What Determines the Miscibility of Ionic Liquids with Water

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What Determines the Miscibility of Ionic Liquids with Water? Identification of the Underlying Factors to Enable a Straightforward Prediction Marco Kla¨hn,* Claudia Stu¨ber, Abirami Seduraman, and Ping Wu Institute of High Performance Computing, 1 Fusionopolis Way, #16-16, Connexis, Singapore 138632, Republic of Singapore ReceiVed: January 4, 2010; ReVised Manuscript ReceiVed: January 22, 2010

Whether an ionic liquid (IL) is water-miscible or immiscible depends on the particular ions that constitute it. We propose an explanation, based on molecular simulations, how ions determine the miscibility of ILs and suggest a straightforward and computationally inexpensive method to predict the miscibility of arbitrary new ILs. The influence of ions on the solvation of water is analyzed by comparing molecular dynamics simulations of water in 9 different ILs with varying cation and anion constituents. The solvation of water in ILs is found to depend primarily on the electrostatic water-ion interaction strength, which, in turn, is determined mainly by two factors: primarily, by the size of the ions and secondarily by the amount of charge on the ion surface that is coordinated with water. It is demonstrated that large ions lead to weaker interactions with water, due to the involved delocalization of the ion charge. A large charge on the ion surface, which is determined by the chemical structure of the ion, strengthens water-ion interactions. We observe that whenever the interaction strength of water with ions exceeds a certain threshold, an IL becomes water-miscible. On the basis of these findings, a simple equation is derived that estimates the water-ion interaction strength. With this equation it is possible to predict most of the observed water-miscibilities of a sample of 83 ILs correctly. A linear increase of the water saturation concentration with the estimated water-ion interaction strength is observed in waterimmiscible ILs, which can be utilized to predict the water concentration in new ILs. 1. Introduction Ionic liquids (ILs) are molten salts with melting points below 100 °C, and in many cases below room temperature. Typical cations are based on an aromatic heterocyclic compound in the center, e.g., imidazole or guanidinium, to which alkyl chains of varying length are attached. The large size of the cations, the resulting delocalization of their positive charge, and their asymmetric structure impede crystallization, which decreases the melting point. Anions are usually compact and inorganic, and are often fluorides or contain fluoroalkyls. ILs exhibit high viscosity, hampered self-diffusion, and negligible volatility due to strong interionic interactions. ILs are also characterized by a high ion conductivity and thermal and chemical stability. These characteristics, together with the possibility to adjust many properties of ILs by an independent variation of cations and anions, have brought massive attention to ILs. As a result, a broad variety of potential applications have been proposed.1–4 The study of the behavior of ILs in the presence of water is of fundamental interest, since contact with ubiquitous water can be hardly avoided. It has been observed that some ILs are watermiscible, while other ILs are water-immiscible, even though their chemical structures might differ only slightly. Even in the case of immiscibility, ILs are generally hygroscopic and capable of solvating substantial amounts of water from air humidity or other accessible sources of water. The amount of water that water-immiscible ILs solvate at thermal equilibrium has been measured by several groups.5–13 The presence of water in ILs * To whom correspondence should be addressed. Phone: (65) 6419 1468. Fax: (65) 6463 2536. E-mail: [email protected] and wuping@ ihpc.a-star.edu.sg.

modifies the characteristics of ILs in many ways: fundamental properties such as density, viscosity, and heat capacity are substantially affected.14–17 Furthermore, the solvation properties of ILs are profoundly altered, where water can act either as a cosolvent to increase the solubility of polar compounds, e.g., alcohols, or as an antisolvent to prevent the solvation of various gases and nonpolar compounds.13,14,18–21 Moreover, water affects the catalytic abilities of ILs by changing reaction barriers, reaction energies and thus also the selectivity of catalyzed reactions.22 Essentially, given the enormous impact of water on IL properties, the variation of the water concentration in ILs provides an additional powerful parameter, with which ILs can be customized. Also, the solubility of ILs in water is of great importance. ILs are usually considered as a potentially green alternative for various conventional molecular liquids. Since the volatility of ILs is negligible, the risk of air-pollution is minimal. However, the solvation of ions in water, especially when water-miscible ILs are used, might pose the risk of water pollution and needs to be addressed. Indeed, it has been found that the solvation of ions from water-immiscible ILs in water is not negligible, even though their solubility was found to be 1-4 orders of magnitude smaller than the solubility of water in ILs.7,9–13,15,23–27 Once these ions are solvated in water, living organisms might be affected due to the adsorption of the cationic lipophilic alkyl chains to the cell membrane.28,29 The toxicity of various ions to aquatic organisms and human cells has been studied by several groups, where also ion modifications with reduced toxicity were suggested (see refs 10 and 30 and references therein). Knowledge of the mutual solubility of ILs and water is also essential for the use of ILs in the treatment of wastewater, which is

10.1021/jp1000557  2010 American Chemical Society Published on Web 02/10/2010

Determining the Miscibility of Ionic Liquids with Water considered to be an important possible application of ILs. When ILs with suitable solvation properties are used, metal ions as well as organic compounds can be extracted from wastewater.6,31 The ions of water-immiscible ILs need to exhibit a minimal solubility in water to be suitable for this and many other applications. Despite the fundamental importance of the above-mentioned properties of ILs, the connection between the ion constituents of the IL and the solubility of water in ILs has not been understood. However, some observations have been made: it has been pointed out by several authors that the influence of the anions on the water solubility is larger than the influence of the cations (e.g., ref 8). Interactions of water with ions can be observed with IR spectroscopic methods, and it was found that water interactions with anions were stronger than with cations.32 Therefore, the identity of the anion often determines the watermiscibility of an IL, where some anions, e.g., halides, nitrate, and methyl sulfonate, strongly facilitate miscibility while other anions, e.g., PF6 and bis(trifluoromethylsulfonyl)imide (Tf2N), usually prevent the mixing with water. Cations still influence the solubility of water as well, even though to a lesser degree: it has been observed that an elongation of cation alkyl chains reduce the solubility of water (see, e.g., ref 18). Furthermore, it has been found that the central cation group plays a role as well. Pyridinium- and pyrrolidinium-based cations impede the solubility of water, compared to imidazolium-based cations, and the solubility was hampered most, when piperidinium-based cations were used.7 Regarding the solvation of ions in water, it has been found that their solubility depends mostly on their hydrophobicity, where large ions tend to be less soluble in water.33 Molecular simulation techniques have been amply applied by numerous groups to study ILs and a broad variety of their properties. These simulations are also an appropriate tool to study the solvation of water in ILs (for an overview, see, e.g., the recent review from Maginn in ref 34). Mixtures of ILs and water were first investigated computationally by Hanke et al. with molecular dynamics (MD) simulations, where the coordination structure of water with ions was analyzed.35 The arrangement of water molecules in imidazolium-based ILs has been studied in various subsequent works by the same group and others. It has been observed that water molecules strongly associated with anions. Furthermore, water molecules in the IL were found to be isolated, while dimers and clusters of water were observed only at very high water concentrations in watermiscible ILs.36–38 In the case of nanostructured ILs, where long alkyl chains aggregate to form nonpolar domains (see, e.g., ref 39), water was found to fluctuate within the polar domains that are formed by the anions and polar groups of the cations.40,41 IL-water interfaces of miscible and immiscible ILs have been studied by Wipff and co-workers, where ion orientations and electrostatic potentials at the interface were analyzed.40,42,43 The solubility of water in ILs was first studied by Lynden-Bell et al., where the excess chemical potential of water in dimethylimidazolium chloride was determined with thermodynamic integration to be 29 kJ/mol.44 Since the chemical potential has not been measured for this system, a confirmation of this value has not been possible so far. The excess chemical potential of water in 1-butyl-3-methylimidazolium hexafluorophosphate was derived with free energy perturbation (FEP),45 where the resulting 23 kJ/mol somewhat overestimated the measured chemical potential of 16 kJ/mol, according to Anthony et al.23 A more accurate value of 19 kJ/mol for the same system was

