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Molecular Dynamics Simulations of Acidic Gases at Interface of Quaternary Ammonium Ionic Liquids Juliana Dariva Morganti, Karina Hoher, Mauro C. C. Ribeiro, Rômulo Augusto Ando, and Leonardo JA Siqueira J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp505853k • Publication Date (Web): 26 Aug 2014 Downloaded from http://pubs.acs.org on August 28, 2014

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of Acidic Gases at Interface of Quaternary Ammonium Ionic Liquids

Juliana D. Morganti,1 Karina Hoher,1 Mauro C. C. Ribeiro,2 Romulo A. Ando,2 and Leonardo J. A. Siqueira1,*

1

Laboratório de Materiais Híbridos

Departamento de Ciências Exatas e da Terra Instituto de Ciências Ambientais, Químicas e Farmacêuticas Universidade Federal de São Paulo Rua São Nicolau, 210 – 2o andar, Diadema - SP – CEP 09913-030

2

Laboratório de Espectroscopia Molecular Instituto de Química Universidade de São Paulo São Paulo-SP – CEP 05508000

*corresponding author: [email protected]

ACS Paragon Plus Environment


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ABSTRACT

Thermodynamics, structure, and dynamics of CO2 and SO2 absorption by ionic liquids based on the bis(trifluoromethylsulfonyl)-imide anion, [NTf2]-, and quaternary ammonium cations have been investigated by molecular dynamics (MD) simulations. The effect of ether-functionalized chains of different lengths in the ammonium cations is emphasized. Oxygen atoms of ether functions in the cation compete with oxygen atoms of anions for interactions with gas molecules. The mole fraction of SO2 is larger than CO2 in a given ionic liquid. The calculation of Gibbs free energy of solvation and profiles of potential of mean force across the gas–liquid interface provide a physical picture consistent with structural effects of gas absorption. The potential of mean force for the gas molecules at interface exhibits a minimum, which is ca. twice deeper for SO2 than CO2, with corresponding effect on residence times of gas molecules in different layers across the interface towards the bulk.

Keywords: Carbon dioxide; Sulfur dioxide; surface; thermodynamics; green house gases


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I. INTRODUCTION

Ionic liquids (IL) as promising materials for gas capture and separation processes is well established in the literature.1-5 Ionic liquids have several advantages, for instance, non-volatility and wide liquid temperature range, and also exhibit a large number of possible structures that can be designed for a specific task.6-8 The significant interaction with pollutant gases, as CO2, was first discussed in the seminal paper of Brennecke et al.,1 who showed it was possible to reach up to 0.72 mole fraction of CO2 (at 40oC and 93 bar) in the ionic liquid 1-butyl-3-methyl-imidazolium hexafluorophosphate, [BMIM][PF6]. Since then, several interesting strategies comprising ionic liquids have been proposed for gas capture, including physical absorption,9,10 chemical absorption by task-specific ionic liquids,2,11 ionic liquids as solvents to absorbent materials,12,13 and ionic liquids supported membranes.14,15 Despite of the potential application of ILs for gas capture and storage, the complex structure at microscopic level prevents the full understanding of mechanisms taking place in the gas/liquid equilibrium, in particular for physical absorption of CO2.3,16 It has been shown that CO2 solubility in ILs is much more dependent on the anion, i.e. cations play a secondary role,4,9,17 but there is no consensus about the explanation for this finding. Some authors attribute to quadrupole interaction between CO2 and anions,18 while others claim that free volume is responsible for CO2 solubility and selectivity.19 Therefore, several experimental and theoretical techniques are being used to unravel the mechanisms involved in the selective interaction of CO2, as well as other gases, with ionic liquids.20


