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Fluid Phase Equilibria 287 (2009) 43–49

Contents lists available at ScienceDirect

Fluid Phase Equilibria

journa l homepage: www.e lsev ier .com/ locate / f lu id

rediction by the ASOG method of liquid–liquid equilibrium for binary andernary systems containing 1-alkyl-3-methylimidazolium hexafluorophosphate

edro A. Roblesa, Teófilo A. Grabera, Martín Aznarb,∗

Department of Chemical Engineering, University of Antofagasta, Angamos 601, Casilla 170, Antofagasta, ChileSchool of Chemical Engineering, State University of Campinas, P.O. Box 6066, 13083-970 Campinas, SP, Brazil

r t i c l e i n f o

rticle history:eceived 20 February 2009eceived in revised form 31 August 2009ccepted 10 September 2009vailable online 17 September 2009

eywords:

a b s t r a c t

Ionic liquids are neoteric, environmentally friendly solvents (since they do not produce emissions)composed of large organic cations and relatively small inorganic anions. They have favorable physi-cal properties, such as negligible volatility and wide range of liquid existence. Moreover, many differentcations and anions can be used to synthesize ionic liquid, so the properties can be designed by the useof selected combinations of anions and cations. Liquid–liquid equilibrium (LLE) data for systems includ-ing ionic liquids, although essential for the design and operation of separation processes, are still scarce.

redictionSOGiquid–liquid equilibriumonic liquids

However, some recent studies have presented ternary LLE data involving several ionic liquids and organiccompounds such as alkanes, alkenes, alkanols, water, ethers and aromatics. In this work, the ASOG modelfor the activity coefficient is used to predict the LLE for 11 binary and 17 ternary systems including theionic liquid 1-alkyl-3-methylimidazolium hexafluorophosphate plus alkanes, alkenes, alkanols, ketones,carboxylic acids and aromatics. New group interaction parameters were determined by using a modifiedSimplex method, minimizing a composition-based objective function. The results are satisfactory, withrms deviations of about 4%.

. Introduction

Ionic liquids (ILs) are ionic compounds made of bulky, asym-etric organic cations and relatively small inorganic anions, whoseelting point is below T = 273.15 K. This is an arbitrary limit defined

n order to organize the dramatically increasing number of pos-ible applications in chemical processes [1–5]. Over the past fewears, research about ionic liquids has increased greatly, mainlyn two directions: as reaction media, especially in homogeneousatalysis, and as solvents for separation processes [6,7]. Particu-arly for this latter purpose, their physical and chemical properties

ake them especially suitable as solvents, potentially substitut-ng the most common volatile organic solvents in the chemicalndustry.

Ionic liquids have low melting temperatures, are liquid atoom temperature, have thermal stability up to high temperatures,ossess high solubility for both polar and nonpolar organic and

norganic substances, exhibit interesting solvation and coordina-ion properties that depend on the nature of the cation and/or anion,nd have very low vapor pressures [3,8,9]; this special characteris-ic of almost null vapor pressure has transformed ionic liquids into

∗ Corresponding author.E-mail address: maznar@feq.unicamp.br (M. Aznar).

378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2009.09.014

© 2009 Elsevier B.V. All rights reserved.

good alternatives as green solvents of future potential and highcommercial interest.

Liquid–liquid equilibrium (LLE) data for multicomponent sys-tems including ionic liquids, although essential for the designand operation of separation processes, are still scarce. However,some recent studies [2,4,5,10–32] have presented ternary LLE datainvolving several ionic liquids and organic compounds such as alka-nes, alkenes, alkanols, water, ethers and aromatics.

Liquid–liquid or solvent extraction is a major industrial pro-cess in the chemical industry that depends on the physical andchemical properties of a solvent to effect the separation of complexliquid mixtures, such as in the recovery of valuable products andthe removal of contaminants in effluent streams. The separationpotential and feasibility of solvents for commercial applicabilityare dependent on physical properties such as boiling point, thermalstability, viscosity, ease of recovery, toxicity and corrosive natureof the solvent.

Liquid–liquid equilibrium data are essential for a proper under-standing of extraction processes. The analysis of the compositionof the two phases in equilibrium supplies considerable information

about mass balance and mass transfer calculations in the design andoptimization of separation processes. In this paper, we have chosenone of the most extensively investigated cation in ionic liquids, thatis, 1-alkyl-3-methylimidazolium, combined with hexafluorophos-phate (PF6) as the anion.