J. Phys. Chem. B, Vol. 114, No. 8, 2010 2857 presented in ref 46 by applying Monte Carlo particle insertion as well as expanded ensemble simulations. The value for the chemical potential was derived from their published Henry’s law constants. Molar enthalpy and entropy were calculated in the same work, and a reasonable agreement with measured data was found. The chemical potential was also calculated for 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide with Monte Carlo simulations.47 The saturation concentration of water in this IL was found to be in good agreement with the experiment. In addition, excess molar volumes and enthalpy of mixing, which are quite difficult to derive from simulations, were calculated for a few ILs.36,47,48 The prediction of the water-miscibility or water saturation concentration of new ILs has not been possible so far without employing computationally expensive methods. The possibility of prediction, however, would facilitate the optimization of ILs, considering the virtually infinite possibilities to modify a given IL and the efforts to synthesize a new version. Therefore, the aim of the present work is to study how the choice of ions influences the solvation of water and how the water-miscibility of an IL can be estimated with a minimal computational effort. We start with MD simulations of water-miscible and waterimmiscible ILs that are brought into contact with a water reservoir, to verify if the simulations are able to reproduce the actually observed miscibilities. After confirming the suitability of the computational model, we proceed to analyze the solvation of water in 9 different ILs with varying cations and anions. Through comparison we identify the two main factors that determine the solvation of water in ILs. These findings are used in the final step to derive a simple model that estimates the water-ion interaction strength in arbitrary ILs. These water-ion interaction strengths are correlated with observed water miscibilities of a large sample of ILs. The found correlation suggests that the water-miscibility of new ILs as well as their water saturation concentration in case of immiscibility can be predicted with the proposed model. 2. Methodology 2.1. Simulated ILs. The following ILs, which contain cations based on imidazole and guanidinium, complemented with nitrate (NO3), tetrafluoroborate (BF4) and hexafluorophosphate anions (PF6), were simulated in this work to study the influence of ions on the solvation of water: 1-butyl-3-methylimidazolium paired with nitrate (BMIM-NO3), tetrafluoroborate (BMIM-BF4), and hexafluorophosphate (BMIM-PF6) as well as 1-methoxyethyl-3-methylimidazolium tetrafluoroborate (MOEMIM-BF4), acyclic butylpentamethylguanidinium paired with tetrafluoroborate (BAGUA-BF4) and nitrate (BAGUA-NO3) and cyclic butyltrimethylguanidinium nitrate (BCGUA-NO3). These ILs were complemented with cyclic tetramethylguanidinium nitrate (MCGUA-NO3) and cyclic heptyltrimethylguanidinium nitrate (HCGUA-NO3) to analyze the influence of a varying alkyl chain length on the solvation of water. The structures of the simulated ions are displayed in Figure 1. Only the abbreviations of the ILs will be used in the following as well as the abbreviation CGUA, which designates all ILs that contain cyclic guanidinium groups, i.e., MCGUA, BCGUA, and HCGUA. 2.2. Applied Force Field. An empirical molecular mechanical (MM) force field was used for all MD simulations to calculate the potential energy of the simulated liquids, using the following standard functional form:

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Kla¨hn et al.

Figure 1. Liquid phase partial charges for five of the ILs that were simulated in this work. Partial charges of other simulated ILs are given in Figure 4 of ref 49 and Figure 2 of ref 54. These partial charges reproduce the electrostatic potential of the ions (ESP charges) in the actual liquid phase, derived with a QM/MM approach. For chemically equivalent atoms, only the average charge is given. Partial charges are given as fractions of the elementary charge. bonds MM Epot )

∑ k (l

ij ij

angles

- l0,ij)2+

i,j

∑k

ijk(φijk

- φ0,ijk)2+

i,j,k

improper

∑

kijkl(θijkl - θ0,ijkl)2 +

i,j,k,l torsions

∑

Eijkl(1 + cos(nijklφijkl - δ0,ijkl) +

i,j,k,l

∑ i,j

[( ) ( ) ]

qiqje2 σij + 4εij 4πε0rij rij

12

-

σij rij

6

(1)

The first three terms in eq 1 are harmonic potentials that describe vibrations along bonds, angles, and out-of-plane vibrations, respectively, and are applied to covalently bonded atoms. The fourth term describes the torsion of molecular groups along a covalent bond and comprises together with the first three terms the so-called bonded interactions. These interactions were used whenever atoms were connected via three or less covalent bonds with each other. The fifth term is the electrostatic Coulomb potential and the last term is a short-range LennardJones potential that includes Pauli repulsion and van der Waals interactions. The last two terms comprise the nonbonded interactions and were applied to atom pairs that are connected via 4 or more covalent bonds or that are not connected with each other. In the case of a separation of four bonds, a dihedral potential as well as the nonbonded potentials were used, where the latter were scaled down with a factor of 0.5. A more detailed description of eq 1 and the used symbols is given elsewhere.49 Guanidinium-based cations and nitrate were simulated with the force field that we developed in our previous work.49 For

imidazolium-based cations as well as for tetrafluoroborate and hexafluorophosphate, a force field based on the work from Lopes et al. was used.50 The water solute was represented in the initial IL-water mixing simulations by the TIP3P model51 and the TIP5P model.52,53 The charge distribution of TIP3P water is represented by three point charges at the atom positions. In TIP5P, two dummy atoms are attached to the oxygen atom, to which the charge of the oxygen atom is transferred to mimic the two electron lone pairs. All subsequent MD simulations relied solely on the TIP5P model, which turned out to provide an improved description of IL-water interactions compared to the TIP3P model, as demonstrated in section 3.1. We like to emphasize that, for all simulated ILs, the charge distribution in the actual liquid phase was used to parametrize the Coulomb potential in eq 1. These charge distributions were already published for the guanidinium-based ILs, except for BAGUA-BF4.49,54 For this IL and all ILs that contain imidazole, the liquid phase charge distributions were derived in this work and used instead of the previously published charge distribution of isolated ions. Additionally, the charge distribution of water, when solvated in the simulated ILs, was derived as well and used for the force field parametrization. 2.3. Derivation of Liquid Phase Charge Distributions. In ILs, ions are subjected to interionic electron charge transfer and internal charge polarization. Therefore, the charge distribution of an isolated ion or ion pair, which is the model that is usually exclusively considered in most force field parametrizations, are not necessarily realistic. We demonstrated that energetic and dynamic properties, in contrast to structural properties, are sensitive to charge reorganization in the liquid phase.49,55 We follow in this work the approach that was applied to our previous

Determining the Miscibility of Ionic Liquids with Water IL simulations to find atomic partial charges and derived liquid phase charge distributions by employing a combined quantum mechanical/molecular mechanical approach (QM/MM). A sample of six different ion clusters, containing six coordinated ion pairs each, was described with density functional theory (DFT) to assess charge transfer. Furthermore, a sample of 12 different single cations and anions, respectively, was treated with DFT to determine the intramolecular polarization. All samples were taken from equilibrated structures of the IL that contained 500 ion pairs in total. The B3LYP hybrid functional and 6-31+G(d) basis set were used, as implemented in the Gaussian 03 code.56–58 All the remaining non-DFT ions in the system were treated with the previously described MM force field, using the MD code GROMACS.59 The QM/MM interface, which is a part of GROMACS, allows charge polarization of the embedded DFT fragment by the electrostatic field that is generated by the external MM fragment. The potential energy of these QM/MM systems was minimized. Atomic partial charges for each DFT fragment from the resulting structures were derived. These partial charges were based on the DFT fragment induced electrostatic potential (ESP charges), according to the CHELPG scheme.60 The charge transfer was estimated by calculating the average total ion charge of the ions in the sample of ion clusters. The average charge distribution of the ions in the liquid was then determined by averaging the atomic ESP charges over the sample of single DFT-ions. These charges were scaled with the previously determined average total ion charge, resulting in the average liquid phase charge distribution of the IL. These charge distributions were used to parametrize the Coulomb potential in eq 1. Details of this procedure are described in ref 49. It should be kept in mind that partial charges are in principle not well-defined properties and that the method chosen to calculate them should be based on their intended purpose. For MD simulations, a realistic representation of electrostatic properties is essential, especially close to the van der Waals surface of ions, which covers the most likely distances between ions. The method described above was chosen according to these requirements. The liquid phase charge distribution, i.e., ESP partial charges, of the ILs BAGUA-NO3, MCGUA-NO3, and BCGUA-NO3 are given in ref 49 and of HCGUA-NO3 in ref 54. All other liquid phase charge distributions are shown in Figure 1. It was found that the internal polarization of BMIM cations in liquid phase was small compared to guanidinium-based cations,49 which led to a charge distribution that is similar to previously published vacuum charge distributions.61,62 The average total ion charges in various simulated ILs is summarized in Table 1. Electron charge is transferred from anions to cations. The amount increases in the case of anions in the order of PF6 < BF4 < NO3, which agrees with the expected anion electrophilicities. In the case of cations, the amount of transferred charge increased in the order of BCGUA < BMIM < BAGUA. The strong electrophilicity of BAGUA cations can be explained with the large positive partial charge of around +0.5 e on the central carbon of the guanidinium group, to which the anion charge was found to be transferred.49 BMIM cations were slightly more electrophilic than CGUA cations, which might be due to the more emphasized localization of positive charge on the ring compound. For BMIM-PF6 total ion charges smaller than one were proposed by other groups. A charge transfer of 0.1 e was estimated in ref 61, based on the charge distribution of an isolated ion pair. In that case, however, charge transfer is likely to be exaggerated due to the lack of surrounding counterions

