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Molecular Design of High CO Reactivity and Low Viscosity Ionic Liquids for CO Separative Facilitated Transport Membranes 2

Akihito Otani, Yong Zhang, Tatsuya Matsuki, Eiji Kamio, Hideto Matsuyama, and Edward J. Maginn Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b00188 • Publication Date (Web): 26 Feb 2016 Downloaded from http://pubs.acs.org on February 29, 2016

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Industrial & Engineering Chemistry Research

Molecular Design of High CO2 Reactivity and Low Viscosity Ionic Liquids for CO2 Separative Facilitated Transport Membranes Akihito Otani,†,‡ Yong Zhang,† Tatsuya Matsuki,‡ Eiji Kamio,‡ Hideto Matsuyama,∗,‡ and Edward J. Maginn∗,† Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA, and Center for Membrane and Film Technology, Department of Chemical Science and Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501, Japan E-mail: [email protected]; [email protected]

Abstract The viscosities of ionic liquids (ILs) that chemically react with CO2 and contain an aprotic heterocyclic anion (AHA) change very little after CO2 absorption, whereas the viscosities of other kinds of reactive ILs increase dramatically after CO2 absorption. This unique property has overcome a major problem with IL-based facilitated transport membranes (FTMs), namely the low CO2 diffusivity caused by the extremely high liquid viscosity. This problem is especially severe at low temperature. In our preliminary experiments, the AHA IL tetrabutylphosphonium 2-cyanopyrrolide ([P4444 ][2 −CNpyrr]) ∗

To whom correspondence should be addressed University of Notre Dame ‡ Kobe University †

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was studied in a FTM and it exhibited good CO2 permeability and CO2 /N2 selectivity. [P4444 ][2 −CNpyrr] does not react as strongly with CO2 as other reactive ILs, however, and its viscosity is still somewhat high. The CO2 separation performance of an IL-based FTM is expected to be better if a lower viscosity IL is used that binds CO2 more strongly. In this work, several AHA ILs were studied and their CO2 reactivity and viscosity were calculated using molecular simulation. The IL triethyl(methoxymethyl)phosphonium pyrrolide ([P222(1o1) ][pyrr]) was predicted to have the highest reactivity and the lowest viscosity of the investigated AHA ILs, suggesting that its use in a FTM will lead to much higher CO2 permeability than previously reported IL-FTM systems such as [P4444 ][2 −CNpyrr]).

Introduction A number of CO2 separation technologies have been developed for the sake of CO2 capture and storage (CCS) especially for CO2 capture from flue gas at fossil fuel combustion sites. 1–7 In fact, there are over 1,000 patents on the subject of CO2 capture. 8 One approach being considered for CCS uses liquid absorbents, which can absorb CO2 either physically or chemically. 1–3 These systems generally consist of a CO2 absorption column and a thermal regeneration column. The CO2 is absorbed at low temperature (∼ 313 K) and desorbed at a higher temperature (∼ 383 K). Amine-based CO2 absorption processes of this type have already been commercialized. 1,9 Although this is a proven technology used to treat industrial gas streams, it is costly, energy intensive and has a large physical footprint. For example an amine system used to capture 90% of the CO2 in flue gas will require about 30% of the power produced by the plant and result in a CO2 capture cost of $40-100/ton CO2 , 10,11 Membrane-based separation of CO2 from flue gas is an attractive alternative to conventional absorption systems due to its operational simplicity, high energy efficiency, compact design and low capital cost. 12–14 A polymeric membrane CO2 separation process proposed by Membrane Technology and Research, Inc. is estimated to capture 90% of CO2 from flue gas 2


