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Modeling Complex Associating Mixtures with [Cn-mim][Tf2N] Ionic Liquids: Predictions from the Soft-SAFT Equation F. Llovell,†,‡ E. Valente,‡ O. Vilaseca,†,‡ and L. F. Vega*,†,‡,§ †
Institut de Ciencia de Materials de Barcelona, Consejo Superior de Investigaciones Científicas (ICMAB-CSIC), Campus de la UAB, 08193 Bellaterra, Barcelona, Spain ‡ MATGAS Research Center (Carburos Metalicos/Air Products, CSIC, UAB), Campus UAB, 08193 Bellaterra, Barcelona, Spain § Carburos Metalicos/Air Products Group, C/Aragon, 300, 08069 Barcelona, Spain ABSTRACT: In a previous work (Andreu and Vega, J. Phys. Chem. B 2008, 111, 16028), we presented a simple model for the imidazolium-based ionic liquids (ILs) with the bis(trifluorosulfonyl)imide anion [Tf2N] in the context of the soft-SAFT equation of state. The model was successfully used to predict the solubility of several gases in these ILs. However, the small amount of experimental data made the predictions less accurate when going into more complex mixtures and one or two fitted binary parameters were needed in some cases. In this work, we have reparameterized our previous model and evaluated its reliability to predict the behavior of these ionic liquids in binary mixtures with other associating compounds. Model parameters for the ionic liquids were estimated using new experimental density data at atmospheric pressure in an extended range of temperatures, from 273 until 473 K, consistent within the range of temperatures previously measured by other authors. The new set of molecular parameters has been tested to predict the density of several members of the family at higher pressures up to 60 MPa with the same degree of accuracy than at atmospheric values. In addition to densitytemperature data, interfacial tensions and the isothermal compressibility of some compounds were predicted in reasonable good agreement with experimental data. The molecular parameters of the pure compounds were used then, in a predictive manner, to describe the behavior of binary mixtures with other imidazolium ionic liquids, changing either the cation or the anion. Predictions for some mixtures with methanol, ethanol, and water were compared with experimental data, providing an excellent description of the systems, with no fitting to mixture data in almost all the cases. The excellent results obtained in this work reinforce the need to have accurate data, showing that molecular based models can be used to assess the validity of these data. In addition, this work also shows that a simple model in which the physics of the system is kept is good enough to describe the complex behavior of associating mixtures of ionic liquids, without the need of additional parameters that may obscure the real physics of the system.
1. INTRODUCTION Room temperature ionic liquids (RTILs) are receiving much attention in recent years from both academia and industry because of their tunable properties and their possible applications in several processes, including separation and extraction among others. Their extremely low volatility, high thermal stability, and wide liquid temperature range make them appropriate solvents for a wide range of industrial applications. In addition, the change of the ionic liquid structure (modifying the anion, the cation, or both) has a significant impact on the solubility of different compounds in them. As a consequence, thousands of combinations are possible and the right anioncation pair can be selected for each particular process. Examples of these applications include drug delivery as active pharmaceutical ingredients,1 solvents for green processing,2 purification processes,3 supercritical fluid applications,4 or novel electrolytes in fuel cells, lubricants, heat transfer fluids, and storage media.5,6 Of particular r 2011 American Chemical Society
interest to the present work is the combination of an alkylimidazolium cation with the bis(trifluoromethylsulfonyl)imide anion [Tf2N] for gas absorption applications. The high solubility exhibited by several gases in these ILs by simple physical absorption, combined with their hydrophobic character versus other common imidazolium ILs with [BF4] and [PF6] anions7 and their low viscosities, make them suitable candidates for gas absorption and other industrial applications. Understanding the origins of the properties of ILs and finding a way to control them by design would provide a wide array of challenges and opportunities to the chemical physics and physical chemistry community, which will further enhance their industrial potential applications. During the last years, many Received: December 28, 2010 Revised: February 21, 2011 Published: March 29, 2011 4387
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The Journal of Physical Chemistry B efforts have been devoted to study different characteristic features, such as the anioncation interactions,8 the nanostructural organization,9,10 and the different conformations of the anion and cation in the liquid phase and crystalline structure.1113 Significant progress has been achieved in the recent years (see the work of Castner Jr. and Wishart14 for an updated summary), but we are still far from a full understanding of the ILs behavior from their components. As the structure and molecular details of the components may play an important role in their final behavior, molecular modeling techniques are excellent tools to be used in this field. As a consequence, several attempts have been done in order to reproduce the main thermodynamic properties of ILs from molecular simulations15 and theoretical approaches16 in recent years. However, the complexity of these molecules limits the predictive capabilities for most of the models available in the literature, while simulations are time-consuming. In the framework of equations of state (EoSs), a number of attempts have been made concerning the modeling of the [Tf2N] imidazolium ionic liquid family; the reader is referred to a recent comprehensive review on the topic.16 Less work has been devoted to modeling the behavior of [Tf2N] alkylimidazolium ILs with other associating systems, like alcohols or water. Among them, we cite the work by Doma nska and Marciniak: they used the NRTL and Wilson equations to correlate the LLE and SLE of [C4-mim][Tf2N] with butanol, hexanol, octanol, and water, among other compounds.17 Nebig et al.18 used the modified UNIFAC to correlate the VLE of ethanol and water (among other compounds) with [C4-mim][Tf2N] too. They also calculated the excess enthalpies and predicted the activity coefficients at infinite dilution. The COSMO-RS model was used by Banarjee et al.19 to predict the VLE of several alkyl-imidazolium-based ILs with the [Tf2N] anion and with acetone, 2-propanol, and water in good agreement with experimental data. Freire et al.2022 used COSMO-RS to study the VLE and LLE of several [Cn-mim][Tf2N] compounds with alcohols and water. Wang et al.23 presented a hetero-SWCF EoS to estimate the vaporliquid equilibrium of several members of the [Tf2N] ILs family in alcohols and water. In their approach, the molecule was divided into two parts: the alkyl group composed of A segments and the ring anion that included B segments. This approach is physically well-sounded and provides very good agreement with experimental data, although three adjustable binary parameters were needed. Yang et al.24 and Xu et al.25 applied lattice-fluid equations that take into account the hydrogen bonding through an exchange energy function and applied them to the description of infinite diluted activity coefficients, vaporliquid and liquidliquid equilibrium thermodynamic properties of several binary mixtures of [Cnmim][Tf2N] and alcohols. Very recently, Tsioptsias et al.26 described the phase behavior of binary systems containing [Tf2N] imidazolium ILs with several alcohols, acetone, and water using the non-random hydrogen-bonding (NRHB) model. According to this methodology, the scaling constants of the ionic liquid were calculated using liquid densities and Hansen’s solubility parameters, while all electrostatic interactions (polar, hydrogen bonding, and ionic) were treated as strong specific interactions. Five parameters were needed to establish the model for pure fluids, although one of them (vsp1) was set to a constant value for each family of compounds. The complex associating mixtures needed two additional parameters considering the cross-associating interactions, plus an adjustable binary interaction kij parameter to correct deviations