J. Phys. Chem. B, Vol. 114, No. 8, 2010 2859 TABLE 1: Average Total Ion Charge in the Liquid Phase as Derived from QM/MM Simulations, Volume, and Mass Density of Simulated ILs IL

|q|a (e)

V (cm3/mol)

F (g/cm3)

BMIM-NO3 BMIM-BF4 BMIM-PF6 MOEMIM-BF4 BAGUA-NO3 BAGUA-BF4 BAGUA-ClO4 MCGUA-NO3 BCGUA-NO3 HCGUA-NO3 BCGUA-ClO4

0.90 0.95 0.97 0.95 0.88 0.85 0.91 0.92 0.92 0.92 0.94

178.9 196.9 217.5 185.7 209.9 230.7 221.6f 149.6 190.3 232.1 203.6f

1.13 (1.16b) 1.15 (1.20c) 1.31 (1.36d) 1.23 1.18 (1.17e) 1.18 1.29f (1.28e) 1.36 (1.36e) 1.29 (1.26e) 1.24 1.39f (1.37e)

a Same average total ion charges were assumed for ILs that differ only by the length of the cation alkyl chain. b Taken from ref 82. c Taken from ref 16. d Taken from ref 83. e Taken from ref 69. f Taken from ref 49.

that could balance the strong pull of charge that is exerted by a single counterion (see also ref 63). A charge transfer of 0.1 and 0.2 e in this IL was later used in simulations to ensure waterimmiscibility of the IL and to fit self-diffusion coefficients to measured values, respectively.42,43,64 Such an adjustment of the total ion charge to compensate inevitable inaccuracies of MM force fields can be advantageous in many cases. However, such a large charge transfer was not actually observed for this IL in the present work. The charge transfer in some other ILs was quite substantial on the other hand, with values up to 0.15 e for BAGUA-BF4 for instance, which justifies our approach to derive charge distributions from the liquid phase. In any event, the derived partial charges together with the other force field parameters were used in simulations to determine IL densities, which are given in Table 1 together with their volume. The calculated densities of guanidinium-based ILs are in good agreement with measured densities, and they are in satisfactory agreement for ILs that contain BMIM cations. The internal polarization of single water molecules solvated in different ILs was derived with the QM/MM approach described above. Water molecules turned out to be more polarized in ILs than in water, due to strong interactions with directly coordinated ions. The variation of the polarization in different ILs is very small. Dipole moments of water ranged from 2.50 D in BAGUA-BF4 to 2.59 D in BMIM-NO3, compared to 2.35 D in TIP3P and 2.29 D in TIP5P. These charge distributions of solvated water were used to parametrize the Coulomb potential in eq 1. 2.4. Specification of MD Simulations. 2.4.1. Mixing of ILs with Water. All MD simulations, except those for the calculation of chemical potentials, were performed with the GROMACS software package.59 For IL-water mixing simulations, a cubic box with 500 ion pairs of BMIM-PF6, BMIM-BF4, and BMIMNO3, respectively, were placed next to a similarly sized box that was filled with 5435 water molecules. These systems contained in total around 30 000 atoms. All three mixing simulations were set up twice: one that contained TIP3P water and another that contained TIP5P water. Full periodic boundary conditions were used, thereby generating two IL-water interfaces, where IL and water were in direct contact with each other. Figure 2a illustrates the setup of these simulations. Furthermore, all hydrogen atoms were treated explicitly, and no degrees of freedom were constrained during the simulations, except those of the dummy atoms in the TIP5P model. Nonbonded interactions were calculated explicitly up to 15 Å, beyond which fast

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Figure 2. van der Waals representation of cations (blue), anions (green) and water molecules (red) of IL-water mixing simulations. ILs are separated from water by two interfaces, because of periodic boundary conditions, that are located in the figure to the left and right of the IL phase. Hydrogen atoms are not displayed for clarity. (a) Initialization of the MD simulation with a complete phase separation of BMIM-PF6 on the left-hand side and water on the right-hand side. (b) Equilibrated structure of water-immiscible BMIM-PF6 after 6 ns of MD simulation at room temperature. Ions are transparent to highlight the position of water in the IL-rich phase. (c) Structure of water-miscible BMIM-BF4 after 6 ns of MD simulation, where the mixing of the two phases was still in progress. MD simulations reproduced the expected watermiscibilities of ILs.

particle-mesh Ewald electrostatics and dispersion energy corrections were used instead.65–67 These simulations were performed in the isothermal-isobaric (NPT) ensemble, where temperature and pressure were adjusted with a Berendsen thermostat.68 The coupling time constants for thermostat and barostat were 0.1 and 1 ps, respectively. Compressibility and target pressure of the barostat were set to 4.5 × 10-5 bar-1 and 1 bar, respectively. A center of mass translation during the simulation was prevented by applying correcting forces. The integration step size of all MD simulations was 1 fs. Atom positions in the IL and water phases were initialized according to equilibrated structures of the pure liquids. The derivation of these equilibrated structures is explained in the next section. Close contacts at the IL-water interfaces were removed by minimizing the potential energy of the system with a steepest gradient method. The resulting structures were used to initialize MD simulations of 3 ns length, at a temperature of 300 K. MD simulations of systems that contained TIP5P water were continued for another 3 ns, resulting in total trajectory lengths of 6 ns. 2.4.2. Water SolWated in ILs Close to Infinite Dilution. In the first step 500 ion pairs of BMIM-NO3, BMIM-BF4, BMIM-

Kla¨hn et al. PF6, MOEMIM-BF4, BAGUA-BF4, BAGUA-NO3, BCGUANO3, MCGUA-NO3, and HCGUA-NO3 were simulated. The initial atom positions were generated by filling a cubic box with copies of one ion pair. The dimension of the box was chosen so that the IL is diluted by about a factor of 10, compared to measured densities. Close contacts between atoms were removed by potential energy minimizations. MD simulations in the NPT ensemble were started from the resulting structures, using the same simulation settings as described above. During the first 400 ps the temperature of the systems was linearly increased to 600 K, after which the simulations were continued at this temperature for another 400 ps. Finally, the temperature was decreased linearly to the target temperature of 300 K during the next 200 ps. This initial heating as well as the initially low density of the ILs enabled a strong diffusion of the ions during the simulations. Therefore, the risk that the comparably immobile IL ions got trapped in local high energy minima of the potential energy surface was substantially mitigated. Subsequently, the MD simulations were continued for 2 ns at 300 K, where the last 500 ps were used for the data analysis. BAGUANO3 and MCGUA-NO3 exhibit melting points above room temperature and therefore represent in the simulations essentially supercooled liquids.69 These nine pure ILs served as reference systems for simulations of ILs that contained water. In these equilibrated structures of pure IL, 10 ion pairs were replaced with 10 water molecules, respectively, to study the solvation of water. The resulting water concentration corresponds to a mole fraction of water of 0.02, for which interactions between water molecules could be neglected. All water molecules were described with the TIP5P model. These IL-water systems were equilibrated at 300 K for 1.5 ns, in which the last 500 ps were used for analysis. 2.4.3. EWaluation of Excess Chemical Potentials of Water in ILs. Excess chemical potentials of water in ILs were derived with the ENZYMIX module of the MD software MOLARIS, developed by Warshel and co-workers, which applies the FEP method.70 In this approach the interaction of the water solute with the IL solvent is adiabatically switched off by slowly reducing the involved Coulomb and Lennard-Jones pair potentials to zero. The following potential energy, Ei, was used for MD simulations:

