Molecular Simulation Study of the Solubility, Diffusivity and

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Molecular Simulation Study of the Solubility, Diffusivity and Permselectivity of Pure and Binary Mixtures of CO and CH in the Ionic Liquid 1n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide 2

4

Samir Budhathoki, Jindal K Shah, and Edward J. Maginn Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b02500 • Publication Date (Web): 18 Aug 2015 Downloaded from http://pubs.acs.org on August 26, 2015

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Industrial & Engineering Chemistry Research

Molecular Simulation Study of the Solubility, Diffusivity and Permselectivity of Pure and Binary Mixtures of CO2 and CH4 in the Ionic Liquid 1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide Samir Budhathoki,† Jindal K. Shah,∗,‡ and Edward J. Maginn∗,¶ Department of Chemical and Biomolecular Engineering, Notre Dame, Indiana 46556, United States, School of Chemical Engineering, Stillwater, Oklahoma 74078, United States, and Deparment of Chemical and Biomolecular Engineering, Notre Dame, Indiana 46556, United States E-mail: [email protected]; [email protected]

∗ To

whom correspondence should be addressed of Notre Dame ‡ Oklahoma State University ¶ University of Notre Dame † University

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Abstract The knowledge of the mixture solubility and diffusivity of gases in ILs is critical for the design of supported ionic liquid membranes (SILMs). Since mixed gas solubilities and diffusivities in ILs are much more difficult to measure than pure gas properties, pure gas solubility and diffusivity data are typically used along with an ideal solubility/diffusivity assumption to estimate permselectivities. It is not clear, however, if the ideal solubility and diffusivity assumptions are valid. In this work molecular dynamics (MD) and Gibbs ensemble Monte Carlo (GEMC) simulations were used to compute the diffusion selectivity and solubility selectivity of CO2 and CH4 in the ionic liquid (IL) 1-n-butyl-3-methylimidazolium bis(trifluoromethyl sulfonyl)imide ([C4 mim]+ [Tf2 N]− ), along with the pure gas solubilities and diffusivities, in order to test the ideal permselectivity assumption. Pure gas solubilities of CO2 and CH4 in [C4 mim]+ [Tf2 N]− at 333 K and pressures ranging from 1-100 bar were found to be in excellent agreement with literature values. Simulated CO2 :CH4 solubility selectivities in [C4 mim]+ [Tf2 N]− at CO2 :CH4 gas phase mole ratios of 4:96, 8:92 and 16:84 were found to be less than the ideal solubility selectivities computed from pure gas solubilities. Self-diffusion coefficients of pure CO2 and CH4 dissolved in the IL were independent of the concentration of the dissolved gases, within the studied pressure range. In CO2 /CH4 -[C4 mim]+ [Tf2 N]− mixtures, self-diffusion coefficients of CO2 and CH4 were similar for all CO2 :CH4 mole ratios. Computed permselectivites were only slightly smaller than the ideal permselectivites computed from pure gas properties. Since the self-diffusion coefficients for CO2 and CH4 are similar, only solubility selectivity was found to influence the overall permselectivity of CO2 over CH4 in the IL.


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Introduction Although natural gas is typically at least 90% CH4 , it also contains some higher hydrocarbons, acid gases such as H2 S and CO2 , and several other impurities such as N2 , O2 and H2 O. 1 From an operational standpoint, impurity concentrations must be reduced prior to the natural gas entering supply lines. 2 CO2 is often a major contaminant, and its removal is usually achieved via absorption with aqueous alkanolamine solvents. 3 The energy required to regenerate alkanolamine solvents is high, 4 and the solvents have other drawbacks such as relatively high volatility, corrosivity, and the tendency to degrade into toxic byproducts. 5 As a result, this technology only allows natural gas to be economically produced up to certain CO2 concentrations, typically around 10-15% of the total volume. If the CO2 content exceeds this level, then the separation process becomes too costly and the natural gas cannot be economically produced. If more effective separation processes were available, then high CO2 -content natural gas reserves could be economically produced. Ionic liquids (ILs) are salts that have melting points below 100◦ C. A large number of experimental 6–14 and computational 15–19 studies have been conducted on the solubility of gases such as CO2 , CH4 , N2 , SO2 , and O2 in various ILs. It has been demonstrated that CO2 has a particularly high solubility in many ILs, 11,20,21 and CH4 has a rather low solubility in these ILs, 7,8,22? ,23 suggesting that these fluids could be useful for carrying out absorption-based CO2 separations. 24–29 There are at least two major drawbacks to the use of ILs as solvents for gas separations. ILs tend to be much more viscous than organic solvents 30 and many of them are also more expensive than commodity solvents. Both of these drawback can be overcome by using ILs in supported ionic liquid membranes (SILMs). 31,32 The high viscosity of ILs reduces mass transfer rates, but this becomes less important when diffusion paths are short, as they are in SILMS. Significantly less IL is required in a SILM than when ILs are used as bulk solvents, thereby mitigating cost concerns. Moreover, the very low volatility of ILs makes them highly stable in supported liquid membrane applications. 33,34 Gas separation performance of SILMs can be described via a solution-diffusion mechanism, in which the permeability of species i, Pi , is given as the product of the solubility (Si ) and the 3 ACS Paragon Plus Environment


