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Modeling the Absorption of Weak Electrolytes and Acid Gases with Ionic Liquids Using the Soft-SAFT Approach F. Llovell,†,‡ R. M. Marcos,§ N. MacDowell,†,∥ and L. F. Vega*,†,⊥ †

MATGAS Research Center, ‡Institut de Ciència de Materials de Barcelona, Consejo Superior de Investigaciones Científicas (ICMAB-CSIC), Campus de la UAB, 08193 Bellaterra, Barcelona, Spain § Departament d’Enginyeria Mecànica, ETSE, Universitat Rovira i Virgili, 43007 Tarragona, Spain ∥ Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, SW2AZ United Kingdom ⊥ Carburos Metálicos, Air Products Group, C/Aragón, 300, 08009 Barcelona, Spain ABSTRACT: In this work, the solubility of three common pollutants, SO2, NH3, and H2S, in ionic liquids (ILs) is studied using the soft-SAFT equation of state with relatively simple models. Three types of imidazolium ionic liquids with different anions are described in a transferable manner using the recently published molecular models (Andreu, J. S.; Vega, L. F. J. Phys. Chem. C 2007, 111, 16028; Llovell et al. J. Phys. Chem. B 2011, 115, 4387), whereas new models for SO2, NH3, and H2S are proposed here. Alkyl-imidazolium ionic liquids with the [PF6]− and [BF4]− anions are considered to be LennardJones chainlike molecules with one associating site in each molecule describing the specific cation−anion interactions. Conversely, the cation and anion forming the imidazolium [Tf2N]− ionic liquids are modeled as a single molecule with three associating sites, taking into account the delocalization of the anion electric charge due to the presence of oxygen groups surrounding the nitrogen of the anion. NH3 is described with four associating sites: three sites of type H mimicking the hydrogen atoms and one site of type e representing the lone pair of electrons. H2S is modeled with three associating sites: two for the sites of type H for the hydrogen atoms and one site of type e for the electronegativity of the sulfur. SO2 is modeled with two sites, representing the dipole moment of the molecule as an associative interaction. Soft-SAFT calculations with the three models for the pollutants provide very good agreement with the available phase equilibria, enthalpy of vaporization, and heat capacity experimental data. Then, binary mixtures of these compounds with imidazolium-based ionic liquids were calculated in an industrially relevant temperature range. Unlike association interactions between the ionic liquids and the pollutant gases have been explicitly accounted for using an advanced association scheme. A single temperature independent energy binary parameter is sufficient to describe every family of mixtures in good agreement with the available data in the literature. In addition, a vapor−liquid−liquid equilibrium (VLLE) region, never measured experimentally, has been identified for mixtures of hydrogen sulfide + imidazolium ionic liquids with the [PF6]− anion at high H2S concentrations. This work illustrates that relatively simple models are able to capture the phase absorption diagram of different gases in ionic liquids, provided accurate models are available for the pure components as well as an accurate equation of state to model the behavior of complex systems.

1. INTRODUCTION In response to ecological, economic, and political developments, the chemical and petroleum industries must more effectively recover acid gases and weak electrolytes from plant effluent streams. The compounds of greatest industrial importance in this area are generally considered to include ammonia (NH3), carbon dioxide (CO2), hydrogen sulfide (H2S), and sulfur dioxide (SO2). Of these, H2S represents an important health hazard, even at modest concentrations. Compounds such as CO2, SO2, and H2S are acid gases and are traditionally removed from gas streams by contacting them with an aqueous solution of organic solvents, often alkanolamines.1 However, the extensive use of volatile organic compounds (VOCs) for gas scrubbing can simply substitute one environmental problem for another.2 Room temperature © 2012 American Chemical Society

ionic liquids are an exciting class of materials which offer a promising alternative to the use of VOCs in gas scrubbing operations. There has been an explosion of interest in ionic liquids. There have been well over 6000 papers published in the last 10 years with the phrase “ionic liquid(s)” in the title.3 Much of the interest in ionic liquids has centered on their possible use as “green” alternatives to volatile organic solvents.4−6 This claim usually rests on the fact that ionic liquids are generally nonvolatile under ambient conditions. Hence, exposure risk to ionic liquids is much lower than it is for a volatile solvent and they have no damaging atmospheric Received: April 8, 2012 Revised: June 4, 2012 Published: June 4, 2012 7709

dx.doi.org/10.1021/jp303344f | J. Phys. Chem. B 2012, 116, 7709−7718

The Journal of Physical Chemistry B

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equation to correlate the solubility of H2S in [C4mim][PF6];20 Jalili and co-workers presented similar calculations for mixtures of H2S in different imidazolium-based ionic liquids with the tetrafluoroborate [BF4]−, hexafluorophosphate [PF6]− and bis(trifluoromethylsulfonyl)imide [Tf2N]− anions;21−23 and Li et al. correlated new measured experimental data of NH3 on several members of the Cnmim[BF4] family.24 Recently, Carvalho and Coutinho25 have used the Flory−Huggins model to evaluate the nonideality of NH3, SO2, and H2S + imidazolium and pyridinium ionic liquid solutions. With the results obtained, they deduced the effect of the enthalpic and entropic contributions that are responsible of the deviations from an ideal solution. The remainder of this paper is structured as follows: we first briefly summarize the soft-SAFT theory. Subsequently, we describe in detail the SAFT models used for the compounds studied in this work. The Results and Discussion section includes a description of the phase diagrams and other thermodynamic properties of interest of each of the solutes and then their solubility on different imidazolium ionic liquids. Finally, some concluding remarks are given in the last section.