Ei ) (1 - λi)EIL+wat + λiEIL

(2)

The potential energy of the IL-water system, EIL+wat, is slowly transformed into the potential energy of the pure IL, EIL, through a coupling parameter, λi. This coupling parameter is stepwise increased from 0 to 1 during the MD simulation, thereby making the water molecule slowly invisible to the rest of the system. When the potential energy is changed from Ei-1 to Ei, the excess chemical potential difference between the two states, ∆µex,i, is given by the Zwanzig equation:

∆µex,i ) -kBT ln〈e-(Ei-Ei-1)/kBT)〉MD with Ei

(3)

In eq 3, T is the temperature and kB is the Boltzmann constant. Equation 3 involves an average over the structure sample that is generated with the MD simulation at step i, using the potential Ei. Equation 3 is only valid for small adiabatic changes of the energy. After the simulation, all small chemical potential changes are added to yield the total excess chemical potential, µex, of the solute:

Determining the Miscibility of Ionic Liquids with Water

µex )

∑ ∆µex,i

J. Phys. Chem. B, Vol. 114, No. 8, 2010 2861

(4)

i

The IL-water simulation setups described in the previous section were used to initialize the FEP calculations. The force fields used in MOLARIS and GROMACS were identical. A cutoff distance for nonbonded interactions of 15 Å was used as well as an integration step size of 1 fs. MD simulations were performed in the isothermal-isochoric (NVT) ensemble, at a temperature of 300 K. The volume of the systems was fixed to the previously determined volume according to the simulations in the NPT ensemble. λ was changed from 0 to 1 in 30 steps, where at each step an MD simulation of 10 ps length was performed, resulting in a total MD simulation length of 300 ps. Some of the results were compared with longer MD simulations that used 30 ps per λ step instead; however, no significant differences were found. Eventually, µex was averaged over the 10 water molecules in the IL to yield the average excess chemical potential of water in all nine IL solvents, respectively. 3. Results and Discussion 3.1. Simulations of IL-Water Mixing. Before water solvation in ILs is analyzed, it is essential to verify that the used force fields provide a realistic representation of water, the ILs, and their mixtures. It has already been demonstrated that the TIP3P and TIP5P models correctly reproduce many properties of pure water. Furthermore, we verified in our previous work the quality of the force fields for pure ILs.49,54,55 Left to scrutinize in this work were the interactions of ILs with water. Therefore, water-immiscible BMIM-PF6 as well as water-miscible BMIMBF4 and BMIM-NO3, were brought into contact with water at room temperature. These ILs present sensitive test cases, since BMIM-PF6, even though immiscible, is highly hygroscopic, while BMIM-BF4 becomes water-immiscible already at 4 °C.71 It can be said that these two ILs mark the line that separates miscible from immiscible ILs. The IL-water miscibilities were investigated with MD simulations using the force fields described above. The initial configuration of the simulation, where IL and water were completely separated, is illustrated in Figure 2a. These mixing simulations were performed twice, with water represented by the TIP3P and TIP5P models, respectively. For the TIP3P model, an exaggeration of the water-ion interactions was observed that led to a mixing of BMIM-PF6 with water, which did not occur when TIP5P water was used instead. The same problem with TIP3P water has been observed previously by Wipff and co-workers.42,43 The densities of water in the two ILs BMIM-PF6 and BMIM-BF4 after 3 ns MD simulations are shown in Figure 3. Even though the IL-water systems did not equilibrate in 3 ns, it is apparent that the TIP3P water concentration in the ILs is higher than the corresponding TIP5P water concentration. The stronger interaction of TIP3P water with ions was probably caused by the larger partial charges on the TIP3P water atoms, compared to TIP5P water. Furthermore, we determined the excess chemical potential of TIP3P water molecules in TIP3P water to be -31.4 kJ/mol. For TIP5P water a value of -25.2 kJ/mol was derived, which is close to the measured value of -26.4 kJ/mol.72 For these reasons, the use of TIP3P water was abandoned in favor of the TIP5P model in all subsequent simulations. The simulations with TIP5P water were continued for another 3 ns, and the resulting water densities are shown in Figure 4. The water concentration in the IL-rich phase, xwat, is shown as a function of time in Figure 5. The IL-water interface regions,

Figure 3. Density profiles of TIP3P-water and TIP5P-water in mixtures of IL and water, after 3 ns of MD simulation at room temperature. The x-axis is perpendicular to the IL-water interfaces, which are centered at around x ) 0 nm and x ) 5.5 nm, with the IL-rich phase at x < 5.5 nm and the water-rich phase at x > 5.5 nm. The corresponding atomic structures are shown in Figure 2. More TIP3P-water than TIP5P-water diffused into the IL-rich phases, and water-immiscible BMIM-PF6 became water-miscible in the simulations when TIP3P water was used. The IL-water systems were after 3 ns simulations not equilibrated, and additional water continued to diffuse into the IL phase.

Figure 4. Density profiles of water (TIP5P) in mixtures of water and water-immiscible BMIM-PF6 and water-miscible BMIM-BF4 and BMIM-NO3, after 6 ns of MD simulation at room temperature. The x-axis is perpendicular to the IL-water interfaces, which are centered at around x ) 0 nm and x ) 5.5 nm, with the IL-rich phase at x < 5.5 nm and the water-rich phase at x > 5.5 nm. The corresponding atomic structures are shown in Figure 2. Both water-miscible ILs were not equilibrated after 6 ns and mixing was still in progress. Phase separation in the equilibrated water-BMIM-PF6 system remained stable throughout the simulation.

centered around x ) 0 and 5.5 nm, were excluded for the calculation of xwat. The width of this interface region was set to 2 nm, according to the water density profile in BMIM-PF6, thereby delimiting the IL-rich phase at x ) 1 and 4.5 nm. The interface region was well distinguishable from the IL-rich phase in the water-BMIM-PF6 system, as can be seen in Figure 4 (see also Figure 2b). A detailed characterization of this interface is given elsewhere.42 In contrast, the interface regions widened during the other two simulations until they almost coalesced in the center of the originally IL-rich phase, which can be seen in Figures 4 and 2c. Therefore, the definition of the interface region width was somewhat arbitrary for the BMIM-BF4 and BMIMNO3 systems. However, the qualitative progression of xwat in these cases, with the IL-rich phase defined as described above, is still instructive. A breakdown of the potential energy changes

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Figure 5. Change of water concentration in water-immiscible BMIMPF6 and water-miscible BMIM-BF4 and BMIM-NO3, during 6 ns of MD simulation. Concentrations are given as mole fractions of water. The water concentration converged to xwat ) 0.2 in BMIM-PF6, which is close to the measured value of 0.24. The water concentration in the other two nonequilibrated systems did not converge after 6 ns, indicating that mixing is still in progress.