4 ase Eq

uaaiUiaiawwlmgfif4

2

ri

f

iE

x

fE

∑

a

3

tmogbnd[

fmint

l

ctc

t

4 P.A. Robles et al. / Fluid Ph

In a rigorous way, any thermodynamic modeling of ionic liq-id containing systems should include a long-range term for thectivity coefficient, such as Pitzer–Debye–Hückel. However, suchpproach needs physical properties such as dielectric constant andonic strength, which have not been obtained yet for ionic liquids.p to date, all thermodynamic modeling in ionic liquid contain-

ng systems have been made with short-range models. Severaluthors [4,12–14,27] have used the NRTL model for the activ-ty coefficient [34] as the standard correlation model for binarynd ternary systems including ionic liquids. More recently, someorks [35–44] using UNIQUAC [45] have been reported. In thisork, LLE data for binary and ternary systems including ionic

iquids are, by the first time, predicted by a group-contributionodel for the activity coefficient, the ASOG model [46–49]. New

roup interaction parameters were determined by using a modi-ed Simplex method, minimizing a composition-based objective

unction. The results are satisfactory, with rms deviations of about%.

. Liquid–liquid equilibrium

The thermodynamic requirement for any type of phase equilib-ium is that the compositions of each species in each phase in whicht appears be such that the equilibrium criterion:

Ii (T, P, xI) = f II

i (T, P, xII) (1)

s satisfied [50]. Introducing the activity coefficient definition intoq. (1) yields:

Ii�

Ii (T, P, xI) = xII

i � IIi (T, P, xII) i = 1, 2, 3 . . . (2)

The compositions of the coexisting phases are the sets of moleractions xI

1, xI2, . . . , xI

c, xII1, xII

2, . . . , xIIc that simultaneously satisfy

q. (2) and

c

i=1

xIi = 1 and

c∑i=1

xIIi = 1 (3)

The activity coefficient �i can be determined with an appropri-te thermodynamic model.

. Analytical solution of groups (ASOG)

A group-contribution method is more effective in predictinghe activity coefficient of the components compared to other

ethods. The effectiveness of this kind of method dependsn the division of the solution into a number of interactingroups. As the mutual behavior of interacting groups cannote determined experimentally, group-contribution thermody-amic models can be used, where the interaction parametersetermined from the behavior of one or several real systems51].

The analytical solution of groups, ASOG [46–49] and UNIQUACunctional-group activity coefficient, UNIFAC [52] methods are

ainly based on the assumption that the contribution to the activ-ty coefficient of component i can be separated into two parts,amely, a combinatorial, entropic part (molecular size contribu-ion) and a residual, enthalpic part (intermolecular forces):

n �i = ln �Ci + ln �R

i (4)

In ASOG, the Flory–Huggins [53,54] equation was used for the

ombinatorial part of the activity coefficient and the Wilson equa-ion [55] was used for the determination of group residual activityoefficients.

The activity coefficient of component, � i, can be calculated byhe following equations, where the superscripts FH and G stand for

uilibria 287 (2009) 43–49

“Flory–Huggins” (combinatorial part) and “groups” (residual part),respectively:

ln �i = ln �FHi + ln �G

i (5)

ln �FHi = 1 + ln

(�FH

i∑NCj=ixj�

FHj

)− �FH

i∑NCj=ixj�

FHj

(6)

ln �Gi =

NG∑k=1

�k,i(ln �k − ln � (i)k

) (7)

In these equations, �FHi

is the measure of the size of moleculei, defined as the number of atoms in the molecule (except forhydrogen atoms), while � k is the residual activity coefficient ofgroup k in the mixture, � (i)

kis the residual activity coefficient

of group k in pure compound i and �k,i is the number of atoms(other than hydrogen atoms) in group k in molecule i. Both theresidual activity coefficients can be calculated by the Wilson [55]equation:

ln �k = 1 − ln

(NG∑l=1

Xlak/l

)−

NG∑l=1

[Xlal/k∑NG

m Xmal/m

](8)

where Xl is the group fraction of group l in liquid solution, given by

Xl =∑NC

i=1xi�l,i∑NCi=1xi

∑NGk=1�k,i

(9)

where �l,i is the number of atoms of the group l in molecule i, NC isthe number of components and NG is the number of groups in themixture. In Eq. (8), ak/l are the group interaction parameters, whichdepend on the temperature as

ak/l = exp(

mk/l + nk/l

T

)ak/l /= al/k (10)

where mk/l and nk/l are the group interaction parameters, whichdepend only on the group pair and not on the temperature.