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using about 16% of plant energy at a cost as low as $23/ton CO2 . 10 Polymeric membranes have been widely investigated for CO2 separation 4,15–17 but it is still difficult to use them in practice due to their relatively low CO2 separation performance. 17 On the other hand, facilitated transport membranes (FTMs) are well-known to have high CO2 permselectivity because they contain chemically reactive CO2 carriers in the membrane. 18,19 These carriers react with CO2 on the surface of the feed side, transport them to the permeate side and finally release CO2 at the permeate side. Although existing FTMs show good performance, their CO2 permeability is strongly affected by the feed gas condition such as temperature, CO2 partial pressure and relative humidity, which limits their practical applicability. 18 Carrier stability is another key limiting factor. Carrier stabilities of the typical FTMs such as a polyvinyl alcohol-polyacrylic acid gel membrane with 2,3-diaminopropionic acid (DAPAFTM) and glycine Na-glycerol based FTM (Gly-FTM) are not good, especially under dry conditions. Conventional FTMs need moisture to maintain their carrier activity. 20,21 Kasahara et al. reported a new class of CO2 separative FTMs that utilize ILs having an amino acid anion. 22–24 The uniqueness of these amino acid-based ionic liquids (AAILs) is their high reaction site density; they bind one CO2 molecule for every amino acid anion. The AAILs are held in the pores of the membrane and act not only as a CO2 carrier but also as the diffusion medium. This uniqueness allows AAIL-FTMs to show excellent CO2 permeability over a wide range of gas conditions including dry condition where other FTMs usually do not work. 18 AAIL-FTMs such as tetrabutylphosphonium glycinate ([P4444 ][Gly]) based FTM, work as FTMs under dry conditions because AAILs absorb a large amount of CO2 under both dry and humid conditions. 22 Also, a long-term stability study of AAILFTMs showed them to be stable up to 130 hours at 373 K. 25 Under dry conditions, however, the CO2 permeability of this AAIL-FTM at room temperature is not as good as at elevated temperature due to the extremely high viscosity of this AAIL after CO2 absorption. Goodrich et al. reported that the viscosity of AAILs increases by two orders of magnitude after CO2 absorption. 26 Other reactive ILs also exhibit large viscosity increases when they react with

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CO2 . 27 It has been found that for these ILs, reaction with CO2 leads to the formation of a network of intermolecular hydrogen bonds, 28 which causes the viscosity to increase rapidly. A new class of reactive IL with aprotic heterocyclic anions (AHAs) has been reported by Gurkan et al. 29 For this particular class of IL, the reactive anion is incapable of forming intermolecular hydrogen bonds, suggesting that the viscosity will be insensitive to CO2 reaction. Indeed it was found that the viscosities of trihexyl(tetradecyl)phosphonium 2-cyanopyrrolide ([P66614 ][2 −CNpyrr]) are about the same before and after CO2 absorption. 29 Wu et al. analyzed the hydrogen bonding network of tetrabutylphosphonium 2-cyanopyrrolide ([P4444 ][2 −CNpyrr]) using molecular dynamics (MD) simulation. 30 They showed that the total number of hydrogen bonding sites of this AHA ILs is much less than on a cation-functionalized TSIL. 28 As a result, the dynamics are insensitive to the extent of reaction with CO2 . In our previous study, a [P4444 ][2 −CNpyrr]-based FTM was investigated for CO2 separation. 24 At around room temperature, the [P4444 ][2 −CNpyrr]-FTM exhibited a CO2 permeability more than 10 times higher than that of a tetrabutylphosphonium glycinate ([P4444 ][Gly])based FTM. The latter IL is the most well-studied AAIL-FTM. It is known, however, that 2-cyanopyrrolide does not bind CO2 as strongly as many other reactive ions, including many amino acid anions. As the binding energy with CO2 increases, the total amount of CO2 absorbed at a given condition increases and the CO2 -complex concentration gradient through the membrane becomes steeper. This results in an overall larger CO2 permeability. It is therefore desirable to find low viscosity AHA ILs that also bind CO2 as strongly as possible. The physical and chemical properties of ILs can be modified by changing the combination of anions and cations. Seo et al. introduced electron-withdrawing and steric hindering substituents on AHA-based ILs to control their CO2 reactivity. 31 Condemarin and Scovazzo found that the viscosity of phosphonium- and ammonium-based ILs were strongly affected by the cation size, with the smaller cation having lower viscosity. 32 Tsunashima and Sugiya compared ILs made with phosphonium and ammonium cations of the same nominal size and found that the viscosity of the phosphonium ILs was lower than that of the corresponding