photochemistry. This nonvolatility also leads to most ionic liquids being nonflammable under ambient conditions. Ionic liquids are often referred as “tunable” or “designer solvents” as it is possible to select desired thermophysical properties of both the “pure” ionic liquid such as liquid range, heat capacities, viscosities, etc. and also absorption capacity and selectivity of the ionic liquid for a given solute by astute selection of the anion and cation. However, this achievement requires not just a posthoc rationalization of ionic liquids’ properties but the ability to predict them. In order to achieve this end, we utilize an approach which is firmly grounded in statistical mechanics and thus has a strong basis in physical chemistry. There are many unanswered questions concerning the physical chemistry of ionic liquids. However, it is still possible to exploit what is known of these systems and, in conjunction with physically based descriptions, produce reliable tools to tackle engineering problems. The statistical associating fluid theory (SAFT)7−9 and its various permutations provide an excellent platform for the estimation and prediction of the thermophysical properties and phase behavior of ionic liquids and their mixtures. In particular, the soft-SAFT equation of state10 has been proven to be successful in the modeling of ionic liquids. In previous contributions, soft-SAFT has been used to study the solubility of CO2,11,12 xenon,12 hydrogen,12,13 CO,13 BF3,14 alcohols,15 and water13,15 in different families of imidazolium-based ionic liquids. In this work, we present a study of the solubility of NH3, SO2, and H2S in a number of imidazolium-based ionic liquids. A key goal of this work is to gain an understanding of the solute−solvent interactions happening in these systems. There have been several previous investigations of the solubility of ammonia, hydrogen sulfide, and sulfur dioxide in ionic liquids,16−25 most of them focused on experimental measurements and the description the solute−solvent interactions. However, to date, there has been little work published concerning the application of physically based approaches to describe these systems, with the exception of the very recently published work of Rahmati-Rostami and co-workers.16 In this work, the authors model the solubility of hydrogen sulfide in six imidazolium ionic liquids using the SAFT-VR and PC-SAFT approaches. After developing a simple molecular model for each compound, they study the influence of the polar contributions and the effect of self- and cross-associating interactions on the calculation of those mixtures when applying both equations. The results obtained for the solubility of H2S, in very good agreement with the experimental data for both equations, are done either using two binary adjustable parameters or one temperature-dependent binary parameter. Among the rest of the contributions on this topic, it is worthy to mention the work of Yokozeki and Shiflett, published in several contributions.17−19 In 2007, they studied the solubility of ammonia in different imidazolium ionic liquids.17 In addition to new experimental data, they presented a model based on the Redlich−Kwong (RK) EoS, with empirical binary interaction parameters fitted to each binary system. The same approach was used in 2009 by the same authors to investigate the ability of ionic liquids to selectively separate SO2 from CO2 using hexylmethylimidazolium [C 6 mim] + with the bis(trifluoromethylsulfonyl)imide anion [Tf2N]−;18 and, again, in 2010, for the separation of a mixture of H2S and CO2 using butylmethylimidazolium [C4mim]+ with hexafluorophosphate [PF6]−19. Jou and Mather used the Krichevsky−Kasarnovsky

2. THEORY SAFT7−9 is a well-known equation of state. Based on Wertheim’s first-order thermodynamic perturbation theory,26−29 it provides a framework in which the effects of molecular shape and intermolecular interactions on the thermodynamic properties of a system are explicitly accounted for. There are several different versions of the SAFT equation (most of them differing in the reference fluid used in the monomer term),10,30−32 and in this work we choose to use the soft-SAFT equation of state,10 as it has been shown to be particularly well suited for describing complex fluid mixtures containing ionic liquids, similar to those investigated in this work.11−15 For associating molecules, the soft-SAFT approach calculates the Helmholtz free energy of the system as a sum of an ideal contribution Aideal, a reference term Aref, for the attractive and repulsive forces between the segments that form the molecules, a chain contribution Achain, which accounts for the connectivity of the segments in the molecules, and a contribution due to site−site intermolecular association Aassoc Atotal Aideal Ares Aref Achain Aassoc − = = + + NkBT NkBT NkBT NkBT NkBT NkBT (1)

where N is the number of molecules, kB is the Boltzmann constant, and T is the temperature. Ares is the residual Helmholtz free energy density of the system. The ideal term is given in the standard form in all SAFT equations and can be easily found in the literature.7,10,13 The reference term of the soft-SAFT EoS is given by a Lennard-Jones (LJ) spherical fluid, considering repulsive and attractive interactions of the monomers in a single contribution. This intermolecular potential includes the segment diameter of the monomers σ and the dispersive energy between segments ε. The equation of Johnson et al.,33 fitted to molecular simulations of Lennard-Jones monomers over a wide range of pressure, temperature, and density, is used here to calculate the free energy of this term. The extension of the reference term to mixtures is done by means of the van der Waals one-fluid theory (vdW-1f), where 7710



