Solubility of Gases in a Common Ionic Liquid from Molecular

Feb 17, 2014 - Piercarlo Fortunato Cardoso , Juan S. L. C. Fernandez , Luiz Fernando Lepre , Rômulo Augusto Ando , Margarida F. Costa Gomes , Leonardo...
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Solubility of Gases in a Common Ionic Liquid from Molecular Dynamics Based Free Energy Calculations Hongjun Liu,† Sheng Dai,†,§ and De-en Jiang*,† †

Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37966, United States

§

S Supporting Information *

ABSTRACT: Solubility of eight common gases in the 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [emim][Tf2N], ionic liquid was systematically investigated based on alchemical free energy calculations from molecular dynamics simulations. The simulated solubilities and trend in terms of Henry’s law constants agree qualitatively with the experiment. Polar gases such as H2S and nonpolar gases with a large quadrupole moment such as CO2 show the highest solubility, while nonpolar gases of small quadrupole moments (such as N2 and H2) are least soluble. The solute−ionic liquid interaction correlates with the observed solubility order. We also examined the temperature dependence of solubility for CO2 and N2 and found that the CO2 solvation in IL is exothermic with a negative solvation enthalpy, while the N2 solvation is endothermic, in agreement with the experiment.

between microscopic structure and macroscopic properties.13,14 Many researches on solvation behaviors in ionic liquid have been reported recently. The first molecular simulation of solvation of small solutes in ionic liquids was presented by Lynden-Bell and co-workers in 2002,15,16 who used the thermodynamic integration method along with molecular dynamics simulations to calculate the excess chemical potential, which can be directly related to the Henry’s law constant. Deschamps et al. used the same technique to investigate the gas solubility trend in several ionic liquids.17−19 The trend is qualitatively reproduced, except that the temperature dependence of simulated solubility of nonpolar gas argon is opposite to the experiment. The recent study of gas solubility in the neat and CO2-reacted ionic liquid also applied the thermodynamic integration.20 They found that the extent of reaction does not have much effect on the solubility of CO2, N2, and O2. Another way to predict gas solubility is through the isotherms using the Gibbs ensemble Monte Carlo (MC) simulation21 or continuous fractional component MC simulation.22 A novel biasing algorithm was used to facilitate the fractional growth or shrinking of solutes and thus to generate complete isotherms.22 It appears that the most popular simulation technique for gas solubility is the Widom insertion.23−26 Easy to implement is probably one major advantage. Shah and Maginn applied the Widom insertion method to estimate the excess chemical potential through sampling the independent configurations generated by the MC simulation.27 Kerle et al. applied both Bennett’s overlapping

1. INTRODUCTION Ionic liquids are organic salts with a melting temperature below 100 °C. They have many attractive properties, such as low volatility, high thermal and chemical stability, good ionic conductivity, and low flammability and corrosivity.1 Through the judicious choice of cation and/or anion, one can design the task-specific ionic liquid with suitable physical and chemical properties. Among numerous potential applications, the use of ionic liquids for CO2 capture is especially promising based on the fact that ion liquid has a negligible vapor pressure and CO2 is more soluble than other gases.2−5 Compared with the conventional amine scrubbing process, an ionic-liquid-based absorbent is energy-efficient and environmentally benign.6−9 Supported ionic liquid membrane is an effective medium to exploit ionic liquid for gas separation. Gas transport through a supported IL membrane is governed by the solution-diffusion mechanism where permeability is a product of solubility and diffusivity. Therefore, it is crucial to choose the suitable ionic liquid to provide fast gas diffusivity and high selectivity to optimize the IL membrane’s performance. Recently, the tetracyanoborate-based ILs have demonstrated the exceptionally high CO2 solubility and high CO2/N2 permeability selectivity.8,10 The high CO2 solubility was attributed to the weak cation−anion interaction in B(CN)4-based ILs.11 A molecular dynamics study showed that N2 diffuses only slightly faster than CO2 in [emim][B(CN)4], suggesting that the high CO2/N2 selectivity observed experimentally is mainly due to the disparity in gas solubility.12 To optimize gas separation application in ionic liquids, it would be necessary to investigate how the structural change affects the physical properties, specifically gas solubility. Molecular simulations are well-suited to study the relationship © 2014 American Chemical Society

