
0.0047 0.0247 0.0171 0.0029 0.0027 NAc NAc NAc
38 25 60 25 60 30 30c 25
0.29 3.35 0.65 0.95 0.15 0.15 1.36 0.46 1.70 13.09 0.51 0.47 1.92 0.64 NAc
0.0222 0.0001 0.0199 0.0073 0.0070 0.0029 0.0030 0.0039 0.0060 0.0103 0.0024 0.0120 0.0043 0.0169 0.0036
0.0011 0.0011 0.0057 0.0048 0.0090 0.0014 0.0003 0.0015 0.0059 0.0170 0.0030 0.0057 0.0064 0.0051 NAc
0.0012 0.0011 0.0057 0.0047 0.0091 0.0015 0.0002 0.0014 0.0058 0.0184 0.0026 0.0052 0.0059 0.0052 NAc
0.0011 0.0011 0.0056 0.0029 0.0090 0.0014 0.0002 0.0015 0.0059 0.0166 0.0031 0.0065 0.0067 0.0052 NAc
10 45 30 35 25 25 70 60 70 35 70 20 35 80 100
1.87 0.94 108.02 0.62 0.62 0.26 4.64 7.36 5.82 1.50
0.0331 0.0436 0.1060 0.0630 0.0434 0.1238 0.0671 0.1456 0.0204 0.1424
0.0168 0.0041 0.0277 0.0199 0.0075 0.0107 0.0073 0.0285 0.0114 0.0197
0.0117 0.0039 0.0267 0.0203 0.0055 0.0052 0.0073 0.0066 0.0068 0.0189
0.0145 0.0041 0.0298 0.0203 0.0068 0.0075 0.0074 0.0078 0.0061 0.0237
30 25 100 40 25 25 35 60 50 27
0.38 0.51 0.44 5.23 25.62
0.1971 0.0045 0.0486 0.0077 0.0040
0.0063 0.0215 0.0082 0.0019 0.0070
0.0083 0.0041 0.0033 0.0024 0.0071
0.0059 0.0043 0.0330 0.0024 0.0070
0 35 25 21 70
14.80 0.78 NAc
0.0190 0.0080 0.0090
0.0122 NAc NAc
0.0122 NAc NAc
0.0122 NAc NAc
0 5 50
NAc NAc NAc 7.99
0.0360 0.0260 0.0870 0.0257
NAc NAc NAc 0.0073
NAc NAc NAc 0.0071
NAc NAc NAc 0.0078
50 100 60
hydrocarbon-based systems24g,h 2.43 66.15 66.71 66.39 3.58 25.95 27.09 26.96 4.99 20.34 20.26 20.39 2.01 0.86 0.87 0.86 0.36 1.96 2.05 2.05 2.50 0.22 0.24 0.22 4.60 NAc NAc NAc 0.70 0.15 0.14 0.14 aromatic-based systems24i 4.17 0.29 0.29 9.69 3.69 4.38 16.40 0.68 0.80 1.43 1.54 1.48 4.48 0.15 0.15 1.47 0.15 0.14 8.28 1.36 1.32 0.28 0.46 0.47 0.60 2.82 3.23 1.63 13.56 15.34 0.73 0.51 0.59 2.80 0.30 0.32 2.62 3.67 4.61 5.79 0.62 0.64 c 3.48 NA NAc water-based systems24a 1.79 2.50 0.93 0.88 105.25 105.65 0.60 0.64 0.70 0.53 0.60 0.27 4.37 4.01 12.54 8.06 4.77 5.00 0.99 0.70
ether-based systems24f 14.29 14.86 0.76 0.82 NAc NAc
mercaptan-based systems29 6.50 NAc NAc NAc 7.80 NAc 3.50 NAc NAc 4.12 7.26 7.31
Deviating compound. b Azeotrope systems. c NA ) not available.
molar excess Gibbs free energy (eq 1), and the vapor pressures of the pure compounds were calculated from the Antoine Pvap i equation.
are the experimental and predicted mole fractions in the ycalc j and Pcalc are the experivapor phase, respectively, and Pexp j j mental and predicted total pressures, respectively.
