Modeling the Absorption of Weak Electrolytes and Acid Gases with

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Modelling the Absorption of Weak Electrolytes and Acid Gases with Ionic Liquids Using the Soft-SAFT Approach Felix Llovell, Rosa M Marcos, Niall Mac Dowell, and Lourdes F. Vega J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp303344f • Publication Date (Web): 04 Jun 2012 Downloaded from http://pubs.acs.org on June 18, 2012

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The Journal of Physical Chemistry

Modelling the Absorption of Weak Electrolytes and Acid Gases with Ionic Liquids Using the Soft-SAFT Approach F. Llovell1,2, R.M. Marcos3, N. MacDowell1,4 and L. F. Vega1,5 1

MATGAS Research Center. Campus de la UAB, 08193 Bellaterra. Barcelona. Spain 2

Institut de Ciència de Materials de Barcelona, Consejo Superior de Investigaciones

Científicas (ICMAB-CSIC), Campus de la UAB, 08193 Bellaterra, Barcelona, Spain 3

Dep. Enginyeria Mecànica. ETSE. Universitat Rovira i Virgili. 43007 Tarragona, Spain 4

Centre for Process Systems Engineering, Dept of Chemical Engineering, Imperial College London, SW2AZ, UK

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Carburos Metálicos/Air Products Group, C/Aragón, 300, 08009 Barcelona, Spain

CORRESPONDING AUTHOR FOOTNOTE e-mail: [email protected], phone: +34 935 929 950, fax: +34 935 929 951

ACS Paragon Plus Environment

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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) while new models for SO2, NH3 and H2S are proposed here. Alkylimidazolium ionic liquids with the [PF6]- and [BF4]- anions are considered to be Lennard-Jones 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 modelled as a single molecule with three associating sites, taking into account the delocalization of the anion electric charge due the presence of oxygen groups surrounding the nitrogen of the anion. NH3 is described with 4 associating sites: 3 sites of type H mimicking the hydrogen atoms and 1 site of type e representing the lone pair of electrons. H2S is modelled with

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associating sites: 2 for the sites of type H for the hydrogen atoms and 1 site of type e for the electronegativity of the sulphur. SO2 is modelled with 2 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 vaporisation 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


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parameter is sufficient to describe every family of mixtures in good agreement with the available data in the literature. In addition, a vapour-liquid-liquid equilibrium (VLLE) region, never measured experimentally, has been identified for mixtures of hydrogen sulphide + 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 behaviour of complex systems.

KEYWORDS imidazolium ionic liquid, sulphur dioxide, hydrogen sulphide, ammonia, vapour-liquid equilibrium and vapour-liquid-liquid equilibrium, molecular-based equations of state.


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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 sulphide (H2S) and sulphur 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 (VOC) for gas scrubbing can simply substitute one environmental problem for another(2). Room temperature ionic liquids are an exciting class of materials which offer a promising alternative to the use of VOC in gas scrubbing operations. There has been an explosion of interest in ionic liquids. There have been well over 6,000 papers published in the last ten years with the phrase ionic liquid(s) in the title(3). Much of the interest in ionic liquids has centred 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 non-volatile 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 photochemistry. This non-volatility also leads to most ionic liquids being non-flammable 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


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ionic liquid for a given solute by astute selection of the anion and cation. However, this achievement requires not just a post-hoc rationalisation 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 provides an excellent platform for the estimation and prediction of the thermophysical properties and phase behaviour of ionic liquids and their mixtures. In particular, the soft-SAFT equation of state(10) has been proven to be successful in the modelling of ionic liquids. In previous contributions, soft-SAFT has been used to study the solubility of CO2(11),(12), Xenon(12), Hydrogen12,(13), CO(13), BF3(14), alcohols(15) and water(13),(15) in different families of imidazolium-based ionic liquids. In this wok, 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 sulphide and sulphur 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 sulphide in 6 imidazolium ionic liquids using


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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 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 [C6mim]+ with the bis(trifluorosulfonyl)imide anion [Tf2N]- (18); and, again, in 2010, for the separation of a mixture

of

H2 S

and

CO2

hexafluorophosphate [PF6]-

using

butylmethylimidazolium

[C4mim]+

with

(19)

. Jou and Mather used the Krichevsky–Kasarnovsky

equation to correlate the solubility of H2S in [C4mim][PF6]

(20)

; Jalili and coworkers

presented similar calculations for mixtures of H2S in different imidazolium-based ionic liquids

with

the

tetrafluoroborate

[BF4]-,

hexafluorophosphate

[PF6]-

and

bis(trifluorosulfonyl)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 Coutinho(25) 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.