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The physical picture seems simpler for sulfur dioxide (SO2) interaction with ionic liquids. It has been shown that there is specific charge transfer interaction between SO2 and the anionic species of ionic liquids.21,22 As higher is the anion basicity, higher its interaction with SO2, and higher is the IL capacity for gas absorption. In contrast to CO2, SO2 can drastically modify structural and dynamic properties of ionic liquids due to the shielding of coulombic interactions and disruption of the IL long-range structure.21,22 In addition to the investigation of the equilibrium structure of gas molecules in the bulk of ILs, it is of great relevance to understand how the gas passes through the IL interface towards the bulk.23-27 Proper to experimental limitations concerning the study of gas/ionic liquid interface, molecular dynamics (MD) simulations have been crucial to address structural and mass transfer at interfaces. Perez-Blanco and Maginn published a systematic MD study showing the behavior of CO2 on the interface of 1n-butyl-3-methylimizazolium bis(trifluoromethylsulfonyl)imide, [BMIM][NTf2], at different pressures and temperatures.23 The main conclusion was that CO2 molecules are rapidly absorbed forming a dense layer with a flat orientation that maximizes their interaction with the IL. Interestingly, the CO2 molecules do not disturb the ionic interactions, so that the ionic ordering is maintained.23 Concerning ether-functionalized ionic liquids, there are some experimental studies on the absorption of CO228,29 and SO2.30 Bara’s group28 evaluated the ability for CO2 absorption by imidazolium based ionic liquids bearing CH2CH2O segments and concluded that the functionalization do not increase the gas absorption. Instead, the number of CO2 molecules absorbed per ionic pair decreases slightly in comparison with the non-functionalized ionic liquid analogue.28 On the other hand, the authors found out that the presence of ether function enhances selectivity for CO2


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separation because the solubility of N2 and CH4 is reduced. In another investigation carried out by a different group,30 it has been found that the presence of ether groups in cations enhances the ability of ILs for SO2 absorption. It is worth noting that the investigated ionic liquids have both physical (due to ether function) and chemical (due to anion) absorption abilities.30 In this work, the behavior of CO2 and SO2 gases on the interface were investigated by MD simulations of a serie of quaternary ammonium ionic liquids with the common bis(trifluoromethylsulfonyl)-imide anion, [NTf2]-. The main focus is to compare the behavior of two different gases in the bulk and at the gas/liquid interface, and also the effect of oxygen atoms in the carbon chain of cations, in order to gain further insight on gas capture and storage by ionic liquids.

II. COMPUTATIONAL DETAILS

MD simulations were carried out with the GROMACS program.31 Figure 1 depicts the structure and group/atom labeling used in this study. The non-bonded interactions were described by a non-polarizable interaction potential given by   12 σ ij  U(r) = ∑ ∑ 4ε ij     rij  i=1 j =i+1 N −1

N

 σ 6  q ⋅ q  ij i j −    + rij   rij   

(1)

where σij and εij are the Lennard-Jones potential parameters, rij is the pair distance, and qi is the atomic partial charge of atom/group i. The CH3 and CH2 were considered as a single body, i.e. a united atom model was assumed for cations. These parameters are available in Table S1 of the supporting information and are the same as those used in previous MD simulations.32-36 The parameters of bonded potentials and their respective equations are provided in Tables S2-S5 (supporting information). The fully


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flexible CO2 and SO2 molecules were modeled with parameters previously used in the simulation of CO2 in ionic liquids and neat SO2.23,37,38 Intramolecular interactions between atom pairs apart by more than three bonds were treated by the non-bonded potential (Eq. 1), whereas a scale factor of 0.5 was applied for intramolecular interactions between pairs exactly separated by three bonds. Lennard-Jones and real space coulombic interactions were cut off at 15 Å. Particle Mesh Ewald (PME) method was employed with interpolation order 6 and 0.8 Å grid spacing. These conditions have been used in previous ionic liquids MD simulations by the Margulis’ group.39,40 The equation of motion was integrated with the leapfrog algorithm by using a time step of 2 fs.

C4

C 5 O2

C3O1

C 7 O3

Figure 1. Structure and labeling of the cations considered in the MD simulations.

