Molecular Dynamics Simulation of Anion Effect on Solubility, Diffusivity

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Molecular Dynamics Simulation of Anion Effect on Solubility, Diffusivity, and Permeability of Carbon Dioxide in Ionic Liquids 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

‡

ABSTRACT: The solubility, diffusivity, and permeability of CO2 in three ionic liquids with a common cation were investigated by molecular dynamics simulations in order to understand the role of the anion in dictating permeability. The three ionic liquids are 1-ethyl-3-methyl imidazolium tetracyanoborate ([emim][B(CN) 4 ]), 1-ethyl-3-methyl imidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf2N]), and 1-ethyl-3-methyl imidazolium tetrafluoroborate ([emim][BF4]). The simulated solubility agrees satisfactorily with experiment with a trend of [emim][B(CN)4] > [emim][Tf2N] > [emim][BF4]. The higher solubility of CO2 in [emim][B(CN)4] appears to be due to weaker cation−anion interaction, higher fraction of larger cavity, larger free volume, and more favorable interaction with CO2. CO2 diffusivity in ILs follows the same trend as solubility. On the basis of the solvation−diffusion mechanism, gas permeability was estimated and compared with experiment. The present work confirms the superiority of tetracyanoborate-based ILs for membrane-based gas separations.

1. INTRODUCTION Ionic liquids (ILs) are promising for CO2 capture thanks to their very low volatility.1−4 Compared with the conventional amine scrubbing process, ionic liquid-based physical absorbent is energy-efficient and environment-benign. Supported IL membranes combining the advantages of membrane with the tunability of ILs offer a potential platform for gas separation.3,5−8 One can judiciously choose cation and anion to improve separation capacity. Recently, the tetracyanoboratebased ILs were found to have high CO2 solubility and high CO2/N2 permeability selectivity.9,10 However, searching for better ILs is still based on the conventional trial-and-error approach. Ideally, it would be more desirable to design ILs that offer higher CO2 permeability and CO2/N2 selectivity. To be able to do that, it is necessary to establish a structure− property relationship for ILs in terms of gas solubility and diffusivity, since the gas permeation through supported IL membranes follows the solvation-diffusion mechanism whereby gas permeability is the product of diffusivity and solubility. Molecular simulations are well-suited to study the relationship between microscopic structure and macroscopic properties.11,12 Various computational methods have been used to study the solvation phenomenon, including Widom insertion,13−17 thermodynamic integration,18−23 and biased Monte Carlo methods.24,25 Even though the Widom insertion method is known to suffer from systematic errors22,25 and convergence and finite-size problems,13 its popularity remains high. Gas solubility predictions usually are qualitatively consistent with experiment, though the temperature dependence of solubility of poorly soluble gases is hard to obtain correctly.20−22,25,26 Our recent work on the gas solubility of a series of gases in [emim][Tf2N] demonstrates that the alchemical free energy calculations equipped with Bennett acceptance ratio analysis27 provide not only the correct solubility trend but also the correct temperature dependence of solubility for both soluble gases and poorly soluble gases.28 © 2014 American Chemical Society

Besides gas solvation properties, gas transport through ILs is also important for the supported IL membrane applications. The majority of experimental data on gas diffusion in ILs was measured as transport diffusivity by the macroscopic techniques.29−32 There are only a limited number of studies on self-diffusion of gas molecules in ILs from simulation15,33,34 or the experiment.35 Previous MD simulations of CO2 and N2 transport in [emim][B(CN)4] suggested that the diffusivity selectivity (that is, the ratio in diffusivity) of CO2/N2 is close to unity.36 Hence according to the solution-diffusion mechanism, the high CO2/ N2 permselectivity (that is, the ratio in permeability) observed experimentally for the B(CN)4-based ILs has been attributed to their higher solubility of CO2. Although the effect of the anion on the solubility trend has been correlated to the computed cation−anion interaction,37 an atomistic prediction of CO2 solubility would be more desirable to test the ability of freeenergy calculations to confirm the experimental trend. Coupled with diffusivity from MD simulations, one can predict gas permeability in ionic liquids without any experimental input. This is an important step toward rational materials design for task-specific ILs. Toward that goal, here we investigate the solubility and transport properties of CO2 in three different ILs sharing a common cation with molecular simulations. The simulated solubility is compared with the experimental data. Analysis from multiple perspectives is performed to explain the solubility trend. Equilibrium molecular dynamics simulations are used to calculate the self-diffusivity of solvated gas molecules in ILs. Then CO2 permeability is evaluated and compared with the experimental values. Received: Revised: Accepted: Published: 10485