5. Vapor-Liquid Equilibria
6. Results and Discussion
The vapor-liquid equilibria prediction, along with the relevant equations, is given in Table 3.The total pressure (P) in kPa is calculated by eq 11. Here, γ1 and γ2 are the activity coefficients obtained by COSMO-RS calculations. The mole fraction in the gas phase (y) is obtained by eq 12. The nonideality in the vapor phase (for ionic liquids only) has been included by using eqs 13 and 14. The measure of the deviation has been calculated using the absolute average deviation (AAD) for mole fraction in the liquid phase (eq 15) and relative absolute average deviation for total pressure (eq 16), where yexp and j
6.1. Sigma Profiles and Potentials for Benchmark Components. Three solvents, namely, hexane, water, and acetone, have been considered for comparison with the reported profiles of Klamt and Eckert.6 The computed profiles are shown in Figure 1a, and the literature profiles are shown in Figure 1b. The sigma potentials (Figure 2a) are then compared with the reported6 sigma potentials (Figure 2b). The molecular polarity is inverted on the negative scale, because positive polarities such as polar hydrogen atoms cause a negative screening charge density, while negative polarities cause a positive screening
Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3213
Figure 4. (a) P-x,y plot for methanol-cyclohexane system (minimumboiling azeotrope).24 (b) P-x,y plot for water-formic acid systems (maximum-boiling azeotrope).24
Figure 3. (a) P-x,y plot for phenol-styrene system at 373.15 K29 (positive deviation from Raoult’s law). (b) P-x,y plot for diethyl ether-chloroform system at 323.15 K24 (negative deviation from Raoult’s Law). (c) P-x,y plot for tert-butyl mercaptan-propane at 333.15 K.29
charge. All σ-values are in e/Å2. Klamt and Eckert6 used TURBOMOLE16 for their COSMO file generation, whereas we have used GAUSSIAN 03. 6.2. Estimation of COSMO Parameters. The aeff parameter has been first optimized using VLE data for non-hydrogenbonding binary mixtures (274 data points) collected from the DECHEMA series24 formed from the 17 simple monofunctional compounds (methyl acetate, butyraldehyde, heptane, acetone, nitromethane, diethyl ether, hexane, 2-butanone, acetonitrile, dimethyl ether, methyl tert-butyl ether, 1-hexene, 1-butene, butane, octane, 1-heptene, and butyronitrile), covering a temperature range from 273.15 to 363.15 K.24 The list of all the associating and nonassociating systems has been shown in Table 4.
For the hydrogen-bonding coefficient (chb) estimation, we used binary mixtures that consisted of any two of the four hydrogen-bonding species (methanol, ethanol, 1-hexanol, and water) or of any of the 17 compounds listed above and one of the four hydrogen-bonding species. The values of all four parameters are shown in Table 5 and are compared with the parameters obtained by different workers. The parameters obtained by Lin and Sandler8 are based on a different training set. The details can be found elsewhere.25 A comparison of the VLE prediction with the COSMO-SAC model8 has been done with systems based on 1-octene, benzene, cyclohexane, and phenol and is shown in in Table 6. 6.3. Validation of Binary VLE Data for Non-IL Systems. The utility of the proposed model is demonstrated by considering the VLE predictions for compounds not included in the parametrization. The DECHEMA data series is used to search for consistent binary-mixture data that contain 1 of the 17 compounds mentioned earlier and 1 of the new compounds listed in Table 7. The COSMO files for all the components are being given as supporting material at the end of this manuscript. The model has then been applied for vapor-liquid equilibria for 116 systems, as shown in Table 7. The accuracy of the results remains the same as in parameter estimation. For the 96 systems, the average deviation is ∼4% in total pressure and 0.025 in mole fraction, excluding the 20 deviating systems. The relative error in vapor-phase compositions can further be reduced by incorporating the nonideality, i.e., fugacity coefficients (φi/φ0) of the vapor phase.
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Figure 5. (a) Sigma profiles of [EMIM][(CF3SO2)2N], [BMIM][(CF3SO2)2N], and [EMIM][C2H5SO4]. (b) Sigma profiles of [MMIM][(CH3)2PO4] and [MMIM][(CF3SO2)2N].