The starting configurations were generated with the program Packmol.41 In the case of bulk simulations, 200 ion pairs and 50 gas molecules were placed in a cubic box of low density. Then, 10 ns long equilibration runs were performed in NPT ensemble at 1 bar and 350 K, with the Berendsen barostat (τ = 5 ps) and V-rescale thermostat (τ = 1 ps) implemented in GROMACS. Further 10 ns long production runs


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were performed in the NVT ensemble at 350 K. In the case of interface simulations, 400 ion pairs were placed in a low-density box with the z-axis twice as larger as the x and y axis. Then, the systems were equilibrated in the NPT ensemble at 350 K and 1 bar for 10 ns, followed by 2 ns equilibration run in the NVT ensemble at 350 K. In the case of C5O2-NTf2 and C7O3-NTf2 ionic liquids, the box dimensions were ad hoc changed in order to keep the equilibrium density and a similar surface area in all the cases. Short simulations in the NVT ensemble were performed in which the x and y box lengths were shortened, whereas the z-axis was lengthened. The configurations of similar surface area were then shifted in z direction, allowing for the presence of two regions with enough volume for 96 CO2 molecules in each region, providing approximately 44 bar of CO2 gas.23 In the case of SO2 simulations, 45 molecules were considered in these regions in order to obtain the density of vapor-liquid coexistence at 350 K.37 Figure 2 shows the starting configuration of C4-NTf2 ionic liquid at the interface with CO2. The box dimensions of the four ionic liquids studied are in Table S6 (supporting information). Before exposing the ionic liquids to the gas molecules, the ionic liquids were equilibrated for 5 ns at vacuum interface. The gas molecules were placed in the empty space by using the Packmol program, and the systems were simulated for 20 ns in the NVT ensemble at 350 K. After every 20 ns, the number of absorbed gas molecules was checked and the systems were filled with the proper number of molecules in order to keep constant density in the gas phase. The last 20 ns of simulation run was performed with the number of gas molecules outside the liquid phase close to 192 (CO2) or 90 (SO2). The simulation runs lasted from 80 to 120 ns.


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Figure 2. Snapshot of the starting configuration of C4-NTf2 at the interface with CO2, visualized with VMD software.42

Free energy calculations. Before performing the solvation free energy calculations, systems composed by either one CO2 or SO2 molecule were inserted in a cubic box of 200 ion pairs of the four ionic liquids and equilibrated for 10 ns at 350 K in the NPT ensemble. The calculation of solvation free energy for CO2 and SO2 were performed by using the Bennett acceptance ratio method,43 as used in the calculations carried out by Costa’s group.44 In the thermodynamic integration scheme, the solvation free energy is calculated by

, where

means average from the

trajectory, H is the Hamiltonian of the system, and λ =1 and λ = 0 denote the neat ionic liquid and the fully solvated gas molecule, respectively. There are 18 different

λ states equally spaced by 0.05 between λ = 1 and λ = 0 . In each λ state it was considered 2000000 steps with a time step of 2 fs. Temperature was kept at 350 K via stochastic dynamics integrations scheme (τ = 1 ps).45 The vanishing of gas molecules was performed in steps, first turning off the electrostatic interactions followed by turning off the van der Waals interactions.


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III. RESULTS AND DISCUSSION

Structure of the bulk.

Equilibrium structure of pure ionic liquids with ether-functionalized ammonium cations has been already investigated in previous works,34-36 so that we discuss here only the effects resulting from gas absorption. Molecules of both of the gases are in close approach to [NTf2]- anions. Figure 3 shows partial radial distribution functions, gαβ(r), for the carbon or the sulfur atom of the gases and the oxygen atoms of anions. The stronger SO2–anion interaction than CO2–anion interaction gives a more intense first peak in gSO(r) than in gCO(r). On the other hand, the anion–gas interaction is only slightly dependent on the length and on etherfunctionalized chains of the ammonium cations.