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2. METHODS All-atom molecular dynamics simulations were performed with the GROMACS version 4.6.1.38,39 ILs were modeled in a periodic cubic box. The force fields of ILs were developed to be consistent with the generalized Amber force field (GAFF)40 following the established procedure that has been successfully applied in many studies.41−46 The all-atom representation of ions is presented in Figure 1. Gas solute molecules were

the ionic liquids using the method suggested by Bara and coworkers.48

3. RESULTS AND DISCUSSION According to the solution−diffusion mechanism of gas permeation in ionic liquids, gas permeability is a product of solubility and diffusivity. By free-energy calculations, we first obtained the solvation free energy of CO2 in the three ILs sharing the same cation (see Table 1). The CO2 solvation free Table 1. Simulated Solvation Free Energy of CO2 in Three ILs at 300 K IL ΔGsol (kJ mol−1)

[emim][B(CN)4]

[emim][Tf2N]

[emim][BF4]

−3.84 ± 0.11

−2.51 ± 0.29

−2.31 ± 0.25

energy becomes more negative or solvation of CO2 becomes more favorable when anion varies from [BF4] to [Tf2N] to [B(CN)4]. Indeed, we found that the B(CN)4-based IL offers the most favorable solvation for CO2. Henry’s law constant is presented in Figure 2a. Note that KH is inversely proportional to solubility: the smaller KH value corresponds to the higher solubility. Volume-based solubility provides another more reasonable perspective in the engineering sense, to compare CO2 solubility in different types of solvents. A comparison of CO2 solubility in the unit of mol L−1

Figure 1. All-atom representation of cation [emim]+ and anions [Tf2N]−, [B(CN)4]−, and [BF4]−. Color codes of atoms: H (white), B (pink), C (gray), N (blue), O (red), F (cyan), and S (yellow).

described in terms of Lennard-Jones plus charges models following the TraPPE model.47 The cross terms were evaluated by the Lorentz−Berthelot mixing rule. The alchemical free energy calculation was applied to calculate the solvation free energy (ΔGsol). Specifically, we implemented a reversible thermodynamic path by creating a series of alchemical intermediate states to facilitate the transition from the initial state (H0: completely decoupled) to the final state (H1: fully interacting). H(λ) = (1 − λ)H0 + λH1

The above expression defines the Hamiltonian as a linear combination of end states as a function of coupling parameter λ. We used the Bennett acceptance ratio (BAR) method27 to extract the free energy difference from neighboring state simulations, as done in the previous work.28 Then the Henry’s law constant KH, as a measure of gas solubility, can be calculated by KH = (RTρ/M) exp(ΔGsol/(RT)), where ρ and M are the density and molecular weight of ionic liquid, respectively. The more negative solvation free energy usually leads to the smaller Henry’s law constant. Molecular dynamics simulations were performed at a pressure of 1 atm and at different temperatures. The temperature dependence of gas solubility can be related to the partial molar solvation enthalpy (ΔHsol) through the following equation: (∂ ln KH)/(∂1/T)P = ΔHsol/R. Gas transport in ILs was studied by standard MD simulations. A system of 20 CO2 molecules inside an IL of 180 ion pairs (corresponding to 10% mole fraction of CO2) was used for the diffusivity study. Self-diffusivity was calculated using the 10 ns trajectory and from the Einstein relation through the slope of mean squared displacement. The estimated error on diffusivity through multiple independent runs is well below 10%. The detailed procedure can be found elsewhere.28,36 We also calculated the fractional free volume of

Figure 2. Simulated Henry’s law constant (a) and CO2 solubility (b) in three ILs compared with experiment9,49,50 at 300 K. 10486