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The remainder of this paper is structured as follows: we first briefly summarise the soft-SAFT theory. Subsequently, we describe in detail the SAFT models used for the compounds studied in this work. The results 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.

2. Theory The Statistical Associating Fluid Theory (SAFT)(7)-(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 A res A ref A chain A assoc − = = + + , Nk BT Nk B T Nk BT Nk BT Nk BT Nk B T


(1)

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where N is the number of molecules, kB is the Boltzmann constant and T is the temperature. A res 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 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 the van der Waals one-fluid theory using the generalized Lorentz-Berthelot mixing rules:

 σ ii + σ jj σ ij = ηij  2 

εij = ξ ij (εii ε jj )

1/ 2

  , 

(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.


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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 :

A chain = ∑ xi ( 1 − mi )ln g LJ , Nk B T i

(4)

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:

 Xa M A assoc = ∑ xi ∑  ln X ia − i  + i , Nk BT 2  2 i a 

(5)

where X ia is the fraction of component i not bonded at sites of type a, and Mi as the number of association sites of type a on component i. The value of X ia comes from the solution of the mass-action equation: X ia =

1 n

s

j =1

b =1

,

(6)

1 + ρ ∑ x j ∑ X b , j ∆ ab ,ij

where ∆ab,ij , includes two association molecular parameters: the site-site bondingvolume of association Kab,ij, and the site-site association energy ε ab,ij . The details of these expressions can be found elsewhere(10). The extension of the associating term to mixtures is straightforward. The unlikeinteraction 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:


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 K ab ,ii (1/ 3) + K ab, jj (1/ 3)   , Κ ab,ij =    2  

(7)

εab,ij = (εab,ii ε ab, jj )

(8)

1/ 2

,

where, Kab,ij is obtained from the mean arithmetic average of the diameters of the pure component volume of association values, while εab,ij is the geometric average of the energy of association 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 treatment based(36) on White’s work(37)-(38). This term incorporates the scaling laws governing the asymptotic behaviour 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: ∞  A total ,i −1 A cross,i  Atotal = ∑ +  Nk B T i =1  Nk B T Nk B T 

(9)

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

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 previously(11)-(13) and as such only the main features are presented here.


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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 behaviour are consistent with a hydrogen bonding fluid, while others are similar to those of simple, non-associating compounds. For example, in ammonia there is approximately a 10% increase in the molar volume on melting, similar to the value for rare gases, while, in contrast, a reduction in the relative volume is observed in the case of H2O.(41) 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 while, in the case of HF and H2O, Tr, is approximately 2.7. The value of Tr for NH3 is 2.07, 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 vapour-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 behaviour 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 (with the exception of mNH3) are fitted to vapour-liquid equilibrium data. Other properties, such as the enthalpy


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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 sulphide (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 sulphur atoms of 92.1º, and a couple of electron pairs on the sulphur atom. However, sulphur is not nearly as electronegative as oxygen and hence hydrogen sulphide 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 self-association(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 SAFTtype 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 3 associating sites: 2 for the sites of type H for the hydrogen atoms and 1 site of type e for the electronegativity of the sulphur (see model in Figure 1b), with only e-H interactions allowed. All the parameters are fitted to liquid density and vapour pressure data of the phase equilibrium diagram. Preliminary calculations (not shown here) have been performed using 2- and 4-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 3-site model instead of a 4-site model (that could consider the two electron pairs of sulphur). Sulphur dioxide (SO2) is a bent molecule surrounded by 4 electron pairs and can be described as a hypervalent molecule. Its structure has some similarities with the NO2


12

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molecule, although in this case, no dimerization has been observed. There are three regions of electron density around the central sulphur 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 non-associating 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 moment in an effective manner with two associating sites of different nature (1 positive and 1 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 modelled 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 vapour 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. 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 behaviour 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 ionpair, 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


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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 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 vapour-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, while in Figure 2b the Clausius–Clapeyron representation of the pressure-temperature diagram is represented. The solid lines correspond to the softSAFT calculations with the renormalization-group term included (crossover softSAFT), accurately capturing the critical region of the phase envelope. In the three cases, very good agreement between the experimental data(56) 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 300K (Figure 2d) in a predictive manner. The calculation of heat capacities is of particular