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in the mean dispersive energy value. Very good agreement was found for all vaporliquid equilibrium calculations, while some deviations were found for liquidliquid equilibrium. To our knowledge, no modeling work for [Cn-mim][Tf2N] þ associating compound mixtures has been published up to date using the statistical associating fluid theory (SAFT) equation of state (EoS). As the soft-SAFT equation provided good results for mixtures of nonassociating compounds with this family of ILs with a simple model,27 it is worth testing the capability of the approach for associating mixtures including these ILs as well. The SAFT EoS name stands for a family of molecular-based EoSs having in common the way in which the chain and the association terms are treated, based on Wertheim’s first-order thermodynamic perturbation theory (TPT1).28,29 The great success of SAFT-type equations is due to their accuracy in providing reliable predictions for systems and properties based on a set of parameters of a molecular model established on statistical mechanics concepts, with physical meaning and independent of the thermodynamic conditions. In fact, SAFT-type equations of state have already been applied with success to the modeling of ionic liquids and their gas solubility using the tPC-PSAFT,3032 the soft-SAFT,16,27,33 and the HeteroSAFT versions.34,35 The aim of this work is to present a complete thermodynamic characterization for the [Tf2N]- imidazolium family of ILs using refined molecular parameters with the soft-SAFT equation of state and to use them to predict the behavior of associating mixtures without any fitting to mixtures, in a predictive manner. The approach we followed in this work is similar to a previous one,27 but at this time, more experimental information is available and it is used to refine the molecular parameters from our previous calculations. Once the molecular parameters of the pure compounds were obtained by fitting to these experimental data, they were used to examine the density behavior at high pressures, the low volatility values, the surface tension, and the isothermal compressibility of the pure components, in order to validate the model. Calculations of mixtures of these ionic liquids with other associating compounds, such as other ILs, alkanols, and water were performed and the results compared to available experimental data in order to assess their predictive capability, also looking for the strengths and limitations of the methodology. The predictive power of soft-SAFT has already been tested and applied to a vast number of complex experimental systems where associating compounds are involved, such as the solubility of hydrogen chloride in n-alkanes,36 the solubility of gases in ionic liquids16,27,33 and ethylene glycol oligomers,37 the mutual solubilities of alkanes and water,38 and the phase behavior of mixtures of refrigerants.39 The rest of the paper is organized as follows: a brief summary of the soft-SAFT equation and the density gradient theory—used for the surface tensions calculations—as well as a short presentation of the molecular models are described in the next two sections. The results section includes a complete thermodynamic characterization of the imidazolium [Tf2N] family, several examples of calculations of mixtures with other associating compounds, and a discussion about the performance of the equation. Some concluding remarks are provided in the last section.
2. THEORY SAFT40,41 is an approach in which the different contributions to the free energy can be explicitly separated in the thermodynamic potential function. In this sense, it is straightforward to 4388
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obtain the different microscopic contributions and relate them to the macroscopic properties of the fluid. SAFT equations are generally written in terms of the residual Helmholtz energy. On the basis of Wertheim’s TPT1 theory,28,29 the SAFT approach has become a very useful tool for describing the behavior of complex systems and for designing purposes. Several refined versions have appeared since its development,40,41 most of them differing in the term used for the reference fluid. Some of the most popular versions include the soft-SAFT,42 the SAFT-VR,43 the PC-SAFT,44 and the SAFT-γ45 equations. Since the background and the basis of SAFT equations have been widely revised during the past years, only the main ideas relevant for this work are retained here. Three excellent reviews about SAFT46,47 and its possible extensions48 can provide more information to the readers. As stated, all SAFT equations are expressed as a sum of different terms to the residual Helmholtz energy. Each term in the equation accounts for a different microscopic contribution to the total free energy of the system. For a system of associating chain molecules, the equation reads a
res
¼ aa ¼ a id
ref
þa
chain
þa
assoc
ð1Þ
where ares is the residual Helmholtz free energy density of the system and aid is the ideal contribution. The terms aref, achain, and aassoc refer to the residual contributions to the free energy due to the monomermonomer repulsive and attractive (dispersion) interactions, to the formation of chains, and to sitesite intermolecular association, respectively. The reference term in the soft-SAFT EoS42,49 is a LennardJones (LJ) spherical fluid. Differing from other SAFT versions, the repulsive and attractive interactions of the monomers forming the chain are accounted for in a single contribution, the LJ term. The reference term includes two molecular parameters that identify the monomer, the segment diameter, σii = σ, and the dispersive energy between segments, εii/kB = ε/kB. The accurate EoS of Johnson et al.50 is used here to calculate the reference term contribution. The extension of the equation to mixtures is performed by applying the van der Waals one-fluid theory with the modified LorentzBerthelot combining rules: σii þ σ jj ð2Þ σij ¼ ηij 2 εij ¼ ξij ðεii εjj Þ1=2
ð3Þ
where η and ξ are the size and energy binary parameters of the mixture, respectively; a value of unity means the equation is used in a predictive manner for mixtures. The other two terms in the equation, the chain and association contributions, come from Wertheim’s theory and are formally identical in the different versions of SAFT. These terms are directly written for mixtures; hence, no extensions are needed. In the soft-SAFT EoS, the chain term is obtained as a function of the chain length of each compound mi and giiLJ(σii), which is the radial distribution function of a fluid of LJ spheres at density Fmonomer = mF, being m = ∑ni=1mixi the chain length of the conformal fluid: n
achain ¼ FkB T
∑ xi ð1 mi Þ ln gLJii ðσiiÞ i¼1
ð4Þ
where F is the molecular density of the system, kB is the Boltzmann constant, T is the temperature, and xi is the mole fraction of component i. We use here the function fitted to