Figure 3. Radial distribution functions for correlations between the carbon (left) or sulfur (right) atoms of gases and oxygen atoms of [NTf2]- anions.


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Among several partial gαβ(r) between gas molecules and cations, the most interesting one is related to atoms in the long chain of cations proper to oxygen atoms in the ether-functionalized ionic liquids. Figure 4 shows that interaction between gas molecules and cations is also significant, and there is no clear difference of gαβ(r) between CO2 or SO2 molecules with a given ammonium cation. The first peak of gαβ(r) splits when ether functions are inserted in the cation. The weak peak at short distance, which is slightly more intense for the CO2–cation partial gαβ(r), indicates growing population of gas molecules close to the cations as more oxygen atoms are available in cations with long ether chain.

Figure 4. Radial distribution functions for correlations between the carbon (left) or sulfur (right) atoms of gases and oxygen atoms of cations chain.

Finer details of the effect of ether-functionalized cations on the interaction between gas molecules and ionic species are provided by the calculation of the


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running number, nαβ(rmax), which is the integral of gαβ(r) up to a given maximum distance. Table I shows that the weak peak at short distance, rmax = 3.7 Å, in the gas– cation gαβ(r) implies a correspondingly small nαβ(rmax) for short range Xg – Oc pairs. Nevertheless, the data in Table I indicate clear trends. As more oxygen atoms in cations with longer chains are available to coordinate gas molecules, the number of oxygen atoms of anions coordinating gas molecules decreases (Xg – Oa). Furthermore, cation – cation interactions change because of the partially negative charge of the oxygen atoms of ether chains, so that nαβ(rmax) increases for Nc – Oc pairs, and nαβ(rmax) decreases for Nc – Oa pairs, as the ether chain increases.

Table I. Running numbers. Xg stand for the C or S atoms of acidic gases. The corresponding rmax considered in the calculation of running number is given in parenthesis. Xg - Oc

Xg - Oa

Nc - Oc

Nc - Oa

(3.7 Å)

(4.5 Å)

(5.5 Å)

(5.5 Å)

C4 – CO2

--

2.2

--

7.5

C3O1 – CO2

0.2

2.4

0.5

7.5

C5O2 – CO2

0.4

2.1

1.2

7.1

C7O3 – CO2

0.6

1.9

1.9

6.7

C4 – SO2

--

2.4

--

7.7

C3O1 – SO2

0.1

2.5

0.4

7.1

C5O2 – SO2

0.2

2.2

1.0

6.8

C7O3 – SO2

0.3

1.9

1.8

6.4

System


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Structure of ionic liquids at interfaces

The main Fig. 5 shows ion–ion correlations of the C3O1-NTf2 ionic liquid exposed to vacuum and CO2 interface, indicating that ionic structure is essentially the same for the ionic liquid at these interfaces. The inset of Figure 5 shows that gαβ(r) of those ions is slightly shifted, comparing vacuum interface and bulk. Previous bulk and vacuum interface MD simulations of different ionic liquids showed similar effect on the ionic structure. 46

Figure 5. Radial distribution functions between nitrogen atoms of ions in C3O1-NTf2 ionic liquids at vacuum (lines) and CO2 interfaces (empty dots). The inset shows the bulk correlations (dashed lines) and at CO2 interface (empty dots).

Number density profiles of each species along the major axis of the simulation box are shown in Figure 6 for some of the simulated systems. Details of the interface regions in the right panels of Fig. 6 show that CO2 molecules (green lines) accumulate more at the interface than SO2 molecules (blue lines), prompting the gas phases with very low density. In contrast, the number of SO2 molecules in the bulk is higher than


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CO2 molecules. The consequence of volume expansion of the ionic liquid is that the interface is more displaced in the SO2 (dotted plus lines) than the CO2 (full lines) containing systems.