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values. The approach described in eqs 5−8 is solved using the procedure of Tan et al.35 In order to describe the long-range fluctuations of the properties of a fluid in the near-critical region, an additional term, Across is added to the soft-SAFT equation. Across is obtained from a renormalization group treatment36 based on White’s work.37,38 This term incorporates the scaling laws governing the asymptotic behavior that appears when approaching the critical point, while reducing to the original equation of state outside the critical region. The crossover term is expressed as a set of recursive equations that incorporate the fluctuations in a progressive way

the residual Helmholtz free energy density of the mixture is approximated by the residual Helmholtz free energy density of a pure hypothetical fluid. This procedure involves the calculation of the size and energy unlike intermolecular potential parameters, obtained with vdW-1f using the generalized Lorentz−Berthelot mixing rules

⎛ σii + σjj ⎞ σij = ηij⎜ ⎟ ⎝ 2 ⎠

(2)

εij = ξij(εiiεjj)1/2

(3)

ηij and ξij are the size and dispersion energy binary adjustable parameters for the species i and j, respectively. They account for differences in size and/or energy of the segments forming the two compounds in the mixture and are usually fitted to binary mixture data. The equation is used in a predictive manner when ηij and ξij are fixed to unity. The chain term is a function of the chain length m and gLJ, the radial distribution function of a fluid of LJ spheres at density ρm = mρ Achain = NkBT

∑ xi(1 − mi)ln gLJ

Atotal = NkBT

⎛

∑ xi ∑ ⎜⎝ln Xia − i

a

Xia ⎞ M ⎟+ i ⎠ 2 2

(5)

Xai

where is the fraction of molecules of component i not bonded at sites of type a and Mi is the number of association sites of type a on component i. The value of Xai comes from the solution of the mass-action equation Xia =

1 1+

n s ρ ∑ j = 1 xj ∑b = 1 Xb , jΔab , ij

(6)

where Δab,ij, includes two association molecular parameters: the site−site bonding-volume of association Kab,ij and the site−site association energy εab,ij. The details of these expressions can be found elsewhere.10 The extension of the associating term to mixtures is straightforward. The unlike-interaction values for the volume and energy of association are described by the classical Lorentz−Berthelot combining rules from pure component parameters, without the addition of any binary parameters Kab , ij

⎛ K (1/3) + K (1/3) ⎞3 ab , ii ab , jj ⎟ = ⎜⎜ ⎟ 2 ⎝ ⎠

εab , ij = (εab , iiεab , jj)1/2

i=1

⎣ NkBT

+

Across, i ⎤ ⎥ NkBT ⎦

(9)

3. MOLECULAR MODELS In this section, a description of the molecular models used for NH3, SO2, and H2S is provided. The models used to represent the ionic liquids have been presented previously11−13 and as such only the main features are presented here. The NH3 molecule, along with hydrogen fluoride (HF) and H2O, is one of the simplest hydrogen bonding molecules in terms of molecular structure. Some aspects of its bulk phase behavior are consistent with a hydrogen bonding fluid, whereas others are similar to those of simple, nonassociating compounds. For example, in ammonia there is approximately a 10% increase in the molar volume on melting, similar to the value for rare gases, whereas in contrast, a reduction in the relative volume is observed in the case of H2O.42 However, a characteristic property of hydrogen bonding fluids is the temperature range of the liquid phase in terms of the temperature ratio between the critical and triple points: Tr = Tc/Tt. The value of Tr for the rare gases is typically less than 2.0, whereas in the case of HF and H2O, Tr is approximately 2.7. The value of Tr for NH3 is 2.07, and thus it seems probable that strong anisotropic interactions are present in liquid NH3.41 There have been published numerous experimental and theoretical studies concerning the physical and chemical properties of ammonia. Often, this has also been done in the context of pollution control, such as in the studies presented by Edwards et al.,42,43 who developed models for the representation of the vapor−liquid equilibria of weak electrolyte solutions. Following a recent publication,44 NH3 is described using four associating sites to describe the hydrogen bonding interactions that characterize the fluid-phase behavior of NH3. Three sites of type H are used to model the hydrogen atoms and one site of type e is used to represent the lone pair of electrons (see model in Figure 1a). Only e−H associating interactions are permitted. Thus, in obtaining an appropriate parameter set for the NH3 model presented here, the soft-SAFT parameters are fitted to vapor−liquid equilibrium data. Other properties, such as the enthalpy of vaporisation and the heat capacity are also calculated in a predictive manner to test the ability of the parameters found to accurately describe other properties of the system. Hydrogen sulfide (H2S) is a self-associating molecule with dipolar and quadrupole moments. Structurally speaking, H2S is similar to water, with an angle between the hydrogen and the sulfur atoms of 92.1° and a couple of electron pairs on the

where xi is the mole fraction. The soft-SAFT EoS uses the expression of Johnson et al.,34 fitted to computer simulation data, to evaluate gLJ. The association term is one of the key contributions of SAFT-type equations of state, as it accounts for strong anisotropic intermolecular interactions, such as hydrogen bonding and other strong, directional, and localized interactions. The contribution for n associating sites on the molecule i is Aassoc = NkBT