computer simulation data for giiLJ(σii), as a function of density and temperature, provided by Johnson et al.51 The association contribution for n sites on the molecule i is obtained from the theory of Wertheim,28,29 as in other SAFT approaches. It can be written in general as n XiR Mi assoc R ð5Þ a ¼ FkB T xi ln Xi þ 2 2 R i¼1
∑ ∑
where XRi is the fraction of molecules of component i not bonded at sites of type R and Mi is the number of association sites of type R on component i. XRi is obtained from a solution of the following mass-action equation: 1 XiR ¼ ð6Þ 1 þ Navog F xj Xjβ ΔRβ, ij
∑j ∑β
The specific sitesite function, ΔRβ,ij, can be approximated by42 ij
ΔRβ, ij ¼ kRβ, ij fRβ, ij gLJ
ð7Þ
where KRβ,ij is the sitesite bonding volume of association and HB /kBT) 1] includes the the Mayer f-function fRβ,ij = [exp(εRβ,ij HB sitesite association energy εRβ /kB. Equations 57 have an analytical solution only for some particular cases when dealing with binary mixtures of complex associating systems. We have used a generalized calculation procedure from the work of Tan et al.52 which provides reliable numerical estimates of the fraction of nonbonded associating molecules, as well as their first- and second-order partial derivatives with respect to temperature, density, and mole fractions. The calculation of interfacial properties has been performed by coupling the soft-SAFT equation with the density gradient theory (DGT) originally proposed by van der Waals53,54 and rediscovered by Cahn and Hilliard.55 The Helmholtz free energy density a of the inhomogeneous fluid is expressed as a function of the mole density and its derivatives with respect to the space coordinates. The function a is expanded in a Taylor series about a0(F), the Helmholtz free energy density of the homogeneous fluid at the local density F, and truncated after the second-order term. This series may not converge, but because of the short range of the intermolecular potential, it is assumed to have at least an asymptotic validity.56 In the absence of an external potential, the expression for the Helmholtz energy of the system reads # Z " 1 cij rFi rFj d3 r ð8Þ A¼ a0 ðFÞ þ i j 2
∑∑
where a0(F) is the Helmholtz free energy density of the homogeneous fluid at the local density F and the integration is performed in the entire system volume; Fi is the molar density of component i. The parameter cij = c for the components i and j is known as the influence parameter.5658 In this work, we have assumed a temperature independent value for c, obtained by fitting to interfacial tension experimental data,59 as previously done in other works.16,39,6062 Considering a planar interface and assuming that the density dependence of the influence parameter can be neglected, an expression that relates the interfacial tension to the square of the density gradient can be derived from eq 8:5355 Z
γ¼ 4389
∑i ∑j
¥ ¥
cij
Z ¥ dFi dFj dz ¼ 2 ½a0 ðFÞ dz dz ¥
∑i Fi μ0i p0 dz
ð9Þ
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Figure 1. Sketch of the model used to describe the [Cn-mim][Tf2N] family of ILs within the soft-SAFT approach. See text for details.
where μ0i and p0 are the equilibrium chemical potential and pressure, respectively, and z is the direction perpendicular to the interface. DGT gives accurate results for interfacial properties provided that the original equation for phase equilibria to which it is coupled is also accurate. Further details on the implementation of the theory can be obtained in the works of Mejía and Segura,60 Kahl and Enders,61 and Vilaseca and Vega.62
3. MOLECULAR MODELS One of the key elements for accurate predictions from molecular-based equations of state is the selection of a reliable coarse-grained model that can represent the basic physical features of the compound to be described. Hence, particular care is taken for each case before any calculation is done with softSAFT. We present here a brief description of the soft-SAFT models used for the [Cn-mim][Tf2N] family, as well as for the rest of the compounds used in the present work. In a previous publication,27 a discussion was provided about the molecular model for [Tf2N] imidazolium ionic liquids according to experimental and theoretical studies, showing evidence that anions and cations are coupled together, forming ionic pairs or ionic clusters63,64 in the bulk fluid state. As mentioned in Andreu and Vega’s work,27 the bulky size and the asymmetric charge distribution of molecular ions soften the Coulomb forces and generate highly directional interactions of shorter range, which can be accurately captured with SAFT approaches.65 Recent simulations also suggest that dispersion forces, specific steric interactions, and, possibly, the formation of short-lived ion pairs reduce the ionic character of these fluids.66 The model used here is based on the previous work27 and is intended to build a simplified coarse-grained model for these molecules, trying to keep their main physical features. Following the previous work, [Cn-mim][Tf2N] ILs are modeled as homonuclear chainlike molecules with three associating sites mimicking the strong interactions between the anion and the cation. The number of associating sites is chosen on the basis of the delocalization of the anion electric charge due to the oxygen groups, enhancing the possibility of interaction with the surrounding cations through them. As a consequence, one associating A type site represents the nitrogen atom interactions with the cation, while two B sites represent the delocalized charge due the oxygen molecules on the anion, allowing only AB interactions between different IL molecules. A sketch of the model is presented in Figure 1. For more details, the reader is referred to ref 27. [BF4] and [PF6] imidazolium ionic liquids were modeled in previous work33 as Lennard-Jones chains with one associating site in each molecule. This assumption was based on results obtained
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from molecular dynamics simulations6769 showing the ion pairing of these systems. This model mimics the neutral pairs (anion plus cation) as a single chain molecule with this association site describing the specific interactions because of the charges and the asymmetry. For more details, the reader is referred to ref 33. Methanol and ethanol have been previously modeled with soft-SAFT,49,70 and the same model is used here for consistency. They are modeled as homonuclear chainlike molecules of equal diameter σ and the same dispersive energy ε. The hydroxyl group in alkanols is mimicked by two square-well sites embedded offcenter in one of the LJ segments, with volume of association κRβ,ij HB = κHB and association energy εHB Rβ /kB = ε /kB. One site of e type corresponds to the lone pairs of electrons, and the other site is of type H, corresponding to the hydrogen atom of the hydroxyl group (only eH bonding is allowed). The pair of electrons is considered with only one site under the assumption that the structure of the molecule does not allow two hydrogen atoms to be associated to the same oxygen due to sterical constraints. Following previous work,38 water is modeled as a single spherical Lennard-Jones monomer (mH2O = 1) with a segment diameter, σ, and energy of interaction between the monomers, ε, with four association sites, two e sites corresponding to the lone pairs of electrons of the oxygen, and two H type sites corresponding to the hydrogen atoms (again, only eH bonding is allowed). A discussion about the number of associating sites for water can be found in the literature;71 a four-site model is seen as the most physically sounded, as it preserves the tetrahedral character of the molecular geometry.