Received: January 6, 2014 Revised: February 12, 2014 Published: February 17, 2014 2719

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distribution method and Widom insertion method to benchmark CO2 solubility in [Cnmim][Tf2N] and concluded that the two methods give the consistent results if the sampling rate for insertion is properly chosen. Arguably, the Widom insertion method is known to be subject to systematic errors, especially for dense solvent and/or larger and strongly interacting solutes.19,22 It also suffers from convergence and finite-size problems.23 The stepwise insertion appears to provide a better route to obtain the solvation free energy. Gradual activation of the solute allows solvent molecules to respond to the presence of solute and reorganize themselves so that the configuration space can be properly sampled. In practice, free energy calculation is separated into three stages. First, a series of alchemical intermediate states are generated, then each state is properly sampled with MC or MD simulations, and finally one of analysis methods, such as the exponential averaging,28 Bennett acceptance ratio,29 weighted histogram analysis method,30 and thermodynamic integration,31 is used to estimate the free energy difference between the states of interest. Here we compute the solvation free energy of various gases in [emim][Tf2N], one of the most studied ILs for which sufficient experimental data are available for comparison, using a thermodynamic path in which interactions of solute and solvent are gradually coupled. The proper alchemical free energy calculation procedure is followed, and Bennett acceptance ratio analysis is performed. The simulated solubility is compared with the experimental data, and temperature dependence of solubility is determined. Our results lead to the consistent gas solubility trend and, more important, the proper temperature dependence, which is incorrectly predicted in previous simulation.18 Correlation between solubility and solute−IL interaction is made. The derived enthalpy and entropy of solvation are discussed.

Figure 1. All-atom representation of the [emim][Tf2N] ionic liquid (center) and the eight gas solute molecules (around). Color codes of atoms: H (white), C (cyan), N (blue), O (red), F (pink), S (yellow), and Ar (green).

solute molecules are described in terms of Lennard-Jones plus charges models. The parameters are tabulated in Table S1. To calculate the gas solvation free energy, we implemented a reversible thermodynamic path by creating a series of alchemical intermediate states to facilitate the transition from the initial state (U0: completely decoupled) to the final state (U1: fully interacting). U (λ) = (1 − λ)U0 + λU1

This expression defines the potential energy as a linear combination of end states as a function of coupling parameter λ. The free energy difference between states can be obtained from its expression in terms of energy difference of simulated systems (free energy perturbation method) or energy derivative with respect to λ (thermodynamic integration method). In this work, we used the Bennett acceptance ration (BAR) method,29 one kind of free energy perturbation, to optimally exploit all data from neighboring state simulations. Note that the BAR method appears to be significantly more efficient than thermodynamic integration or exponential averaging.38 The interactions between solute and solvent were turned on separately: first the Coulombic part and then the LennardJones part. It has been suggested that separate stages are needed for the high-quality data. For the smooth electrostatics, a few coupling parameters (0, 0.2, 0.4, 0.6, 0.8, and 1) were found to be sufficient; the much slowly converging LennardJones coupling interactions were conducted in a step of 0.05 from λ = 0 to λ = 1. The soft-core potential was used to circumvent the singularity problem of linear scaling and accuracy concern of λk scaling.39,40 Molecular dynamics simulations were performed at a pressure of 1 atm over a wide temperature range between 300 and 400 K. All simulations were simulated in a periodic cubic box with the GROMACS version 4.6.1.41,42 The GAFF parameters were converted to the GROMACS topology and coordinate format files using the ACPYPE Python script. The system consists of 100 ionic liquid ion pairs with one solute molecule, generated by the genbox utility. After preparation of solvated system, the procedure below was performed to equilibrate the system. The steepest-descent minimization was followed by the L-BFGS steps. Langevin dynamics with fixed