⎡ Atotal, i − 1

∑⎢

The reader is referred to previous work for more details about its implementation in the soft-SAFT equation.39,40

(4)

i

∞

(7) (8)

where Kab,ij is obtained from the mean arithmetic average of the diameters of the pure component volume of association values and εab,ij is the geometric average of the energy of association 7711



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moment in an effective manner with two associating sites of different nature (one positive and one negative). This approach has been followed for other polar molecules, such as HCl,52 obtaining a good representation of the phase diagram of the fluid. Hence, SO2 is modeled as an associating molecule with two specific interaction sites (see Figure 1c). As it was described previously, the molecular parameters of those molecules are fitted to liquid density and vapor pressure at equilibrium. In a first approach, only data ranging at temperatures between 70 to 95% of the critical temperature Tc are used. Once the molecular parameters without the renormalization group treatment are obtained, the data around the critical region are added and then only the crossover parameters L and ϕ are optimized (keeping the previous parameters constant). The molecular parameters obtained for the three compounds are provided in Table 1. Table 1. Optimized Molecular Parameters for the Acid Gases Involved in This Worka

Figure 1. Image of the structure for (a) ammonia (NH3), (b) hydrogen sulfide (H2S), and (c) sulfur dioxide (SO2) and sketch of the model used to describe the molecule within the soft-SAFT approach. See text for details.

H2Sb SO2c NH3d

Mw [g·mol−1]

m

σ [Å]

ε/kB [K]

εab/kB [K]

Kab [Å]3

34.08 64.06 17.04

1.706 2.444 1.418

3.060 2.861 2.974

225.8 228.3 280.5

673.8 1130.0 2160.5

500.6 601.0 483.0

See text for details. bH2S crossover parameters: ϕ = 6.60 and L = 1.20σ [Å]. cSO2 crossover parameters: ϕ = 7.10 and L = 1.18σ [Å]. d NH3 crossover parameters: ϕ = 4.75 and L = 1.00σ [Å]. a

sulfur atom. However, sulfur is not nearly as electronegative as oxygen and hence hydrogen sulfide is not as polar as water. As a consequence, comparatively weak intermolecular forces exist for H2S. Cabaleiro-Lago concluded from ab initio calculations that in H2S clusters there is a low tendency for selfassociation.45 This was also confirmed by Pecul, who estimated the H2S−H2S binding energy (due to the formation of a hydrogen bond) to be between −3766 and −6276 J/mol, far from a typical hydrogen bond value of −25.000 J/mol.46 With this in mind, several models with a different number of associating sites can be proposed. Some contributions with SAFT-type equations of state have been published using zero, one, two, three, and four associating sites for H2S.47−50 We have chosen a model with three associating sites: two for the sites of type H for the hydrogen atoms and one site of type e for the electronegativity of the sulfur (see the model in Figure 1b), with only e−H interactions allowed. All of the parameters are fitted to liquid density and vapor pressure data of the phase equilibrium diagram. Preliminary calculations (not shown here) have been performed using two- and four-site models, achieving similar results. Similar observations have also been made by other authors.47,48 In light of the weak intermolecular forces observed in H2S, we have chosen to retain the three-site model instead of a four-site model (that could consider the two electron pairs of sulfur). Sulfur dioxide (SO2) is a bent molecule surrounded by four electron pairs and can be described as a hypervalent molecule. Its structure has some similarities with the NO2 molecule, although in this case, no dimerization has been observed. There are three regions of electron density around the central sulfur atom. The SO2 molecule is characterized by a relatively small polar moment, including dipolar and quadrupolar interactions. Some authors have noticed that the polar effect is very slight on the phase diagram and have decided to model SO2 as a nonassociating molecule.51 As there is not clear evidence in either direction, we have decided to account for the polar interactions in the soft-SAFT model, mimicking the dipole