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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 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 350K, significantly below the critical temperature of ammonia and sulphur dioxide and slightly below the critical region of hydrogen sulphide. Within this range of temperature, the performance of soft-SAFT 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 renormalization-group term in order to speed up the process. In this case, the soft-SAFT molecular parameters shown in Table 1 remain unchanged, as they accurately reproduce the phase envelope far from the critical region. These parameters’ 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


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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 modelling 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 crossassociating possibilities, as those ionic liquids are modelled 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 equations (7)-(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 283.4K till 355.8K. 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


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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 data(17) of the mixture in the range of studied temperatures (283.4-343.6K). 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 vapour 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 323K (ξ=0.910) and has been 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 data(17),(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 power 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 behaviour of solutions of strongly polar fluids(57), and suggests that solubility in ionic liquids is entropy driven, confirming the indications noted in the work of Carvalho and Coutinho(25).


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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]anion(18) and a very recent contribution with data at 293K 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 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 crossedinteraction values. Figure 5a shows the solubility of SO2 in [C6mim][Tf2N] at different temperatures from 298.1K till 348.1K. The calculation 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 data(18) in the whole range of evaluated conditions. Although the value of ξ corrects deviations in the ε from the pure component parameters (see Equations (2) and (3)) , the fact that it deviates from unity may indicates that, in addition to correcting


18

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the energy interaction, it also corrects, in an indirect manner, the values of the association parameters, as the interactions should be weaker than in the pure components. In other words, the relatively large deviation of ξ from unity may also indicate that the calculated cross-association parameters of the mixture from the pure component parameters are too high and predict a higher absorption of SO2. This remark 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 preferred 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 293.15K(58). We have modelled both mixtures using the soft-SAFT 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, a ξ value of 0.955 and 0.965 has 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 behaviour 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 H2S molecule was modelled using three associating sites, one site e’ representing the sulphur 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


19


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Page 20 of 40

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 sulphur 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 modelled with 3 sites (1 A site and 2 B sites), we consider cross-association interactions between the sulphur 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 sulphide (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 Shiflett(19) had demonstrated that H2S + [C4mim][PF6] systems follow a Type V phase behaviour, according to the classification of van Konynenburg and Scott(61), by measuring VLLE (vapour–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 298K till 403K, has been described in very good agreement with the experimental data(19),(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 and 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 reference(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


20

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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] while 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 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 available experimental data for those mixtures. The ionic liquids model developed in a very recent work has been used here in a transferable manner, while 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 available


21


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Page 22 of 40

experimental data, including the critical region, once the crossover term was added to soft-SAFT. The molecular parameters fitted to vapour-liquid equilibria were used in a 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 modelling approach is careful consideration of the appropriate cross-associating interactions among the different molecules. In general, good agreement is found for all the vapour-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 vapour-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 behaviour. 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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Acknowledgements F. Llovell 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 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 CTQ200805370/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 Mac Dowell thanks the Natural Environment Research Council (NERC) of the UK for funding a post-doctoral research grant (Grant Number NE/H01392X/1).


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TABLES Table 1. Optimized molecular parameters for the acid gases involved in this work. See text for details.

Mw

m

σ

ε/kB

εab/kB

Kab

[g·mol-1]

-

[Å]

[K]

[K]

[Å]3

H2S*

34.08

1.706

3.060

225.8

673.8

500.6

SO2♦

64.06

2.444

2.861

228.3

1130.0

601.0

NH3§

17.04

1.418

2.974

280.5

2160.5

483.0

* H2S crossover parameters: φ =6.60 and L= 1.20σ [Å] ♦ SO2 crossover parameters: φ = 7.10 and L= 1.18σ [Å] § NH3 crossover parameters: φ = 4.75 and L= 1.00σ [Å]


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Table 2. List of molecular parameters for the different ionic liquids used in this work. All the parameters of this list are taken from previous works (see last column).

Mw

m

σ

ε/kB

εab/kB

Kab

[g·mol-1]

-

[Å]

[K]

[K]

[Å3]

[C2mim][BF4]

197.97

3.980

3.970

415.0

3450

2250

(11)

[C4mim][BF4]

226.02

4.495

4.029

420.0

3450

2250

(11)

[C6mim][BF4]

254.07

5.005

4.110

423.0

3450

2250

(11)

[C4mim][PF6]

284.18

4.570

4.146

418.0

3450

2250

(11)

[C6mim][PF6]

312.23

5.095

4.210

423.0

3450

2250

(11)

[C2mim][Tf2N]

391.32

6.023

4.069

394.6

3450

2250

(15)

[C4mim][Tf2N]

419.34

6.175

4.211

399.4

3450

2250

(15)

[C6mim][Tf2N]

447.36

6.338

4.334

404.2

3450

2250

(15)


Ref.