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ammonium ILs. 33 Moreover, Tsunashima and Sugiya also reported that a small phosphonium cation with a methoxy group, triethyl(methoxymethyl)phosphonium ([P222(1o1) ]+ )), had extremely low viscosity. 33 Despite these promising results, predicting viscosity trends in ILs is difficult. In some cases, smaller ions actually lead to higher viscosities 34 and the addition of substituents that should reduce the interactions between ions can end up increasing viscosity. 35 Molecular simulations are an attractive means for obtaining the physical properties of ILs given only the structure and chemical composition of the ions. These simulations can be used to “screen” compounds for desired properties as well as to obtain a better physical understanding of the relationship between properties such as viscosity and the chemical structure of the ions. In this study, density functional theory (DFT) calculations were employed to compute the CO2 reactivity with different AHA ILs, and MD simulations were used to estimate the densities, mobilities and viscosities. The objective was to find AHA ILs with strong CO2 binding energy and low viscosity, which should lead to better performance in terms of selectivity and permeability for FTMs.

Methodology Molecular Dynamics Simulation In the present study, AHAs with/without substituents including (pyrrolide ([pyrr]– ), pyrazolide ([pyra]– ), 2-methoxypyrrolide ([2 −Mtpyrr]– ), 3-methoxypyrrolide ([3 −Mtpyrr]– ) and 2-cyanopyrrolide ([2 −CNpyrr]– )) were studied as candidate AHAs. These anions were paired with two candidate cations: tetraethylphosphonium ([P2222 ]+ ) and triethyl(methoxymethyl)phosphonium ([P222(1o1) ]+ ), the latter of which is expected to lower the viscosity because of its ether oxygens. 36 The chemical structures of the anions and cations are shown in Figure 1.

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force field (GAFF). 37 The partial atomic charges were computed from ab initio calculations in the gas phase using the restrained electrostatic potential (RESP) method. 38 The electronic structure calculations and geometry optimization were carried out with Gaussian 09 39 at the B3LYP/aug-cc-pVTZ level of theory. The total charge on an ion was constrained to ± 1.0 e. We note that GAFF does not have appropriate force field parameters for the bond between AHA and CO2 in the case of the reacted species, so these parameters were obtained by fitting to the ab initio calculations. Additional details are provided in the Supporting Information. Recent ab initio MD studies of a variety of ILs indicate that about 20% of the charge is shared with other ions due to the charge transfer between ions and polarization caused by the environment in the bulk phase. 40 To account for this, the partial atomic charges on each ion were uniformly scaled by a factor of 0.8. The MD simulation package LAMMPS 41 was employed to carry out isothermal-isobaric (NpT) ensemble simulations and canonical (NVT) ensemble simulations. The Nos´e-Hoover thermostat 42 was used to control the temperatures at 350, 400, 450 and 500 K, with a time constant (damping parameter) of 0.1 ps. For the NpT simulations, the extended Lagrangian approach was used to set the pressure at 1 atm, with a time constant of 0.1 ps. The cutoff for nonbond interactions was set to 12 Å, with a long-range van der Waals tail correction and the Ewald 43 method with an accuracy of 10−4 for Coulombic interaction. Initial configurations were generated by randomly inserting 140 - 180 ion pairs into a large periodic simulation box using the Packmol package. 44,45 The number of ion pairs was varied depending on the molecular size in order to have box lengths of at least 40 Å in all simulations. During operation of a FTM, the ratio of reacted to unreacted AHA ILs will vary along the length of the pore because the CO2 partial pressure is higher at the feed side of the membrane and lower at the permeate side. Therefore, five different compositions were simulated to represent different extents of reaction: 0 % reacted (100 % unreacted), 25 % reacted, 50 % reacted, 75 % reacted and 100 % reacted. Each system was relaxed by performing an energy minimization. After the energy minimization, a 2 ns NpT simulation was carried out to

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determine the density. This was followed by a 10 ns NVT run at the proper density, where the self-diffusion coefficient of the ILs was computed. Twenty snapshots were extracted from the NVT simulation trajectory. A 3 ns NVT simulation was carried out starting with each of the 20 snapshots with a new random velocity seed. These independent trajectories were used to estimate the viscosity. Velocities and coordinates were dumped every 500 fs and stress tensors every 5 fs.

