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Fluid Phase Equilibria 294 (2010) 15–30

Contents lists available at ScienceDirect

Fluid Phase Equilibria

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

odeling ionic liquids and the solubility of gases in them:ecent advances and perspectives

ourdes F. Vegaa,b,c,∗, Oriol Vilasecaa,b, Fèlix Llovellb, Jordi S. Andreua,b

MATGAS Research Center, Campus de la UAB, 08193 Bellaterra, Barcelona, SpainInstitut de Ciència de Materials de Barcelona, Consejo Superior de Investigaciones Científicas (ICMAB-CSIC), Campus de la UAB, 08193 Bellaterra, Barcelona, SpainCarburos Metálicos – Air Products Group, C/Aragón, 300 Barcelona, Spain

r t i c l e i n f o

rticle history:eceived 19 November 2009eceived in revised form 7 February 2010ccepted 9 February 2010vailable online 13 February 2010

eywords:onic liquids

a b s t r a c t

The fascinating properties of ionic liquids, their versatility for different applications and their highlynon-ideal behavior have promoted the study of these systems from different perspectives. This articleprovides an overview of the different approaches that have been applied to describe the thermodynamicbehavior of ionic liquids and the solubility of selected compounds in them, including carbon dioxide,hydrogen, water, BF3 and other compounds. The paper deals with some of the most recent and refinedapproaches involving physical models developed to characterize the ionic liquids. Emphasis is put on themodels based on statistical mechanics, highlighting the advantages of these models versus classical ones.

O2 solubilityeak complexationolecular-based models

lassical equationsattice modelsoft-SAFT

New modeling results involving the chemical association of BF3 in ionic liquids and interfacial propertiesof selected ionic liquids within the framework of soft-SAFT are also presented. It is seen that the greatadvance in the refined modeling tools allows not only quantitative agreement with known experimentaldata, but also a guide to some of the physics governing the behavior of these systems, a step forward intodeveloping ad hoc ionic liquids for specific applications.

© 2010 Published by Elsevier B.V.

PC-PSAFTWCF

. Introduction

Ionic liquids, also known as liquid electrolytes, ionic melts, ionicuids, liquid salts, or ionic glasses, is a term generally used to refero salts that form stable liquids. Nowadays it is considered that any

rganic salt that is liquid below 100 ◦C falls into this category. Theyre usually formed by a large organic cation like quaternary ammo-ium, imidazolium or pyridinium ions combined with an anion ofmaller size and more symmetrical shape such as [Cl]−, [Br]−, [I]−,

Abbreviations: AMQs, additive molar quantities; COSMO-RS, COnductor likecreening MOdel for Realistic Solvents; EoS(s), equation(s) of state; GC, group contri-ution method; IFP, Institut Francais du Pétrole; IL, ionic liquid; LJ, Lennard–Jones;LE, liquid–liquid equilibrium; LLV, liquid–liquid–vapor; NRTL, nonrandom two-iquid model; NRTL-SAC, nonrandom two-liquid segment activity coefficient model;C, perturbed chain; PCM, polarizable continuum model; PR, Peng–Robinson; pVT,ressure–volume–temperature; RK, Redlich–Kwong; RST, Regular Solution Theory;AFT, Statistical Associating Fluid Theory; SLE, solid–liquid equilibrium; SWCFs,quare-well for chain fluids equation; tPC-PSAFT, truncated Perturbed Chain Polartatistical Associating Fluid Theory; UNIFAC, universal functional activity coefficientodel; UNIQUAC, universal quasi-chemical approach; vdW, van der Waals; VLE,

apor–liquid equilibrium.∗ Corresponding author at: MATGAS Research Center, Campus de la UAB, 08193ellaterra, Barcelona, Spain. Tel.: +34 935 929 950; fax: +34 935 929 951.

E-mail addresses: vegal@matgas.com, lvega@icmab.es (L.F. Vega).

378-3812/$ – see front matter © 2010 Published by Elsevier B.V.oi:10.1016/j.fluid.2010.02.006

[BF4]−, [PF6]−, [Tf2N]−, etc., although some symmetric cations arealso combined with asymmetric anions to form ionic liquids. Inspite of their strong charges, their asymmetry frustrates them frombeing solid below 100 ◦C and this is why they remain liquid at theselow temperatures.

It is believed that the first synthesized ionic liquid reported inthe literature is ethanolammonium nitrate, published by Gabriel[1]. However, one of the earlier known truly room-temperatureionic liquids was [EtNH3]+[NO3]−, the synthesis of which was pub-lished in 1914 [2,3]. Much later, different ionic liquids based onmixtures of 1,3-dialkylimidazolium or 1-alkylpyridinium halidesand trihalogenoaluminates, initially developed for their use as elec-trolytes, were to follow [4,5]. Ionic liquids remained unused foryears, mostly because of their moisture sensitivity and their acid-ity/basicity (the latter can sometimes be used as an advantage).However, when in 1992, Wilkes and Zawarotko [6] reported thepreparation of ionic liquids with a new set of alternative, ‘neutral’,weakly coordinating anions such as hexafluorophosphate ([PF6]−)and tetrafluoroborate ([BF4]−), a much wider range of applications

for ionic liquids were envisioned, and this has been a field of con-tinuous growth since then.

There are some key properties of these compounds that makethem particularly attractive for different applications: in fact, theirextremely low volatility has become one of their most important

16 L.F. Vega et al. / Fluid Phase Equilibria 294 (2010) 15–30

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ig. 1. Number of publications about ionic liquids published in journals included inhe Web of Science List, year by year in this decade.

enefits compared to volatile organic solvents used as traditionalndustrial solvents. High thermal and electronic stability, high ioniconductivity, a wide liquid temperature and good solubility char-cteristics complete the list of advantages versus other traditionalompounds for different applications.

As already mentioned, a huge amount of different ionic liq-ids can be synthesized through the combination of an organicr inorganic anion and an organic (or inorganic) cation, and theumber of new synthesized ionic liquids continues to grow inces-antly. For instance, just regarding the imidazolium family, therere over 30,000 1,3-functionalized entries recorded in the CASatabase. Further scope for derivatization beyond ramification of

inear alkyl-substituents, for example with branched, chiral, fluori-ated, or an active-functionality, can yield further useful materials.he degree and type of substitution renders the salts low melting,argely by reducing cation–anion Coulombic interactions and dis-upting ion–ion packing [7]. In this way, the specific properties ofn ionic liquid can be almost selected ad hoc, in order to have aompound with the most appropriate characteristics for a specificpplication.

Among an uncountable amount of different possibilities [8],he use of ionic liquids as media for CO2/gas separations appearsspecially promising, as CO2 is more highly soluble than the restf the gases. Process temperature and the chemical structures ofhe cation and the anion have significant impacts on gas solubil-ty and gas pair selectivity. In addition to their role as a physicalolvent, ionic liquids might also be used in supported ionic liquidembranes as a highly permeable and selective transport medium.verall, they are considered environmentally friendly compounds

even if it depends on the selection of the cation and the anion) thatan be used in catalytic reactions [9], gas and liquid separations,leaning operations, electrolyte or fuel cells or even as lubricantsnd heat transfer fluids [10,11]. A summary of capabilities and limi-ations of ionic liquids in CO2-based separations respect to a varietyf materials is provided in a very recent and detailed contributiony Bara et al. [12].

Fig. 1 depicts the number of contributions in scientific Journalsncluded in the Web of Science related to ionic liquids versus theear of publication in the last decade. The blooming of publicationsn ionic liquids in the last years is due, in part, to the popular-zation of these compounds done by Rogers and Seddon (see, fornstance, Ref. [13]) and the review paper published by Welton 10ears ago [10]. It should be mentioned that, in spite of their poten-ial for several industrial applications, the list of published works is

ore related to synthesis, characterization and modeling of theseaterials, than to applications, being the list of industrial applica-

ions still very short. As an example of the distribution of works,ig. 2 shows the allocation of topics devoted to different aspectsf ionic liquids presented in the last International Symposium on

Fig. 2. Distribution of topics related to the presentations about ionic liquids at the17th International Symposium on Thermophysical Properties. See text for details.