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diffusivity (Di ). Hence, permselectivity for species i over species j, βiPj , is defined as

βiPj =

Pi = βiDj × βiSj . Pj

(1)

βiDj and βiSj are diffusion selectivity and solubility selectivity, defined as βiDj =

βiSj =

S

D i

Dj

i

Sj

P,T

=

(2)

P,T

x /y i

i

x j /y j

P,T

(3)

where x and y are mole fractions of species in the liquid and vapor phase, respectively. It is to be noted that in the derivation of the solution-diffusion mechanism, negligible interfacial resistance is assumed. It is clear from eq 1 that knowledge of the mixture solubility and diffusivity of gases in ILs is critical for the design of SILMs. Several experimental and simulation studies have reported the solubility 12–14,35,36 and self-diffusion coefficients 37,38 of pure CO2 in a widely studied and common IL, 1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C4 mim]+[Tf2 N]− ). To our knowledge, only Raeisis and Peters 23 and Ramdin et al. 22 have reported the solubility of CH4 in this particular IL, and there are no CH4 diffusion data. Only Ramdin et al. 39 have measured the solubility of CO2 /CH4 mixtures in [C4 mim]+ [Tf2 N]− . Since mixed gas solubilities and diffusivities in ILs are much more difficult to measure than pure gas properties, pure gas solubility and diffusivity data are typically used along with an ideal solubility/diffusivity assumption to estimate permselectivities. Some groups have developed correlations to compute ideal CO2 /CH4 solubility selectivitiy and permeability in imidazolium-, 40–42 as well as in ammonium- and phosphoniumbased 41 ILs. It is not clear, however, if the ideal solubility and diffusivity assumptions are valid. This is because gas separation conditions are not necessarily ideal, as pressures can be large, and the presence of more than one solute contributes to the non-ideality of the system. The objective of


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this work is to use atomistic Monte Carlo (MC) and molecular dynamics (MD) simulations to compute diffusion selectivity and solubility selectivity of CO2 and CH4 in [C4 mim]+ [Tf2 N]− , along with the pure gas solubilities and diffusivities, in order to test the ideal permselectivity assumption.

Simulation Methods Force Field An all atom-force field of the following functional form was used for the simulations

Vtot =

∑

kb (r − r0 )2 +

bonds

+

∑

kθ (θ − θ0 )2

angles

∑

kγ [1 + cos(nγ − δγ )]

dihedrals

+

∑

kψ [1 + cos(nψ − δψ )]

improper N−1 N

+

∑∑

i=1 i< j

(

qi q j + 4πε0 ri j

4ε i j

"

σi j ri j

!12

−

σi j ri j

)

!6 # (4)

where the terms have their usual meaning. 43 For [C4 mim]+[Tf2 N]− , the force field parameters for bonds, angles and improper terms and the Lennard-Jones parameters were obtained from the Generalized Amber Force Field (GAFF). 44 The details regarding the derivation of charge and dihedrals parameters for [C4 mim]+[Tf2 N]− can be found elsewhere. 38 The TraPPE 45 force field was used for CH4 and CO2 . For the calculation of diffusion coefficients, CO2 was made flexible using the bond and angle parameters derived from the work of Shi and Maginn. 16 Based on the previous studies 38,46,47 that have shown that charge scaling enhances the dynamics of the ILs, a uniform scaling of 0.8 was used for the cation and anion charges.