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FIGURE CAPTIONS Figure 1. Image of the structure for a) Ammonia (NH3) b) Sulphur dioxide (SO2) c) Hydrogen sulphide (H2S), and sketch of the model used to describe the molecule within the soft-SAFT approach. See text for details. Figure 2. Vapour-liquid equilibrium diagram of ammonia (circles), sulphur dioxide (diamonds) and hydrogen sulphide (squares). a) Temperature-density diagram b) Vapour pressure in the Clausius-Clapeyron representation. c) Enthalpy of vaporisation d) Isobaric Heat Capacity at 300K. The experimental data (symbols) are taken from NIST Chemistry Webbook(56), while the solid lines are the soft-SAFT calculations with the crossover term included. Figure 3: Solubility of NH3 in a) [C4mim][PF6] at 283.4K (crosses), 298.6K (squares), 324.6K (circles), 347.2K (diamonds) and 355.8K (triangles). b) [C2mim][Tf2N] at 283.4K (squares), 299.4K (circles), 323.4K (diamonds) and 343.6K (triangles). All experimental data (symbols) in both figures are from reference(17) while the lines are the soft-SAFT EoS with ξ=0.920 in Figure 3a, and ξ=0.900 in Figure 3b. Figure 4: Solubility of NH3 in the [Cnmim][BF4] family. Pressure-composition diagram for the a) NH3 + [C2mim][BF4] at 283.4K (crosses), 298.6K (squares), 324.6K (circles), 347.2K(diamonds) and 355.8K (triangles). b) NH3 + [C4mim][BF4] at 298K (crosses), 313K (squares), 323K (circles), 347K (diamonds) and 355K (triangles) c) NH3 + [C6mim][BF4] at 298.2K (squares) 313K (circles), 323K (diamonds) and 333K (triangles). Experimental data (symbols) are from references(17),(24) while all the lines are the soft-SAFT EoS with ξ=0.910.


30

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Figure 5. Solubility of SO2 in a) [C6mim][Tf2N]. Pressure-composition diagram at 298.15K (circles), 323.15K (diamonds) and 348.15K (triangles) using a ξ=0.910 adjusted to 323.15K. Experimental data (symbols) are taken from reference(18). b) [C4mim][BF4] (diamonds) and [C4mim][PF6] (triangles) using a ξ=0.955 and ξ=0.965, respectively. Experimental data from reference(58). Figure 6: Solubility of H2S in a) [C4mim][PF6] at 298.15K (stars), 323.15K (squares), 343.15K (circles), 373.15K (diamonds ) and 403.15K (triangles). Experimental data(20) are symbols while the lines are the soft-SAFT EoS calculations with ξ=0.900 b) [C6mim][PF6] at 323.15K (squares), 333.15K (circles), 343.15 (diamonds) and 373.15K (only prediction). Experimental data are symbols(22) while the lines are the soft-SAFT EoS predictions using the transferred value optimized for H2S + [C4mim][PF6] of ξ=0.900. Figure 7: Solubility of H2S in the [Cnmim][BF4] family at 313K (squares), 323K (circles), 333K (diamonds) and 343K (triangles). a) Pressure-composition diagram for a H2S + [C4-mim][BF4] mixture. Experimental data from reference(21) a) Pressurecomposition diagram for H2S + [C6mim][BF4] mixture. Experimental data from reference(22). In both figures, a binary adjustable parameter ξ=0.920 has been used. Lines are the soft-SAFT EoS calculations. Figure 8: Solubility of H2S in the [C4mim][Tf2N] family at 303.15K (crosses), 313.15K (squares),

323.15K

(circles),

333.15K

(diamonds)

and

343.15K

(triangles).

Experimental data (symbols) are from reference(21) while the lines are the soft-SAFT EoS with ξ=0.890.


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Figure 1: Llovell et al.

a) NH3

b) H2S

c) SO2


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a)

b)

c)

d)


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a)

b)


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Figure 4: Llovell et al. a)

b)

c)


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a)

b)


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a) VLLE

b) VLLE


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a)

b)


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ToC Graphic Cnmim[Tf2 N]

Cnmim[PF6] Cnmim[BF4]

+ C2 mim[Tf 2N]

VLLE + C4mim[PF6 ]


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Modeling the Absorption of Weak Electrolytes and Acid Gases with

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