2. METHODS Molecular simulation is a tool of choice to investigate the solubility phenomenon. Two elements need to be specified: the force field that describe the solvent−solvent and solute−solvent interactions and the technique from which free energy can be calculated. First, we developed the force fields of solvent ILs consistent with the generalized Amber force field (GAFF)32 following the established procedure that has been successfully applied in many studies.33−35 Briefly, the total energy is expressed in terms of bond stretching, angle bending, dihedral torsion, and van der Waals and electrostatic interactions. The all-atom representation of ions is presented in Figure 1. Atom type, bond, angle, and improper terms were taken directly from the GAFF, while partial charges were computed from the ab initio calculation on individual ion using the restrained electrostatic potential method. The resulting partial charges were scaled uniformly with a factor of 0.8 to take into account polarizability and charge transfer. This simple practice has been shown to better describe the dynamics of ILs.36,37 We also found here that the simulated CO2 solubility is improved from the scaling when compared with the experimental value. Most of dihedral terms were also taken from the GAFF. Several dihedrals of interest were further refined to match the difference of the ab initio energy (from a single point energy calculation at the MP2/6-311+g(d,p) level) and molecular mechanics energy (using the force field parameters with the selected dihedral set to zero). All force field parameters for ionic liquid are provided in the Supporting Information. Gas 2720

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volume was first run at 400 K for 100 ps with the initial velocities taken from the Maxwell distribution. The high temperature improves the efficiency of reaching the equilibrium. Then the Berendsen barostat was added to the integrator to adjust the volume for 200 ps. After equilibration, the production was conducted using the Parrinello−Rahman barostat for 5 ns, and the resulting configuration was used to start the alchemical free energy calculations. For lower temperatures, the simulated annealing was conducted and then followed by the long production runs. Simulations at alchemical intermediate states were implemented in parallel with the stochastic dynamics integrator. For each λ, the equilibration lasts 1 ns, and the production needs 5 ns. After the simulations were done, we extracted the free energy difference from the output data using the GROMACS BAR tool to otain the solvation free energy ΔGsol. Henry’s law constant KH, as a measure of gas solubility in a liquid at infinite dilution, is directly related to the free energy of solvation ΔGsol through the thermodynamic relation KH =

Figure 2. Free energy difference as a function of coupling parameter λ for CO2 in [emim][Tf2N] at 300 K. The data points show the free energy differences from two neighboring states, plotted at the midpoint, at an interval of Δλ = 0.2 for the Coulombic contribution and Δλ = 0.05 for the van der Waals contribution.

⎛ ΔG ⎞ RTρ exp⎜ sol ⎟ ⎝ RT ⎠ M

both the Coulombic and van der Waals contributions over λ, we can then get the free energy of solvation and the solubility. 3.2. Simulated Solvation Free Energy and Gas Solubility in Terms of Henry’s Law Constant at 300 K. The gas solubility trend is presented in Figure 3 along with the

where M is the molecular weight and ρ is the density of the pure ionic liquid, which is equal to that of solution in the limit of infinite dilution. The effect of temperature on gas solubility can be related to the partial molar solvation entropy ΔSsol and solvation enthalpy ΔHsol through the van’t Hoff equation: d ln x ΔH = dT RT 2

where x is mole fraction solubility. With the definition of the Gibbs free energy ΔG = ΔH − T ΔS

and the reaction isotherm equation ΔG = −RT ln x

one can determine ΔHsol from the plot of ln(KH/p0) vs T as follows: ⎛ ∂ ln(K /p0 ) ⎞ H ⎟ ΔHsol = −RT 2⎜ ∂T ⎠P ⎝

The entropy of solvation is given as ΔSsol =

Figure 3. Comparison of simulated gas solubilities (open circles) in terms of Henry’s law constant in [emim][Tf2N] with experimental values (filled circles) at 300 K.46−49

ΔHsol − ΔGsol T

3. RESULTS AND DISCUSSION 3.1. Choosing the Coupling Parameters for the Coulombic and van der Waals Contributions. The key parameter in the free energy calculations is the resolution of the coupling parameter, λ. Figure 2 displays a representative free energy difference of CO2 as a function of λ in [emim][Tf2N] at 300 K. Summation over all intermediates states (different λ’s) ranging from the decoupling to coupling leads to the solvation free energy ΔGsol. Smooth monotonic variation for the Coulombic alchemical transition is evident, indicating that five intermediate states are enough to obtain the free energy difference of the Coulombic coupling. The van der Waals part first increases, then decreases with λ, and reaches the maximum at λ ∼ 0.2. It appears that Δλ = 0.05 is sufficiently fine to properly recover the van der Waals contribution. By adding