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Monte Carlo (MC) Simulations Isothermal- isobaric (NPT) Gibbs ensemble Monte Carlo (GEMC) simulations were performed using the Monte Carlo package Cassandra 48 to calculate the solubility of CO2 , CH4 , and their mixture in [C4 mim]+[Tf2 N]− . CO2 and CH4 solubilities in [C4 mim]+[Tf2 N]− were calculated at pressures ranging from 1-50 and 5-100 bar, respectively. CO2 and CH4 mixture solubilities in [C4 mim]+[Tf2 N]− were calculated at a pressure of 100 bar with different CO2 /CH4 mole ratios in the gas phase. All the simulations were performed at 333 K. Thermal equilibration of the system was achieved by translation of center-of-mass (COM) of molecules or ions, rotation around the COM about a randomly chosen x, y or z axis and regrowth moves altering conformation of cations and anions. The fragment-based sampling approach 48 was adopted for the regrowth moves. Volume fluctuations were carried out for the simulation box containing ionic liquid and gas molecules and the gas phase simulation box independently. The maximum allowable volume displacement magnitude varied at each pressure and was optimized during equilibration runs to achieve an overall 50% acceptance rate for the volume moves. Gas molecules were exchanged between the two boxes to enforce equality of chemical potential. Since insertion and deletion of gas molecules into or from dense ionic liquid phase result in high energetic penalty, configurational bias sampling 48 was carried out to improve the efficiency of these moves. The probability of performing translation, rotation and regrowth moves was set to 30% for each of the moves. Volume fluctuations were attempted on an average at 0.5% frequency while exchange of molecule was attempted for 9.5%. At least 40 M MC moves were carried out to compute averages. Standard deviation in the solubility was computed by carrying out three simulations for which the starting configuration was the same but a different initial random seed was used to generate the Markov chain.

Molecular Dynamics (MD) Simulations After determining the solubilities of CO2 , CH4 and CO2 /CH4 mixtures in [C4 mim]+[Tf2 N]− from MC simulations (see results), mole fractions of pure and mixed gases were used to construct the initial configurations for MD simulations. Self-diffusion coefficients of the gases and ions were 6 ACS Paragon Plus Environment

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subsequently calculated. MD simulations were performed using the software LAMMPS. 49 For the MD simulations, initial configurations were generated by inserting 250 pairs of IL and the corresponding number of gas molecules based on their mole fractions into a periodic cubic box. Subsequently, the energy of the system was minimized using a conjugate gradient technique. Random velocities were then assigned, and the systems were allowed to equilibrate to a desired temperature of 333 K for 40 ps in the canonical (NVT) ensemble. The temperature of the systems was maintained by using the Nosé - Hoover thermostat 50 with a damping factor of 0.1 ps. NVT simulations were followed by isothermal isobaric (NPT) simulation for 10 ns, and the system pressures were maintained using the extended Lagrangian approach 51 with a damping factor of 1 ps. Volumes from the last 2 ns of NPT simulation were averaged and used to perform an NVT simulation for 40 ps, followed by a microcanonical (NVE) simulation for 20 ns, from which the trajectories were taken for computation of self-diffusivities. The Lennard-Jones and electrostatic interactions were truncated at 12 Å. Long range electrostatic interactions were handled using the particle-particle particle-mesh Ewald method. Coordinates were recorded every ps for the IL and every 0.1 ps for CO2 and CH4 . A 1 fs time-step was used.

Results and Discussion CO2 solubility Solubilities of CO2 in [C4 mim]+[Tf2 N]− computed at 1, 2, 5, 10, 20, 50 and 80 bar and 333 K are shown in Figure 1. Solubility values computed in this work agree very well with the experimental 12–14 results at pressures up to 50 bar, suggesting that the force field used in this work can accurately predict the solubility of CO2 in [C4 mim]+ [Tf2 N]− . Solubility values also agree well with the simulation results from Singh et al. 36 up to 20 bar and Ramdin et al. 22 for all pressures except 50 bar. At 50 and 80 bar, however, the solubilities are somewhat higher than those computed by Singh et al. This may be due to the well known difficulties of getting convergence at high pressures, where sampling becomes difficult. We believe the results presented here are accurate 7 ACS Paragon Plus Environment


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because each of the three independent simulations yielded a consistent number of CO2 molecules absorbed. The Henry’s Law constant for CO2 was estimated to be 51.4 ±1.6 bar, based on a linear fit of the absorption isotherm from 0-5 bar. Carvalho et al. 13 and Jacquemin et al. 52 have reported the Henry’s Law constant for CO2 in [C4 mim]+ [Tf2 N]− at 333 K to be 46.5 bar and 50.76-51.08 bar, respectively, consistent with the computed value.