4. RESULTS AND DISCUSSION A. Pure Components. As stated, we have recalculated the molecular parameters for the [Tf2N] imidazolium family using new available data. The parametrization was done following the same assumptions as in our previous work:27 the molecular parameters m, σ, and ε/kB were obtained by fitting to selected experimental density data from the literature. The association parameters were transferred from those of 1-alkanols,49 as done for the case of the [BF4] and [PF6] imidazolium ionic liquid families and in ref 27, in order to decrease the degrees of freedom of the system for fitting. These associating values were chosen as a first approximation, and they were kept constant for the whole family, assuming that the alkyl chain length of the cation does not affect the strength of the associating bonds (as previously done for large enough 1-alkanols). The validity of this assumption was checked by comparison with experimental data, providing excellent results, in spite of the simplicity of the assumptions.27 As already mentioned, one of the main issues when modeling ionic liquids is the scattering in the experimental data found in the literature.72 After a detailed revision of literature data, we have used information from a recent contribution of Tariq et al.,73 that includes experimental data for a wide variety of members of the [Tf2N] family, from C2 until C14, in the whole liquid temperature range (before thermal degradation appears) at atmospheric pressure. The choice was based on the extended temperature range investigated (from 293 until 473 K) and also because of their agreement with other published data in the range where other data were available.7477 Results for the temperature density fitting are shown in Figure 2a, while the molecular parameters are provided in Table 2. Experimental data for the first member of the series, [C1-mim][Tf2N], was also included and taken from another publication,74 in order to complete the 4390
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Table 1. Optimized Molecular Parameters for the Compounds Used in This Work, except for the [Tf2N] Family, Together with the References from Which These Parameters Were Taken Mw (g 3 mol1)
Figure 2. Single-phase properties for the [Cn-mim][Tf2N] family. (a) Temperaturedensity diagram for [Cn-mim][Tf2N] from n = 1 (right) to n = 14 (left), except for n = 11 and n = 13, at atmospheric pressure. [C2-mim][Tf2N] to [C8-mim][Tf2N] compounds are used in the molecular parameters fitting procedure, while the rest of the family is predicted with the correlations. The symbols are experimental data from refs 73 and 74. (b) Pressuredensity diagram predictions for [C2mim][Tf2N] (squares), [C4-mim][Tf2N] (circles), [C6-mim][Tf2N] (triangles up), and [C8-mim][Tf2N] (crosses). [C2-mim][Tf2N] and [C8-mim][Tf2N] are evaluated at 293, 333, and 393 K, and the experimental data is taken from the work of Gardas et al.77 [C4-mim][Tf2N] is calculated at 298 and 328 K, while [C6-mim][Tf2N] calculations are done at 298 and 333 K, according to the available experimental data.76 In both figures, solid lines represent the soft-SAFT calculations.
series. As done in previous work, the molecular parameters m, σ, and ε/kB for the [Cn-mim][Tf2N] family are correlated with the molecular weight, while the other two parameters (volume and energy of association) are kept constant for the whole family: m ¼ 0:0056Mw þ 3:8337
ð10Þ 3
mσ3 ¼ 1:9733Mw þ 366:33ðÅ Þ
ð11Þ
mε=kB ¼ 3:3986Mw þ 1043:3ðKÞ
ð12Þ
The correlations were obtained using the molecular parameters from [C2-mim][Tf2N] until [C8-mim][Tf2N], both included. The density AAD% for this series of ILs is 0.09%. None of these parameters are temperature dependent.