To substantiate our findings, we report sample prediction. We have chosen the systems in which we have both positive as well as negative deviation from Raoult’s law. Figure 3a shows the VLE data for phenol (1)/styrene (2) at T ) 373.15 K. COSMO-RS predicts a positive deviation from Raoult’s law. Similarly, Figure 3b illustrates the prediction of negative
Figure 6. (a) Sigma potential of [EMIM][(CF3SO2)2N], [BMIM][(CF3SO2)2N], and [EMIM][C2H5SO4]. (b) Sigma potentials of [MMIM][(CH3)2PO4] and [MMIM][(CF3SO2)2N].
deviation from Raoult’s law for the diethyl ether (1)/chloroform (2) system at T ) 323.15 K. In Figure 3c, the VLE predictions for the tert-butyl mercaptan (1)/n-propane (2) system at T ) 333.15 K are shown. Klamt and Eckert6 reported that the UNIFAC model26 cannot be used for this system because the functional-group parameters for mercaptans are not available.
Table 8. Binary VLE Predictions Using COSMO-RS for [EMIM][(CF3SO2)2N] with Acetone, 2-Propanol, and Water at 353.15 K acetone
2-propanol a
x
ypred
Pexp
0.013 0.038 0.068 0.339 0.402 0.465 0.525 0.584 0.637 0.685 0.726 0.763 0.795 0.897 0.938 0.967 0.984 0.993 0.997 0.999 1.000
0.966 0.989 0.994 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.14 3.48 6.07 39.81 50.26 61.86 74.28 87.87 101.46 114.73 127.22 138.75 149.16 183.74 196.92 205.80 210.74 213.25 214.40 214.94 215.16
a
Data from ref 13.
water a
Ppred
x
ypred
Pexp
1.28 3.72 6.76 41.66 52.23 64.00 76.49 90.11 103.58 116.86 128.99 140.56 150.97 185.36 198.56 207.01 211.44 213.57 214.48 214.91 215.13
0.012 0.024 0.036 0.049 0.061 0.095 0.135 0.185 0.239 0.295 0.412 0.740 0.752 0.936 0.975 0.986 0.992 0.996 0.998 0.999 1.000
0.974 0.987 0.991 0.994 0.995 0.997 0.998 0.998 0.999 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.73 3.21 4.84 6.50 8.08 12.54 17.88 24.43 31.42 38.61 52.86 82.08 82.82 89.96 91.14 91.52 91.86 92.05 92.16 92.21 92.26
Ppred
x
ypred
Pexp a
Ppred
1.68 3.30 4.91 6.63 8.20 12.56 17.54 23.51 29.66 35.70 47.26 72.69 73.48 85.74 88.86 89.80 90.33 90.69 90.87 90.96 91.06
0.029 0.060 0.089 0.145 0.193 0.270 0.351 0.439 0.520 0.597 0.661 0.717 0.768 0.810 0.843 0.870 0.892 0.910 0.924 0.935 0.945
0.989 0.990 0.991 0.993 0.993 0.993 0.993 0.964 0.994 0.995 0.995 0.996 0.997 0.997 0.998 0.998 0.998 0.999 0.999 0.999 1.000
3.19 6.45 9.54 15.32 20.15 34.27 40.72 47.33 47.35 47.36 47.36 47.36 47.37 47.37 47.38 47.38 47.39 47.38 47.37 47.38 47.37
3.40 6.55 9.72 16.41 21.93 33.25 40.53 47.66 47.97 48.78 48.81 48.98 49.95 50.73 51.14 51.28 51.95 52.08 52.08 52.55 52.87
Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3215 Table 9. Binary VLE Predictions Using COSMO-RS for [BMIM][(CF3SO2)2N] with Acetone, 2-Propanol, and Water at 353.15 K acetone x
ypred
Pexpa
0.056 0.089 0.146 0.422 0.504 0.575 0.693 0.741 0.783 0.872 0.892 0.907 0.934 0.941 0.973 0.990 0.996 0.999 1.000