Figure 1: Comparison of calculated CO2 solubility in [C4 mim]+ [Tf2 N]− at 333 K and available experimental values (Aki et al., 14 Carvalho et al., 13 Raeissi et al. 12 ) and previous simulation values (Ramdin et al. 22 and Singh et al. 36 ). Dashed line is a linear fit to our data up to 5 bar, from which a Henry’s Law constant was computed. Data below 15 bar are shown in inset for clarity.

CH4 solubility The computed CH4 solubilities at different pressures and 333 K are shown in Figure 2. The simulation results are compared to the experimental results of Raeissi and Peters 23 and simulation results of Ramdin et al. 22 The computed solubilities from this work are slightly greater than the previous experimental and simulation values up to 50 bar. Above 50 bar, the solubilities agree well with the literature values, within the estimated uncertainties. A Henry’s Law constant of 331 8 ACS Paragon Plus Environment

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Figure 2: Comparison of CH4 solubility in [C4 mim]+ [Tf2 N]− with available literature values, Raeissi et al. 23 and Ramdin et. al. 22 Dashed line is a linear fit to our data up to 20 bar pressure from which a Henry’s Law constant was computed. ±11 bar was calculated for CH4 in [C4 mim]+ [Tf2 N]− from a linear fit of the data ranging from 0-20 bar. The experimental Henry’s Law constant of 541 bar was calculated from a linear fit of the data ranging from 15.9-49 bar. Ramdin et al. have reported the Henry’s Law constant of CH4 in [C4 mim]+ [Tf2 N]− to be 524 bar, which indicates a lower solubility than that observed in the present work. One of the reasons for such a discrepancy in the Henry’s Law value between this work and the literature values is due to the range of data used for the linear fit. The Henry’s Law constant obtained from a linear fit of the data at large pressures is larger than those obtained from the data at lower pressures due to the curvature of the isotherm at high pressure.

CO2 /CH4 mixture solubility The solubility of CO2 /CH4 mixtures in [C4 mim]+ [Tf2 N]− was computed at 333 K and 100 bar with different CO2 :CH4 gas phase mole ratios. Results are shown in Figure 3. Actual compositions, along with the solubility selectivity computed from eq 3, are provided in Table 1. Table 1 also provides ideal selectivities computed in two different ways. In the first method, the liquid 9 ACS Paragon Plus Environment


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phase composition in the mixture at a given partial pressure was assumed to be the same as the composition obtained from a pure gas isotherm at a total pressure equal to the partial pressure. In other words, the gases were assumed to be absorbing completely independent of one another. The following equation was used to compute the ideal selectivity = βiS,ideal j

(xi /yi ) pi ,T (x j /y j ) p j ,T

(5)

where pi and p j are partial pressures of species i and j respectively.

Figure 3: CO2 /CH4 mixture solubility isotherm in [C4 mim]+ [Tf2 N]− at 333 K and different partial pressures in the gas phase. Total pressure is 100 bar. For the second method, the ideal selectivity was determined by taking the ratio of Henry’s Law constants

βiS,H j =

H j

Hi

.

(6)

Since the Henry’s Law constant is by definition an infinitely dilute property, there is no composition dependence for this ideal selectivity. The results in Table 1 show that the computed solubility selectivity is relatively insensitive to