Thermophysical Properties [14]. As observed in the figure, 42% ofthe presentations were dedicated to modeling (22% to theory and20% to molecular simulations), while 33% of the contributions dealtwith the measurement of some specific properties and the remain-ing 25% dealt with applications. This average share of topics is alsofound in other similar conferences and in the open literature.

As inferred from the literature, there is a gap between theamount of published works and the academic groups working inionic liquids, and the amount of processes used at industrial scale.Before analyzing the causes for this gap, we will briefly revisethe main industrial processes already available. The first indus-trial process involving ionic liquids, the BASIL process (BiphasicAcid Scavenging utilizing Ionic Liquids), was announced in 2003,by BASF. The process is used for the production of the generic pho-toinitiator precursors alkoxyphenylphosphines [15]. As stated byBASF, the BASIL process economically avoids the problems resultingfrom solids generation by making use of ionic liquids to scavengeacids. Instead of using a tertiary amine, a 1-alkylimidazole is usedto scavenge the produced acids. As the imidazole reacts with theacid, an alkylimidazolium salt is formed which is an ionic liquid atthe reaction temperature. As a liquid, the alkylimidazolium salt canbe easily removed by liquid–liquid phase separation. In addition,economic reclamation of the 1-alkylimidazole through deprotona-tion is possible. Another industrial application of great success isthe use of ionic liquids for cellulose processing [16]: cellulose isinsoluble in water and most common organic liquids; before ionicliquids proved to work, CS2 was used to dissolve cellulose for pro-cessing. As 0.2 billion tones of cellulose are used as feedstock forfurther processing, the amount of CS2 to be used is far from beingan eco-friendly technology. However, it has been proved that witha solution up to 25 wt% with [bmim][Cl] at 100 ◦C the cellulosefibers can be cracked or modified. The presence of water in theionic liquid significantly decreases the solubility of cellulose. Afterprocessing, water is added to the cellulose ionic liquid solution andthe modified cellulose can be separated. The water is evaporatedand the ionic liquid is recovered and can be re-used, making it agreen process. Some other uses of industrial applications involvethe Dimersol–Difasol process, proposed by the Institute Francaisdu Pétrole (IFP): the Dimersol process is a traditional way to dimer-ize short chain alkenes into branched alkenes of higher molecularweight. The IFP developed an ionic liquid-based add-on to this pro-cess called the Difasol process, which is operating at a pilot planscale (see Ref. [17] for more details on this and other industrial

processes).

However, the list of successful industrial applications is stilltoo short, compared to the amount of research work done in thearea. As mentioned, there is a clear gap between the academic

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L.F. Vega et al. / Fluid Pha

se of ionic liquids and the few industrial applications. This factas already addressed in a recent report entitled “Accelerating

onic liquid commercialization” [18]. Six barriers were identified toe circumvented for the commercialization of ionic liquids. Thesearriers include: (1) process engineering, as most of the ionic liq-id studies to date have been performed at the laboratory scalender conditions that do not adequately represent operating condi-ions for full-scale industrial applications. Further work is requiredo know the industrial processing equipment for reactors or sep-rators incorporating ionic liquid processes; (2) environmental,afety and health issues: although ionic liquids have no detectableapor pressure and this provides a basis for clean manufacturing“green chemistry” –, each ionic liquid is likely to be classified

s a “new chemical” and may require significant environment,afety and health studies prior to widespread use; (3) economicenefit analyses: ionic liquid applications that have broad chem-

cal industry impact only become a reality when the economiesf these applications are favorable and well understood. Detailedconomic benefit analyses of ionic liquid processes are neces-ary and must be based on process engineering data (barrier 1);4) fundamental understanding of compositional structure versuserformance: ionic liquid commercialization requires discoveryesearchers to not only develop fundamental understanding ofonic liquid synthesis and properties, but to impart these liquids

ith the chemical processing features needed for important indus-rial applications and markets. Developing an understanding of theeactions that form ionic liquids, ionic liquid chemical and phys-cal properties, mechanisms/functions in catalysis and separationystems, and interactions with other materials (e.g., container ves-els) is essential to their usefulness in industrial applications. Sincehe combinations of ions for potential ionic liquids are virtuallynfinite, this is a needed but expensive and time-consuming task;5) ionic liquid manufacturing: as manufacturing of ionic liquids toate has primarily been done on a small scale, the ability to techni-ally and economically scale up the manufacturing process needso be demonstrated before ionic liquids will be used in industrial-cale volumes. Industry is unlikely to adopt this technology if thexpenses of producing bulk ionic liquids remain at their currentevel; (6) institutional issues: in general, industry has been slowo focus on the application of ionic liquids and slow to recognizeheir potential economic value. Also, ionic liquid researchers fre-uently lack insight into the specific details of industrial processesnd applications. This fundamental disconnect between discoveryesearchers and industry, also common to many new product androcesses, contributes significantly to slow the ionic liquid tech-ology growth and route into commercialization.

Hence, steps should be taken towards overcoming these barriersnd make ionic liquids readily available for industrial applica-ions. In order to overcome some of the aforementioned barrierst is important to develop tools that will allow for fundamentalnderstanding of compositional structure versus performance (tourmount barrier (4) on the list). The vast amount of possible ioniciquids and the type of required information needed make the mod-ling tools excellent candidates to advance in this field. However,hese are extremely non-ideal systems, with charged and asym-

etric compounds and, hence, most classical equations will failn capturing their physico-chemical properties, unless the specificnteractions are taken into account since the inception of the model.

Great advance in the understanding of ionic liquids, and theelationship between their structure and the properties, has beenone thanks to the molecular simulation work done by several

esearchers, including the works of Maginn and co-authors [19–24],adua and Canongia-Lopes with co-workers [25–30] and Rey-astro et al. [31,32], among others (see the book published byaginn [23], the recent review of the same author [24] and theork of Bhargava et al. [33] for an extensive bibliography on molec-

ilibria 294 (2010) 15–30 17

ular simulation studies done in the field). These simulation resultshave greatly helped in understanding the local structure of ionicliquids, the solubility of some given compounds in them, and theirtransport properties. Although very useful from this perspective,the vast amount on computational time required to obtain theseproperties precludes the use of molecular simulations as standardtools to characterize these systems for screening purposes beforeselecting an optimum one for a given application. Hence, the useof equations of state or models that reliably provide fast calcula-tions remains an excellent alternative for a quick description of theselected ionic liquids.

This contribution aims to review the different modelingapproaches that have been used in order to describe the phasebehavior of ionic liquids and their mixtures, highlighting the mostimportant efforts done in the last years from the statistical mechan-ics point of view, as the use of lattice models, group-contributionequations, and SAFT-based approaches, including the soft-SAFTequation [34], the truncated Perturbed Chain Polar SAFT (tPC-PSAFT) equation [35] and the square-well for chain fluids (SWCFs)equation [36]. Some new results for the application of soft-SAFTwith a relatively simple model to new properties and systems arealso presented here.

The rest of the paper is organized as follows. Section 2 is devotedto the description of the most recent and refined efforts towardsthe modeling of ionic liquids, with special attention to the physi-cal model behind them, together with the systems that have beendescribed with them. New results are presented related to theapplication of the soft-SAFT approach to two challenging cases:(1) the description of interfacial tensions of pure ionic liquids and(2) the description of the weak chemical complexation betweena chemical compound and an ionic liquid, focused on the absorp-tion of BF3 in [C4mim][BF4] ionic liquid at different temperatures.Finally, some concluding remarks are provided in last section.

2. Modeling theories for ionic liquids

As explained in the previous section, accurate models for theappropriate description of thermodynamic properties of ionicliquids are needed. Several different theoretical approaches, corre-lations and equations of state (EoS) have been used for that purposein recent years. Due to the huge amount of contributions publishedin the last years we have decided to present the information in atabular form (see Table 1), which shows a summary of all of them,highlighting the equation used, the cations and anions that wereconsidered, and the main properties discussed in the given paper.We have classified them according to the “molecular model” used todescribe the ionic liquid in the different approaches: classical cubicequations, activity coefficient and group contribution methods,quantum chemistry calculations and statistical mechanics-basedmolecular approaches. A sketch of each one of the models for aspecific ionic liquid is presented in Table 2. We will summarizenext the main approaches, with emphasis on their advantages andlimitations versus other approaches.