m
σ (Å)
ε/kB (K)
εHB/kB (K)
κHB (Å3)
ref
H2O
18.01
1.000 3.154 365.0
2388
2932 38
methanol
22.04
1.491 3.375 220.4
3213
4847 49
ethanol
46.07
1.740 3.635 234.8
3387
2641 49
[C4-mim][PF6]
226.02
4.495 4.029 420.0
3450
2250 33
[C4-mim][BF4]
284.18
4.570 4.146 418.0
3450
2250 33
These correlations enable the equation to predict the thermodynamic behavior of other members of the series, not included in the fitting procedure. We have checked the validity of the correlations predicting the temperaturedensity diagram of [C1-mim][Tf2N], [C9-mim][Tf2N], [C10-mim][Tf2N], [C12mim][Tf2N], and [C14-mim][Tf2N], also shown in Figure 2a. As it can be seen, the agreement with experimental data has a similar degree of accuracy as that for the other members fitted to the data, with a density AAD% of 0.17%. The influence of the pressure on the behavior of some members of the [Tf2N] family has been checked with this approach, and results are presented in Figure 2b. The pressuredensity diagram for [C2 -mim][Tf2N], [C4-mim][Tf2N], [C6-mim][Tf2N], and [C8-mim] [Tf2N] up to a pressure of 60 MPa has been predicted using the previously optimized parameter values. Several isotherms in the range from 293 until 393 K have been plotted and compared to experimental data.76,77 As seen in the figure, the agreement between the data and the predictions with soft-SAFT is very good (average AAD% of 0.28%) with no loss of accuracy when increasing the pressure values. This fact enhances the validity of the model and the approach, adding confidence to the rest of the calculations performed here. We have also checked the validity of the parameters to predict the vapor pressure of some selected ILs of the family for which there is available experimental data.78 Results are presented in Figure 3. As stated in the Introduction, it is well-known that one of the key properties of ionic liquids is their negligible vapor pressure. At the range of application of ionic liquids, vapor pressure values are so close to zero that almost no experimental measurements are available, as the values are of the same order as the accuracy of the equipment. However, Zaitsau et al.78 were able to measure some vapor pressure values for several imidazolium [Tf2N] members by the integral effusion Knudsen method in the temperature range 450500 K, before thermal degradation starts; results are shown in Figure 3. The symbols represent the vapor pressure measurements for [C2-mim][Tf2N], [C4-mim][Tf2N], [C6-mim][Tf2N], and [C8-mim][Tf2N], while the dashed lines correspond to the soft-SAFT predictions using the previous parametrization27 and the solid lines are the predictions with the current set of parameters. We have also included a dotted line corresponding to correlated data for [C2-mim][Tf2N], using eq 3 from the recent work of Lovelock et al.79 The equation was developed calculating several vapor pressures using indirect methods from measurements of the amount of ionic liquid desorbed at certain conditions. Comparisons of soft-SAFT predictions to experimental data show significant deviations. Our calculations are 2 orders of magnitude higher compared to the data of Zaitsau and 1 order of magnitude higher compared to the correlated data of Lovelock et al. However, it should be kept in 4391
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Table 2. Optimized Molecular Parameters for the [Cn-mim][Tf2N] Seriesa Mw (g 3 mol1)
m
σ (Å)
ε/kB (K)
εHB/kB (K)
κHB (Å3)
ref
[C1-mim][Tf2N]
377.29
5.947
3.992
391.08
3450
2250
74
[C2-mim][Tf2N]
391.32
6.023
4.069
394.60
3450
2250
73
[C3-mim][Tf2N]
405.33
6.101
4.143
397.00
3450
2250
73
[C4-mim][Tf2N]
419.34
6.175
4.211
399.40
3450
2250
73
[C5-mim][Tf2N]
433.35
6.247
4.277
401.80
3450
2250
73
[C6-mim][Tf2N]
447.36
6.338
4.334
404.20
3450
2250
73
[C7-mim][Tf2N]
461.45
6.418
4.395
407.60
3450
2250
73
[C8-mim][Tf2N] [C9-mim][Tf2N]
475.48 489.49
6.489 6.575
4.450 4.501
410.00 411.70
3450 3450
2250 2250
73 73
[C10-mim][Tf2N]
503.50
6.653
4.551
414.00
3450
2250
73
[C12-mim][Tf2N]
531.52
6.810
4.645
418.45
3450
2250
73
[C14-mim][Tf2N]
559.54
6.967
4.731
422.69
3450
2250
73
Parameters for the members from n = 2 to n = 8 were obtained by fitting to experimental data. Parameters corresponding to n = 1 and from n = 9 to n = 14 have been obtained using the correlations presented in eqs 1012. See text for details. References correspond to the experimental data used in the fitting.
a
Figure 3. Vapor pressures for [C2-mim][Tf2N] (squares), [C4-mim][Tf2N] (circles), [C6-mim][Tf2N] (triangles up), and [C8-mim][Tf2N] (crosses). The symbols represent the experimental data,78 while the dotted lines stand for the vapor pressure correlated data for [C2mim][Tf2N] from ref 79, the dashed lines are the soft-SAFT calculations with the previous parametrization (see ref 27), and the solid lines are the soft-SAFT predictions with the new molecular parameters.
mind that the measured values are of the range 0.0010.1 Pa and a difference of 1 or 2 orders of magnitude still provides results close to zero. It should also be noted that these are pure predictions, as the vapor pressure information was not used in the fitting procedure. The possibility of fitting the molecular parameters to these data was also considered, but the idea was discharged because of the uncertainty associated with the data. As can be observed in Figure 3, there is not a clear pattern for the experimental data (all the values are similar, but [C4-mim][Tf2N] has apparently a slightly lower vapor pressure than [C6-mim] [Tf2N] and [C2-mim][Tf2N]). Note that the results with the new parameters are closer to the experimental data than the ones originally proposed by Andreu and Vega.27 We have complemented the characterization of the [Tf2N]ionic liquids family with the calculation of the interfacial tension for some of the members for which there is available experimental data. This is a key property for processes in which heat or mass transfer are involved. Figure 4 shows the interfacial tension as a function of temperature for [C2-mim][Tf2N], [C4-mim] [Tf2N], [C6-mim][Tf2N], [C8-mim][Tf2N], and [C10-mim]
[Tf2N]. The so-called influence parameter c has been fitted to these data for each compound, and its values are reported in Table 3. Using this information, a parabolic equation with a molecular weight dependence can be determined. As observed experimentally, the value of the interfacial tension decreases as the alkyl chain length of the cation increases, contrarily to the behavior of other organic compounds.62 Nevertheless, these compounds are exceptional in terms of interfacial phenomena, as they show an almost constant value when the alkyl chain length increases beyond [C7-mim][Tf2N]. Very good agreement between the experimental data59 and the soft-SAFT þ DGT calculations is found in all cases, with an AAD% lower than 0.60% in all cases. More information on the interfacial, critical, and surface behavior of this family and other imidazolium ionic liquid families can be found in a forthcoming contribution.80 A final test to check the robustness of the proposed model involves the calculation of some second-order thermodynamic derivative properties. It has been shown that ionic liquids have an unusual behavior when facing some second-order derivative properties81 and some insight can be obtained from their calculation with molecularbased equations of state. Figure 5 depicts the isothermal compressibility kT for [C2-mim][Tf2N], [C7-mim][Tf2N], and [C8-mim][Tf2N]. The compressibility has been directly calculated from the soft-SAFT equation, through the inverse of the derivative of the pressure with the density of the ionic liquid at constant temperature: DP ¼ F ð13Þ k1 T DF T It is important to remark that no adjustable parameters are used, with these calculations being a prediction from the molecular parameters fitted to temperaturedensity data. In the absence of experimental data, a comparison with the calculated data of Gardas et al.77 using the Tait equation fitted to experimental densities is presented. The Tait equation is an integrated form of an empirical equation representative of the isothermal compressibility behavior. Gardas et al.77 used the following Tait correlation: C F kT ¼ ð14Þ B þ P FðT, P ¼ 0:1MPaÞ where B and C were parameters fitted to density data. A comparison between our predictions and the results found by Gardas et al. 4392
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Figure 4. Interfacial tensions for [C2-mim][Tf2N] (squares), [C4mim][Tf2N] (circles), [C6-mim][Tf2N] (triangles up), [C8-mim][Tf2N] (crosses), and [C10-mim][Tf2N] (diamonds). The symbols are experimental interfacial tension data,59 and the lines represent the soft-SAFT calculations.