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Table 1: CO2 /CH4 solubility selectivity in [C4 mim]+ [Tf2 N]− at 333 K and total pressure of 100 bar. CO2 /CH4 mole percent compositions are in gas phase. Uncertainties computed from three independent simulations are indicated by subscripts in all tables. For example, 0.0381 = 0.038 ± 0.001 yCO2 0.0381 0.0752 0.1594 0.4175 0.7441 0.8641

yCH4 0.9622 0.9242 0.8405 0.5836 0.2571 0.1361

S βCO 2 /CH4 6.28 0 7.59 6.14 6.35 5.61 5.42

S,ideal βCO 2 /CH4 10.21 9.017 7.637 5.00 2.871 –

S,H βCO 2 /CH4

6.444

composition, varying from 5.4 at the highest CO2 concentrations to 7.5 at low CO2 concentrations. The ideal selectivity computed from pure gas isotherms shows more variability with composition (ranging from about 3 to 10), while the ideal selectivity computed from the ratio of Henry’s Law constants is roughly equal to an average of the composition-dependent solubility selectivity. For a CO2 :CH4 mole ratio of 4:96, the amount of CO2 absorbed is lower than what is observed in the pure CO2 system at the same CO2 partial pressure. Conversely, the total amount of CH4 absorbed in the mixture is slightly greater than that for pure CH4 system. This means that at this ratio, CO2 slightly facilitates the absorption of CH4 and CH4 retards the absorption of CO2 . As the ratios of CO2 :CH4 increase, the total amount of CO2 and CH4 absorbed is reduced relative to the pure systems. Petermann et al. 53 have measured CH4 /CO2 solubility in a different IL (1ethyl-3-methyl imidazolium ethyl sulfate ([C2 mim]+ [EtSO4 ]− )) and found that there is only slight enhancement of CH4 solubilities and slight deterioration of CO2 solubilities when compared to pure gas solubilities. To our knowledge, only Ramdin et al. 39 have reported CO2 /CH4 mixture solubilities in [C4 mim]+ [Tf2 N]− at different CO2 /CH4 compositions. Since they have reported data at different pressures, direct comparison to our results was not possible. However, at low pressure conditions (< 50 bar), they observed that mixed gas solubilities were similar to the pure gas solubilities, and they deviated at higher pressures, consistent with our results. Also, similar to our study, their ideal solubility selectivity computed from the ratio of Henry’s constant is similar 11 ACS Paragon Plus Environment


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to the solubility selectivity for the binary gas-IL mixtures. In our case, ideal solubility selectivity computed from eq 5 is larger than the solubility selectivity up to 16:84 CO2 :CH4 mole ratio. Ramdin et al. 39 have reported the real CO2 /CH4 selectivity of ∼ 8 at 333 K, which is very close to the values computed in this work up to CO2 :CH4 mole ratio of 42:60.

Molar Volume Computed molar volumes for [C4 mim]+[Tf2 N]− in equilibrium with pure gases as well as binary gas mixtures at different solute compositions are shown in Fig 4. Molar volumes decrease linearly with increasing solute concentration by roughly 47% for CO2 from 1 bar to 80 bar, and 14% for CH4 from 5 to 100 bar. For the binary systems, mixture molar volume decreases with an increase in CO2 concentration by about 37%. For similar mole fraction of CH4 and CO2 in pure systems, mixture molar volumes are about equal and within the estimated uncertainties. The ratio of mixture volume to the molar volume of pure [C4 mim]+[Tf2 N]− for both pure gas and binary gas systems is less than unity, indicating that there is no expansion of [C4 mim]+[Tf2 N]− upon absorption of gases. This is typical behavior for ILs 14,16,54,55 since at 333 K and infinite dilution CO2 and CH4 have small partial molar volumes of 39 ±5 and 38 ±4 cm3 /mol, respectively, as opposed to the large molar volume of [C4 mim]+[Tf2 N]− (293 ±1 cm3 /mol). These results are consistent with those obtained for this and related systems. For example, Aki et al. 14 and Harris et al. 56 have reported the experimental molar volume of [C4 mim]+ [Tf2 N]− to be 298.7 ± 0.5 cm3 /mol and 298.8 cm3 /mol respectively. Kumełan et al. 57 have reported the partial molar volume of CO2 and CH4 in [C6 mim]+ [Tf2 N]− at 333 K to be 41.8 ± 0.8 and 35.9 ± 7.1 cm3 /mol, respectively. Shi and Maginn 16 have computed the partial molar volume of CO2 in [C6 mim]+ [Tf2 N]− to be 40.7 ±1 cm3 /mol. Along with the low partial molar volume of solute gases, the negligible volume expansion of ILs upon gas absorption can be attributed to other factors. For instance, some studies 58–60 have suggested that dissolved gas molecules occupy interstitial spaces formed by the network of ions, while others suggest that ILs do not have cavities large enough to accommodate the solutes. Cavities large enough for dissolution of solute gases are created in the 12 ACS Paragon Plus Environment