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atm−1 at ambient conditions (Figure 2b) clearly shows the trend of [emim][B(CN)4] > [emim][Tf2N] > [emim][BF4]. Comparison between simulation and experiment as seen in Figure 2b indicates that although the CO2 solubilities in [emim][B(CN)4] and [emim][BF4] are overestimated by as high as 30%, a qualitatively correct trend is obtained. The temperature dependence of CO2 solubility is presented in Figure 3. All three ILs show the similar pattern of

Figure 4. Center of mass (COM) radial distribution functions of cation and anion of the three ILs.

interaction, thereby making it easy for CO2 to squeeze into the interstitial cavities inside the ionic liquid. Cavity distribution is a direct way to characterize how a liquid structure accommodates the solute molecules.51 We computed the cavity distribution of ILs by choosing 1000 random points per frame of the trajectory and calculating the smallest distance to all atomic sites of ILs. The resulting probability distribution shown in Figure 5 defines the

Figure 3. Temperature dependence of CO2 solubility in terms of Henry’s law constant in the three ILs. Statistical error bars from the simulation are indicated at each data point; lines are for guiding the eye.

temperature dependence: the Henry’s law constant increases or solubility decreases with temperature. It has been shown that solvation of polar gases or gases with a large quadrupole moment is an exothermic process with a relatively large solubility and the solvation of nonpolar gases is endothermic with a vanishingly small solubility.28 The ΔHsol values derived from Figure 3 are listed in Table 2. One can see that the Table 2. Enthalpy of Solvation of CO2 in ILs, ΔHsol (kJ mol−1), from Simulation along with the Experimental Values49,50 IL

[emim][B(CN)4]

[emim][Tf2N]

[emim][BF4]

simulation experiment

−14.2 N/A

−13.8 −13 ± 1

−12.9 −13 ± 0.2

Figure 5. Cavity distribution in the three ILs at 300 K.

possibility of a randomly chosen point locating at a distance of R from the center of the nearest atom. As shown in Figure 5, the probability of observing larger voids follows the trend that [emim][B(CN)4] > [emim][Tf2N] > [emim][BF4], though the difference in cavity distributions between [emim][Tf2N] and [emim][BF4] is rather small. [emim][B(CN)4]’s cavity distribution is obviously shifted toward larger sizes than [emim][Tf2N] and [emim][BF4], indicating a greater fraction of larger cavities in [emim][B(CN)4]. In addition, we also computed the fractional free volume (FFV) of the three ILs in the traditional meaning of the definition following the method of Bara et al.48 The computed FFVs are 0.1326, 0.1155, and 0.1116 for [emim][B(CN)4], [emim][Tf2N], and [emim][BF4], respectively. Hence, both cavity distribution and free volume appear to correlate with the simulated and experimental CO2 solubility trend so that larger cavity and higher free

solvation enthalpy of CO2 is negative for all three ILs, indicating a favorable interaction between CO2 and the ILs. In addition, the trend of the enthalpy of solvation correlates well with that of the solubility: [emim][B(CN)4] has the most favorable interaction for CO2 and, hence, the highest CO2 solubility. Previously, we have correlated the solubility of CO2 in ILs with the cation−anion interaction, computed from the gasphase ionic-pair interaction energy.37 Here to understand deeper the solubility trend from the liquid structure, we calculated the radial distribution function between cations and anions. The center-of-mass radial distribution functions are presented in Figure 4. The peak height and position of g(r) follow the sequence of [emim][B(CN)4] < [emim][Tf2N] < [emim][BF4]. Higher peak with smaller r indicates stronger interaction, so [emim][B(CN)4] has the weakest cation−anion 10487

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volume lead to higher CO2 solubility. Here we note that both cavity distribution and free volume are purely a geometrical analysis without considering the charges on the ions or the interaction sites for CO2. Detailed analysis of the structure of CO2 inside the ionic liquid can be found in previous studies.33−36 We next obtained CO2 diffusivity from the Einstein relation through the slope of mean squared displacement in the MD trajectory. The resulting diffusivities for CO2 in different ILs are reported in Figure 6. The accompanying cation and anion

Figure 7. CO2 permeability in the three ILs at 300 K. One Barrer = 3.348 × 10−16 mol m−1 s−1 Pa−1.