2.1. Classical models

A first effort towards the thermodynamic characterization ofionic liquids was done by the use of relatively simple cubic EoS. Inthis case the ionic liquid is “modeled” as a whole molecule witha certain volume and cohesive energy, but no specification about

its structure nor its association effects are explicitly considered (asketch of the model is presented in Table 2 – see Table 2b).

The Peng–Robinson (PR) EoS [37] was used in a pioneering workof Shariati and Peters to model the solubility of fluoroform in 1-ethyl-3-methylimidazolium hexafluorophospate, [C2mim][PF6], in

18 L.F. Vega et al. / Fluid Phase Equilibria 294 (2010) 15–30

Table 1Summary of published modeling works in ionic liquids, including the references. See text for details.

EoS [BF4] [PF6] [Tf2N] Other anions Properties discussed

Cation: [Cnmim] ImidazoliumPR [38] [40] [41] Solubility of fluroform (CF3H) and CO2

up to 367 K and 50 MPa.Study of the specific solvationinteractions of CO2 + IL.

RK [43], [45], [52] [45,46], [48],[52]

[44,45],[50–52], [54]

[45], [47], [49],[52,53]

Solubility of CO2, SO2, H2, ammonia,trifluoromethane in selected ionicliquids at various thermodynamicsconditions. Binary and ternary phasediagrams with C6H6 and C6F6. Globalphase behavior of CF3H. VLE for theternary systems with SO2/CO2 andCO2/H2.

RST [55–57],[59,60]

[60–62] [55–62] [59–62] Gas solubilities of CO2 andhydrocarbons in imidazolium ionicliquids at low pressures.

NRTLE-NRTLNRTL1NRTL-SACUNIQUAC

[71–74],[76], [81],[87],[96,97],[103–105],[107]

[74–76][81],[86], [100],[103–105][107]

[71,72],[74],[77–79],[87–89],[104–107]

[68],[73,74],[80],[82–85],[87],[90–95],[97–99],[101],[103–105],[107]

SLE and LLE of alcohols, water, ketones,thiophene and hydrocarbons from275 K till the boiling point of thesolvent.Ternary mixtures of aromatics, alkanes,alkenes, alcohols and ketones attemperatures in the range 293–323 K.Activity coefficients of aliphatic andaromatic esters and benzylamine.Phase stability analysis in a binarymixture with water.

GC + correlationsUNIFAC

[108–113][117]

[108–113][114], [117]

[108–113] [108–113][115–117]

Density, surface tension, viscosity,speed of sound, liquid heat capacityand transport properties of a widevariety of ionic liquids.Solubility of hydroflorocarbons.Solubility of [C(12)mim][Cl] innumerous alcohols.Structural and interactions parametersfor dialkylimidazolium-based ILs.

COSMO-RS [125–126] [121],[125,126],[129]

[125,126],[129]

[118],[120–130]

VLE and LLE of alcohols, hydrocarbons,ethers, ketones and water.

Latticemodels

[133,134],[137],[140,141]

[133,134],[137],[140,141]

[134,135],[137], [140]

[134,135],[138]

Solubility of CO2 and CF3H at highpressure up to 100 MPa. VLE and LLEequilibrium diagrams at temperaturesfrom 313 to 343 K. Solubility of C7

hydrocarbons with ethylsulfate anions.

GC-EoS [144], [147] [144] Solubility of CO2. Phase diagrams andphase transitions of ternary mixturesof an organic compound, CO2 andbmim[BF4]

SWCFsHomonuclear[148] andheteronuclear[149]

[148,149] [148,149] [148,149] [148] Molar volumes; solubility of CO2,propane, propylene, butane, benzene,cyclohexane, propanol, 2-propanol,acetone and water in a range oftemperatures from 298 in a range oftemperatures from 298 till 368 K andpressures up to 15 MPa.

Hetero-SAFT [150] [150] [150] Densities of pure ionic liquids from 293to 415 K and up to 650 bar.

PHST [154] [154] [154] Henry’s constants for 20 differentsolutes (hydrocarbons and gases).

tPC-PSAFT [155–158] [155–157] [155–157] Molar volumes, solubility of CO2, O2,CF3H, benzene, benzaldehyde. VLE forternary mixtures of water–CO2–[NO3]and 1-hexane-trans-3-hexene-[PF6]

Soft-SAFT [160] [160] [161] Solubility of CO2, H2 and Xe in therange 293–473 K and pressures up to100 MPa.

L.F. Vega et al. / Fluid Phase Equilibria 294 (2010) 15–30 19

Table 1(Continued).

EoS [BF4] [PF6] [Tf2N] Other anions Properties discussed

Cation: [Py+] PyridiniumNRTL

E-NRTLUNIQUAC

[87], [105] [68], [87],[105,106]

[68,69], [98] SLE, LLE and VLE of binary mixturesbetween several pyridiniums withalcohols and thiophene.Activity coefficients of quaternaryammonium salts in water.Phase stability analysis in a binarymixture with water.

GC + correlationsUNIFAC

[110], [113],[117]

[110] [110],[112,113]

[110], [113],[117]

Viscosity, liquid heat capacity andtransport properties of a widevariety of pyridinium ionic liquids.

COSMO-RS [129] [129] [129] Mutual solubilities of water andhydrophobic ionic liquids.

Cation: [H4S+] SulfoniumNRTL [68] SLE and LLE of the mixture

[EtS3][Tf2N] with thiophene.

NRTLelectrolytes

[98] Activity coefficients of quaternaryammonium salts in water.

Cation: [H4P+] PhosphoniumRST [62] [62] CO2 gas solubility in

room-temperature ionic liquids.

NRTLNRTL1NRTL2UNIQUAC

[105] [105] [102], [105] SLE and LLE with alcohols, benzeneand alkylbenzenes.

COSMO-RS [131] Solubility of water intetradecyltrihexylphosphonium-based ionicliquids.

Cation: [H4N+] AmmoniumRST [62] CO2 gas solubility in

room-temperature ionic liquids.

0], [89

a5

P

Ptb

a

b

xtupcvstd

w

NRTL [7

range of temperatures from 309 to 367.5 K and pressures up to0 MPa [38]. The equation reads:

= RT

v − b− a

v(v + b) + b(v − b)(1)

being the pressure, v the volume, T the temperature, and a and bhe parameters obtained with quadratic mixing rules as modifiedy Adachi and Sugie [39]:

=∑∑

xixj

√aiaj[1 − kij − �ij(xi − xj)] (2)

=∑∑

xixj

(bi + bj

2(1 − lij)

)(3)

being the mole fraction, with kij, �ij and lij as three binaryemperature-dependent parameters. ai and bi were obtained bysing the critical temperature, pressure and acentric factor of theure compounds. No information about the way to obtain the criti-al parameters for [C2mim][PF6] was given in the paper. In general,ery good agreement in the whole range of temperatures and pres-

ure was achieved, although the use of three binary parameters,emperature dependent, limits the predictive power of the proce-ure.

Very recently, Carvalho et al. [40,41] also used the PR equationith the Wong–Sandler mixing rules, using the UNIQUAC model to

] SLE of alkanes and aromatics.Activity coefficients at infinitedilution of hydrocarbons, alcohols,esters, and aldehydes.

calculate the activity coefficients to describe Henry’s constants ofCO2 with [C2mim][Tf2N] and with [C5mim][Tf2N], achieving goodagreement with the measured data. In this case, the critical param-eters were taken from the work of Valderrama and Robles [42],who proposed a group contribution method to estimate the criticalproperties of 50 different ionic liquids.

Shifflet and Yokozeki have published a considerable amount ofexperimental contributions where they measured the solubilitiesof different compounds in a variety of ionic liquids and, later, theyused the simple Redlich–Kwong (RK) equation of state to modelthem [43–54]:

P = RT

v − b− a(T)

v(v + b)(4)

a =∑∑

xixj

√aiaj

(1 + �ij

T

)(1 −

(lijlji(xi + xj)ljixi + lijxj

))(5)

b =∑∑

xixj

(bi + bj

2(1 − kij)(1 − mij)

)(6)

In the above model, there are a maximum of four binary inter-action (temperature-independent) parameters: lij, lji, mij and �ij foreach binary pair. However, in most of the works, only two or threeparameters were necessary. Pressure–temperature–composition

20 L.F. Vega et al. / Fluid Phase Equilibria 294 (2010) 15–30

Table 2Sketch of the different models, for a selected ionic liquid, following different theoretical approaches. Image of the molecule and COSMO-RS model taken from reference [186].Sketch of GC-EoS taken from reference [144].

eacic

pTi

xperimental data was used to obtain their values. The values ofi and bi were estimated, as in the previous case, by using theritical parameters of the pure compounds. In these works, crit-cal information about ionic liquids was obtained through groupontribution methods.