0.992 0.995 0.997 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
4.92 7.27 12.82 49.81 65.45 80.91 112.26 126.60 140.78 172.53 179.77 185.16 194.48 196.86 207.00 211.93 213.96 214.72 215.04
2-propanol Ppred
x
5.28 8.58 14.67 53.75 69.50 85.20 116.27 130.83 144.47 175.33 182.37 187.59 196.67 198.92 208.48 212.85 214.25 214.91 215.13
0.037 0.074 0.115 0.340 0.424 0.505 0.644 0.699 0.750 0.862 0.879 0.898 0.937 0.957 0.972 0.989 0.996 0.999 1.000
water
ypred
Pexpa
Ppred
x
ypred
Pexpa
Ppred
0.990 0.995 0.997 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3.85 7.25 11.58 37.42 47.22 56.32 70.28 75.21 79.20 86.25 86.98 87.83 89.41 90.16 90.60 91.33 91.71 91.92 91.99
4.21 8.32 12.79 35.99 44.03 51.45 63.38 67.82 71.81 80.19 81.45 82.86 85.82 87.40 88.62 90.07 90.69 90.96 91.06
0.049 0.097 0.192 0.264 0.342 0.458 0.563 0.657 0.733 0.793 0.839 0.874 0.923 0.939 0.950 0.960 0.967 0.972 0.977
0.989 0.991 0.993 0.995 0.998 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
5.32 10.18 20.07 27.00 34.49 43.68 46.31 46.66 46.82 46.94 47.00 47.05 47.07 47.09 47.11 47.12 47.13 47.15 47.15
4.67 9.21 18.19 24.97 32.12 42.58 51.12 57.44 60.91 61.97 61.30 59.65 57.49 55.35 53.44 52.05 50.79 49.97 49.46
Table 10. Binary VLE Predictions Using COSMO-RS for [MMIM][(CH3)2PO4] with Acetone, 2-Propanol, and Water at 353.15 K acetone
tetrahydrofuran
water
x
ypred
Pexpa
Ppred
x
ypred
Pexpa
Ppred
x
ypred
Pexpa
Ppred
0.046 0.080 0.193 0.308 0.535 0.602 0.634 0.684 0.823 0.868 0.896 0.917 0.933 0.946 0.969 0.995 0.996 0.997 0.999 1.000
0.996 0.998 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
10.11 19.13 46.11 80.35 169.57 190.77 205.73 212.47 215.99 215.85 215.74 215.65 215.56 215.48 216.68 215.45 216.84 215.47 216.93 216.82
9.49 16.20 42.44 78.56 154.23 180.58 197.50 203.97 207.35 207.22 207.11 207.02 206.94 206.86 208.01 206.83 208.17 206.85 214.91 215.13
0.021 0.051 0.230 0.291 0.359 0.435 0.512 0.634 0.651 0.689 0.705 0.750 0.800 0.850 0.893 0.926 0.992 0.995 0.998 1.000
0.988 0.994 0.997 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 1.000 1.000 1.000 1.000
9.67 21.23 97.54 124.04 150.34 157.67 157.75 157.87 157.86 157.85 157.82 157.81 157.84 157.83 157.83 157.82 157.84 157.84 157.84 157.86
10.23 22.93 103.88 130.74 157.11 154.38 162.40 162.48 162.61 162.60 162.59 162.55 162.54 162.58 162.56 162.56 162.55 162.58 162.58 162.58
0.037 0.078 0.432 0.555 0.656 0.738 0.886 0.909 0.910 0.927 0.929 0.947 0.962 0.974 0.996 0.998 0.999 0.999 0.999 1.000
0.972 0.989 0.998 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 1.000 1.000 1.000 1.000
0.09 0.14 1.57 3.45 6.74 11.56 30.72 34.41 34.28 37.59 37.99 41.07 43.45 45.09 47.48 47.75 47.77 47.78 47.81 47.82
0.10 0.16 1.81 3.97 7.75 13.29 35.33 39.57 39.42 43.23 43.69 47.23 49.97 51.85 54.60 54.91 54.94 54.95 54.98 54.99
a
Data from ref 13.