In this work, for the calculation and discussion on the 1-alkyl-3-methylimidazolium hexafluorophosphate containing systems,two new groups, the imidazolium ring (Imid) and the hexaflu-orophosphate anion (PF6), are proposed. New group interactionparameters for CH2/Imid, CH2/PF6, C = C/Imid, C = C/PF6, OH/Imid,OH/PF6, CO/Imid, CO/PF6, ArCH/Imid, ArCH/PF6, CyCH/Imid,CyCH/PF6, COOH/Imid, COOH/PF6 and Imid/PF6 have been deter-mined from 28 binary and ternary systems using the procedurebelow.

4. Parameter estimation

Group interaction parameters were estimated using the For-tran code TML-LLE 2.0 [56]; the procedure is based on the Simplexmethod proposed by Nelder and Mead [57], and consists in theminimization of a concentration-based objective function, S [58].

S =D∑k

M∑j

N−1∑i

[(xI,exp

ijk− xI,calc

ijk)2 + (xII,exp

ijk− xII,calc

ijk)2]

(11)

Here, D is the number of data sets, N and M are the number of com-

ponents and tie lines in each data set and superscripts I and II referto the two liquid phases in equilibrium, while superscripts ‘exp’ and‘calc’ refer to the experimental and calculated values of the liquidphase concentration. With these parameters, LLE calculations canbe made.

P.A. Robles et al. / Fluid Phase Equilibria 287 (2009) 43–49 45

Table 1The values of �k,i and �FH

i.

N Compound �k,i �FHi

CH2 C C OH CO ArCH Imid PF6 CyCH COO COOH

1 Heptane 7 0 0 0 0 0 0 0 0 0 72 Nonane 9 0 0 0 0 0 0 0 0 0 93 Undecane 11 0 0 0 0 0 0 0 0 0 114 Dodecane 12 0 0 0 0 0 0 0 0 0 125 Hexadecane 16 0 0 0 0 0 0 0 0 0 166 1-Hexene 4 2 0 0 0 0 0 0 0 0 67 1-Heptene 5 2 0 0 0 0 0 0 0 0 78 Ethanol 2 0 1 0 0 0 0 0 0 0 39 1-Propanol 3 0 1 0 0 0 0 0 0 0 4

10 2-Propanol 2.8 0 1 0 0 0 0 0 0 0 411 1,3-Propanediol 3 2 0 0 0 0 0 0 0 0 512 1-Butanol 4 1 0 0 0 0 0 0 0 0 513 1-Pentanol 5 1 0 0 0 0 0 0 0 0 614 2-Butanone 3 0 0 2 0 0 0 0 0 0 515 Benzene 0 0 0 0 6 0 0 0 0 0 616 Toluene 1 0 0 0 6 0 0 0 0 0 717 m-Xylene 2 0 0 0 6 0 0 0 0 0 818 [bmim][PF6] 5 0 0 0 0 5 7 0 0 0 1719 [hmim][PF6] 7 0 0 0 0 5 7 0 0 0 1920 [omim][PF6] 9 0 0 0 0 5 7 0 0 0 2121 Ciclohexane 0 0 0 0 0 0 0 6 0 0 6

000

mtn

r

TA

22 Propionic acid 2 0 0 023 Vynil propionate 2 2 0 024 n-Hexane 6 0 0 0

Comparisons between experimental and calculated data can beade through root mean square (rms) absolute deviations between

he experimental and the calculated composition of each compo-

ent in both phases. These rms deviations are given by

ms = 100

√∑Mn

∑N−1i (xI

exp − xIcalc)

2 + (xIIexp − xII

calc)2

2MN(12)

able 2SOG group interaction parameters mk/l and nk/l .

k l

CH2 C C OH

m n m n m

CH2 0 0 1.3286 −995.4 −41.25C C −1.524 713.8 0 0 −0.159OH 4.7125 −3060 10.576 −4545.3 0CO −1.7588 169.6 0 0 −0.328ArCH 0.7297 −176.8 0 0 2.2682Imid 3.6123a −29.013a 4.3495a 0.0196a 2.1066PF6 7.2605a −1096.9a −0.51205a 290.23a 4.2233CyCH −0.1842 0.3 0 0 0COO −0.36990 162.60 −3.4011 1149.1 0COOH −10.9719 4022.0 0 0 0

k l

Imid PF6 CyCH

m n m n m

CH2 −2.3117a 33.103a 0.51570a −326.79a 0.1530C C −0.60827a −14.233a −0.45924a −5.1805a 0OH −5.4567a 810.11a −71.794a 122.97a 0CO −3.2046a −15.733a 0.17382a −18.763a −2.719ArCH −0.95171a −8.1351a 0.65181a −10.178a 0Imid 0 0 4.5219a 213.97a 1.0133a

PF6 4.3496a −3.9826a 0 0 4.1983a

CyCH −0.95502a −196.36a −3.1521a 136.72a 0COO −0.09406a 350.72a 6.8088a −11628.0a 0COOH −0.26986a −128.75a 2.5309a −216.69a 0

a Estimated in this work.