Table 3. Optimized Influence Parameter for the Compounds Studied in This Work compound
1019c (J m5 mol2)
[C2-mim]-[Tf2N]
15.932
[C4-mim]-[Tf2N]
17.952
[C6-mim]-[Tf2N]
22.278
[C8-mim]-[Tf2N]
28.037
[C10-mim]-[Tf2N]
35.733
revealed qualitative agreement for all the compounds investigated. The compressibility of [C7-mim][Tf2N] and [C8-mim][Tf2N] was in very good agreement with the correlated data from the Tait equation (compressibility AAD% of 3.57 and 2.67%, respectively), while the predicted values of [C2-mim][Tf2N] were slightly underpredicted, with an AAD% of 10.0%, although they followed the right pattern in the whole range of temperature. B. Binary Mixtures of Ionic Liquids. The binary mixtures of ionic liquids investigated consist of two different ionic liquids with either a common cation or a common anion. From a molecular perspective, the mixtures are conceptually very simple, as the complexity associated with the inclusion of either a non-IL component or two completely different ILs is removed, and a highly ideal behavior would be expected. However, some authors confirm there is experimental evidence that some binary mixtures of ILs are heterogeneous (liquidliquid phase separation may occur) when the cations differ largely.82 Hence, some deviations from ideality may be expected and it is interesting to check the ability of the model and the selected parameters to capture these features. B.1. Influence of the Cation. We have modeled a series of mixtures of imidazolium [Tf2N]- compounds with different alkyl chain lengths in the cation. The molecular parameters of the pure compounds are used to reproduce the behavior of binary mixtures without adding any additional information from them, in a predictive manner. Cross-associating values were calculated using the classical combining LorentzBerthelot rules for the associating energy and volume, with no fitting parameters. As described in section 3, the [Cn-mim][Tf2N] ILs were modeled using three associating sites, one A site representing the nitrogen
Figure 5. Predicted isothermal compressibility kT for [C2-mim][Tf2N] (squares), [C7-mim][Tf2N] (circles), and [C8-mim][Tf2N] (crosses). The symbols are calculated data using the Tait equation fitted to experimental densities,77 and the lines are the soft-SAFT predictions.
atom interactions with the cation and two B sites representing the delocalized charge due to the oxygen molecules on the anion (see Figure 1). Each type of associating site is identically defined, and only AB interactions between different IL molecules are allowed. Then, when calculating cross-associating values with another [Tf2N] IL with one A0 site and two B0 sites, only AB0 and A0 B associations are allowed. Hence, AA0 and BB0 interactions are set to zero. In this particular case, as the associating parameters are kept constant for the whole [Cn-mim][Tf2N] ILs family, the cross-associating energy and volume parameters have the same values as the self-associating parameters. The densitycomposition diagrams of the mixtures [C2-mim][Tf2N], [C4-mim][Tf2N], [C6-mim][Tf2N], and [C8-mim][Tf2N] with [C10-mim][Tf2N] at two temperatures, 298.15 and 318.15 K (from top to bottom), are shown in Figure 6a and b. Very good agreement between the experimental data82 and the softSAFT predictions is observed in all cases, with an average AAD% ranging between 1.27 and 3.12% in the worst case. Deviations from ideality (the experimental data shows some positive excess volume values along the composition axis) are captured by the model without the need of any fitting to mixture data. Similar conclusions can be extracted from Figure 6c, where the densitycomposition diagram of [C2-mim][Tf2N] and [C4-mim][Tf2N] with [C8-mim][Tf2N] is presented. B.2. Influence of the Anion. We present the next results concerning a series of mixtures of ILs changing the anion. In particular, we have checked the influence of the anion by keeping the same cation ([C4-mim]þ) and having mixtures of [C4-mim] [Tf2N] with two different anions: [BF4] and [PF6]. The molecular model developed for these mixtures follows the same patterns described above. Care was taken when considering the cross-associating interactions. [BF4] and [PF6] imidazolium ionic liquids are modeled with one associating site, A0 type, representing the whole cationanion interaction where the charges are involved. We have assumed that this site may interact with the B sites of the [Tf2N] IL but not with the A site, due to sterical effects. In fact, the nature of the sites is positivenegative, and the allowance of the AA0 interaction would be physically feasible, although it is assumed that, in practice, it will not happen for the reason already mentioned. 4393
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Figure 7. Influence of the anion on an imidazolium ionic liquid. Density-composition diagram of the mixtures [C4-mim][Tf2N] þ [C4-mim][BF4] (diamonds) and [C4-mim][Tf2N] þ [C4-mim][PF6] (circles) at two temperatures of 298.15 and 318.15 K (from top to bottom). The symbols represent experimental data,82 while the lines are the soft-SAFT predictions.