6.3.a. Azeotrope Prediction. A total of 33 azeotropic systems have been studied. This includes 16 alcohol-, 3 aldehyde-, 10 ketone-, and 3 water-based systems and 1 nitrogen-based system. The methanol (1)/cyclohexane (2) system at T ) 323.15 K in Figure 4a is predicted as the minimum-boiling azeotrope. Similarly, in Figure 4b, the water (1)/formic acid (2) system is predicted as the maximum-boiling azeotrope by COSMO calculations. The prediction of both minimum- as well as maximum-boiling azeotrope are indicated in Table 7 using superscripted b notation. The overall relative absolute average deviation for azeotropic systems is ∼5% in total pressure and ∼0.04 for mole fraction. 6.3.b. Deviating Systems. It can be observed that, out of the 20 deviating systems, polar compounds contribute the most. Systems containing alcohols (methanol, ethanol, propanol, and hexanol), ketones (acetone, pentanone, n-methyl pyrolidone, and dimethylformamide), aldehydes (acetaldehyde, propionaldehyde, and furfural), acids (acetic acid), and water have higher deviations as compared to nonpolar ones, which is consistent with previous work.9 The relative absolute average deviations in total pressures are 6%, 8%, and 6% with alcohols, aldehydes, and ketones, respectively. This error could be reduced by finetuning the COSMO parameters.
There is a significant deviation for systems based on water (3.5% in pressure and ∼0.08 in mole fraction), e.g., with acetaldehyde, dimethyl sulfoxide, 2-butanone, formaldehyde, and acetic acid. This is consistent with the fact that the screening charge densities of water are overpredicted, which results in the greater value of the activity coefficient in the other compound.9 For the acetic acid-hexanol and propionic acidethyl acetate systems, the high deviations in mole fraction (of 0.127 and 0.115, respectively) are attributed to the dimerization of the carboxylic acids, which has not been taken into account in COSMO calculations. Grensemann and Gmehling9 have also reported high deviations for amine-water systems, which tallies with our computed deviation of ∼20% in pressure for the triethylamine-water system. 6.4. Prediction of VLE for Ionic Liquid Systems. 6.4.a. Sigma Profiles and Potentials for Ionic Liquids. For the ionic liquids, the sigma charge densities have been defined earlier by Klamt and co-workers10 as the summation of the cation and anion profile. However, we have adopted the geometry optimization approach similar to that of Meng et al.27 and Singer and co-workers28 A sequential geometry optimization approach has been used, starting with the imidazolium ring and adding successive alkyl groups until the desired cation is constructed.
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The anion is then added to the cation via a dummy atom and reoptimized to obtain the minimum energy confirmation. Frequency calculations have been performed after each level to verify the stability. The sigma profile of ionic liquid has been obtained for the molecule as a whole. The σ-profiles for [MMIM] [(CF3SO2)2N], [EMIM] [(CF3SO2)2N], [BMIM][(CF3SO2)2N], [MMIM][(CH3)2PO4], and [EMIM][C2H5SO4] have been shown in Figure 5 parts a and b. The two vertical dashed lines are the locations of the cutoff values for the hydrogen-bond donor (σhb < -0.0082 e/Å2) and acceptor for σhb > 0.0082 e/Å2. [EMIM][(CF3SO2)2N] has a sharp peak at 0.002 and another lesser one at 0.01. Both the peaks correspond to the negatively charged [(CF3SO2)2N] anion. The peaks on the negative side are due to the positive charges on the carbon atoms of the imidazolium ring. The sigma profile for [BMIM][(CF3SO2)2N] overlaps with that of [EMIM][(CF3SO2)2N]. For hydrogen bonding, the screening charge densities should lie between -0.0082 to +0.0082 e/Å2. The lesser peak at 0.01 being greater