Figure 6. Number densities of ions, CO2 and SO2 gases molecules. The dotted plus lines and full lines are results obtained in simulations at CO2 and SO2 interfaces, respectively.

The bump observed in the density profiles at interfaces is higher for cations than anions. Concerning those cations at interface, the anisotropic molecular structure implies orientational order, in particular for the ammonium cation with one long chain. This is clearly seen in Figure 7, which shows the density profiles for each atom of cations at interface. The long chain of the cations points outwards the ionic liquid, so that the density profile of the end chain atoms overlap with the density profile of gas molecules that accumulate at the interface. Previous MD simulations of alkyl


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imidazolium based ionic liquids at interface with vacuum or CO2 also describe the occurrence of non-polar layer on the surface, in which the alkyl chain points outward the liquid phase.23 It is worth remembering that three of the ionic liquids studied here bear ether-functionalized chains, so that it is interesting to investigate the structure of polar chains at interface. The width of chain layers at interface were estimated by measuring the distance between the peaks of N and Ct densities shown in Figure 7: C4 – 4.16 Å; C3O1 – 2.90 Å; C5O2 – 4.08 Å; C7O3 – 5.31 Å. Therefore, the widths of cation chains at the interface of C3O1-NTf2 and C5O2-NTf2 ionic liquids are smaller than the layer of the alkyl chain in C4-NTf2, whereas that of C7O3-NTf2 is only ~ 1.30 Å larger. In case of all-trans conformation of the C7O3 cation, the N-Ct distance would be 11.7 Å, with C-O and C-C bond length 1.40 and 1.53 Å, respectively. These findings point out that the ether chains of cations are coiled. In fact, a characteristic feature of neat poly(ethylene oxide), PEO, and polymer electrolytes is the helicoidal structure of the polymer due to gauche OCCO conformers.47-49 Hence, the relative thin layer of chains of ether-functionalized ionic liquids is a manifestation of gauche conformation of OCCO dihedra.


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Figure 7. Number densities of CO2 molecule (dashed lines) and the chain atoms of cations at CO2 interface.

An alternative way of visualizing the distribution of ions and gas molecules is a plot of number density map of a given specie at the gas-liquid interface. Figure 8 shows examples of number density maps of ions and gas within a 5 Å width slice of the surface for the C3O1-NTf2. The uncertainties of number density maps of gases are around 10% of the average densities encoded by the colors. In the first 1.0 ns of exposure of C3O1-NTf2 to the gases, the ions are located in well-defined regions of the x-y plane (yellow-red spots), whereas the distribution of both gases is less defined on the surface. These findings are due to slow and fast dynamics of ions and gases, respectively. The number density maps of gases indicate that some places have high concentration of SO2 and CO2. In the CO2 case, the yellow ellipse in Fig. 8 encloses a region of high density of CO2, which is located in a region of low density of C3O1


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cations (black spots in the C3O1 density map). The red spots of CO2 and SO2 on the surface slice arise from gases molecules with longer time occupancies deeper into the slice and closer to the liquid phase (see Figure S1 in the Supporting Information). It is worth noting that the red-yellow spots of gases are mainly located where there is low density of ions, although closer to the neighborhood of yellow-red spots of NTf2 anions. Similar behaviors have been found for the other three ionic liquids interfaces (not shown).

Figure 8. Number density maps of ions and gas molecules on the surface of the C3O1NTf2 ionic liquid. Yellow indicates high density, red medium, and purple/black indicates low density.

Maps of densities of C7O3-NTf2 were also obtained for the next 5 Å slice from the surface deeper into the liquid phase. The yellow and green ellipses in the bottom panels of Fig 9 show that SO2 molecules populate regions that are cations rich. This inner slice corresponds to the z-axis range of high concentration of [NTf2]- that screens the high concentration of cation on the surface. Proper to the strong cation-


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anion interaction, the SO2 molecules in this inner slice look for another favorable site of interaction, such as the oxygen atoms of the ether chains. It should be noted that CO2 molecules in this inner slice of the ionic liquid still occupy places of low density of cations and closer to the anions (light-blue ellipses in the top panels of Fig. 9).