Figure 6. Influence of a change in the alkyl chain of the cation on an imidazolium [Tf2N]- ionic liquid. Density-composition diagram of the mixtures (a) [C2-mim][Tf2N] þ [C10-mim][Tf2N] (squares) and [C6mim][Tf2N] þ [C10-mim][Tf2N] (triangles), (b) [C4-mim][Tf2N] þ [C10-mim][Tf2N] (circles) and [C8-mim][Tf2N] þ [C10-mim][Tf2N] (crosses), and (c) [C2-mim][Tf2N] þ [C8-mim][Tf2N] (circles) and [C4-mim][Tf2N] þ [C8-mim][Tf2N] (squares). All graphics are done at two temperatures of 298.15 and 318.15 K (from top to bottom). The symbols represent experimental data,82 while the lines are the soft-SAFT predictions.
The influence of the anion on an imidazolium ionic liquid is presented in Figure 7. A densitycomposition diagram of the mixtures [C4-mim][Tf2N] þ [C4-mim][BF4] and [C4-mim][Tf2N] þ [C4-mim][PF6] at two temperatures of 298.15 and 318.15 K (from top to bottom) is shown. As for the other
mixtures, some positive volume deviations from ideality are observed. These deviations are well captured by the soft-SAFT EoS in a predictive way, being in agreement with the measured experimental data82 with an AAD% below 1.50%. C. Solubility of Methanol and Ethanol in [C4-mim][Tf2N]. The solubility results of short alcohols (methanol and ethanol) in [C4-mim][Tf2N] were also modeled with soft-SAFT. These mixtures are challenging from a modeling perspective, as alcohols are associating molecules with a hydroxyl group that will interact with the ionic liquid. As described before, the hydroxyl group of the alcohols is modeled using two associating sites, one for the hydrogen (H = A0 ) and one for the electron pair of the oxygen (e = B0 ). Here again, we have made several assumptions considering the possible effective cross-associating interactions. We have allowed the oxygen electron pair in the alcohol (site B0 ) to interact with site A of [C4-mim][Tf2N] ionic liquid, while site A0 , representing the hydrogen in the alcohol, was allowed to interact with the two B sites of the ionic liquid. In order to keep the process as predictive and simple as possible, we have still applied the LorentzBerthelot combining rules for the calculation of the cross-associating values, and we have also considered that AB0 = A0 B, having the same association volume and strength. Solubility results of methanol in [C4-mim][Tf2N] are shown in Figure 8a at four different temperatures of 298, 303, 308, and 313 K. Good agreement is found between the soft-SAFT predictions and the measured experimental data83 in the whole range of compositions. The AAD% remained below 5% at all temperatures. The calculated solubility is slightly underpredicted at both temperatures at intermediate compositions, although predictions closely follow the trend of the experimental data. The pressurecomposition diagram of the ethanol þ [C4-mim] [Tf2N] mixture is calculated at the same four temperatures and plotted in Figure 8b. Once again, good agreement is obtained from the soft-SAFT predictions, although the vapor pressures are more underestimated than in the case of methanol (AAD% around 10%). It is important to remark that the value of this work remains on the ability to predict the behavior of complex associating mixtures with this degree of accuracy without any fitting to mixture data. Although quantitative agreement with 4394
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Figure 8. Solubility of alcohols in [C4-mim][Tf2N] at 298 K (squares), 303 K (diamonds), 308 K (circles), and 313 K (triangles): (a) pressurecomposition diagram of a methanol þ [C4-mim][Tf2N] mixture; (b) pressurecomposition diagram of an ethanol þ [C4mim][Tf2N] mixture. The symbols are experimental data,83 while the lines are the soft-SAFT predictions.
Figure 9. Solubility of water in [Cn-mim][Tf2N]: (a) pressure composition diagram of a water þ [C2-mim][Tf2N] mixture at 292.75 K (squares), 303.20 K (diamonds), 323.35 K (circles), and 353.15 K (triangles). Experimental data taken from refs 84 and 85; (b) pressurecomposition diagram of a water þ [C4-mim][Tf2N] mixture at 353.15 K. The symbols are experimental data.85 In both graphics, lines are the soft-SAFT predictions.
experimental mixture data can be obtained with the use of one or two binary parameters, the predictive capability of the model would be lost in this case. D. Solubility of Water in [Cn-mim][Tf2N]. Results concerning the challenging mixture containing water and [Cn-mim][Tf2N] are presented next. In fact, this is the most important binary mixture to model, considering that water is present in most ionic liquids to be used in all industrial processes. It is also important to study the relevance of water impurities in the phase and transport behavior of ILs, as even a small amount of water content may change the properties of the IL. A similar approach to the one taken for alcohols was followed to build the interaction matrix of association. As stated before, water is modeled with four associating sites, two H = A0 sites accounting for the two hydrogen atoms of the molecule and two e = B0 sites accounting for the oxygen electron pair. We assume an interaction between the two hydrogen atoms (A0 sites) of water and the two B sites of the ionic liquid, as well as an interaction between the two electrons (B0 sites) of water and the A site in the ionic liquid. We consider, again, that the volume and strength of association is the same for the AB0 and A0 B interactions. The AA0 and BB0 interactions were set to zero. Following this approach, we have first checked the solubility of water in [C2-mim][Tf2N] at several temperatures, and results are
depicted in Figure 9a. Vaporliquid equilibrium diagrams at 292.75, 303.15, 323.20, and 353.15 K were predicted using the soft-SAFT equation. Comparison with experimental data84,85 shows a reasonable good agreement in the whole range of compositions, with vapor pressure predictions slightly underestimating the vaporliquid equilibrium region. The small vapor pressure values tend to increase the AAD%, which are found to be between 5.67 and 11.46%. A liquidliquid region has been detected over the constant pressure three-phase line. The patterns found here coincide with those found for methanol and ethanol. Similar results can be seen in the pressurecomposition diagram of a water þ [C4-mim][Tf2N] mixture at 353.15 K, shown in Figure 9b. The symbols represent experimental data,85 while the lines are the soft-SAFT predictions, again in very good agreement with the experimental measurements (AAD% of 9.79%). The phase change is found at approximately the same pressure and composition as the available data. These results are striking considering that the cation and anion of the IL are modeled as a single molecule and, also, the particular characteristics of water; they reinforce the robustness of the model and the approach. Finally, we have also checked the strength of the model by calculating the liquidliquid equilibria (LLE) of these 4395
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Figure 10. Liquidliquid equilibria of water þ [Cn-mim][Tf2N] systems. Mutual solubilities of water in [C2-mim][Tf2N] (squares), [C4-mim][Tf2N] (circles), and [C6-mim][Tf2N] (triangles), and vice versa, at atmospheric pressure. Calculations are done with two temperature independent binary parameters η = 0.820 and ξ = 0.922, fitted to the water-rich phase of the H2O þ [C4-mim][Tf2N] mixture and used in a predictive manner for the ionic liquid-rich phase and for the other two mixtures. The experimental data is taken from ref 22, and the solid lines are the soft-SAFT calculations.