than the cutoff value (i.e., σhb > +0.0082 e/Å2) contributes to the formation of hydrogen bonds (Figure 6a). This peak leads to negative values of µ(σ) for σhb < -0.0082 e/Å2, because extra free energy is gained from forming hydrogen bonds when adding a hydrogen-bond donor segment. Thus, if a strong hydrogen bond is formed, the net restoring free energy (µ(σ)) should be negative. The peaks in the negative side are all greater than σhb (σhb > -0.0082 e/Å2 ); thus, they do not contribute to the hydrogen bonds. [EMIM][C2H5SO4] has no peak for σhb < -0.0082 e/Å2, indicating the absence of hydrogen bonds. In the positive region, a relatively smaller peak at σ ) 0.015 e/Å2 shows the formation of hydrogen bonds in the negative direction of its sigma potential (Figure 6a). In all the ionic liquids, the peaks in the region of -0.0082 to +0.0082 e/Å2 are due to the misfit interactions of the surface segments. The sigma profiles for [MMIM][(CH3)2PO4] and [MMIM][(CF3SO2)2N] are very similar. Both have strong peaks on the positive side due to the presence of anions (Figure 5b). However, neither peaks are located at σhb < -0.0082 e/Å2. The [(CF3SO2)2N] anion forms a relatively low peak at 0.012 e/Å2, which is responsible for its hydrogen bonding as evident from its sigma potential (Figure 6b). 6.4.b. VLE Prediction. Gmehling and co-workers13-15 have measured the experimental binary VLE data of ionic-liquidbased systems comprising alkylmethylimidazolium cation. Predictions have been done for 13 binary systems by varying both the alkyl group on the cation as well as the anion. These ILs have been paired with acetone, 2-propanol, water, cyclohexane, benzene, and tetrahydrofuran. The results of all the COSMO predictions have been summarized in Tables 8-12 and are shown in Figure 7 parts a-e. Our root-mean-square deviations for COSMO-RS systems have been compared with those reported for WILSON, NRTL, and UNIQUAC models in Table 13. Although the COSMO-RS deviations are relatively larger, they lie in the expected range of accuracy for a priori predictions. In all the VLE calculations, a vapor pressure of 1 × 10-3 mm of Hg has been used for ILs. This order of magnitude is comparable to that reported by Paulechka et al.31 for [BMIM][(CF3SO2)2N]. In Figure 7a, [EMIM][(CF3SO2)2N]-acetone and [EMIM][(CF3SO2)2N]-2-propanol show a homogeneous mixture with the IL. [EMIM][(CF3SO2)2N]-acetone shows a negative deviation, while [EMIM][(CF3SO2)2N]-2-propanol predicts a positive deviation from Raoult’s Law. In Figure 7b, the [EMIM][(CF3SO2)2N]-water system predicts a miscibility gap for the
Table 11. Binary VLE Prediction Using COSMO-RS for [MMIM][(CF3SO2)2N] with Benzene and Cyclohexane at 353.15 K. (d: data from ref 15) cyclohexane x 0.001 0.003 0.005 0.006 0.007 0.014 0.022 0.036 0.048 0.080 0.133 0.175 0.398 0.481 0.646 0.718 0.806 0.875 0.978 0.990 0.998 1.000 1.000 a
benzene
ypred
Pexp a
Ppred
x
ypred
Pexp a
Ppred
0.963 0.971 0.978 0.982 0.989 0.994 0.996 0.997 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.998 0.999 0.999 1.000 1.000
1.08b
1.20 4.23 6.12 8.45 10.38 19.69 31.12 52.28 67.05 86.91 90.14 90.18 90.13 90.13 90.11 90.92 92.87 93.91 97.37 98.27 98.99 99.18 99.18
0.009 0.017 0.036 0.046 0.198 0.248 0.354 0.413 0.622 0.665 0.704 0.738 0.876 0.911 0.971 0.996 0.998 0.999 1.000
0.991 0.995 0.998 0.999 0.998 0.999 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.36 2.58 5.23 6.56 28.08 35.26 50.32 58.97 89.15 94.68 98.98 101.13 101.08 101.09 101.11 101.10 101.10 101.09 101.10
1.76 2.44 5.06 6.91 30.56 32.29 62.69 64.69 91.94 95.63 99.90 100.13 100.45 100.53 100.61 100.62 100.82 100.92 101.02
3.62b 5.48b 7.32b 9.87b 18.44 28.98 48.01 62.78 95.50 99.27 99.32 99.26 99.26 99.24 99.22 99.12 99.16 99.19 99.18 99.15 99.13 99.10
Data from ref 15. b Indicates extrapolated values.