The group of Noble and co-workers have published a very com-lete series of papers where they applied the Regular Solutionheory (RST) to estimate gas solubilities of CO2 and hydrocarbonsn several imidazolium, ammonium and phosphonium ionic liq-

uids [55–62]. RST results from the premise that non-ideality inliquid solutions is due to differences in short-range attractive forcesbetween the molecules present. Hence, the authors assumed thatshort-range forces dominate in ionic liquids because of their weaklattice energies, resulting from low Coulombic forces that are sig-

nificantly delocalized, with a low degree of nucleophylicity [63].The reader is referred to the work of Scovazzo et al. [55] and ref-erences therein for more details. The set of publications by Nobleand co-authors differ from each other on the way used to estimate

se Equ

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i

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l

w

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L.F. Vega et al. / Fluid Pha

he solubility parameter, directly related to the cohesive energyensity ıS [55–61]:

S =(

(�Hv − RT)zVS

)1/2

(7)

ith z being the compressibility factor and Vs the molar volumef the solvent. For ionic liquids, as there are no measurable vaporressures, the heat of vaporization is taken as the enthalpy of vapor-

zation at the salt’s melting point:

Hvmelt = CT (Tmelt) (8)

here Tmelt is the salt’s melting point temperature and CT is aalt category specific constant. A new parameter KT = (CT − R)z isssumed to be constant for each ionic liquid, so the cohesive energyensity of the ionic liquids becomes:

IL =(

KT Tmelt

V IL

)1/2(9)

More recently, Scovazzo and co-workers [62] have estimated ıIL

n ionic liquids from surface tension measurements.In summary, one of the main advantages of using these equa-

ions is that they are straightforward to use and they are presentn any process simulator. However, several parameters, tempera-ure and composition dependent are needed, in most of the cases,o make them readily accessible for ionic liquids’ calculations. Thiss due to the fact that in general classical equations are missingn important part of the physical nature of ionic liquids. Even if thenion and cation are considered as a neutral pair, they exhibit polar-ty and hydrogen bonding ability, two facts not taken into accountn an explicit manner in cubic EoSs. In addition, a major drawbackn the use of cubic EoSs is the fact they require critical parametersf the ionic liquids, which can only be obtained indirectly and witharge uncertainties. This fact limits the predictive ability of thesequations, and they are used for correlation purposes.

.2. Activity coefficient models and group contribution methods

As a consequence of the limitations already highlighted for cubicoS, several authors have decided to model ionic liquids using sev-ral excess Gibbs energy models, such as the Wilson’s equation [64],he nonrandom two-liquid model (NRTL) [65] and UNIQUAC [66],r group contribution methods as UNIFAC [67].

NRTL and UNIQUAC are well known activity coefficient mod-ls, very useful for liquid–liquid equilibria calculations. The binaryctivity coefficients of the NRTL model are given by

n �1 = x22

[�21

(G21

x1 + x2G21

)2

+ �12G12

(x2 + x1G12)2

](10)

n �2 = x21

[�12

(G12

x2 + x1G12

)2

+ �21G21

(x1 + x2G21)2

](11)

here

12 = exp (−˛�12) and G21 = exp (−˛�21) (12)

12, �21 and ˛ are three parameters adjusted to experimentalolubility data of the ionic liquids. In general, �12 and �21 are tem-erature dependent, while ˛ is usually set to a constant uniquealue.

Concerning UNIQUAC, parameters ri and qi, related to the num-er of segments and external contacts of the molecule of type i,

espectively, are usually related to the molar volumes of the ioniciquids following relatively simple expressions.

Among the classical excess Gibbs models, Domanska and co-orkers have published several works, where they have used NRTL

o model the solid–liquid and liquid–liquid equilibria of several

ilibria 294 (2010) 15–30 21

ionic liquids and different solvents, like alkanes, alkanols, tiopheneor water [68–71]. For solid–liquid equilibria (SLE), they used a sim-plified general thermodynamic equation relating temperature, TSLE,and the mole fraction of the ionic liquid, x1, in the respective sol-vent:

ln xi = −�Hmelt

R

(1

TSLE− 1

Tmelt

)+ ln � (13)

where �Hmelt is the enthalpy of melting of the pure ionic liquidand � is the activity coefficient of the ionic liquid in the solution,calculated by means of the excess Gibbs free energy (GE) by usingthe Gibbs–Duhem equation.

Shiflett and Yokozeki, already mentioned for their use of theRedlich–Kwong equation, have also used NRTL in some of theircontributions, in order to correlate their measured data and tomodel the LLE of refrigerants and fluorinated compounds in imi-dazolium ionic liquids [72–79]. Several other groups [80–97]have also employed the NRTL equation to study the vapor–liquidand liquid–liquid equilibria of hydrocarbons and water in ILs,being able to correlate the data with a good degree of accu-racy. Furthermore, some modified versions from the original NRTLmodel have also been employed. Belzève et al. [98] have usedthe electrolyte-NRTL version for modeling imidazolium and pyri-dinium salts. Domanska et al. also used Wilson, UNIQUAC, NRTL,NRTL1 and NRTL2 equations with parameters derived from thesolid–liquid equilibrium to describe the solubility of alcohols, aro-matics, alkanes and cyclohydrocarbons in ionic liquids [99–102].Banerjee et al. [103] have used the polarizable continuum model(PCM) to estimate the parameters for the UNIQUAC model. Thisapproach was used to calculate the structural parameters for25 dialkylimidazolium-based ionic liquids and the interactionparameters for seven ionic liquid-based ternary systems. Simoniet al. [104,105] have studied the liquid–liquid equilibrium ofionic liquid systems using NRTL, electrolyte-NRTL, NRTL-SAC andUNIQUAC methods. The same authors have later refined theirapproach considering an asymmetric framework in which dif-ferent phases have different degrees of electrolyte dissociation,and are thus represented by different Gibbs free energy models[106,107].

Concerning the use of group contribution methods, also knownas group additivity relationships, they are useful for correlatinga material property with the chemical composition and state ofmatter of a substance and are becoming more popular for model-ing ionic liquids. The basic assumption made is that the physicalproperty of a material is a sum of contributions from each of thematerial’s component parts. Then, the properties of known materi-als are correlated with their chemical structure, in order to identifythe basic groups and their additive molar quantities (AMQs), whilethe properties of unknown materials are estimated through directaddition of AMQs from constituent chemical groups, or through theuse of additive quantities to estimate parameters in more accuratecorrelations. This was the idea followed by Gardas and Coutinho,who published a series or articles [108–113], where they devel-oped a second-order group additivity method, whose parameterswere applied to different correlation equations for the estima-tion of thermodynamic and transport properties of ionic liquids.In particular, predictive methods for density [108], surface tension[109], viscosity [110], speed of sound [111], liquid heat capacity[112] and transport properties [113] were applied to imidazolium-,pyridinium-, and pyrrolidinium-based ionic liquids (ILs) containing[PF6], [BF4], [Tf2N], [Br], [EtSO4], or [CF3SO3] as anions.

The UNIFAC model has also been used by other authors[114–118] to model mixtures of ionic liquids with alkanes,cycloalkanes, alcohols, water and other solvents.

One of the most valuable features of all these methods is theirapplicability to multicomponent systems under the assumption

2 se Equ

tstaata

2

tRvitt(iipp

ebftTctiaagta

apgsaTo

hlwsapL[

icwtu

2

mtt

2 L.F. Vega et al. / Fluid Pha

hat local compositions can be described in this case by a relation-hip similar to that obtained for binary systems. However, one ofhe main disadvantages of these methods is that they depend onn extremely large amount of experimental data. Furthermore, thebsence of the volume and surface parameters poses a hindrance inhe calculation of the binary interaction parameters for UNIQUACnd UNIFAC models.