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IL by rearrangement of ions. 16,61

Figure 4: Molar volumes of CO2 -[C4 mim]+[Tf2 N]− (a), CH4 -[C4 mim]+[Tf2 N]− (b), and CO2 /CH4 -[C4 mim]+[Tf2 N]− (c) mixtures at 333 K and different mole fractions of solute species, and molar volumes of pure [C4 mim]+[Tf2 N]− (d) at different pressures. Note that mole fractions in Figure c correspond to the mole fraction of CO2 in binary gas-IL mixtures.

Energy of Interaction Solute-IL and solute-solute interaction energies for pure gas and binary gas-IL mixtures were computed to investigate which interactions are dominant in the system, and how different the interaction energies are in pure gas-IL mixtures compared to binary gas-IL mixtures. Both van der Waals and electrostatic interaction energies are listed in Tables 2 and 3 respectively. Table 2: IL-solute and solute-solute electrostatic interaction energies (kJ/mol) of CO2 [C4 mim]+[Tf2 N]− and CO2 /CH4 -[C4 mim]+[Tf2 N]− mixtures per mole of solute gas at 333 K. P(bar) 50 100 100

xCO2 0.49 0.0443 0.331

xCH4 0 0.1797 0.0722

cat-CO2 -4.264 -0.731 -3.823

cat-CH4 – – –

an-CO2 -1.412 -0.171 -1.385

an-CH4 – – –


CO2 -CO2 -0.381 -0.0116 -0.191

CH4 -CH4 – – –

CO2 -CH4 – – –


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Table 3: IL-solute and solute-solute van der Waals interaction energies (kJ/mol) of CO2 [C4 mim]+[Tf2 N]− , CH4 -[C4 mim]+[Tf2 N]− and CO2 /CH4 -[C4 mim]+[Tf2 N]− mixtures per mole of solute gas at 333 K. P(bar) 50 50 100 100

xCO2 0.49 0 0.0443 0.331

xCH4 0 0.1056 0.1797 0.0722

cat-CO2 -10.64 – -1.952 -9.377

cat-CH4 – -10.314 -7.538 -1.421

an-CO2 -12.81 – -2.286 -11.51

an-CH4 – -10.71 -7.522 -1.452

CO2 -CO2 -1.293 – -0.0333 -0.662

CH4 -CH4 – -0.121 -0.1883 -0.0173

CO2 -CH4 – – -0.0435 -0.1933

It is observed that CO2 has significant van der Waals interactions with both the cation and anion, and smaller but still favorable electrostatic interactions with the cation and anion. CH4 has similar and favorable van der Waals interactions with the cation and anion. At the highest solute concentrations, there is minimal solute-solute interactions. Since CH4 has no partial charge, there is no electrostatic interaction for CH4 . Self-Diffusion Coefficients Self-diffusion coefficients were calculated from the Einstein relationship 1 h|r(t) − r(0)|2i t→∞ 6t

D = lim

(7)

where r(t) is the position of a center of mass of the species at time t and r(0) is the position at time t = 0. The brackets h...i represent the ensemble average over the configurations of the system and time. The slopes of the mean squared displacements from 1-2 ns were used in the calculations. Computed self-diffusion coefficients of CO2 -IL and CH4 -IL mixtures at different gas mole fractions are shown in Figure 5. Self-diffusion coefficients of CH4 /CO2 -IL systems as a function of the ratio of CO2 to CH4 mole fractions in liquid phase are shown in Figure 6. Figures 5 and 6 show that self-diffusion coefficients of CH4 and CO2 are an order of magnitude larger than that of the cation and anion. For pressures below 5 bar (the Henry’s Law regime, corresponding to the mole fractions below 0.1) in CO2 -IL mixtures, self-diffusion coefficients of the cation, anion and CO2 are independent of pressure. At 10 bar, the self-diffusion coefficient of CO2 remains 14 ACS Paragon Plus Environment