due to water-IL mixing is shown and described in Figure S1, Supporting Information. The progression of xwat, according to Figure 5, suggests that the MD simulation of 6 ns length was insufficient to equilibrate the BMIM-BF4 and BMIM-NO3 systems and that, at the end of the simulation, mixing with water was still in progress. While BMIM-BF4 mixed readily with water at the beginning of the simulation, the influx of water into BMIMNO3 was initially slow but eventually proceeded to a very high influx rate toward the end of the simulation. The influx of water into BMIM-NO3 might have been initially impeded by the strong counterion attraction in this IL (see also Figure S1). On the contrary, the water-BMIM-PF6 system equilibrated after about 4 ns of MD simulation. This is indicated by the convergence of xwat toward a water saturation concentration in the IL-rich phase of xwat ) 0.2 mol fractions of water. Measured values of xwat in BMIM-PF6 range from 0.16 to 0.30, where an average value of xwa ) 0.24 can be derived from these measurements, which agrees well with the value derived from our simulation.7,43 Despite of the chemical similarities of the three simulated ILs that involve identical cations, simulations correctly reproduced the water-immiscibility of BMIM-PF6 and its water saturation concentration. Furthermore, the simulations also suggest the miscibility of BMIM-BF4 and BMIM-NO3 with water, in accordance with measurements. These results demonstrate that the applied force fields are capable of providing a realistic model to describe IL-water interactions. Generally, miscibility and water saturation concentration in ILs depend on the free energy changes that are involved when water is transferred from the water-phase into the IL. By reproducing the measured excess chemical potential of water in BMIM-PF6, as demonstrated in the next section, the quality of the force field was confirmed additionally. With these encouraging results in mind, we confidently proceeded to analyze the interactions of water with various different ILs to identify the factors that determine water-miscibility of ILs. 3.2. Analysis of Water-IL Interactions. The energetics of single water molecules solvated in nine different ILs, close to the limit of infinite dilution, was analyzed. The average water-ion interaction strength in these ILs, i.e., the sum of

Kla¨hn et al.

Figure 6. Interaction energies of water with cations, Ewat-cat, and anions, Ewat-an, as well as the excess chemical potential, µex, of water in nine different simulated ILs. The numbers at the end of the upper bars are the total interaction energies of water with the IL, i.e., Ewat-cat + Ewat-an, respectively. The abbreviations of the ILs are explained in section 2.1. Values of µex follow the trend of Ewat-cat + Ewat-an.

Coulomb and van der Waals interactions between water and surrounding ions, are shown in Figure 6. The corresponding potential energy terms were derived from MD simulations of the ILs, in which single water molecules were solvated, as described in section 2.4.2. Furthermore, the average excess chemical potential of water in ILs, µex, was derived. The method described in section 2.4.3 was applied to evaluate these chemical potentials, which also takes into account the reorganization of the IL-solvent upon solvation of water as well as entropic effects. These results are also displayed in Figure 6. The obtained interaction energies of water with anions were a factor of 1.4-3.8 larger than with cations, which is in line with numerous previous observations. The water-anion interaction strength increased in the order of PF6 < BF4 < NO3, which is consistent with the findings from the mixing simulations (see also Figure S1) as well as with IR measurements in which anion-water interaction strengths were measured.73 The water-cation interaction strength increased in the order of AGUA < CGUA < MOEMIM < BMIM and HCGUA < BCGUA < MCGUA. The latter relation means that the water-cation interaction strength diminished with increasing alkyl chain length of the cation, which is confirmed by measurements as well.18 The interaction energy of water with a particular ion was barely influenced by the identity of the counterions. Values of the calculated chemical potentials of water varied from -17 kJ/mol in BAGUA-BF4 to -26 kJ/mol in MCGUANO3 and follow the trend of the water-ion interaction energies, Ewat–IL ) Ewat-cat + Ewat-an. Regarding the three ILs that involve BMIM, water exhibits a smaller chemical potential, |µex|, in water-immiscible BMIM-PF6 than in the other two watermiscible ILs, as expected. For BMIM-NO3, which is known to mix with water more readily than BMIM-BF4, the largest chemical potential was derived. A comparison with experimental data is possible in the case of BMIM-PF6, for which Henry’s law constant of water vapor, H, was measured by Anthony et al.23 H can be converted to µex, in the limit of infinite dilution of the solute, via H ) FRTe µex/RT, where F is the density of the

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TABLE 2: 2. McGowan Volume of Cations and Anions, and Number of Water-Cation and Water-Anion Close Contacts in Simulated ILs IL

Vcat (cm3/mol)

Van (cm3/mol)

Nwat-cat

Nwat-an

BMIM-NO3 MCGUA-NO3 BCGUA-NO3 HCGUA-NO3 BMIM-BF4 MOEMIM-BF4 BAGUA-NO3 BMIM-PF6 BAGUA-BF4

125.9 118.0 160.3 202.6 125.9 117.7 179.6 125.9 179.6

25.8 25.8 25.8 25.8 46.9 46.9 25.8 48.3 46.9

3.9 4.9 4.8 5.0 3.7 3.4 5.2 3.2 4.5

1.7 1.5 1.3 1.4 1.8 1.9 1.4 2.2 1.6

solvent. The resulting measured chemical potential is -16.2 kJ/ mol. We obtained in our calculations a value of µex ) -18.3 kJ/mol in this IL, which is in satisfactory agreement with the measurement. Furthermore, the Henry’s law constants of two octyl-substituted imidazolium-based ILs, namely C8MIM-BF4 and C8MIM-PF6, were measured as well in the same work.23 After conversion to |µex| it can be seen that in C8MIM-PF6 the chemical potential of water was 2.9 kJ/mol lower than in C8MIM-BF4. This value can be compared to the chemical potential difference of water in our simulated systems BMIMPF6 and BMIM-BF4. The small contribution of the alkyl chains to µex should basically cancel out in the chemical potential difference. The calculated value of ∆µex ) 2.1 kJ/mol compares well with the measured value and provides a further confirmation of the applied computational approach. When water molecules are solvated by the IL, the formation of solute cages in the solvent requires energy that is made available by favorable interactions of water with surrounding ions. Both energy contributions, as well as entropic changes of the solute and solvent, were taken into account when the excess chemical potentials were evaluated. The small values of µex, compared to values of Ewat-IL, indicate that a substantial amount of energy was used to form the water-accommodating cavities in ILs. Considering the strong electrostatic attraction of counterions in ILs, this is not surprising. Also a considerable entropy penalty due to the reduced mobility of water, caused by a tight coordination to ions, might be involved. In any event, despite of the substantial cavity formation energy, the qualitative trend of µex is basically determined by the largest of its contributions, Ewat-IL, according to the results in Figure 6. That, in turn, means that the interaction strength of water with ions is the main factor that determines the solubility of water in ILs and thereby water-IL miscibility. This hypothesis will be confirmed later in section 3.4.2 with the help of experimental data. A computational analysis of the cage formation energy and entropic effects, and how both are influenced by particular ions, deserve special attention, but that is beyond the scope of the present work. An inspection of the qualitative trend of Ewat-IL implies a correlation with the ion size. In the following we use the McGowan method rather than a more sophisticated computational method to estimate ion volumes, because its simplicity will ease the application of the empirical equation that will be derived in section 3.4.1.74 McGowan volumes are simply calculated by adding the element specific volumes of all atoms in the compound, which are listed in ref 74, and by subsequently subtracting 6.56 cm3/mol for each present covalent bond, while bond orders are ignored. This method was originally developed for neutral molecules; however, its application can be extended to ions, where volume changes due to additional or missing electrons are taken into account.75 Here, cations were treated

Figure 7. Comparison of the interaction strength of water with ions, Ewat-cat and Ewat-an, in nine different ILs, with the size of the involved ions, Vcat and Van. Ion volumes were estimated with the McGowan method.74 The influence of the counterion on the water-ion interaction strength modified the values of Ewat-ion slightly, therefore some ions are represented by more than one data point in the plot. Generally, the interaction strength increases with the reciprocal ion volume.