0 0 0 0 3 50 0 0 3 0 70 0 0 0 0 6

5. Results and discussion

The values of �k,i and �FHi

of the 24 substances are listed in

Table 1.

The group interaction parameters are shown in Table 2. In thistable, the values marked with (*) were estimated by the procedureabove, while the other values were taken from Kojima and Tochigi[44].

CO ArCH

n m n m n

7686.4 2.6172 −865.1 −0.7457 146.05 −248.2 0 0 0 0

0 −0.7262 2.9 −0.5859 −939.13 1.3 0 0 0 0

−1111.5 0 0 0 0a 16.823a 5.1906a −49.170a 3.4086a 11.133a

a 108.79a 3.2109a 0.02313a 2.5962a 9.1764a

0 3.2821 −1042.6 0 00 0 0 0 00 0 0 0 0

COO COOH

n m n m n

2.1 −15.262 515.00 9.7236 −3797.50 −5.8807 −9.0000 0 00 0 0 0 0

4 428.0 0 0 0 00 0 0 0 0−1.2254a −16.280a 297.29a 4.9387a −233.63a

−4.2888a 5.0689a −30.095a −5.7735a −159.57a

0 0 0 0 00 0 0 0 00 0 0 0 0

46 P.A. Robles et al. / Fluid Phase Equilibria 287 (2009) 43–49

F1l

t[Apa

pca

Da

datvtmea

F[

NRTL, with deviations about 1.4% between experimental and calcu-lated compositions; more recently, Santiago et al. [44] modeled theLLE for 50 ternary systems (408 tie lines) containing ionic liquidsby using UNIQUAC, with deviations about 1.75%.

ig. 1. Liquid–liquid equilibrium of [hmim][PF6] + 1-alcohols. Experimental [22]: (+)-propanol; (�) 1-butanol; (�) 1-pentanol and (�) [bmim][PF6] + 1-pentanol. ASOG:

ines.

Fig. 1 shows the comparison between the experimental andhe predicted LLE for three [hmim][PF6] + 1-alcohols systems andbmim][PF6] + 1-pentanol. From this figure, we can observe thatSOG can predict accurately the behavior of the ionic liquid-richhase, while the behavior of the alcohol-rich phase is predicted inless accurate way.

Fig. 2 shows the comparison between the experimental and theredicted LLE for the binary system [bmim][PF6] + 1-butanol. Theonclusion is similar, the ionic liquid-rich phase is well predictednd the prediction for the alcohol-rich phase is poorer.

Figs. 3–7 show the same comparisons for five ternary systems.epending of the system, the ASOG predictions can be consideredccurate.

For a more general view of the results, Table 3 shows the rmseviations between experimental and calculated compositions forll 28 systems, comprising 277 tie lines, according to Eq. (12), withhe values always below 10% and generally below 5%. The globalalue for rms was about 4%. From these deviations, we can conclude

hat ASOG was able to predict the phase behavior of the experi-

ental data with a good precision. However, these results are, asxpected, inferior to those obtained with molecular models suchs NRTL and UNIQUAC. For example, Aznar [1] modeled the LLE for

ig. 2. Liquid–liquid equilibrium of [bmim][PF6] (1) + 1-butanol (2). Experimental26]: *; ASOG: —.

Fig. 3. Liquid–liquid equilibrium of [hmim][PF6] + benzene + heptane at 298.15 K.Experimental [14]: (�); ASOG: �.

24 ternary systems (184 tie lines) containing ionic liquids, by using

Fig. 4. Liquid–liquid equilibrium of 2-propanol + 2-butanone + [bmim][PF6] at298.15 K. Experimental [11]: �; ASOG: �.

Fig. 5. Liquid–liquid equilibrium of cyclohexane + 2-butanone + [hmim][PF6] at298.15 K. Experimental [11]: �; ASOG: �.

P.A. Robles et al. / Fluid Phase Eq

Fig. 6. Liquid–liquid equilibrium of cyclohexane + 2-butanone + [omim][PF6] at298.15 K. Experimental [11]: �; ASOG: �.