Viscosity Calculation The shear viscosity, η, was calculated from the following Green-Kubo relation 46 V η= kB T

Z

∞ 0

hταβ (t0 + t) · ταβ (t0 )idt

(2)

where V is the volume of the system, kB is the Boltzmann constant and T is the temperature. Here, the angle bracket h...i indicates the ensemble average over all time origins t0 , and ταβ represents the stress tensor of element αβ. Eqn (2) was calculated by taking the average over six independent terms of the stress tensor, including τxy , τyz , τxz , 0.5(τxx − τyy ), 0.5(τyy − τzz ) and 0.5(τxx −τzz ). 47–49 Theoretically, the stress tensor autocorrelation function decays to zero in the long time limit and the integral in Eqn (2) reaches a constant value, which corresponds to the calculated shear viscosity. In practice, however, the running integral shows fluctuations at long times due to the accumulation of random noise from the correlation function. 48–50 Viscosity is a collective property so very long trajectories are needed. An alternative way to improve the accuracy is to run multiple independent trajectories and take the average of the running integrals. 51–53 In this work, we employed this time-decomposition method 51 and ran 20 independent NVT simulations with each trajectory 3 ns long. The first 1 ns of the trajectory was considered equilibration and discarded, while the final 2 ns were used to estimate the integral in 2.

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Reaction Enthalpy Estimation The reaction enthalpy of each AHA was estimated using the Gaussian 09 package. 39 Optimized geometries and energies of the AHAs, CO2 and AHA-CO2 complexes were computed at the B3LYP/6-311+G(d,p) level, with a tight force convergence criterion. Reaction en◦ thalpies at 298 K (∆Hrxn (298)) were calculated using the following equation

◦ ∆Hrxn = HAHA−CO2 − (HAHA + HCO2 )

(3)

Materials and Synthesis Triethylphosphine (1 M in THF), 2-cyanopyrrole (>96%), and anion-exchange resin (Amberlite IRN78 hydroxide form) were purchased from Sigma Aldrich (St. Louis, MO, USA). Bromomethyl methyl ether (>95%) was purchased from Tokyo Chemical Industry Co. (Tokyo, Japan). Hexane (>96%) was purchased from Wako Pure Chemicals Industry Ltd. (Osaka, Japan). All of regents were used as received. [P222(1o1) ][2 −CNpyrr] was synthesized by nucleophilic addition and neutralization using the following procedure. Bromomethyl methyl ether (6.30 g, 0.050 mol) was mixed with triethylphosphine (50 mL, 0.050 mol) for 6 hours at 353 K to carry out the nucleophilic addition. The product triethyl(methoxymethyl)phosphonium bromide ([P222(1o1) ][Br]), was crystallized in 500 mL hexane for 12 hours at room temperature. The white precipitate was dried at 333 K and the obtained crystallized [P222(1o1) ][Br] was dissolved into 150 mL of milli-Q water (Millipore). The [Br]– anion of [P222(1o1) ][Br] solution was exchanged to [OH]– by anion-exchange resin (80 g) to form [P222(1o1) ][OH]. After removing the anion-exchange resin by filtering, 2-cyanopyrrole (4.60 g, 0.050 mol) was added to [P222(1o1) ][OH] aqueous solution and stirred for 24 hours at room temperature. After the reaction, the solution was evaporated to remove the solvents at 313 K. The structure of the products were evaluated by 1 H NMR (ECZ 400S, JEOL RESONANCE Inc.) spectroscopy (details in the Supporting Information). 9



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Viscosity Measurements The viscosity of the [P222(1o1) ][2 −CNpyrr] was measured with an electro-magnetically spinning sphere viscometer (EMS-1000W, Kyoto Electronics Manufacturing Co., Ltd.) with an uncertainty of ±3%, using a metallic sphere at a constant rotation speed of 1000 rpm. The measurements were carried out in the temperature range of 303 to 373 K (± 0.1 K).