in this particular case as neutral molecules, since the volume reduction due to the missing electron is negligible compared to the total cation size. The volumes of the smaller anions were taken from ref 75. The resulting McGowan volumes for cations and anions are listed in Table 2. The water-ion interaction energies, Ewat-cat and Ewat-an, are compared with the corresponding ion volumes, Vcat and Van, in Figure 7. A correlation of ion volume and interaction strength with water is apparent, i.e., water favors interactions with small ions. The strongest interaction energies with values between 40 and 43 kJ/mol were obtained for the smallest ion, NO3. These values decreased substantially to values between 28 and 33 kJ/ mol in the case of BF4 and PF6. Interactions of water with cations, generally weaker than with anions, were strongest when small BMIM and MOEMIM cations were involved, with values between 16 and 19 kJ/mol. The interaction with the larger cation CGUA decreased from 14 to 11 kJ/mol due to an elongation of the alkyl chain. Finally, the weakest interaction was obtained when BAGUA was involved, the largest ion in the simulations, with values between 9 and 11 kJ/mol. The stronger interaction with small ions can be understood readily by considering the dominant Coulomb interactions between a water molecule and an ion. These Coulomb interactions are weak, when the average distance between the dipole of the water and the ion charge is increased, which is the case for large ions. In other words, water prefers to interact with ions that provide a localized charge that can be brought into close contact with the water molecule. According to Figure 7, the ion size seems to be the prime factor that determines the interaction strength with water. A closer look, however, reveals that another important factor is involved as well. In BMIM-BF4 and MOEMIM-BF4, for instance, the interaction of water with BF4 was 4-5 kJ/mol stronger than with PF6 in BMIM-PF6, even though both anions are of similar size. That the interaction of water is indeed stronger with BF4 than with PF6 has been confirmed in measurements before.76 Inspecting the contributions to Ewat-an, according to the simulations, the stronger interaction of water with BF4 was simply caused by the larger partial charges on the fluorine atoms. These atoms exhibit an atomic partial charge of -0.5 e each, compared to -0.4 e in the case of PF6, as can

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Kla¨hn et al. The number of close contacts between ions and water were quantified with radial distribution functions (RDFs) that were derived from the MD simulations. The RDFs for pairs of water oxygen atoms and cation hydrogen atoms, gwat-cat, as well as for pairs of water hydrogen atoms and anion oxygen/fluorine atoms, gwat-an, were calculated. From these RDFs, the number of close contacts, Nwat-cat and Nwat-an, can be derived as a function of the maximum distance up to which atom pairs are still considered to form a close contact, rmax, using the following equation:

Nwat-ion ) 4πFion Figure 8. Two main factors that determine the interaction strength of water with ions. (a) Water-ion interaction strength is primarily determined by the ion size: Water interaction with small ions is stronger than with large ions, because the charge is more localized, i.e., the average distance between the electric water dipole and the ion monopole is small. (b) Water-ion interaction strength is secondarily determined by the surface charge of the ion: Water interacts favorably with ions that exhibit large surface charges, i.e., large partial charges on atoms that are in direct contact with water, than with ions that exhibit small surface charges. The surface charge of an ion is determined by its chemical structure.

be seen in Figure 1. These large partial charges on the surface of BF4 led to stronger interactions with the water dipole. Since the ion sizes are similar in this case, the different watermiscibilities of these ILs, in fact, can be attributed to the different anion surface charges. In this context, we also like to remind that all partial charges that were used in the simulations of this work were based on the IL charge distribution of the actual liquid phase. The two main factors that determine water-ion interaction strength are summarized in Figure 8. The findings of this section also explain why water preferably interacts with anions in ILs. In most ILs that have been synthesized, anions are substantially smaller than cations. Furthermore, anions exhibit larger surface charges than cations. While on fluorine and oxygen atoms of anions typical surface charges vary between -0.4 and -0.8 e, the surface charges on cation hydrogen atoms vary between 0.1 and 0.2 e. Both, the small size and the large surface charge, result in strong attraction between water and anions. Therefore, it is plausible that the water-miscibility of ILs is determined more by anions than cations, assuming that the solubility of water is mainly determined by the strength of water-ion interactions. The findings of this section also constitute the basis with which the approach to predict water-miscibility of ILs will be derived in section 3.4. Before we turn to this approach, the alternative notion that the internal IL structure could determine water solubility will be scrutinized in the next section. 3.3. Impact of the IL Structure on the Solvation of Water. 3.3.1. Influence of the Coordination Structure of Water and Ions. It was demonstrated in the last section that the magnitude of the ion surface charge, together with the ion size, determines the water-ion interaction strength. The influence of the size of the ion surface area that is in direct contact with water was not considered so far. The size of this surface area is proportional to the number of hydrogen bonds between the ion and water. Hydrogen bonds basically connect water oxygen atoms and cation hydrogen atoms as well as water hydrogen atoms and anion hydrogen acceptor atoms, i.e., oxygen and fluorine atoms. Since the covalent contribution to these hydrogen bonds is very small in ILs, compared to electrostatic attraction, we prefer to use in the following the more general expression “close contact” instead of hydrogen bond.

∫0r

max

gwat-ion(r)r2dr

(5)

Here, Fion designates the cation hydrogen atom density or anion oxygen/fluorine atom density, respectively. The resulting values for N, in the case of rmax ) 3 Å, are given in Table 2. A comparison of values for Nwat-cat and Nwat-an with the corresponding water-ion interaction strengths, Ewat-cat and Ewat-an in Figure 6, shows that a large number of water-ion close contacts is related to weak water-ion interactions. For instance, in BMIM-NO3, Nwat-cat and Ewat-cat are 3.9 and -19 kJ/mol, respectively, while in BAGUA-NO3 Nwat-cat and Ewat-cat are 5.2 and -9 kJ/mol. This seemingly surprising result, in which a larger number of water-cation close contacts led to weaker interactions, can be simply explained by the larger number of hydrogen atoms in BAGUA cations. This cation contains 24 hydrogen atoms that can coordinate with anion oxygen atoms, compared to only 15 hydrogen atoms in BMIM. The larger number of hydrogen atoms translates to a larger hydrogen atom density in BAGUA-NO3, which increases the number of water-cation close contacts. A larger number of hydrogen atoms per cation, on the other hand, also corresponds to a larger cation size, which leads to weaker interactions with water, as explained in the previous section. That means that it was indeed the cation size and not the number of close contacts that determined the interaction strength with water. The findings for other cations as well as for anions were similar. Also interesting is a comparison of the interaction strength of water with anions in BMIM-BF4 and in BMIM-PF6. In the case of BMIM-BF4, Nwat-an and Ewat-an are 1.8 and -32 kJ/mol, respectively, while in the case of BMIM-PF6, Nwat-an and Ewat-an are 2.2 and -28 kJ/mol. The difference in Ewat-an is comparably small, because of the similar anion volume. The smaller partial charge on the PF6 fluorine atoms resulted in a somewhat weaker interaction with water, as explained before. This was not compensated by the larger number of close contacts. Therefore, the ion volume and surface charge are by far more important in determining the water-ion interaction strength than the structural details of the particular water-ion coordination that is realized in the IL. 3.3.2. Influence of Preformed CaWities. It has been suggested that interstices or preformed cavities in the IL solvent could facilitate the accommodation of small molecules and thereby improve the solvation of water.45 For instance, the solubility of water in BMIM-PF6 could be lower than in BMIM-BF4, because the slightly larger PF6 anions would fill more interstices in the IL. Preformed cavities in ILs have indeed already been observed in simulations; however, their influence on IL properties remains unclear.55,77 Preformed cavities that are sufficiently large to accommodate water were located and quantified in the three ILs BMIM-PF6, BMIM-BF4, and BMIM-NO3 to scrutinize their relevance for the solvation of water. A sample of 10 structures from MD simulations of the pure ILs was generated for each IL, respectively. Subsequently, the simulation boxes that contained