Fig. 7. Liquid–liquid equilibrium of heptane + ethanol + [omim][PF6] at 298.15 K.Experimental [33]: �; ASOG: �.

Table 3Root mean square rms deviations in binary and ternary systems.

N System Reference ND �x (%)

1 [bmim][PF6] + 1-butanol [26] 05 0.992 [bmim][PF6] + 1-propanol [22] 14 3.033 [bmim][PF6] + 1-butanol [22] 14 3.434 [bmim][PF6] + 1-pentanol [22] 14 2.095 [hmim][PF6] + 1-propanol [22] 11 2.696 [hmim][PF6] + 1-butanol [22] 14 2.457 [hmim][PF6] + 1-pentanol [22] 14 2.738 [omim][PF6] + 1-propanol [22] 08 8.349 [omim][PF6] + 1-butanol [22] 10 4.02

10 [omim][PF6] + 1-pentanol [22] 12 5.2611 1,3-Propanediol + [bmim][PF6] [24] 08 1.4112 Nonane + toluene + [bmim][PF6] [2] 03 8.9213 Nonane + m-xylene + [bmim][PF6] [2] 05 7.1314 Undecane + toluene + [bmim][PF6] [2] 04 8.1615 [hmim][PF6] + benzene + heptane [14] 05 3.0716 [hmim][PF6] + benzene + dodecane [14] 13 3.5017 [hmim][PF6] + benzene + hexadecane [14] 13 3.8118 [hmim][PF6] + ethanol + 1-hexene [13] 12 5.3919 [hmim][PF6] + ethanol + 1-heptene [13] 07 4.0620 Ethanol + 2-butanone + [bmim][PF6] [23] 06 7.4821 2-Propanol + 2-butanone + [bmim][PF6] [23] 11 2.2422 Ciclohexane + 2-butanone + [hmim][PF6] [31] 11 1.5123 Ciclohexane + 2-butanone + [omim][PF6] [31] 10 1.9724 [bmim][PF6] + propionic acid + n-hexane [32] 04 3.9925 [bmim][PF6] + vynil propionate + n-hexane [32] 05 6.3726 Hexane + ethanol + [hmim][PF6] [33] 13 4.6327 Hexane + ethanol + [omim][PF6] [33] 16 4.8328 Heptane + ethanol + [omim][PF6] [33] 15 2.84

Global 277 4.24

uilibria 287 (2009) 43–49 47

6. Conclusion

Binary and ternary LLE data for 28 systems and 277 tie linesincluding ionic liquids of the kind 1-alkyl-3-methylimidazoliumhexafluorophosphate were predicted by the ASOG model for theactivity coefficient. The group interaction parameters were esti-mated by minimization of a composition-based objective functionusing the Simplex method. The results of the prediction were satis-factory, with rms deviations between experimental and calculatedequilibrium compositions always below 10% and, in most cases,below 5%, with a global value of about 4%. It can be concluded thatthe ASOG model is able to predict the LLE of binary and ternarysystems including these ionic liquids with a good precision.

List of symbolsak/l group interaction parameters, temperature dependentc componentD number of data setseqs equationsf fugacitymk/l, nk/l group interaction parameters, temperature independentM number of tie linesNC number of componentsNDP number of data pointsNG number of groups in the mixtureP pressureS objective functionT absolute temperaturex mole fraction in liquid phaseX group mole fraction

Greek letters� group activity coefficient� activity coefficient� number of groups

Superscripts/subscriptsC combinatorialFH size contributionG group contribution(i) standar state (pure component i)I, II liquid phaseR residual1, 2, i, j molecule 1, 2, i, and jcalc calculated valueexp experimental valuek, l, m group k, l, and mk, i group k in molecule i

AbbreviationsASOG analytical solutions of groupsLLE liquid–liquid equilibriumrms root mean square absolute deviationsUNIFAC universal functional activity coefficient

Acknowledgements

P.A. Robles is grateful to the National Council for Scientificand Technological Research (CONICYT-Chile) for grant 21070448.

T. Graber acknowledges the National Council for Scientific andTechnological Research (CONICYT-Chile), for grant FONDECYT1085059/2008. M. Aznar is the recipient of a fellowship fromthe National Council of Scientific and Technological Development(CNPq-Brazil).

4 ase Eq

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

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[

[

[

[

[

[

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[

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[

[

[

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8 P.A. Robles et al. / Fluid Ph

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