Results and Discussion Reaction Enthalpy Ab initio electronic structure calculations have provided the most directly predictive description of chemically reactive IL-CO2 systems. 29,31,54 Quantum chemistry computations can provide essential information such as molecular structure and reaction energies quite accurately. The structure of the unreacted and CO2 reacted anion were calculated at the B3LYP/6-311+G(d,p) level and the results are shown in the Supporting Information. The computed reaction enthalpies are listed in Table 1. The difference between the calculated results in the current work and those at the B3LYP/6-311++G(d,p) level using Gaussian 03 reported by Wu et al. are less than 0.7%. 54 For comparison, the experimental reaction enthalpy of CO2 with a 30 wt% monoethanolamine solution and with a 30 wt% Nmethyldiethanolamine solution at 313 K is -80 kJ mol−1 and -60 kJ mol−1 , respectively. 55 Table 1: Calculated reaction enthalpies of various AHAs. Calculations were carried out at the B3LYP/6-311+G(d,p) level. Anions [pyrr]– [pyra]– [2 −Mtpyrr]– [3 −Mtpyrr]– [2 −CNpyrr]–

◦ ∆Hrxn (kJ mol−1 ) -98.8 -74.2 -62.7 -93.8 -34.5

The pyrrolide anion is planar and aromatic. 56 The reactivity of its N center is strongly 10


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affected by the inductive effect of substitutions and π conjugation effect of the ring. According to Table 1, [2 −CNpyrr]– has the weakest binding with CO2 of all the AHAs investigated in this study because of the strong electron withdrawing cyano group. The steric effect is another important factor which controls the reactivity of AHA anions. For [2 −Mtpyrr]– and [3 −Mtpyrr]– , [2 −Mtpyrr]– showed 31.1 kJ mol−1 higher reaction enthalpy due to the steric effect of the substituent group at the 2 position. In the study of 2-substituted cyanopyrrolide and 3-substituted cyanopyrrolide, the reaction enthalpy of CO2 reaction differed by 21 kJ mol−1 , mainly because of the steric effect. 29 Because the -OCH3 group is bulkier than the cyano group, the steric effect is larger in these systems. [2 −CNpyrr]– was designed to have a moderate CO2 binding energy to reduce the cost of CO2 desorption in an absorption-based CO2 separation system. In contrast, the FTMbased CO2 separation system needs a highly reactive AHA-IL to achieve a large driving force by steepening the concentration gradient. In order to maintain high reactivity at high temperature (around 373 K), AHA ILs with reaction enthalpies under -70 kJ mol−1 are preferred. 54 Based on this criterion, all [pyrr]– , [pyra]– and [3 −Mtpyrr]– are satisfactory as FTM carriers. High reactivity usually means slower desorption rate and lower CO2 permeability. However, for the three steps of permeation (CO2 absorption on the feed side of the membrane, CO2 -carrier complex diffusion through the membrane and CO2 desorption on the permeate side), diffusion through the membrane is the rate-determining step of IL-FTMs. 24 Higher reactivity is required to achieve larger permeability, and lower viscosity is required to increase diffusion. Among the AHA anions investigated in this study, [pyrr]– has the lowest (most negative) reaction enthalpy, indicating that it has the potential to realize the largest driving force.