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the same while it increases slightly for both the cation and anion compared to the value at lower pressures. For the CH4 -IL system, the dynamics of all species remain the same for the pressure range studied. In our previous study, 38 we have shown that at higher concentration of CO2 in [C4 mim]+ [Tf2 N]− , the self-diffusion coefficients of CO2 and IL increase with an increase in CO2 concentration because of the fluidization of the system by the presence of CO2 resulting in a decrease in mixture density. Self-diffusion coefficients for CH4 -[C4 mim]+[Tf2 N]− mixture are also expected to follow the same trend (i.e. increase monotonically with an increase in solute concentration) because addition of CH4 in IL results in a decrease of mixture density. In this study, the self-diffusion coefficients of the cation, anion and gases in pure gas-IL mixtures show no dependence on pressures, because there is not enough dissolved gas. Additionally, self-diffusion coefficients of the cation and anion for CO2 -IL and CH4 -IL mixtures are identical at the same concentration of CO2 and CH4 . There are very few reports in the literature that have reported self-diffusion coefficient of CO2 in [C4 mim]+ [Tf2 N]− . Baltus et al. 37 have reported a CO2 selfdiffusion coefficient of 10.3 × 10−12 m2 /s in [C4 mim]+ [Tf2 N]− at 323 K and infinite dilution. Even at lower temperature, this experimental value is greater by around 48% than those computed in this work. In our previous work 38 in investigating the dynamics of CO2 -[C4 mim]+ [Tf2 N]− , simulation self-diffusion coeffcients of all the species were found to be less than the experiment by about 50 %. In the same work, it was also observed that the simulation self-diffusion coefficient of the pure IL at 333 K was around 50 % smaller than that measured by a pulsed field gradient (PFG) NMR. This was attributed to the absence of polarizability and charge transfer due to the use of a fixed charge models inherent in simulations. For CO2 /CH4 -[C4 mim]+[Tf2 N]− mixtures, self-diffusion coefficients of all the species increase with increasing concentration of solute molecules because of the reason stated above. Self-diffusion coefficients of CO2 and CH4 are similar at a given composition regardless of their concentrations in the IL. If the Stokes-Einstein relation for diffusion is valid, one expects that self-diffusivities for similar sized molecules will be similar, which is what we observe. Cation self-diffusion coefficients were greater than the anion self-diffusion coefficient for all cases. This



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is typical dynamic behavior for imidazolium-based ionic liquids. Cations show faster dynamics along the plane of the ring at temperatures above 400 K, as demonstrated by Ribeiro and Urahata; 62 at temperatures below 400 K, their preferential mobility is along the direction of alkyl chain as shown by Liu and Maginn. 46

Figure 5: Self-diffusion coefficients of CO2 , CH4 and ions in CO2 -[C4 mim]+[Tf2 N]− and CH4 [C4 mim]+[Tf2 N]− mixtures at 333 K as a function of solute mole fraction in the mixture.

Permeability and Permselectivity From the computed solubilities and self-diffusivities, the pure gas permeability can be estimated using the following equation P=

Dt IL V ∗H

(8)

where Dt is the transport diffusion coefficient, VIL is the ionic liquid molar volume and H is the Henry’s Law constant. In the Henry’s Law regime, Dt is equal to the self-diffusion coefficient. 63 In the pure gas systems, CO2 permeability was computed to be 1071 ±312 Barrer while CH4 permeability was 136 ±26 barrer (1 Barrer = 3.348 * 10− (16) mol/(m*s*pa)). Scovazzo 41 has reported an experimentally measured CO2 permeability of 1344.4 Barrer in [C4 mim]+ [Tf2 N]− at 303 K. To our knowledge, there are no published literature data on CH4 permeability in [C4 mim]+ 16 ACS Paragon Plus Environment

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Figure 6: Self-diffusion coefficients of CO2 , CH4 and ions in CO2 /CH4 -[C4 mim]+[Tf2 N]− mixture at 333 K as a function of ratio of CO2 to CH4 mole fraction in the mixture. [Tf2 N]− . The mixed gas system is outside the Henry’s law regime, and the self-diffusion coefficients showed a strong dependence on solute concentration. Since the use of self-diffusivity in eq 8 is only valid in the Henry’s Law regime, permeabilities of CH4 and CO2 in the binary gas mixture were not computed. Because CH4 and CO2 have similar self-diffusion coefficients at all CO2 :CH4 mole ratios, however, it is likely that the permselectivity is dominated by the solubility selectivity. This is consistent with the results of Scovazzo, 41 who computed a diffusivity selectivity of CO2 vs CH4 of 0.94 using permeability and solubility selectivity data in various ILs. As a result, eq 1 was used to compute the permselectivities listed in Table 4. Also listed are ideal permselectivities, which were computed by taking ratio of pure gas permeabilities. The two permselectivities are similar. Scovazzo 41 has developed the following model to estimate CO2 /CH4 permselectivity in ILs at 303 K P = βCO 2 /CH4