experimental data for eight common gases. Comparison between simulation and experiment shows a qualitative agreement, with the correct order of magnitude of solubility; moreover, the solubility trend of various gases is properly predicted except for C2H4 and C2H6. H2S and CO2 show a greater solubility (or smaller Henry’s law constant) than the other gases. In contrast, nonpolar gases with small quadrupole moments like N2 and H2 are least soluble in [emim][Tf2N]. The similar solubility trend was also experimentally observed in [hmpy] [Tf2N].43 Here we note that the experimental solubilities of poorly soluble gases (N2 and H2) have a rather large error bar.44 Moreover, both underestimated gas solubility17,19 and overestimated gas solubility23,45 were reported in previous simulations. Such a discord suggests that it is of great challenge using molecular simulations to 2721

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Table 1. Coulombic (q) and van der Waals (vdW) Interactions (in Units of kJ mol−1) of Solute−Cation (S−C), Solute−Anion (S−A), and Solute−IL (S−IL) in [emim][Tf2N] at 300 K S−C q S−C vdW S-A q S-A vdW S-IL

H2S

CO2

C2H4

C2H6

Ar

CH4

N2

H2

0.5 −15.1 −5.8 −16.7 −37.1

−6.6 −12.6 −4.8 −17.3 −41.3

2.2 −13.3 −3.9 −17.2 −32.2

2.5 −16.6 −2.8 −20.4 −37.3

0 −6.7 0 −9.8 −16.5

1.1 −9.9 −1.4 −12.1 −22.3

−1.4 −6.2 0.8 −10.2 −17.0

0.4 −2.6 −1.0 −3.7 −6.9

quantitatively predict the gas solubility in ionic liquids. At the present stage, our goal is to achieve a qualitatively correct trend and understand what factors dictate the trend, as we analyze next. 3.3. Correlation of Solubility with Physical Properties. The distribution of spontaneous cavity size and the associated cavity formation free energy in different ionic liquids have been used to clarify the solubility difference of CO2,24,50 but such an analysis is not helpful to explain the trend of various gases in the same ionic liquid. Moreover, Lin and Freeman have already pointed out that the correlation between fractional free volume and solubility is weak at best.51 Polarizability as a way to implicitly describe the solute−solvent interaction was suggested to serve a metric to correlate the gas solubility in [bmim][PF6].44 A similar correlation is to directly relate solubility to the interaction between solute and solvent, one of quantities that can be readily accessible in the simulations. We can separate the interactions into individual parts: Coulombic and van der Waals interactions of solute−cation and solute−anion, and then combine them into the total solute−IL interaction. The resulting values are listed in Table 1. As can be seen, the van der Waals contribution is much larger than the Coulombic contribution for both solute−cation and solute−anion interactions. This is true for every single gas molecule studied, irrespective of its polarizability. One can also see that solute interacts more strongly with anion than it does with cation. The favorable interaction between solute and anions might explain the general wisdom that anion is the dominant factor in determining gas solubility in ionic liquids. A recently proposed metric,23 which takes the solute−IL interaction, cation−anion interaction, and molar density into account, can be reduced to this simple criterion for the same IL. The correlation between solubility and solute−IL interaction for various gases in [emim][Tf2N] is shown in Figure 4. One can see that the stronger solute−solvent interaction generally leads to the higher gas solubility. There are several outliers in Figure 4, such as H2S, C2H6, and, to a lesser extent, Ar. This could be caused by the entropic contribution which might be also important in dictating the solubility for some gases; it could also be due to that commonly used force field models as employed here were not able to accurately describe the solute− solvent interaction for those gases. Further study is warranted. 3.4. Temperature Effect on Solubility. The temperature dependence of solubility for CO2 and N2 is presented in Figure 5. We chose CO2 and N2 here because the two gases show opposite dependence of solubility on the temperature. One can see that the trend of solubility versus temperature is in agreement with the experiment for both CO2 and N2 from the present simulations. The simulated CO2 solubility is in excellent agreement with experiment and a recent simulation using the Widom insertion method,39,46 while the N2 solubility in terms of mole fraction is underestimated by around 60%. Such a deviation from experiment is not uncommon in the

Figure 4. Correlation between simulated Henry’s law constant and the solute−IL interaction energy from Table 1.