For consistency with our previous work, we use here the same molecular models for the ionic liquids already described in detail in previous papers.12−15 The use of these models to describe the behavior of these new challenging mixtures will assess their robustness and transferability. An important feature of the model used for ionic liquids in the soft-SAFT approach is that they are considered as a tightly bonded ion-pair, based on ion pairing results observed in molecular dynamics simulations.53−55 Alkyl-imidazolium ionic liquids with the [PF6]− and [BF4]− anions are considered to be homonuclear chainlike molecules with one associating site in each molecule that describe the specific cation−anion interactions due to the charges and the asymmetry. The model for the [Tf2N]− imidazolium family has three associating sites, in order to consider the delocalization of the anion electric charge due the presence of oxygen groups surrounding the nitrogen of the anion. Hence, [Cn-mim][Tf2N] ionic liquids have one associating A type to represent the nitrogen atom interactions with the cation, while two B sites represent the delocalized charge due the oxygen molecules on the anion. Only AB interactions between different ionic liquids molecules are permitted. Here, it is important to note that we define the sites as of type A and B (and not as H or e) because they are representing an interaction more than a well-defined positive or negative charge (hydrogen or an electron). All of the parameters of the ionic liquids have been taken from previous contributions and are included in Table 2 for completeness.

4. RESULTS AND DISCUSSION A. Pure Components. In Figure 2, the vapor−liquid phase diagrams of SO2, H2S, and NH3 molecules are shown. In Figure 2a, the temperature-density equilibrium diagram of these three molecules is depicted, whereas in Figure 2b the Clausius− Clapeyron representation of the pressure−temperature diagram 7712



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Table 2. List of Molecular Parameters for the Different Ionic Liquids Used in This Worka [C2mim][BF4] [C4mim][BF4] [C6mim][BF4] [C4mim][PF6] [C6mim][PF6] [C2mim][Tf2N] [C4mim][Tf2N] [C6mim][Tf2N] a

Mw [g·mol−1]

m

σ [Å]

ε/kB [K]

εab/kB [K]

Kab [Å3]

ref

197.97 226.02 254.07 284.18 312.23 391.32 419.34 447.36

3.980 4.495 5.005 4.570 5.095 6.023 6.175 6.338

3.970 4.029 4.110 4.146 4.210 4.069 4.211 4.334

415.0 420.0 423.0 418.0 423.0 394.6 399.4 404.2

3450 3450 3450 3450 3450 3450 3450 3450

2250 2250 2250 2250 2250 2250 2250 2250

11 11 11 11 11 15 15 15

All of the parameters of this list are taken from previous works (see last column).

Figure 2. Vapor−liquid equilibrium diagram of ammonia (circles), sulfur dioxide (diamonds) and hydrogen sulfide (squares). (a) Temperature density diagram, (b) vapor pressure in the Clausius−Clapeyron representation, (c) enthalpy of vaporization, and (d) isobaric heat capacity at 300 K. The experimental data (symbols) are taken from NIST Chemistry Webbook,56 and the solid lines are the soft-SAFT calculations with the crossover term included.

molecular parameters used for SO2, H2S, and NH3 are those presented in Table 1. Once molecular parameters for the pure compounds are obtained, the next step involves the study of the absorption of those three molecules on different ionic liquids with the same soft-SAFT approach. Current industrial processes where ionic liquids can be used to separate those compounds occur at a range of temperature between 280 and 350 K, significantly below the critical temperature of ammonia and sulfur dioxide and slightly below the critical region of hydrogen sulfide. Within this range of temperature, the performance of softSAFT without the crossover treatment is identical to that with the corrections for the critical point. Hence, the following calculations have been done without using the renormalizationgroup term in order to speed up the process. In this case, the

is represented. The solid lines correspond to the soft-SAFT calculations with the renormalization-group term included (crossover soft-SAFT), accurately capturing the critical region of the phase envelope. In the three cases, very good agreement between the experimental data56 and the soft-SAFT optimized results are achieved. The validity of the molecular parameters is further tested by calculating the enthalpy of vaporisation (Figure 2c) and the heat capacity at 300 K (Figure 2d) in a predictive manner. The calculation of heat capacities is of particular interest, as they represent a strong test for any equation of state. In fact, this information has been used to discriminate between several ammonia models. As observed in the figures, the soft-SAFT calculations provide excellent agreement when compared to the available data.56 The 7713