5483 (VRT IL )1.09

(9)

where VRT IL is the IL molar volume in cm3 /mol. Using the molar volume of [C4 mim]+ [Tf2 N]− from this work, the CO2 /CH4 permselectivity at 333 K was computed to 11.2, which is about 17 ACS Paragon Plus Environment


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twice as large as the permselectivities computed in this work. Such differences in permselectvites obtained from the eq 9 and eq 1 could be attributed to the fact that the correlation was developed for a temperature of 303 K, while the simulations were performed at 333 K. Also, the At lower temperatures, the solubility selectivity (and hence the permselectivity) is expected to be larger. Table 4: Permselectivities of CO2 over CH4 in CO2 /CH4 -[C4 mim]+[Tf2 N]− mixture at 333 K and 100 bar, and at different CO2 :CH4 mole ratios in the gas phase yCO2 0.0381 0.1594 0.4175 0.7441

yCH4 0.9622 0.8405 0.5836 0.2571

P βCO 2 /CH4 6.49 6.04 6.05 5.65

P,H βideal

7.95

Summary and Conclusions MC and MD simulations were used to compute the solubility and self-diffusion coefficients of CO2 , CH4 and mixtures of CO2 and CH4 in the ionic liquid [C4 mim]+[Tf2 N]− at 333 K and varying pressures. The computed solubilities and self-diffusion coefficients were used to evaluate the CO2 /CH4 solubility selectivities and permselectivities in [C4 mim]+[Tf2 N]− . Solubilities of pure CO2 and CH4 in [C4 mim]+[Tf2 N]− were found to be in good agreement with previous experimental and simulation results. It was observed that the solubilities of CO2 and CH4 in CO2 /CH4 -[C4 mim]+ [Tf2 N]− mixtures are reduced compared to the pure gas solubilities at higher CO2 concentrations, confirming that the CO2 /CH4 -[C4 mim]+ [Tf2 N]− system is slightly non-ideal. The self-diffusion coefficients of CO2 , CH4 and IL were found to increase in systems with large gas concentrations. In agreement with previous experimental and simulation studies, this observation was explained by the added solutes caused a fluidization of the system and a resulting decrease in mixture density. CO2 /CH4 solubility selectivities in the binary gas-IL mixtures were found to be slightly smaller 18 ACS Paragon Plus Environment

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than the solubility selectivities computed from the pure gas isotherms, while they were similar to the ideal solubility selectivity computed from Henry’s Law constants. CO2 /CH4 permselectivties in binary-gas IL mixtures were not affected by the gas phase compositions and were found to be slightly smaller than the ideal permselectivity. Similar to previous studies, it was observed that diffusivity of solute gases are similar and therefore do not play a major role in determining the permselectivities, even at pressure as large as 100 bar and varying gas compositions. Although the CO2 /CH4 -[C4 mim]+[Tf2 N]− ] mixture is slightly non-ideal, the solubility selectivities and permselectivites are not very different from the ideal solubility selectivity and ideal permselectivity. Hence, it can be concluded that for systems similar to those of this study, important properties such as solubility selectivity and permselectivity can be safely estimated from pure gas-IL data.

Acknowledgement Funding for this work was provided by the National Science Foundation (CBET-0967458 and ACI-1339785) and the Stanford Global Climate and Energy Project. Computational resources were provided by the Notre Dame Center for Research Computing (CRC). J. K. S. acknowledges partial funding from CRC and Oklahoma State University.

Supporting Information Available Solubility, self-diffusion coefficients and molar volume data for CO2 -[C4 mim]+[Tf2 N]− , CH4 [C4 mim]+[Tf2 N]− , and CO2 /CH4 -[C4 mim]+[Tf2 N]− mixtures are provided. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Molecular Simulation Study of the Solubility, Diffusivity and

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