.3. Quantum chemistry calculations

Unimolecular quantum mechanical calculations, by means ofhe conductor-like screening model for real solvents COSMO-S [119], have also been used by several authors to predictapor–liquid and liquid–liquid equilibria for systems involvingonic liquids and a wide variety of solvents [118,120–131]. In con-rast to the group contribution methods, COSMO-RS calculates thehermodynamic data from molecular surface polarity distributionsTable 2c), resulting from quantum chemical calculations of thendividual compounds in the mixture, without the need of exper-mental data. Although time-consuming, one advantage of thisrocedure is that the quantum chemical calculations have to beerformed just once for each molecule or ion of interest.

Most of these works were done by the use of the COSMOth-rm program [132]. This program describes all the interactionsetween molecules as contact interactions of the molecular sur-aces, and relates them to the screening charge densities, � and �’,he most significant descriptors of the interacting surface pieces.he COSMO output provides the total energy of a molecule in itsonductor environment and the 3D polarization density distribu-ion on the surface of each molecule. This information acts as annput for the statistical thermodynamic calculations therein afternd it is independent of the solvent dielectric constant and temper-ture. The COSMO-RS method depends only on a small number ofeneral or, at most, element-specific adjustable parameters (prede-ermined from known properties of a small set of molecules) thatre not specific for functional groups or type of molecules.

For ionic liquids, the cation and the anion are treated as sep-rated compounds with the same mole fraction during all therocedure. In the work of Banerjee et al. [127,128], a sequentialeometry optimization approach was used, and the charge den-ities were constructed starting with the imidazolium ring anddding successive alkyl groups until the desired cation was built.hen, the anion was added to the cation via a dummy atom re-ptimized to obtain the minimum energy configuration.

Concerning the application of this methodology, several authorsave focused in the description of LLE systems involving ionic

iquids and alcohols, hydrocarbons, ethers or ketones [120–126],hile other researchers studied the VLE of ionic liquids with the

ame solvents and water [125–131]. In most of the cases, thispproach provided qualitative predictions of the thermodynamicroperties of these systems, although some model limitations forLE predictions were found, especially for the anions influence126].

As outlined, a main advantage of this method is that no exper-mental data is needed, being their main limitation the extensiveomputational time and also that in some cases the comparisonith experimental data is only qualitative. In spite of this, having a

ruly predictive tool is a great step towards the characterization ofn-synthesized ionic liquids.

.4. Statistical mechanics-based approaches

The capabilities of lattice models, chain fluid theories and otherolecular-based approaches are attracting more and more scien-

ists and engineers until the point that they are becoming standardools for engineering purposes. The advantage of building a model

ilibria 294 (2010) 15–30

for the molecule describing the physics of the system is relatedto a major predictive ability, hence enhancing the possibility ofextending the range of application of the equation.

In the next subsections, we outline the latest and more refinedefforts towards the modeling of ionic liquids and their solubili-ties. We have selected some physical approaches that have beenrecently used for this purpose due to their potential for predictingother properties.

2.4.1. Lattice modelsAs ionic liquids are usually composed of cations and anions with

long alkyl chains or a long chainlike structure and, considering theirnegligible vapor pressures, they seem to share features of the poly-mer systems. In that sense, several authors have tried to model ionicliquid by the use of lattice models, assuming that the fluid structurecan be approximated by a solid-like structure (see Table 2d).

Several scientific groups have followed this approach: Ally etal. [133] used an irregular ionic lattice model, consisting of a twoparameter model in which CO2 is considered the “solute” andthe ionic liquids is the “solvent”, to predict carbon dioxide vaporpressure and solubility in several imidazoliums. Yang et al. [134]have successfully correlated infinite diluted activity coefficients,vapor pressures of solvents and liquid–liquid equilibria of ionicliquids solutions with a modified lattice model, which takes intoaccount the hydrogen bonding through an exchange energy func-tion. Tome et al. [135] have modeled high pressure experimentaldensities of imidazolium ionic liquids by means of the Sanchez-Lacombe equation of state [136]. Kim et al. [137] have used a groupcontribution form of a nonrandom lattice-fluid model to predictsolubilities of carbon dioxide in ionic liquids. Bendova and Wagner[138] have described the liquid–liquid equilibria in systems 1-ethyl-3-methylimidazolium ethylsulfate + C7 hydrocarbons usinga molecular-thermodynamic lattice model proposed by Qin andPrausnitz [139].

In a recent work, Hu and co-authors [140] have extended andapplied a recently developed lattice-fluid equation that includedholes into the close-packed lattice model [141], to the description ofthermodynamic properties of the [Cnmim][BF4] and [PF6] familiesand the solubility of CO2 in them. Based on the chemical associationtheory, the resulting lattice fluid equation was expressed as

p = T{

−ln(1 − �) + z

2ln

[2z

(1r

− 1)

� + 1]}

− z

2�

− z

41

T(3�4−4�3 + �2)− z

121

T2(10�6−24�5+21�4 − 8�3 + �2)

+ r − 1 + �

rT�2

[[1 + D(1 − �)]2 − 1

[1 + D(1 − �)][1 + D�(1 − �)]

](14)

where

D = exp(

1

T

)− 1 (15)

z being the coordination number, T the reduced temperature, p thereduced pressure and � the reduced density.

With this approach, each pure fluid is characterized by fourmolecular parameters: the coordination number (z), the segmentalvolume (v∗), the segment number (r) and the temperature-dependent interaction energy (ε). For vapor–liquid binary mixturecalculations, mixing rules are applied and a binary adjustableparameter kij appear in the calculations. Xu et al. applied this modelto the calculation of 48 different pure ionic liquids and 40 binary

mixtures [140]. z and v∗ have a fixed and constant value for allfluids, while the others were adjusted to experimental data. Forliquid–liquid calculations, a parameter Cr describing the effect ofthe mixture composition on the chain length parameter r was fur-ther used, and a satisfactory correlation was obtained.

se Equ

2

dfiippItHf

eaae

omCcd

gT(uvpdf

tratnpd

a[d

tosqpe

2

oooh

pgB

tion [152], developed by the group of Economou and co-workersto deal with systems as complex as ionic liquids. In the tPC-

L.F. Vega et al. / Fluid Pha

.4.2. Group contribution EoSThe group contribution equation of state approach (GC-EoS) was

eveloped in the 80s by Skjold-Jorgensen [142]. This method differsrom previous GC methods (UNIFAC) from the way the GC concepts applied. In Section 2.2, an activity coefficient model with a built-n group contribution method was used for calculation of mixturearameters of an EoS through appropriate mixing rules. Here, EoSarameters are evaluated using a built-in group contribution rule.

n this case, the EoS is based in the generalized van der Waals func-ion combined with the local composition principle. The residualelmholtz energy of the system is evaluated through the sum of a

ree-volume term and an attractive term:

ares(T, �)RT

= af v(T, �)RT

+ aattr(T, �)RT

(16)

The free-volume term is described by the Mansoori and Lelandxpression for hard spheres and includes the hard-sphere temper-ture dependent diameter parameter [143]. The attractive part isgroup contribution version of a density dependent NRTL type

xpression.In 2007, Breure et al. [144] studied the solubilities of the homol-

gous families [Cnmim][PF6] and [BF4] with CO2. Ionic liquids wereodeled as a sum of different functional groups, containing one

H3 group, nCH2 groups (depending on the length of the alkylhain) and a new functional group consisting of the methylimi-azolium cation plus the anion (see Table 2e).

The GC-EoS contains an important amount of pure group androup-group interaction parameters that need to be parameterized.he free-volume term includes the critical hard-sphere diameterdc). Breure et al. have followed the work of Espinosa et al. [145] andsed a correlation using information of the van der Waals molecularolume (r). In the free-volume term, the volume Rk and surface Qkarameters of [Cnmim][PF6] and [Cnmim][BF4] were calculated byividing the anion in constituent units whose information could beound in the literature [146].

Concerning the attractive term, pure group and binary interac-ion parameters for many gases and solvent groups were alreadyeported in the literature. The attractive parameter (gii) for thenions and the binary interaction parameters kij and ˛ij betweenhe anion and the paraffin groups were calculated by fitting infi-ite dilution coefficients of alkanes in the ionic liquids. The binaryarameters between the anions and CO2 were fitted to bubble pointata of CO2 in the ionic liquid.