solubility simulations, especially for the less soluble gases.18,19 As suggested,17 the disagreement might arise from that the force field model is unable to properly capture the interactions between solute and solvent molecules in these low-solubility gas systems, and the solute−solvent interaction parameters need to be further refined against more accurate experimental data. The temperature dependence of solubility is thermodynamically related to the enthalpy of solvation. For CO2, solubility decreases (increase of Henry’s law constant) with increasing temperature, indicating an exothermic solvation. Such an exothermic solvation of CO2 is also found in previous simulations for [bmim][PF6],23 [Cnmim][Tf2N],52 and phosphonium cyanopyrrolide [P4444][CNpyr].20 Nonpolar gases with low solubility, specifically N2 here, show an increasing solubility (decrease of Henry’s law constant) in [emim][Tf2N] with temperature, a characteristic of endothermic solvation. A recent free energy simulation using the Widom’s particle insertion method showed an opposite temperature dependence of solubility for Ar, another low-solubility gas, in [bmim][BF4] or [bmim][PF6], yielding an incorrect sign of solvation enthalpy.17,18 Similarly, Shi et al. applied the continuous fractional component Monte Carlo method to compute isotherms and found N2 solvation in [hmim][Tf2N] to be exothermic.22 In contrast, our simulated solubility for N2 shows correct temperature dependence indicating an endothermic solvation with a positive solvation enthalpy. To further clarify the solubility of poorly soluble gas, H2 solubility was also calculated at several temperatures, and the temperature dependence of H2 solubility was found to be similar to that of N2; that is, the solvation of H2 is endothermic, as expected. 2722

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Figure 6. Enthalpy (upper panel) and entropy (lower panel) of solvation of CO2 and N2 in [emim][Tf2N].

Figure 5. Temperature dependence of Henry’s law constant of CO2 (upper panel) and N2 (lower panel) in [emim][Tf2N].

4. CONCLUSIONS We have systematically investigated the solubility of eight common gases in [emim][Tf2N] through the alchemical free energy calculations with Bennett acceptance ratio analysis using the molecular dynamics simulations. This method presents not only the correct gas solubility trend for various gases but also the correct temperature dependence of solubility for both polar and nonpolar gases. The simulated solubilities qualitatively agree with experiment within the order of magnitude. H2S and CO2 show the highest solubility, while nonpolar gases (like N2 and H2) are least soluble. We have also correlated the interaction of solute−ionic liquid with the observed solubility order. The stronger solute−IL interaction generally leads to the higher gas solubility in ionic liquid. The temperature dependence study for CO2 and N2 shows that solvation of polar/ quadrupole gases is exothermic, while solvation of nonpolar gases such as N2 is endothermic. Overall, the results demonstrate that molecular simulation is a powerful technique to investigate the gas solvation phenomenon in ionic liquids. Our alchemical free energy calculations could be a good alternative to other widely used free energy methods for predicting gas solubility in ionic liquids.

Next we analyze the solubility−temperature relationship for CO2 and N2. The Henry’s law constant can be fitted to the power series in 1/T to smooth the curve ⎛K ⎞ A A ln⎜ H0 ⎟ = A 0 + 1 + 22 T T ⎝p ⎠

where p0 is the standard-state pressure. The fitting parameters A0, A1, and A2 are given in Table S3 of the Supporting Information. Once the analytical expression for KH is obtained, the enthalpy and entropy of solvation can be derived accordingly (see the Methods section). Our simulated enthalpies of solvation (Figure 6) are in reasonable agreement with the experimental values of −12 ± 1 kJ mol−1 for CO2 and 8 ± 3 kJ mol−1 for N2.46 As explained by Noble and coworkers,46 the solvation enthalpy can be separated into the two parts: the condensation enthalpy of solute and the mixing enthalpy of condense solute with solvent. The former is generally negative, while the latter is always positive and its magnitude depends on solubility. For the poorly soluble gases such as N2, the mixing enthalpy is large, leading to a positive solvation enthalpy. For the more soluble gases such as CO2, the mixing enthalpy is expected to be smaller; therefore, the condensation enthalpy is a dominant factor and results in a negative solvation enthalpy.46

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ASSOCIATED CONTENT

S Supporting Information *

Force field parameters and supplementary tables and figures. This material is available free of charge via the Internet at http://pubs.acs.org. 2723

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph 1 (865) 574-5199 (D.J.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract DEAC02-05CH11231.

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