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soft-SAFT molecular parameters shown in Table 1 remain unchanged, as they accurately reproduce the phase envelope far from the critical region. These values are used together with the two additional crossover parameters only when approaching the critical region. B. Solubility of NH3 on Imidazolium Ionic Liquids. The solubility of ammonia in different imidazolium ionic liquids has been reproduced with the soft-SAFT equation and compared to available experimental data. In those mixtures, it is important to consider cross-associating interactions between the associating sites of both molecules. It is expected that cross-association will play an important role on the prediction of the thermophysical properties. Hence, as in previous works,13,15 we explicitly consider crossed-association interactions between NH3 and the ionic liquids. Mixtures with imidazolium ionic liquids with the [PF6]− or [BF4]− anions are described following the same approach. As we are modeling the cation−anion pair with one only associating site A, the dual positive-negative nature of this site allows a possible interaction either with the nitrogen atom (site e) of ammonia, or with the three hydrogen atoms (sites H) of ammonia and the site A in the ionic liquid. Hence, Ae and AH interactions are allowed. Mixtures with imidazolium ionic liquids with the [Tf2N]− anion have more cross-associating possibilities, as those ionic liquids are modeled with three sites (one A site and two B sites). We consider cross-associating interactions between the nitrogen atom of ammonia (site e) and the two B sites of the ionic liquid (eB) and between the three hydrogen atoms of ammonia (sites H) and the site A of the ionic liquid (AH). Other cross-associating possibilities (Ae or BH) are not permitted in this case. The possible crossed interactions have been established based on previous results obtained for the [Tf2N]− family with other associating systems such as water and alcohols,15 where excellent predictions for VLE and LLE diagrams were obtained following the same cross-associating interactions hypothesis. In all cases, as shown in eqs 7 and 8, the cross-associating interaction values are calculated following the Lorentz−Berthelot combining rules with no adjustable parameters, in a predictive manner from the association parameters of the pure compounds. Figure 3a shows the solubility of NH3 in [C4mim][PF6] at different temperatures ranging from 283.4 until 355.8 K. We found that a value of ξ = 0.920 gave quantitative agreement at all temperatures. This value accounts for the differences in the cohesive energy of both molecules. A similar performance is obtained in Figure 3b, where the solubility of NH3 in ethylmethylimidazolium [C2mim]+ with the [Tf2N]− anion is shown. Once again, a single temperature independent energy parameter (ξ = 0.900) is enough to reproduce the experimental data17 of the mixture in the range of studied temperatures (283.4−343.6 K). Although the general agreement is very good, some deviations are observed at the highest temperatures and lowest ammonia compositions. Close inspection of the experimental data reveals that the data trends at low compositions do not reach a nearly zero vapor pressure value when the ionic liquid is pure. Hence, this could be a possible cause of disagreement between the calculations and the measurements. In Figure 4, results concerning the absorption of NH3 on the [Cnmim][BF4] family are depicted. The ξ parameter has been adjusted for NH3 + [C4mim][BF4] (Figure 4b) at an intermediate temperature of 323 K (ξ = 0.910) and has been

Figure 3. Solubility of NH3 in (a) [C4mim][PF6] at 283.4 (crosses), 298.6 (squares), 324.6 (circles), 347.2 (diamonds), and 355.8 K (triangles) and (b) [C2mim][Tf2N] at 283.4 (squares), 299.4 (circles), 323.4 (diamonds), and 343.6 K (triangles). All experimental data (symbols) in both figures are from ref 17, whereas the lines are the soft-SAFT EoS with ξ = 0.920 in panel a, and ξ = 0.900 in panel b.

used to predict, in a transferable manner, the solubility at other temperatures and for other mixtures with ionic liquids of the same family, with [C2mim][BF4] (Figure 4a) and [C6mim][BF4] (Figure 4c). In all cases, good agreement is achieved between the experimental data17,24 and the soft-SAFT calculations. Here, we should remark that better agreement can be achieved modifying the ξ values, but that would result in a loss of transferability of the equation. As a general conclusion, it is remarkable to note that the unlike dispersive interactions appear to be very important in controlling the solubility of even quite strongly polar compounds such as NH3 in a relatively wide range of imidazolium-based ionic liquids. This is distinct from previous observations of solubility behavior of solutions of strongly polar fluids57 and suggests that solubility in ionic liquids may be entropy driven, confirming the indications noted in the work of Carvalho and Coutinho.25 C. Solubility of SO2 on Imidazolium Ionic Liquids. The solubility of SO2 on ionic liquids has also been studied, and the results compared with the scarce available experimental data. Only data with the [TF2N]− anion18 and a very recent contribution with data at 293 K for [C4mim][PF6] and [C4mim][BF4] have been found.58 Regarding the cross interactions between SO2 and the ionic liquids, molecular dynamic simulations and Raman spectroscopy measurements of Ando et al.59 and Siqueira et al.60 showed that there are no strong interactions between the imidazolium ionic liquid and 7714



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Figure 5a shows the solubility of SO2 in [C6mim][Tf2N] at different temperatures from 298.1 to 348.1 K. The calculation

Figure 5. Solubility of SO2 in (a) [C6mim][Tf2N]. Pressure− composition diagram at 298.15 (circles), 323.15 (diamonds), and 348.15 K (triangles) using a ξ = 0.910 adjusted to 323.15 K. Experimental data (symbols) are taken from ref 18. (b) [C4mim][BF4] (diamonds) and [C4mim][PF6] (triangles) using ξ = 0.955 and 0.965, respectively. Experimental data from ref 58.