Figure 9. Number density maps of ions and gas molecules calculated within a 5 Å slice below the surface of C7O3-NTf2.

Thermodynamics of gas absorption.

Table 2 shows the mole fraction of CO2 and SO2 molecules absorbed by the four ionic liquids simulated at 350 K. We considered a given molecule as absorbed as long as it is located in the region in between the two peaks of the density profiles shown in Fig. 6. The calculated mole fraction of CO2 dissolved in C4-NTf2 ionic liquid is 0.36, which is in good agreement with the experimental value of ~0.4 at 333 K and pressure around 44 bar.17 In the authors knowledge, there are no experimental


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data available of CO2 or SO2 solubility in the ether-functionalized ionic liquids considered in this work. The mole fraction of CO2 is essentially the same in ionic liquids with or without ether function in short chains. The slightly higher mole fraction of CO2 in C7O3-NTf2 is probably due to the large molar volume of this ionic liquid, so that more gas molecules can be absorbed. Despite of the lower pressure of SO2 than CO2 in the MD simulations, the SO2 mole fractions are ca. 0.50, i.e. the investigated ionic liquids have the ability to absorb more SO2 than CO2. Therefore,

∆Gsolv is much more negative for SO2 than CO2 absorption. This finding is in line with the results of equilibrium structure of strong SO2 interactions with anions and oxygen atoms of the ether chain of cations. The trend of ∆Gsolv with the length of cation chain exhibits some outlined values because of difficulty of accurate calculation of ∆Gsolv by MD simulations.

Table 2. Solvation free energy of gases and mole fraction of gas absorbed. System

∆Gsol (kJ mol-1)

Mole fraction of gas absorbed

C4 – CO2

-0.32 ± 0.11

0.36

C3O1 – CO2

-0.56 ± 0.33

0.37

C5O2 – CO2

-0.1 ± 0.25

0.36

C7O3 – CO2

-0.26 ± 0.19

0.41

C4 – SO2

-7.46 ± 0.30

0.50

C3O1 – SO2

-7.75 ± 0.43

0.48

C5O2 – SO2

-7.96 ± 0.44

0.52

C7O3 – SO2

-7.63 ± 0.37

0.45


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We used the number density of CO2 and SO2 molecules to calculate potential of mean force, PMF, according to the equation:50

w(z) = RT ln

ρ (z) , ρo

(2)

where ρ(z) is the gas density at a given point on the z-axis, and ρo is the gas phase density. Profiles of PMF along the z-axis were calculated by using configurations of the last 10.0 ns of the simulations runs. Figure 10 shows the interface region of the PMF profiles calculated for the different systems simulated in this work. The negative valley of PMF at the interface is deeper for SO2 than CO2 absorption, and it deepens further as more oxygen atoms are available in cations with longer chains. The PMF remains significantly negative for SO2 towards the bulk, but it is positive for some liquids and oscillates near zero for CO2. We recall that the PMF calculated here considers the density number of CO2 accounting for the amount of CO2 that was absorbed. The positive values of PMF in the interior of some liquids suggest that longer simulations with addition of CO2 in the gas phase are still required in order to have the proper equilibrium of CO2. Nevertheless, the difference between CO2 and SO2 PMF is consistent with differences in ion–gas equilibrium structures and the small ∆Gsolv for CO2, and it will imply a dynamical counterpart discussed in the next section.


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Figure 10. Potential of mean force calculated from number densities of gas molecules.