aqueous mixtures. Figure 10 depicts the LLE of the previous mixtures at atmospheric pressure, showing the mutual solubilities of water in [C2-mim][Tf2N], [C4-mim][Tf2N], and [C6-mim][Tf2N], and vice versa. Unfortunately, we were unable to obtain reasonable predictions from soft-SAFT when compared to the available experimental data;22 important deviations (not shown here) were obtained in the water-rich phase. The solubility calculations of ionic liquid in water provided lower values than the experimental measurements. Quantitative agreement could be reached by the use of two adjustable binary parameters η = 0.820 and ξ = 0.922 (see eqs 2 and 3). These binary parameters were adjusted to the water-rich phase of the aqueous [C4-mim][Tf2N] mixture and used in a predictive manner for the ionic liquid-rich phase. The same values were transferred to the [C2-mim][Tf2N] and [C6-mim][Tf2N] aqueous mixtures, and very good agreement was achieved in all cases.
5. CONCLUSIONS In the context of the soft-SAFT equation, a new set of molecular parameters for the [Cn-mim][Tf2N] ILs has been obtained using new experimental data over a wide range of temperatures and pressures. The new set has been used to check the robustness of the model for predicting other thermodynamic properties of the pure fluids and also the mixtures behavior. The model provides quantitative agreement for pressuredensity data, and it allows a better prediction of the low vapor pressure values of this ILs family, compared to previous work. Interfacial tensions have also been estimated using the density gradient theory coupled with soft-SAFT, in excellent agreement with experimental data. In addition, the isothermal compressibility was found to be in good agreement with calculations performed through indirect experimental measurements. The model has been used in a predictive manner to check the capability of soft-SAFT in capturing the thermodynamic behavior of several complex associating mixtures. Cross-associating interactions were explicitly considered, and a matrix of interactions was built for each particular case. The behavior of binary
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mixtures of ionic liquids with different cations and anions was found to be in excellent agreement with the available experimental data. The slight deviations from ideality were well captured by the molecular model. Quantitative agreement between predictions and experimental data of mixtures of short-chain alcohols in [Tf2N] ILs was found in the whole range of compositions, with some slight underestimation of the vapor pressure at intermediate compositions. A similar pattern was reproduced when modeling aqueous mixtures of ionic liquids. Vaporliquid equilibrium of water with [Cn-mim][Tf2N] was predicted in very good agreement with experimental data. Concerning liquidliquid equilibria calculations, the prediction without using binary parameters had only qualitative agreement, and two adjustable binary parameters were necessary to quantitatively reproduce this equilibrium. The binary parameters were adjusted to the water-rich phase of the aqueous [C4-mim][Tf2N] mixture and used in a predictive manner for the ionic liquidrich phase. The behavior of the mixtures [C2-mim][Tf2N] and [C6-mim][Tf2N] with water was predicted with these transferred parameters, attaining very good agreement with experimental data. The excellent results obtained in this work reinforce the need to have accurate data, showing that molecular based models can be used to assess the validity of these data. In addition, this work also shows that a simple model (a coarse-grained-type model) in which the physics of the system is kept is good enough to describe the complex behavior of associating mixtures of ionic liquids, without the need of additional parameters that may obscure the real physics of the system. The relative good results obtained should not hide the idea of the limitations of a model where the cation and the anion are not considered in an independent manner. We have seen here that the current model can be extended to the calculation of mixtures with reliability but a step forward should be given in order to better capture and understand the physics of the dissociation phenomena expected in water, and also for developing a fully predictive model for other ionic liquids.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Phone: þ34 935 929 950. Fax: þ34 935 929 951.
’ ACKNOWLEDGMENT F.L. acknowledges a JAE-Doctor fellowship from the Spanish Government. This work has been partially financed by the Spanish government, Ministerio de Ciencia e Innovacion, under projects CTQ2008-05370/PPQ and NANOSELECT and CENIT SOST-CO2 CEN2008-01027 (a Consolider project and CENIT project, respectively, both belonging to the Ingenio 2010 program). Support from Air Products and additional support from the Catalan government, under project 2009SGR-666, is also acknowledged. ’ REFERENCES (1) Dean, P. M.; Turanjanin, M.; Yoshizawa-Fujita, M.; MacFarlane, D. R.; Scott, J. L. Cryst. Growth Des. 2009, 9, 1137. (2) Sun, N.; Rahman, M.; Qin, Y.; Maxim, M. L.; Rodriguez, H.; Rogers, R. D. Green Chem. 2009, 11, 646. (3) Yokozeki, A.; Shiflett, M. B. Appl. Energy 2007, 84, 351. 4396
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