Table 12. Binary VLE Prediction Using COSMO-RS for [EMIM][C2H5SO4] with Benzene and Cyclohexane at 353.15 K cyclohexane x
ypred
Pexpa
0.002 0.005 0.007 0.010 0.030 0.041 0.057 0.081 0.186 0.231 0.285 0.340 0.580 0.601 0.671 0.878 0.933 0.983 0.999
0.969 0.987 0.990 0.993 0.997 0.998 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
3.12 5.97 8.73 11.45 16.25 16.27 16.27 16.27 16.26 16.25 16.25 16.25 16.24 16.25 16.24 16.23 16.25 16.29 16.29
a
benzene Ppred
x
ypred
Pexpa
Ppred
3.43 6.57 9.60 12.60 17.05 17.28 17.90 17.90 17.89 17.88 17.88 17.88 17.86 17.88 17.86 17.85 17.88 17.92 17.92
0.001 0.002 0.003 0.004 0.005 0.011 0.018 0.055 0.096 0.159 0.239 0.333 0.527 0.606 0.645 0.666 0.718 0.731 0.813 0.893 0.947 0.978 0.989
0.941 0.946 0.951 0.958 0.963 0.975 0.984 0.995 0.997 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999
0.05b 0.07b 0.13b 0.18b 0.28 0.57 0.92 2.54 4.25 6.84 9.82 12.88 15.98 15.98 15.98 15.98 15.97 15.97 15.95 15.94 15.95 15.96 15.97
0.03 0.08 0.12 0.19 0.29 0.6 0.97 2.74 4.59 7.39 10.31 13.52 17.26 17.26 17.26 17.26 17.25 17.09 17.07 17.06 17.07 17.08 17.09
Data from ref 15. b Indicates extrapolated values.
IL. Negative deviation with Raoult’s law is predicted for the [MMIM][(CH3)2PO4]-water system (Figure 7b). However, the COSMO-RS prediction with water is poorer with all the IL systems in terms of total pressure (∼10%) (Table 13). This is mainly due to the overprediction of the activity coefficients and is consistent with the prediction of Grensemann and Gmehling,9 for 18 non-IL-based binary systems. Grensemann and Gmehling, in their COSMO-RS(Ol) formulation, have corrected this overprediction for non-IL systems by scaling the screening charge density of water by a factor of 0.905. Using the same scaling factor, the total pressure COSMO-RS prediction gets further reduced to 8%.
Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006 3217
Figure 7. (a) VLE of [EMIM][(CF3SO2)2N] + acetone and [EMIM][(CF3SO2)2N] + 2-propanol at 353.5 K.13 (b) VLE of water with [EMIM][(CF3SO2)2N] and [MMIM][(CH3)2PO4], at 353.5 K.13-14 (c) VLE of acetone, tetrahydrofuran + [MMIM][(CH3)2PO4] at 353.5 K.14 (d) VLE of cyclohexane[MMIM][(CF3SO2)2N] at 353.5 K.14 (e) VLE of benzene-[EMIM][C2H5OSO3] at 353.5 K.15
The [MMIM][(CH3)2PO4]-tetrahydrofuran (Figure 7c) system shows a positive deviation from Raoult’s law and a miscibility gap for x > 0.4, whereas for [MMIM][(CH3)2PO4]water system (Figure 7b), the miscibility gap ends at x ) 0.4. This allows [MMIM][(CH3)2PO4] to be an extractive solvent for the separation of water/THF mixtures. A similar strategy cannot be applied for water/acetone mixtures, since both have a negative deviation from Raoult’s law and their miscibility gap gets overlapped (Figure 7c). In [MMIM][(CF3SO2)2N]-cyclohexane (Figure 7d) and [EMIM][C2H5OSO3]-benzene systems (Figures 7e) (Tables 11 and 12), the prediction shows that there are large regions which show a flat behavior in the P-x diagram.
This indicates a large miscibility gap with the ionic liquid. The fact that cyclohexane has a larger miscibility gap (high activity coefficient) with [MMIM][(CF3SO2)2N] as compared to benzene is used for the separation of aliphatics from aromatics by liquidliquid extraction.32 It has also been reported that the solubility of cyclohexane in ionic liquid increases on increasing the alkyl length of the cation.15 Benzene shows a miscibility on account of its unsaturated bonds, leading to strong solute-solvent interaction. The nonideality of the vapor phase has been incorporated using eqs 13 and 14. The molar volume of the pure liquid (V) and the second virial coefficients (B1) are taken from ref 33.