Determining the Miscibility of Ionic Liquids with Water these structures were filled with small adjoining cubes of 2 Å edge size. All cubes that overlapped with at least one of the atoms in the IL, which were represented by spheres with atom-specific van der Waals radii, were removed. The volume of the remaining cubes was added to give the percentage of unoccupied space in the ILs. Hence, small isolated cavities with a volume below 8 Å3 were excluded. Since cavities of that size are too small to be occupied by water, they are not relevant for this analysis. The largest amount of unoccupied space was obtained for BMIM-PF6, where 1.05% of the total volume remained unoccupied, followed by BMIM-BF4 with a value of 0.80% and BMIM-NO3, with a value of 0.45%. With a water volume of 18 cm3/mol, these preformed cavities in BMIM-PF6 could accommodate up to 0.11 mol fractions of water and in the case of BMIM-NO3 only up to 0.05 mol fractions. Since the solubility of water is the lowest in BMIM-PF6 and largest in BMIM-NO3, the results of this analysis do not support the idea that preformed cavities are important for the solubility of water. Furthermore, the amount of unoccupied space seems to be insufficient to store larger concentrations of water. On the basis of these findings, we did not consider cavities as an essential ingredient for the prediction of water-miscibilities of ILs. These results are also in line with a simulation work, in which cavities were not found to cause the high solubility of CO2 in ILs.78 3.4. Prediction of Water-IL Miscibility and Water Saturation Concentration. 3.4.1. Estimation of the Water-Ion Interaction Strength. According to the results in this work, the solvation of water in ILs mainly depends on the water-ion interaction strength. The interaction strength in turn depends on the size of the ions and the ion surface charge that is in direct contact with water, as explained before. A model to estimate water-ion interaction strengths, which is based on these assumptions, is introduced in this section. An equation is derived from this model, which can be used to predict the miscibility of new ILs with water, while only minimal computational effort is required for its application. The proposed water-ion interaction model is schematically shown in Figure 9a. One water molecule is coordinated to one cation and one anion. Ions are described as spheres with a volume that is estimated according to the McGowan method. Furthermore, the electron charge density of the ions is assumed to be constant within the sphere and can thus be represented by a single point charge in the center of the sphere. A part of this ion charge is transferred to the ion surface, by placing a second point charge on the part of the ion surface that is closest to the water molecule. The sum of the ion center charge and the surface charge is +1 e for the cation and -1 e for the anion. Three point charges are placed at the atom positions of the water molecule. A Coulomb potential is used to calculate the interaction energy of the three water point charges with the two point charges of the cation and anion, respectively. This model takes into account the size of the ions and the magnitude of the surface charge that is in direct contact with the water molecule, as demanded by the previous analysis. Details of the described model, together with geometric specifications, are shown in Figure 9b. The oxygen atom of water carries the charge -Q and the two water hydrogen atoms carry the charge +Q/2. The two surface charges are called qcat and qan, leaving the charges 1 - qcat and -1 - qan in the center of the cation and anion, respectively. The geometry of the water molecule is specified by the oxygen-hydrogen bond length, d, the water bond angle, φ, as well as by the van der Waals radii of the oxygen atom and the hydrogen atoms, RO and RH. The radii of the ion spheres, rcat and ran, can be derived from their

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Figure 9. (a) Scheme of model to estimate the interaction strength of water with ILs. A water molecule is coordinated to one cation and one anion. Both ions are treated as spheres with a volume according to the McGowan method. Point charges are placed in the center of the spheres, with charges of +1 and -1 for cations and anions, respectively. A part of these charges is transferred to the ion surface that is in direct contact with the water molecule. These surface charges are designated as qcat and qan. (b) Details of the water-IL interaction model with geometric specifications. Shown are the ion centered charges, 1 - qcat and -1 - qan, the two ion surface charges, qcat and qan, the charge of the water oxygen atom, -Q, and the charge of the two water hydrogen atoms, +Q/2. Also shown are the hydrogen-oxygen bond length of water, d, and the water bond angle, φ. The distance between water oxygen atom and cation surface charge as well as the distance between water hydrogen atom and anion surface charge is called p. The distance between the cation center charge and the water oxygen atom is the sum of cation radius, rcat, and the van der Waals radius of the oxygen atom, RO. Similarly, the distance between the anion center charge and the water hydrogen atom is the sum of the anion radius, ran, and the van der Waals radius of the hydrogen atom, RH.

McGowan volume via r ) (3V/4π)1/3. The distance between the water oxygen atom and the cation surface charge, qcat, as well as the distance between the water hydrogen atoms and the anion surface charge, qan, are called p. With these specifications, the water-ion interaction strength, Ewi, can be calculated with a Coulomb sum, with the help of some simple geometric considerations, as shown in Figure 9b: 4πε0 2

e

2

Ewi )

-Q(1 - qcat) + RO + rcat Q (1 - qcat) 2

(d sin φ2 ) + (d cos φ2 + R

+

2

2

O

)

+ rcat

Q q 2 cat



-Q(-1 - qan) φ + 2

(R

H

(

+ ran)2 - d sin

φ 2

)

2

φ 2 Q (-1 - qan) 2 +2 + RH + ran

-Qqan φ d cos + 2

 (

φ p - d sin 2 2

-Qqcat + p

+

d2 + p2 + 2dp cos

d cos

2

2

)

Q q 2 an +2 p

(6)

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Kla¨hn et al.

The specifications for water, namely d ) 0.96 Å, φ ) 104.5°, RO ) 1.4 Å, and RH ) 1.0 Å, were substituted into eq 6 in the next step. The charge Q was set to 0.9, according to the previously determined dipole moment of water in ILs. The close contact distance, p, was set to 2 Å, which is a typical value for a hydrogen bond length. This leaves only the ion sizes and surface charges, rcat, ran, qcat, and qan as parameters in eq 6. With the approximations RO + rcat . d and RH + ran . d, the following equation for Ewi (in kJ/mol) can be derived:

(

Ewi ) -738

1 - qcat (rcat + 1.67)

2

+

1 + qan

)

(ran + 1.26)2 161qcat + 111qan

(7)

We would like to emphasize that all coefficients in eq 7 were directly derived from eq 6 with the parameter values described above, i.e., no other data was used and no fitting of the coefficients in eq 7 was performed. While the first two terms in eq 7 estimate the interaction of water with the electric monopole of the ions, the last two terms describe the interaction of water with the surface charges. 3.4.2. Application and Verification of the Ion-Water Interaction Model. The water-ion interaction strength, according to eq 7, was estimated for a sample of ILs and compared with measured water saturation concentrations and watermiscibilities to verify the proposed water-ion interaction model. The sample includes 83 different ILs and involves 28 different cations and 18 different anions.4,5,7,9,18,23,26,27,30,79,80 Cations in the sample are based on either imidazolium, pyridinium, pyrrolidinium, or piperidinium, to which alkyl chains of varying length were attached, involving in some cases also fluoroalkyl, allyl, and methoxyehtyl groups. The diversity of anions in the sample is illustrated in Figure S2. The list of ILs can be found in the Supporting Information in Table S1, together with the McGowan volume and radius of the constituting ions. Also, the water-miscibility of these ILs, and in case of immiscibility the measured water saturation concentrations as well, are given in Table S1. The McGowan radii of monatomic halide anions somewhat overestimate the distance between ion and water. Therefore, in this special case, the anion radius, ran, was chosen so that ran + RH, i.e., the distance between the halide ion and the water hydrogen atoms, reproduced the actually measured distances according to ref 81. Equation 7 contains 4 parameters, two of which are the ion radii that were readily estimated with the McGowan method. The choice of the two ion surface charges, qcat and qan, required some more consideration. When a water molecule diffuses into the IL, it is safe to assume that it strives to coordinate with the part of the ion that exhibits the largest surface charge, in an effort to optimize its solvation. The ion surface charges are the partial charges on the atoms that are directly coordinated with water. That means that qcat and qan should be equal to the largest partial charge, carried by an ion atom that is capable of coordinating with water. While the value of this charge varies considerably from anion to anion, the value and variation of this charge is small in the case of cations, as can be seen, for example, in Figure 1. Therefore, we were content to use an average surface charge of qcat ) 0.1 for all cations to simplify matters. In the case of anions, where the interaction model is required to capture the anion specific variation of the surface charge, qan was derived directly from the anion charge distribution. The charge distributions of all anions that are listed in Table S1, excluding monatomic halides, were determined with DFT,