Very recently, Kuhne et al. [147] have used the same approachnd extended it to the calculation of ternary mixtures ofC4mim][BF4] + organic solute + CO2, being able to qualitatively pre-ict liquid–vapor and liquid–liquid phase transitions.

This methodology presents similar advantages and disadvan-ages than the other group contribution methods. On one hand,nce the functional groups have been established, it provides atraightforward way to calculate multicomponent mixtures in auite accurate way. On the other hand, a significant number ofarameters must be fitted and, as a consequence, a large set ofxperimental data is required.

.4.3. The square-well chain fluids (SWCF) equation of stateThe SWCF EoS has also been used for the modeling and study

f ionic liquids. Wang et al. [148] correlated the pVT behaviorf several ionic liquids and some mixtures with gases with onlyne temperature-independent adjustable parameter, using the

omonuclear version of this equation.

In a more recent contribution [149], the hetero-SWCF EoS wasresented, and the molecule was divided in two parts: the alkylroup composed of A segments and the ring anion that includedsegments (see Table 2f). The residual Helmholtz energy of the

ilibria 294 (2010) 15–30 23

system was calculated as

ares(T, �)RT

= ahscf (T, �)RT

+ aattr(T, �)RT

+ aassoc(T, �)RT

(17)

where the superscripts hscf, attr and assoc refer to hard-spherechain fluid, attractive interaction and association interaction,respectively. The hscf contribution is expressed by the effectivetwo-particle cavity correlation function:

ahscf

RT= r

ar(a = 0)

RT∑K

i ri

−K∑

i=1

M∑j=1

M∑k=j

xirjk(i) ln y2ejk

−K∑

i=1

M∑j=1

M∑k=1

M∑l=j

xirjkl(i) ln y2ejkl (18)

M being the number of segment types and ar(a = 0) thecontribution from the monomers calculated from theMansoori–Carnahan–Starling–Leland equation [143]. As eachheteronuclear chain consists of two types of segments, there arethree different nearest-neighbor pairs and six different next-nearest-neighbor pairs, that are used to calculate the effectivecavity correlation function y2e

jkand y2e

jkl. More details can be found

in Ref. [149].Each segment is modeled using three parameters: the chain

length r, the attractive energy ε/k and the segment diameter �.The model parameters for the alkyl chain were taken from thosefor hydrocarbons, available in literature, while the imidazoliumring-anion block as well as the binary interaction parameters ABbetween segments, were fitted to experimental volumes of ionicliquids. The work includes several mixtures of compounds withionic liquids (alkanes, alcohols, aromatics, water, etc.). In this case,three adjustable binary parameters are needed (AB, AS, BS), cor-responding to the interaction between segments AB and betweeneach segment with the solvent S. The parameter AB was refittedand included with the rest using the fugacity coefficients of thesolvent in the liquid and the vapor phases.

This approach is physically well sounded and provides verygood agreement with experimental data when tested. However,it requires at least three adjustable parameters for binary mixturesthat do not follow any trend, losing predictive power when tryingto use it at other conditions or for other similar systems.

Lately, Ji and Adidharma [150] have used a similar approach toestimate the density of several [BF4], [PF6] and [TfN2] imidazoliumionic liquids. In particular, they have employed a heterosegmentedSAFT, referred as SAFT1 [151]. They have divided the ionic liquidin four different parts, considering the anion, the cation head, themethyl group and the alkyl chain as independent compounds withtheir molecular parameters. The spherical segments representingthe cation head and the anion have one association site, which canonly cross-associate. This complex model provides excellent agree-ment with experimental data, although a considerable amount ofadjustable parameters are required even for pure compounds.

2.4.4. The truncated Perturbed Chain Polar Statistical AssociatingFluid Theory (tPC-PSAFT)

tPC-PSAFT [35] is a refined version of the original PC-SAFT equa-

PSAFT equation, dipolar interactions of the ionic liquid, quadrupolarinteractions for CO2, and the Lewis acid–base type of associationbetween the anion of the ILs and the CO2 molecule are explicitlyconsidered. As in any SAFT approach the total Helmholtz energy ofthe system is evaluated as a sum of different contributions:

2 se Equ

wtfqTtpa

ctwaItitsc

aTuziswarodteaTttiahb

[ouc[dfm

ittdci

4 L.F. Vega et al. / Fluid Pha

ares(T, �)RT

= ahs(T, �)RT

+ achain(T, �)RT

+ adisp(T, �)RT

+ aassoc(T, �)RT

+ apolar(T, �)RT

(19)

here ahs accounts for the hard-sphere contribution, achain forhe chain formation, adisp for the dispersion interaction, aassoc

or the association effects and apolar for the dipole–dipole,uadrupole–quadrupole and cross dipole–quadrupole interactions.he hard-sphere, chain, association and dispersion terms are iden-ical to those proposed for the original PC-SAFT [152], while theolar term corresponds to a Padé approximant proposed by Stellnd co-workers [153], also used in other versions of SAFT:

apolar (T, �)RT

= mapolar

2

1 − (apolar3 /apolar

2 )(20)

The higher order terms of the polynomials are truncated; as aonsequence, a new effective polar interaction diameter is used toake the spatial extent of the polar interactions into account. Ase can see, polar contributions were explicitly considered in this

pproach, in order to capture the polarity effects in the ionic liquid.n a similar manner, Qin and Prausnitz [154] also reflected con-ributions from induction, dipole–charge and quadrupole–chargenteractions using the Perturbed–Hard–Sphere Theory to correlatehe behavior of volatile nonelectrolytes, obtaining the Henry con-tant for 20 different solutes. No association was considered in theirase.

Economou and co-authors first modeled the ionic liquid ascombination of two different species (anion and cation) (see

able 2g). The size and energy of the cations could be obtainedsing the PC-SAFT molecular parameters obtained from alkylben-ene family (those corresponding to the same alkyl chain lengthn the molecules than for the imidazolium ring). For the size andhape of the anions available literature parameters were used,hile the dispersive energy was estimated with the Mavroyannis

nd Stephen equation. Finally, they used the standard combiningules in order to calculate the volume and the energy parametersf the molecule, and the segment number was fitted to ionic liquidensity experimental data. For the dipole moment of ionic liquidhey used the value from methanol. Additionally, they also mod-led the Lewis acid–base association between the CO2 moleculesnd the anion of the IL as a specific cross-association interaction.hese cross-association parameters (energy and volume of associa-ion) between the ionic liquid and the CO2 were estimated throughhe experimental enthalpy and entropy of dissolution of CO2 inonic liquids [155]. When studying the solubility in water, cross-ssociation was also calculated from the experimentally measuredydrogen bonding, while the association volume was assumed toe the same as the volume between water molecules.

Economou and co-workers have published several works155–158] where they applied this methodology to the calculationf thermodynamic properties and solubilities of several ionic liq-ids with different solutes, obtaining very good agreement whenomparing to experimental data. In the most recent contributions157,158], they calculated ternary mixtures of water–CO2 and twoifferent ionic liquids ([bmim][NO3] and [HOPmim][NO3]). The dif-erent binary kij interaction parameters were fitted to ternary data,

aking them temperature dependent.This is clearly a sound and robust method to describe the behav-

or of ionic liquids and the mixtures of several compounds with

hem, with great potential for predictions. The main limitation ishe complexity of the model itself, which requires a high number ofifferent (physical, though) parameters, and the fact that an explicitross-association between the CO2 molecule and the ionic liquidss required.

ilibria 294 (2010) 15–30

2.4.5. The soft-SAFT equation of stateThe soft-SAFT equation of state [34] is another successful version

of the original SAFT [159] that uses a Lennard–Jones intermolecularpotential as the reference fluid. As other SAFT-type equations, it iswritten in terms of the total Helmholtz energy of the system. Whenapplied to ionic liquids, the residual Helmholtz energy is written as

ares(T, �)RT

= aLJ(T, �)RT

+ achain(T, �)RT

+ aassoc(T, �)RT

+ apolar(T, �)RT

(21)

where the superscript LJ accounts for attraction and repulsionforces between monomers, following a Lennard-Jones intermolec-ular potential, and chain, assoc and polar have the same meaningthat the one explained in the previous subsection.