Experimental studies have shown that the ability of an ionic liquid to absorb CO2 is mainly dominated by the nature of the anion, rather than the cation.4,9,17 Therefore, it is reasonable to compare the results obtained here with those obtained for different ionic liquids with the same anion. For instance, the PMF of CO2 in ionic liquids based on the 1-butyl-3-methylimidazolium cation, BMIM, calculated with the umbrella sampling algorithm exhibits a valley of -3.0 kJmol-1 close to the interface, and the PMF oscillates around zero in the bulk.23,26 In the case of SO2, the valley of PMF obtained from the MD simulations of BMIM-BF4 is ca. 10.0 kJmol-1 deeper than the ones we have obtained in this work.24 This difference might be related to the different nature of anions. In fact, Dang et al.25 obtained different deeps of the PMF valleys of CO2 on the surface depending on the anion, -10.0 and -3.0 kJ/mol, for


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BMIM-BF4 and BMIM-NTf2, respectively. In the case of SO2 absorption, the numerical difference between the PMF calculated in this work and by Dang’s group24 is also due to different properties of [NTf2]- and [BF4]- anions.

Dynamics of gas absorption.

Table 3 shows the diffusion coefficients of cations, anions, and acidic gases calculated for the bulk simulations, in which 50 molecules of CO2 or SO2 in cubic boxes containing 200 ion pairs were considered. The first two rows of Table 3 show that ionic diffusion increases as the ammonium cation becomes more flexible when oxygen atoms are inserted, while keeping the same chain length, as already addressed in a previous publication of our group.35 Dcation and Danion decrease as expected for longer chains, although the diffusion coefficients for the pure ionic liquid with the C7O3 cation are slightly higher than the C4 cation. Increase of Dcation and Danion take place when gases are dissolved. It is worth noting that the effect of gas absorption on ionic diffusion is higher for SO2 than CO2, even though the diffusion coefficient of SO2 is lower than CO2 in a given ionic liquid. Also, the box volume of a given ionic liquid is essentially the same with either CO2 or SO2 dissolved in. Therefore, the fast diffusion of ions in SO2 is related to effective shielding of ionic interactions in SO2 because of the strong anion–SO2 interaction. It was shown above that there is a significant population of SO2 molecules interacting with the atoms of the flexible C7O3 chain. Thus, the high diffusion coefficients in the last row of Table 3 are the consequence of highly mobile SO2 molecules in these soft domains of the ionic liquid with the long C7O3 chain. Even though the diffusion coefficient of CO2 also increases in the C7O3 system in comparison with ionic liquids of shorter chain, the increase of


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Page 22 of 42

CO2 mobility is not enough to increase anion and cation diffusion coefficients in the C7O3 ionic liquid.

Table 3. Diffusion coefficients of cations, anions, and gases at 350 K calculated in the bulk simulations. Dcation

Danion

Dgas

(10-7 cm2 s-1)

(10-7 cm2 s-1)

(10-7 cm2 s-1)

C4

1.47 ± 0.21

1.13 ± 0.24

-

C 3 O1

2.82 ± 0.23

2.12 ± 0.18

-

C 5 O2

2.31 ± 0.14

1.97 ± 0.17

-

C 7 O3

1.52 ± 0.27

1.33 ± 0.25

-

C4 – CO2

2.31 ± 0.18

2.33 ± 0.16

50.3 ± 4.02

C3O1 – CO2

3.12 ± 0.22

2.53 ± 0.18

52.9 ± 6.12

C5O2 – CO2

2.74 ± 0.18

2.76 ± 0.08

51.4 ± 3.21

C7O3 – CO2

2.55 ± 0.17

2.02 ± 0.19

71.8 ± 7.56

C4 – SO2

3.06 ± 0.22

3.05 ± 0.18

49.3 ± 2.32

C3O1 – SO2

3.50 ± 0.08

3.20 ± 0.21

36.4 ± 2.05

C5O2 – SO2

2.56 ± 0.50

2.10 ± 0.28

36.9 ± 5.77

C7O3 – SO2

3.83± 0.20

3.50 ± 0.57

62.7 ± 8.83

System

Residence time correlation functions, Cres(t), were calculated for CO2 and SO2 molecules in different slices of 5 Å width along the z-axis and close to the interface: C res (t) = hi (t) h (0) ,