Figure 7 also indicates that the simulation results are not accurate enough to offer a quantitative agreement with the experiment. To be able to achieve a quantitative agreement, one needs to predict both solubility and diffusivity accurately. Since we are using force-field-based molecular dynamics simulations for both solubility and diffusivity predictions, the most probable source of major error comes from the force field. It has been shown that polarizable force fields can more accurately predict transport properties,53 but at a greater expense (roughly an order of magnitude slower than the conventional force field as employed in the present work). There are also recent developments in advanced force fields such as force-matching,54 ForceBalance,55 and symmetry-adapted perturbation theory.56 With the development of advanced hardware such as the graphic processing unit (GPU), exciting opportunities lie ahead in applying those advanced force fields to achieve quantitative agreement with the experiment in predicting gas diffusivity, solubility, and permeability in ionic liquids and other separation media.

Figure 6. Self-diffusivities of CO2, cation, and anion in the CO2-IL mixtures at 300 K.

diffusivities are also included for comparison. CO2 diffuses much faster than cation/anion, while cation always diffuses faster than anion. According to the Einstein−Stokes relation, the less viscous fluid leads to the more active dynamics. This is exactly what we have observed: diffusivity of ions follows the trend of [emim][B(CN)4] > [emim][Tf2N] > [emim][BF4] which inversely relates to the experimental viscosity (19.5 mPa· s, 30.1 mPa·s, and 36.9 mPa·s for [emim][B(CN)4],9 [emim][Tf2N],50 and [emim][BF4],52 respectively). With solubility and diffusivity available, one can readily evaluate the gas permeability (P) using the solution-diffusion mechanism: P = Dt/(VmKH), where Dt is transport diffusivity for gas molecules, Vm is the molar volume of the IL, and KH is the Henry’s law constant. At the low concentrations studied here, transport diffusivity of solute can be approximated by its self-diffusivity. The predicted permeability (Figure 7) follows the trend of [emim][B(CN)4] > [emim][Tf2N] > [emim][BF4], in agreement with the experiment, although the simulated CO2 permeability in [emim][B(CN)4] is overestimated by 100%,9 while CO2 permeabilities in [emim][Tf2N] and [emim][BF4] are underestimated by 45% and 49%, respectively. The results above now provide a qualitative picture of the [emim][B(CN)4] IL in offering the highest CO2 permeability. Namely, CO2 has both the highest solubility and the fastest diffusivity in [emim][B(CN)4]. In other words, the [B(CN)4] anion is a good choice for both thermodynamic and dynamic considerations in terms of CO2 solvation and diffusion. Whether or not another anion can surpass [B(CN)4] in both considerations remains unknown. The present work suggests that MD simulations can at least provide a qualitative prediction in terms of an IL’s performance.

4. CONCLUSIONS We have calculated the CO2 solubility of [emim][B(CN)4], [emim][Tf2N], and [emim][BF4] through the alchemical free energy calculations with Bennett acceptance ratio analysis using the molecular dynamics simulations. This method provides the correct gas solubility trend, showing that the [B(CN)4] anion has the most favorable solvation for CO2. Analysis of the solvation enthalpy, cavity distribution, free volume, and cation− anion interaction also shows that the [B(CN)4] based IL tends to have more favorable interaction with CO2, higher portion of larger cavities, greater free volume, and weaker cation−anion interaction. Hence the [B(CN)4] anion is indeed special in solvating CO2, giving the highest solubility. MD simulation also revealed that CO2 has the highest diffusivity in [emim][B(CN)4] among the three ILs, due to its lowest viscosity. With simulated solubility and diffusivity, we obtained CO 2 permeability which follows the trend of [emim][B(CN)4] > [emim][Tf2N] > [emim][BF4], consistent with experiment. The present work demonstrates that all-atom MD simulations can now provide a qualitatively correct trend of gas permeability in ionic liquids, but quantitative comparison is still not satisfactory. More accurate force fields are probably needed for further improvement in quantitative prediction of gas solubility, diffusivity, and permeability in ionic liquids. 10488

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 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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dx.doi.org/10.1021/ie501501k | Ind. Eng. Chem. Res. 2014, 53, 10485−10490