Figure 10. Comparison of estimated water-ion interaction strengths according to eq 7, Ewi, and measured water saturation concentrations, exp xwat , given in mole fractions of water, for a sample of 83 ILs. Large values of Ewi correlate with high water concentrations in the IL, up to a point where mixing of the IL with water occurs. (a) ILs are categorized by the value of Ewi to be in one of 3 groups: for Ewi > -117 kJ/mol exp water and IL are immiscible and xwat increases linearly with Ewi. For -124 kJ/mol < Ewi < -117 kJ/mol the phase separation of IL and water becomes unstable. For Ewi < -124 kJ/mol water and IL are miscible. (b) Magnification of the region in Figure 10a in which IL and water are immiscible, together with a linear regression line according to eq 8.

using the functional B3LYP and the basis set 6-31+G(d). The geometries of the anions were optimized in vacuum, and from the resulting geometries the ESP charges were calculated using the CHELPG scheme. The obtained charges are shown in Figure S2. The largest negative partial charge of each anion is listed in Table S1 as qan. In the case of monatomic anions, the entire anion charge was placed into the anion center. Interesting are the large negative partial charges on anion groups such as, -CO2, -SO3, and -SO2-, compared to the charges on the often involved fluoroalkyl groups. For example, in the case of the commonly used Tf2N anions, water coordinates much more likely with one of the SO2 groups, whose oxygen atoms exhibit a partial charge of -0.56 e, rather than with one of the fluorine atoms that carry only small charges of -0.12 e. This assumption has been confirmed also by MD simulations of BMIM-Tf2N, in which water was indeed found close to the SO2 groups.40 With this in mind, it should be expected that only the nonfluoroalkyl groups in larger anions influence the solubility of water in the IL. In Figure 10a, measured water saturation concentrations, xexp wat, were plotted against the corresponding values of Ewi, listed in Table S1, according to eq 7. Indeed, the water-miscibilities of ILs strongly correlated with the estimated water-ion interaction strengths. According to a visual inspection of Figure 10a, the

Determining the Miscibility of Ionic Liquids with Water plot can be divided into three regions. For weak water-ion interactions with Ewi > -117 kJ/mol, ILs and water are immiscible. Furthermore, xexp wat increases linearly with Ewi, which is plausible, since stronger water-ion interactions should allow the absorption of a larger quantity of water. For strong water-ion interactions with Ewi < -124 kJ/mol, ILs and water become miscible. At these interaction strengths, a sufficient amount of water is absorbed by the IL to overcome the interionic interactions, resulting in a mixing of the two phases. For a narrow range of medium values of Ewi, roughly between -117 and -124 kJ/mol, miscibility cannot be predicted. In this region of the plot, the ILs are either miscible or they are immiscible but exhibit a very high concentration of water. Only 12 ILs in the sample were found to fall into this category. It is likely that miscibility in this region of the plot also depends on how the water-IL equilibrium is established in the experiment. Some experiments involve especially long equilibration times and intense stirring, enabling mixing of the two phases that would have otherwise not occurred. For BMIM-PF6, a value of Ewi ) -113 kJ/mol was calculated, which classifies this IL correctly as immiscible. For BMIM-BF4 a value of Ewi ) -122 kJ/mol was determined, classifying the separation of water and IL phases as unstable. Since BMIM-BF4 is water-miscible at room temperature but immiscible at 4 °C, as mentioned before, this classification seems to be very reasonable. BMIM-NO3, with a value of Ewi ) -136 kJ/mol, is correctly classified as a miscible IL. The region of the plot in Figure 10a in which ILs are immiscible is enlarged in Figure 10b. Using a linear regression line, the water saturation concentration in immiscible ILs can be estimated from Ewi with exp xwat ) -0.0189Ewi - 1.91,

for

Ewi > -117kJ/mol (8)

Considering the large data set of ILs that encompassed a large variety of different ions and keeping in mind the simplicity of the proposed water-ion interaction model and that no parameters in eq 7 were fitted to measured data, the observed correlation in Figure 10 is remarkable. The obtained correlation confirms that the ingredients of the interaction model, the ion sizes and surface charges, were indeed sufficient to predict the water-miscibility of ILs. It furthermore demonstrates that the water-ion interaction strength indeed determines the trend of the excess chemical potential of water in ILs. Equations 7 and 8 can be used to predict the miscibility and water saturation concentration of new ILs, without the need to perform computationally expensive molecular simulations. In fact, only the derivation of the anion surface charges, qan, requires a computational treatment. Fortunately, deriving an anion charge distribution with the method explained above is computationally very inexpensive and straightforward to carry out. For instance, the charges of all 15 anions together, shown in Figure S2, were calculated within 2 days, using a single processor. Values of Ewi for new ILs need to be compared with the data shown in Figure 10 to enable a categorization of the IL. The absolute value of Ewi is not meaningful by itself. Therefore, new values for qan should be calculated with the same DFT functional, basis set, and ESP scheme to ensure a maximum comparability of the derived Ewi with the data presented in this work. 4. Conclusion It was demonstrated with molecular simulations that the water-ion interaction strength determines qualitatively the trend

J. Phys. Chem. B, Vol. 114, No. 8, 2010 2867 of the excess chemical potential of water in ILs and thereby also the miscibility of ILs with water. This interaction strength in turn is primarily determined by the size of the ions. Interactions of water with small ions are more favorable because of the localization of the ion charge. The second factor that determines water-ion interactions is the magnitude of the charge on the ion surface atom that is directly coordinated with water. This charge in turn depends on the chemical structure of the ion. A strong internal polarization of the ion, which leads to larger partial charges on its surface atoms, results in more favorable interactions with water. This also implies, for example, that the water saturation concentration in ILs can be minimized by using ions that are large and that exhibit minimal partial charges on their surface. On the basis of these findings, a water-ion interaction model was proposed to derive an equation that estimates the water-ion interaction strength. The only parameters of this equation are the volume and surface charge of the ions. The validity of the model was demonstrated by classifying a large sample of ILs correctly as being miscible or immiscible ILs, merely based on their estimated water-ion interaction strengths. Thereby, it is also established that the solvation of water in ILs is primarily determined by electrostatics. Additionally, a linear relationship between water-ion interaction strength and water saturation concentration was found for immiscible ILs. The proposed model can be applied with a minimum of computational effort to predict the miscibility of a new IL: first, McGowan volumes of cations and anions are determined from tables, and, second, the ion surface charge is determined from the ion charge distribution, using a computationally inexpensive DFT calculation. With these parameters, the water-ion interaction strength is estimated by evaluation of eq 7. Miscibility of the IL at room temperature is predicted for values below -124 kJ/mol, and immiscibility is predicted for values above -117 kJ/mol. A clear distinction cannot be made by the model for values in between. If immiscibility is predicted, eq 8 can be used to estimate the water saturation concentration in the IL at thermal equilibrium. A refined version of eq 7 might be able to improve the quality of the predictions further. However, a verification of such an improved equation would be hampered by the limited accuracy of the experimental data, due to difficulties in establishing the equilibrium of the water-IL systems. A generalization of the proposed model to predict the miscibility of ILs with other small polar solutes such as CO2 would also be promising. In any event, the proposed method to predict the watermiscibility of ILs is computationally inexpensive, especially when compared to the time-consuming calculation of chemical potentials with molecular simulations. This model provides guidelines to aid the considerable efforts that are being made to optimize water-related properties of ILs. Acknowledgment. We gratefully acknowledge the provision of computing facilities by the Institute of High Performance Computing (IHPC) and the financial support from the Agency for Science, Technology and Research (A*STAR) of Singapore. Supporting Information Available: Complete ref 58; table listing McGowan volume and radius of cations and anions, anion surface charge, estimated water-IL interaction energy, and measured water-miscibility for a sample of ILs (Table S1); potential energy changes upon mixing of initially separated ILs and water, after 6 ns MD simulations at room temperature (Figure S1); and atomic partial charges for the 15 anions that are included in the list of ILs in Table S1, excluding halide

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