(3)

where the Heaviside function hi(t) = 1 if the gas molecule i is found in the corresponding slice, and hi(t) = 0 otherwise. Figure 11 shows Cres(t) calculated for both gases at the gas–liquid interface, and for other two regions towards the liquid phase, as illustrated in the schematic picture on the top of Fig.11. The decay rate of Cres(t) in the surface region (slice 1) is lower for SO2 than CO2. It is worth mentioning


22

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that Cres(t) in this region accounts for adsorption and desorption phenomena of gases on the surface. The difference between SO2 and CO2 residence times can be correlated with the corresponding PMF close to the surface. In the gas phase, the PMF for both the gases is set to zero as reference, so that in order to desorption takes place the SO2 molecules need to overcome a higher energy barrier than CO2, ~ 9 kJ mol-1 and ~ 4 kJ mol-1, respectively. Therefore, the slow decay rate of Cres(t) for SO2 is the dynamical counterpart of more negative ∆Gsolv and PMF, and stronger anion–SO2 structures, in comparison with CO2. Concerning the slices 2 and 3 in Fig. 11, the inner the slice, the slower is the decay rate of Cres(t) for both the gases. Although there is a clear effect of ether chain length on diffusion coefficients of gas molecules, it is hard to infer from the decay rate of Cres(t) the corresponding chain length effect.

Figure 11. Normalized auto-correlation functions of residence time for CO2 and SO2 within different 5 Å width slices at the surface as indicated in the top figure.


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Page 24 of 42

IV. CONCLUSIONS

We have studied by molecular dynamics simulations four tetraalkylammonium ionic liquids as CO2 and SO2 absorbers. The SO2–anion interaction is stronger than CO2–anion interaction. The gas–anion interaction is not very dependent on the length of the chain of quaternary ammonium cations. The gas–cation interaction increases in ether-functionalized systems because of relatively short-range interactions between gas molecules and oxygen atoms of the ether chain. Cations with long ether chain have more oxygen atoms available to coordinate gas molecules, so that less oxygen atoms of [NTf2]-anions coordinate gas molecules. Number density profiles give a detailed view of population of ions and gas molecules across the interface. For the ionic liquids investigated in this work, CO2 accumulates more than SO2 at gas–liquid interface, whereas the number of SO2 molecules is higher than CO2 molecules in the bulk. The long ether chain of the ammonium cation, although coiled at the interface, points toward the gas phase, so that the end atoms of the chain overlap into the region in which gas molecules accumulate at the interface. The comparison of probability maps of occurrence of ions and gases on the surface indicates that gas molecules are close to [NTf2]- anions in regions of low density of ions. In case of SO2 molecules in a region just below the interface into the liquid phase, one can discern a population of SO2 molecules close to oxygen atoms of ether chains of cations. Thermodynamic consequences of these structural effects include a higher mole fraction, a more negative ∆Gsolv, and a more negative potential of mean force for SO2 than CO2 absorption in a given ionic liquid. The dynamical consequence is a significant increase of ionic diffusion after gas absorption, the effect on ionic


24

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diffusion being higher for SO2 than CO2 absorption. In line with more negative ∆Gsolv and potential of mean force for SO2 than CO2 absorption, the residence time of SO2 molecules at the interface is longer than CO2 molecules in a given ionic liquid.

ACKNOWLEDGMENTS

The authors acknowledge FAPESP and CNPq for financial support.

Supporting Information Available: Table S1 - Non-bonded parameters of intermolecular interaction potential. Table S2 to S5 – Intramolecular parameters used in the simulations. Table S6 – Box dimensions of the ionic liquids at interface with gases. Figure S1 - Number density maps of ions and CO2 molecules calculated at the interface of C3O1-NTf2. This material is available free of charge via the internet at http://pubs.acs.org.

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