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Ind. Eng. Chem. Res., Vol. 45, No. 9, 2006
Table 13. Comparison of RMSD with Different Modelsa experimental data fit with model system
Wilson RMSD (%)
NRTL RMSD (%)
a priori prediction
UNIQUAC RMSD (%)
COSMO-RS (this work)
acetone 2-propanol water
[EMIM][(CF3SO2)2N]13 1.03 1.13 1.41 2.24 1.13 1.44 8.01 2.45 2.25
2.7 3.8 9.8
acetone 2-propanol water
[BMIM][(CF3SO2)2N]13 1.49 1.62 1.59 1.96 1.33 1.43 8.81 1.05 1.07
3.5 4.0 9.8
[MMIM][(CH3)2PO4]13 acetone tetrahydrofuran water
6.2 4.5 8.3
5.1 4.6 10.6
Greek Symbols
benzene cyclohexane
[MMIM][(CF3SO2)2N]15 1.45 1.45 4.16 4.16
8.92 6.26
benzene cyclohexane
[EMIM][C2H5OSO3]15 6.78 6.78 17.8 17.8
9.75 6.94
a
pi(σ) ) probabilistic surface charge distribution for pure component (i) pS(σ) ) probabilistic surface charge distribution for mixture (S) P ) total pressure in Kpa q ) normalized area parameter r ) normalized volume parameter reff ) radius of the standard surface segment (aeff) in Å rn ) radius of the nth segment R ) universal gas constant in J/(mol K) SG ) Stavermann-Guggenheim term T ) temperature in K V ) liquid molar volume in cm3/mol x ) mole fraction in liquid phase y ) mole fraction in gas phase z ) coordination number ) 10
RMSD (%) ) 100x(1/n)∑n(Pexp-Pcalc/Pexp)2.
However, the change in fugacity coefficients is negligible and within 2%. The vapor-phase prediction for all the systems shows that the vapor mole fractions are in the range of 0.990-1.00, indicating that the ionic liquid does not go into the vapor phase. Even at pressures as low as 0.003 Pa, the ionic liquid does not go into the vapor phase. However, the vapor-phase prediction could not be validated, since the experimental vapor-phase compositions have not been reported by the workers.13-15
σ ) screening charge density in e/Å2 R′ ) misfit constant in kJ/mol/Å2 σhb ) cutoff screening charge density for hydrogen bonding in e/Å2 σdon ) screening charge density for hydrogen-bond donor in e/Å2 σacc ) screening charge density for hydrogen-bond acceptor in e/Å2 τ(e(R)) ) dispersion coefficient in kJ/mol/Å2 for element R µS(σ) ) sigma potential in kJ/mol/Å2 for a surface segment in solution S Γi(σ) ) segment activity coefficient for pure component (i) ΓS(σ) ) segment activity coefficient for mixture (S) γiS ) component activity coefficient in the mixture (S) φi ) fugacity coefficient of the component in mixture φ0 ) fugacity coefficient of the component in pure state
7. Conclusions An a priori phase equilibria model has been developed along the lines of COSMO-RS and COSMO-SAC. The predictions are very good for a large number of systems containing a variety of functional groups. The model is also carefully able to predict the low- and high-boiling azeotrope formation. Finally, the predictions have been tried on ionic liquids, and these predictions, being a priori, are fairly close to the results of the Wilson, NRTL, and UNIQUAC models based on total pressure. Supporting Information Available: Appendixes I and II give the COSMO files for 50 nonionic liquids components and 5 ionic liquids generated by GAUSSIAN 03. This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature List of Symbols aeff ) effective contact surface area of a segment in Å2 aR ) molecular surface on atom R B ) The second virial coefficients in cm3/mol chb ) hydrogen-bonding coefficient dmn ) distance between the mth and nth segment Emisfit ) misfit interaction energy Ehb ) hydrogen-bonding interaction energy EvdW ) van der Waals (vdW) interaction energy k ) Boltzmann constant M ) no of points ni ) contribution of molecule i to the surface segments in the solution
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ReceiVed for reView October 6, 2005 ReVised manuscript receiVed February 14, 2006 Accepted March 8, 2006 IE051116C