Using the soft-SAFT EoS, Andreu and Vega were able to accu-rately describe the solubility of carbon dioxide, hydrogen, carbonmonoxide and xenon in the alkylimidazolium family [Cnmim]+ withn = 2, 4, 6 and 8 with different fluorinated anions such [BF4]−, [PF6]−,and [Tf2N]−, achieving quantitative agreement with experimentaldata [160,161]. The objective of these works was to recover theoriginal spirit of the SAFT approach and keep the model as simpleas possible while retaining the main physics of the problem. In thissense, the model used in soft-SAFT for ionic liquids is simpler thanthe one used in the other versions of SAFT mentioned here (SWCFand tPC-PSAFT).

Based on the concept of ion pairing of these systems, as observedin molecular dynamics [162–164], ionic liquids were modeled as LJchains with one (for the [BF4] and [PF6] anions) and three (for the[Tf2N] anion) associating sites in each molecule. This model mimicsthe neutral pairs (anion plus cation) as a single chain molecule withan only association site describing the specific interactions becauseof the charges and the asymmetry (see Table 2h). In this sense, onlyassociating forces between ionic liquids pairs, as well as van derWaals forces, were taken into account for the ionic liquids, while thequadrupolar term was included for molecules showing quadrupo-lar interactions. In particular, no specific association between theCO2 molecule and the ionic liquids was needed to quantitativelyreproduce the solubility of this compound in these ionic liquids, asin the work of Qin and Prausnitz [154] and contrary to the assump-tion of the tPC-PSAFT EoS. Given the excellent results obtained withsoft-SAFT with no CO2–ionic liquid association, it can be inferredthat the specific interaction between the anion and CO2 is alreadytaken into account within the specificity of the model. However,this is not the case of the solubility of BF3 in ionic liquids, where aclear BF3–ionic liquid 1:1 weak interaction is observed, taken intoaccount into the model with a cross-association interaction (shownlater in the present work).

The chain length, size and energy parameters of the ionic liquidswere obtained by fitting to available density–temperature data,obtaining a correlation with the molecular weight of the com-pounds. The association parameters were transferred from thoseof the alkanols [165], thus avoiding further fitting. The correlationof the three first parameters and the fixed value of the associa-tion parameters allow the calculation of ionic liquids of the familynot included in the fitting procedure or for which experimentaldata is not available. When calculating the solubility with car-bon dioxide, quadrupolar interactions were taken into accountthrough the molecular parameters Q and xp, defined as the frac-tion of segments in the chain that contain the quadrupole. Q wasfitted but similar values were obtained from those of literature

[166,167] and xp, it was fixed to 1/3 for carbon dioxide, thus mim-icking the molecule as three segments with a quadrupole in one ofthem.

Fig. 3a shows the temperature–density of [Cnmim]+ with n = 2,4, 6 and 8 with [BF4]− as obtained with soft-SAFT and the model just

L.F. Vega et al. / Fluid Phase Equilibria 294 (2010) 15–30 25

Fig. 3. Thermodynamic characterization for some [BF4] imidazoliums. (a)Temperature-density diagram for [C2mim][BF4] (circles), [C4mim][BF4] (squares),[[(t

dapb[ctdaTdasaww

Table 4Optimized influence parameters for the compounds studiedin this work. See text for details.

Ionic liquid 1019c (J m5 mol−2)

TMa

C6mim][BF4] (diamonds) and [C8mim][BF4] (triangles). Experimental data from168]. (b) Surface tension as a function of temperature for the same ionic liquidsexcepting [C2mim][BF4]). Symbols represent experimental data [175,176] whilehe lines are soft-SAFT with density gradient theory calculations.

escribed. The selected molecular parameters for each ionic liquidre taken from Ref. [160] and reported here in Table 3 for com-leteness. As it can be observed, excellent agreement is achievedetween the theory (lines) and the experimental data (symbols)168]. We present here new results completing the thermodynamicharacterization of these compounds by adding the calculation ofheir surface tension. In this case, the soft-SAFT Eos is coupled toensity gradient theory [169,170], following the work by differentuthors [165,171–174], in order to obtain interfacial properties.he required molecular parameters are those obtained from theensity–temperature data, used in a transferable manner, with the

dditional influence parameter c (see Table 4). Results are pre-ented in Fig. 3b, where solid lines correspond to the calculationsnd symbols represent experimental data [175,176]. In agreementith the experimental data, a decreasing interfacial tension valueith alkyl chain length has been obtained. This behavior is very

able 3olecular parameters for the [Cnmim][BF4] family and the BF3 model used in the soft-

djusted to the associating site for cross-association, also added to the modeled ionic liqu

m � [Å] ε/kB [K] kHB

[C2mim][BF4] 3.980 3.970 415.0 3450[C4mim][BF4] 4.495 4.029 420.0 3450[C6mim][BF4] 5.005 4.110 423.0 3450[C8mim][BF4] 5.570 4.170 426.0 3450BF3

a 2.321 2.889 128.7 8000

a Parameters L/� and are crossover parameters, only used when the crossover term i

[C4mim][BF4] 13.468[C6mim][BF4] 15.034[C8mim][BF4] 14.067

surprising as it is contrary to the other chemical families where theinterfacial tension increases with the chain length. Deetlefs et al.[177] suggested that the increase of the cation size and the increas-ing diffuse nature of the anion negative charge results in a moredelocalized charge leading to a decreasing ability to form hydrogenbonds. Besides, these tendencies can also be affected by entropiceffects leading to distortions on the expected results [176].

Another example of the capabilities of a simple, physically soundand reliable approach is presented next. Although a great effort hasbeen devoted to develop ionic liquids for capturing CO2, most ofthe published work on ionic liquids for this purpose show highersolubilities than other gases, but still very low solubilities com-pared to the industrial amines process used today to capture CO2.Through the different experimental, and also simulation and mod-eling works, it has been shown that the solubility of CO2 in theseknown ionic liquids is mainly due to van der Waals forces, and noweak chemical interactions have been observed so far.

However, the weak complexation of ionic liquids with somecompounds has been observed experimentally. Tempel et al.[178] demonstrated that a reversible complexation of Lewis basicgases like BF3 with ionic liquids is possible, permitting the useof ionic liquids as a transport media that allows the reversibleabsorption and desorption of this dangerous compound. Theyinvestigated the absorption of PH3 and BF3 in two differentionic liquids, the 1-butyl-3-methylimidazolium trichlorodicuprate[C4mim][Cu2Cl3] and the 1-butyl-3-methylimidazolium tetraflu-oroborate [C4mim][BF4], respectively. The experimental resultsshowed the possibility to store and transport large amounts of gasesin small volumes at low pressures.

We have applied the same methodology described previously(soft-SAFT with a simple model) to see if the general modelwas able to capture this behavior as well. For this purpose, aBF3 model was built based on liquid density and vapor pressureexperimental data taken from the DIPPR® database [179]. In thiscase, the BF3 was modeled as a non-associating compound withfour molecular parameters: m, the length of the chain, �, theLennard–Jones diameter of each spherical segment forming themolecule, ε, the LJ energy for each segment, and Q, the quadrupole.The quadrupole–quadrupole interactions between BF3 moleculeswere taken into account by fixing the quadrupole term accord-ing to the experimental value reported elsewhere [180]. Followingprevious approaches for molecules with non-zero quadrupole, like

CO2 and N2, the fraction of the molecule (xp) associated to thequadrupole was set to 0.25. Molecular parameters are summarizedin Table 3 and the phase diagram of this molecule is presentedin Fig. 4a and b. The molecular parameters and L correspond

SAFT EoS. The fourth and fifth columns for the BF3 case correspond to the valuesid.

[Å3] εHB/kB [K] Q [C m2] L/�

2250 – – –2250 – – –2250 – – –2250 – – –4730 3.15 × 10−40 1.29 6.90

s included in the soft-SAFT equation (dashed line in Fig. 4).