procedure is exactly the same previously described for the ammonia solubility and, as such, will not be described again here. A single binary energy parameter ξ = 0.910 is enough to have an excellent agreement with the experimental data18 in the whole range of evaluated conditions. Although the value of ξ corrects deviations from the mean dispersive energy value obtained from the pure component parameters (see eqs 2 and 3), the fact that it deviates from unity may indicate that, in addition to correcting the energy interaction, it also corrects, in an indirect manner, the values of the association parameters, as the interactions should be weaker than those in the pure components. In other words, the relatively large deviation of ξ from unity may also indicate that the calculated crossassociation parameters of the mixture from the pure component parameters are too high and predict a higher absorption of SO2. This is in agreement with the previous observations of Ando et al.59 and Siqueira et al.60 and suggests the use of lower parameter values of cross-association. However, we have decided to continue using predictions for association and correcting the deviations for the mixture with just one temperature independent energy binary parameter. A recent paper by Jin et al. presented new data on the solubility of SO2 in [C4mim][PF6] and [C4mim][BF4] at

Figure 4. Solubility of NH3 in the [Cnmim][BF4] family. Pressure− composition diagram for the (a) NH3 + [C2mim][BF4] at 283.4 (crosses), 298.6 (squares), 324.6 (circles), 347.2 (diamonds), and 355.8 K (triangles); (b) NH3 + [C4mim][BF4] at 298 (crosses), 313 (squares), 323 (circles), 347 (diamonds), and 355 K (triangles); and (c) NH3 + [C6mim][BF4] at 298.2 (squares) 313 (circles), 323 (diamonds), and 333 K (triangles). Experimental data (symbols) are from refs 17 and 24, whereas all of the lines are the soft-SAFT EoS calculations with ξ = 0.910.

the SO2 molecule. The selected molecular model for SO2 allows the possibility of considering cross-association between the sites of SO2 and those of the ionic liquids. For the [Cnmim][Tf2N] family, we have taken into account interactions between the positive site of SO2 (site +) and the two B sites of the ionic liquid (+B) and between the negative site of SO2 (site −) and the site A of the ionic liquid (−A). For the [Cnmim][PF6] or [BF4] families, we allow a possible interaction of the ionic liquid site either with the positive or negative site of SO2. As a first approach, trying to make the methodology as predictive as possible, we have used the Lorentz−Berthelot combining rules for the calculation of the crossed-interaction values. 7715



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293.15 K.58 We have modeled both mixtures using the softSAFT equation, and the results obtained are shown in Figure 5b. The triangles correspond to the [C4mim][PF6] data and the diamonds to the [C4mim][BF4] data. Here, ξ values of 0.955 and 0.965 have been used, respectively. Once again, the binary parameter is lower than 1, and similar conclusions to those obtained in Figure 5a can be addressed, although in this case the deviations are not as significant as before. Otherwise, it is gratifying that simple models within the SAFT approach can be used to accurately describe the solubility behavior of such complex fluid mixtures, without taking into account other interactions or additional terms into the equation. D. Solubility of H2S on Imidazolium Ionic Liquids. The solubility of H2S in ionic liquids is described in this section. Recall that the H2S molecule was modeled using three associating sites: one site e′ representing the sulfur negative charge and two H′ sites representing the two hydrogen atoms of the molecule. The same assumptions previously employed for the ammonia−ionic liquids interactions have been followed here. Mixtures with imidazolium ionic liquids with the [PF6]− or [BF4]− anions, with one only associating site A, are allowed to interact either with the sulfur atom (site e′) or with the two hydrogen atoms (sites H′) of H2S. When dealing with imidazolium ionic liquids with the [Tf2N]− anion, which are modeled with three sites (1 A site and 2 B sites), we consider cross-association interactions between the sulfur atom of hydrogen sulfide (site e′) and the two B sites of the ionic liquid (e′B) and between the two hydrogen atoms of hydrogen sulfide (sites H′) and the site A of the ionic liquid (AH′). As before, other cross-associating possibilities (Ae′ or BH′) are not allowed. Figure 6 shows the equilibrium of H2S with some [Cnmim][PF6] compounds. Yokozeki and Shiflett19 had demonstrated that H2S + [C4mim][PF6] systems follow a type V phase behavior, according to the classification of van Konynenburg and Scott,61 by measuring VLLE (vapor−liquid− liquid equilibrium) data at high H2S concentrations. Hence, in Figure 6a, the VLE and VLLE of H2S with [C4mim][PF6] at different temperatures, ranging from 298 to 403 K, have been described in very good agreement with the experimental data19,21 using a constant binary ξ energy parameter. The ξ value has been fitted to an intermediate temperature of 323.15 K for the H2S + [C4mim][PF6] mixture and transferred to other temperatures to predict the VLLE diagram. It is striking to observe that the VLLE diagram found at high compositions of H2S is predicted in such good agreement with the experimental data. Unfortunately, we have not been able to close the VLLE gap at low temperature, as it should be expected from the results shown in ref 19. The ξ value has been transferred to the H2S + [C6mim][PF6] mixture (see Figure 6b), achieving also good agreement at all temperatures for the VLE calculations, demonstrating the transferability of our approach. Further, we also present predictions at higher temperatures, and we have also predicted the formation of another VLLE area (never measured experimentally yet) with a similar size of the one seen for the H2S + [C4mim][PF6] mixture. Figure 7 contains results for the absorption of H2S in imidazolium ionic liquids with the [BF4]− as the anion. Figure 7a is devoted to the VLE of H2S + [C4mim][BF4], whereas in Figure 7b we represent the VLE of H2S + [C6mim][BF4]. Once again, an accurate description is achieved with the same binary parameter value for the two mixtures. In this case, it is