26 L.F. Vega et al. / Fluid Phase Equilibria 294 (2010) 15–30

F(w

tor[tlapta

pbfcnBcait

Fig. 5. VLE diagram for the system BF3 + n-butane at 195.49 K obtained from the

for other binary systems. Note also that soft-SAFT was able to cap-ture the behavior of this mixture without assuming any specificinteraction between BF3 and n-alkane. Unfortunately, the data forBF3 mixtures is very scarce in the literature and no further compar-

ig. 4. Phase diagram for the BF3 compound. (a) Vapor–liquid equilibria diagram.b) Pressure–temperature diagram. Symbols are experimental data taken from [179]hile the solid line corresponds to the soft-SAFT model.

o the inclusion of a specific renormalization-group treatment inrder to consider the inherent density fluctuations in the criticalegion into soft-SAFT, in a version known as crossover soft-SAFT181,182]. The dashed line of the figure corresponds to the calcula-ion using the crossover soft-SAFT equation of state, while the solidine corresponds to the original soft-SAFT equation. Quantitativegreement is found for the whole range of liquid temperature andressure when the crossover term is used, while the original equa-ion describes well both densities, except in the near critical region,s expected.

In order to test the BF3 model and parameters we checked itserformance in mixtures with other well known compounds, n-utane in this case. As at these conditions the mixture is far awayrom its critical point, the soft-SAFT version used is the one withoutrossover, making the calculations faster. The parameters for pure-butane were taken from reference [183]. Results for the mixture

F3 + n-butane at 195.49 K are depicted in Fig. 5. The dotted linesorrespond to predictions from pure component parameters, and,s shown in the figure, the equation is unable to capture the behav-or of the mixture unless two binary parameters, close to unity, areaken into account (� = 0.925 and � = 0.95). As already observed with

soft-SAFT EoS. The dotted line corresponds to the prediction without fitting, thedashed line to the description with a binary energy parameter and the full line withtwo binary parameters. The symbols correspond to experimental data taken fromreference [179]. See text for details.

several other mixtures, this is due to the asymmetry in size (the �parameter) and van der Waals attractive energy (the � parameter)between the two different compounds integrating the mixture. Infact, similar results were obtained for the same system with a simi-lar EoS [184], although in the soft-SAFT case the binary parametersare slightly closer to unit.

The good agreement obtained for the BF3 + n-butane mixturewith experimental data validates the molecular parameters of BF3

Fig. 6. Absorption isotherms for the system [C4mim][BF4] + BF3 at three differenttemperatures. Symbols represent the experimental data from Ref. [178]. Comparisonbetween original calculations with no association (dashed lines) and association(solid lines). See text for details.

L.F. Vega et al. / Fluid Phase Equ

Fig. 7. Absorption isotherms for the system [C4mim][BF4] + BF3 at three differenttemperatures. The solid lines are the prediction from soft-SAFT when the cross-as

iotwf[ape

ambictcme[cBtaFeattc

ettaapc

r chain length (SWCF)T temperature

ssociation model is used. Same data and symbols as in Fig. 6, but with a differentcale.

sons could be made. Hence, the next step was to test the validityf the model for the mixture with ionic liquids. When applyinghe model used to describe the [Cnmim][PF6] and [BF4] familiesith CO2 and other gases, and also the BF3 + n-butane mixture we

ound that the model is not able to reproduce the behavior of thebmim][BF4] + BF3 mixture (dashed lines in Fig. 6). Note that a log-rithm scale has been used in the plot to highlight that the modelrovides several orders of magnitude deviations with respect toxperimental data (symbols).

It is thought that the higher absorption of BF3 in [C4mim][BF4] isctually due to a weak 1:1 interaction [178]. Within the soft-SAFTodel this type of interaction (stronger than van der Waals forces,

ut weaker than chemical bonds, and with specific directions)s modeled as a cross-association interaction between the twoomponents. In this case two additional parameters are required,hose concerning the cross-association. In order to check if theross-association model was able to capture the behavior of thisixture, we have transferred the volume cross-association param-

ters from our previous work on perfluoroalkanes + O2 mixtures185], where a cross-association of this kind was found. The energyross-association parameter was used as a fitting parameter to theF3 + ionic liquid mixture. In the absence of experimental data,hese association parameters could be obtained with the help ofb initio calculations. Results with these parameters are shown inig. 6 (solid lines) and in Fig. 7. An excellent agreement betweenxperimental data and results obtained from soft-SAFT with cross-ssociation is observed at all temperatures, with the same accuracyhan other mixtures with CO2. These results reinforce the fact thathere is association in the mixture, and that the model is able toapture it in a simple manner.

Although the results obtained from soft-SAFT are also veryncouraging, given the relative simplicity of the model, its predic-ive power and the agreement obtained with experimental data,he main limitation of the approach is that it considers the anionnd cation as a unique molecule. Considering the cation and anion

s two independent species will empower the equation with moreredictive power, especially for conditions at which the ionic liquidan dissociate, such as aqueous mixtures.

ilibria 294 (2010) 15–30 27

3. Conclusions and future directions

A summary of recently published modeling works in ionic liq-uids has been presented here, emphasizing some of the mainadvantages and limitations of each of them for predictive pur-poses. Particular attention has been paid to the most refinedapproaches involving a physical description of the compound. Adetailed list of the works published, with the systems investi-gated has been provided in a tabular form, providing a generaloverview of the available techniques and systems investigated upto now.

As inferred from the amount of work published up to now andrevised in this work, several steps have been taken towards devel-oping tools for advancing in the fundamental understanding ofionic liquids, relating their structure to their properties. This isparticularly true in the case of molecular-based methods, as theirphysical background allows for extrapolations and predictions atother conditions and for similar systems. In particular, we haveshown that a SAFT-based equation provides not only solubility data,but also interfacial properties. In addition, it has also been shownthat soft-SAFT, with a simple model, is able to describe the weakchemical complexation found in BF3 with ionic liquids, with a sim-ple cross-association model, while no specific association betweenCO2 and ionic liquids is needed to quantitatively describe the sol-ubility of CO2 in them.

Further developments are still needed in order to extend thepredictive power of the model, focusing on the parameters trans-ferability and the ability of the equations to explore all regions ofthe phase diagram, as well as other properties. This should includean independent model for the anion and the cation in order tomake the model more transferable, in a group contribution manner.In addition, the models should be simple enough for engineeringcalculations.

List of symbolsa Helmholtz free energy densityCN carbon numberCr binary parameter to measure the effective chain length

for LLE (lattice model)CT salt category specific constantc influence parameterdc critical hard-sphere diametergii attractive parameterkHB volume of associationkB Boltzmann constantkij binary interaction adjustable parameterGij Gibbs energy�H enthalpyKT parameter (in the RST model)L cutoff length (crossover parameter)m number of LJ segments, chain lengthMw molecular weightNA Avogadro’s numberP pressurep reduced pressureQ quadrupoleQk group volume parameter (GC method)R ideal gas constantRk group surface parameter (GC method)r segment number (lattice model)r vdW molecular volume (GC method)

T reduced temperatureZ compressibility factorz coordination number (lattice model)

2 se Equ

xy

G˛ıεε�

�

����v��

SaaccdefhhiLprr

Smi

A

sLiSpCts0

R

8 L.F. Vega et al. / Fluid Pha

mole fractioncavity correlation function

reek letters

ij binary interaction parameterscohesive energy densityinteraction energy

HB association energysize parameter of the generalized Lorentz–Berthelot com-bining rulesaverage gradient of the wavelet function (crossoverparameter)compressibilitychemical potentialenergy parameter of the generalized Lorentz–Berthelotcombining rulesdensity

˜ reduced densityi activity coefficient

surface tension∗ segmental volume (lattice model)

segment diameterij binary interaction parameter (NRTL model)

uperscriptsssoc association termttr attraction termhain chain termross crossoverisp dispersion

effectivev free-volume terms hard-sphere termscf hard-sphere chain fluid term

d ideal termJ Lennard–Jonesolar polar termef reference termes residual term

ubscriptselt melting

,j the specific compound i or j in a mixture

cknowledgements

Discussions with J.A.P. Coutinho, C. Rey-Castro, B. Peter-on, D. Tempel and C.J. Peters are gratefully acknowledged. F.lovell acknowledges a JAE-Doctor fellowship from the Span-sh Government. This work has been partially financed by thepanish government, Ministerio de Ciencia e Innovación, underrojects CTQ2008-05370/PPQ, NANOSELECT and CENIT SOST-CO2EN2008-01027 (a Consolider project and a CENIT project, respec-ively, both belonging to the Ingenio 2010 program). Additionalupport from the Catalan government, under projects SGR2005-0288 and 2009SGR-666, is also acknowledged.

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