Figure 6. Solubility of H2S in a) [C4mim][PF6] at 298.15 (stars), 323.15 (squares), 343.15 (circles), 373.15 (diamonds), and 403.15 K (triangles). Experimental data20 are symbols while the lines are the soft-SAFT EoS calculations with ξ = 0.900. (b) [C6mim][PF6] at 323.15 (squares), 333.15 (circles), 343.15 (diamonds), and 373.15 K (only prediction). Experimental data are symbols,22 whereas the lines are the soft-SAFT EoS predictions using the transferred value optimized for H2S + [C4mim][PF6] of ξ = 0.900.

interesting to observe that the ξ value of 0.920 is close to that obtained for mixtures with the [PF6]− anion. To our understanding, the interactions between H2S and ionic liquids with either the [PF6]− or the [BF4]− anion are apparently of a very similar nature, although it is important to notice that H2S is more soluble in ionic liquids containing the [BF4]− anion than those containing the [PF6]− anion. Finally, Figure 8 shows the solubility of H2S in [C2mim][Tf2N] at different temperatures. Even if the nature of the [Tf2N]− anion is quite different from the anions showed before, good agreement with experimental data is again achieved with a binary energy parameter quite close to the values previously obtained (ξ = 0.890).

5. CONCLUSIONS The solubility of NH3, SO2, and H2S in three imidazolium ionic liquids families has been described with the soft-SAFT equation of state and results compared to the available experimental data for those mixtures. The ionic liquids model developed in a very recent work has been used here in a transferable manner, whereas accurate molecular models have been developed for NH3, SO2, and H2S. The pure fluid phase diagrams of those three compounds were reproduced in excellent agreement with 7716



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predictive manner to obtain enthalpies of vaporisation and isobaric heat capacities in excellent agreement with experimental data, showing the robustness of the model and the parameters. The optimal sets of molecular parameters were then used to examine the solubility of these three pollutants in different families of imidazolium-based ionic liquids. A key to the success of the modeling approach is careful consideration of the appropriate cross-associating interactions among the different molecules. In general, good agreement is found for all of the vapor−liquid equilibrium calculations studied using a single temperature-independent binary parameter for a whole family of ionic liquids with each compound. Furthermore, for the particular case of H2S + [C4mim][PF6], a vapor−liquid−liquid equilibrium (VLLE) region experimentally observed in the H2S rich section of the isothermal phase diagram is well reproduced. This information has been used to predict a VLLE region in the H2S + [C6mim][PF6], never experimentally measured. As the alkyl chain of the cation is increased, it is possible to expect the same VLLE region, even in a higher range of compositions, considering that the ionic liquid will tend to approach an alkane-like behavior. These results show, once more, than in spite of the a priori simplicity of the approach the soft-SAFT equation of state is able to provide reliable results for complex ionic liquids systems using a minimum amount of experimental information and the appropriate level of physical description of the molecules. Further, the parameters of the equation are transferable, making it a powerful tool with which to tackle important engineering challenges.

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Figure 7. Solubility of H2S in the [Cnmim][BF4] family at 313 (squares), 323 (circles), 333 (diamonds), and 343 K (triangles). (a) Pressure−composition diagram for a H2S + [C4mim][BF4] mixture. Experimental data from ref 21. (b) Pressure−composition diagram for H2S + [C6mim][BF4] mixture. Experimental data from ref 22. In both panels, a binary adjustable parameter ξ = 0.920 has been used. Lines are the soft-SAFT EoS calculations.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +34 935 929 950. Fax: +34 935 929 951. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS F.L. acknowledges a JAE-Doctor fellowship from the Spanish Government that allowed starting this work and a TALENT contract from the Catalan Government that has permitted him to finish it. Helpful discussions with Prof. J.A.P. Coutinho about the nature of the solubility of those compounds in ionic liquids and with Jordi Andreu about the ammonia model are fully appreciated. This work has been partially financed by the Spanish government, Ministerio de Ciencia e Innovación, under projects CTQ2008-05370/PPQ and CENIT SOST-CO2 CEN2008-01027 (a CENIT project belonging to the Ingenio 2010 program). Additional support from the Catalan government, under project 2009SGR-666, and from Carburos Metálicos, Air Products Group, is also acknowledged. N.M. thanks the Natural Environment Research Council (NERC) of the U.K. for funding a postdoctoral research grant (Grant No. NE/H01392X/1).

Figure 8. Solubility of H2S in the [C4mim][Tf2N] family at 303.15 (crosses), 313.15 (squares), 323.15 (circles), 333.15 (diamonds), and 343.15 K (triangles). Experimental data (symbols) are from ref 21, whereas the lines are the soft-SAFT calculations EoS calculations with ξ = 0.890.

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