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Density All calculated densities and molar volumes are listed in the Supporting Information. The computed densities are lower than 1 g cm−3 , typical of many phosphonium-based ILs. 30,57–59 As Wu reported, the calculated density of each AHA IL decreases with increasing temperature, whereas the calculated densities of the AHA ILs increase linearly with an increase in the mole fraction of the reacted ILs. 30 AHA ILs with the [P222(1o1) ]+ cation had higher calculated densities than the corresponding ILs with the [P2222 ]+ cation. This phenomenon was also observed in the experimental studies. 60,61 In the study of aliphatic quaternary ammonium salts with perfluoroalkyltrifluoroborates, Zhou reported that the densities of ILs with [CF3 BF3 ]– and [C2 F5 BF3 ]– anions increase about 5% by substituting an alkyl group with an alkoxy substituent. 61 The same amount of increase is observed in the calculated density in the current work. These results indicate that the effects of the methoxymethyl group are properly described in the current work. In FTMs, the density of reaction sites is very important. If the size of CO2 carriers is small, the number of carriers per unit volume increases, and consequently so does the FTM performance. Therefore, AHA ILs with small molar volume are preferable. As shown in the Supporting Information, the molar volumes of ILs with [pyrr]– and [pyra]– anions are smaller than those of other ILs. From this point of view, [pyrr]– - and [pyra]– -based AHA ILs could be good candidates for efficient AHA IL-FTMs.

Viscosity Viscosity Calculation We previously reported that the accuracy of viscosity calculation can be improved by averaging the running integrals of the Green-Kubo relation (Eqn (2)) over multiple independent NVT simulations. 51 As mentioned above, 20 independent NVT simulations were carried out in this study and the averaged running integrals were used to calculate the viscosity. An

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example of such a calculation is shown in Figure 2. Because of the noise in the stress tensor autocorrelation function, the 20 running integrals start to deviate from one another at around 50 ps and the deviation becomes large at long time. Clearly, it is difficult to estimate the viscosity for this system from a single run. On the other hand, the averaged running integral shows smooth behavior. The average of the 20 running integrals and corresponding uncertainty are plotted in Figure 2. The standard deviation as a function of time was calculated by the following equation. v u u σ(t) = t

N

1 X (η(t)i − hη(t)i)2 N − 1 i=1

(4)

The result indicates that the error becomes larger at long times due to the accumulation of noise. As shown in Figure 2, the averaged running integral converged after roughly 200 ps, while individual trajectories start to diverge after this time. A systematic way of estimating the shear viscosity from the Green-Kubo relation is to fit the running integral in Eqn (2) to a function. This method can reduce the undesired effect of the noise in the long time region. An empirical double-decay exponential autocorrelation function of the form

η(t) = Aατ1 (1 − e−t/τ1 ) + A(1 − α)τ2 (1 − e−t/τ2 )

(5)

has been suggested before, where A, α, τ1 and τ2 are fitting parameters. 48,49 In this work, we employed Eqn (5) for the viscosity estimation and the cutoff time was determined by considering the relation between viscosity and standard deviation following our previous report. 51 The cutoff time tcutof f was chosen to be the time when σ(t) reaches 30% of viscosity. Detailed procedures and a discussion and all calculation results may be found in the Supporting Information. The computed viscosity was compared with available experimental data. The measured

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viscosity of [P222(1o1) ][2 −CNpyrr] and the corresponding computational results are plotted in Figure 3. The simulations were performed at elevated temperatures due to the fact that the viscosities at low temperatures were too high to be reliably computed. Because of the limitations of the experimental apparatus, the highest temperature we were able to measure viscosities was 373 K. In order to estimate the experimental viscosities at elevated temperatures, and thereby compare them with simulation results, the Vogel-Fulcher-Tammann (VFT) equation

η = AT

0.5

k exp T − T0

(6)

was used where A, k and T0 are fitting parameters. 24,58,62,63 The experimental data were fit to the VFT equation (Eqn (6)) using the Levenberg-Marquardt algorithm and are shown in Figure 3 as a dashed curve. The fitting results are A = 3.30 ×10−3 mPa s K−0.5 , k = 795 K and T0 = 209 K. The computations slightly underestimate the viscosity at low temperatures, but as the viscosity gets smaller at high temperatures, the absolute difference between the experimental and computed viscosity becomes small. Extents of Reaction The calculated dependence of the viscosity on the extent of reaction is shown in Figure 4 for the [P2222 ][pyrr] system. Similar behavior was observed for the other AHA ILs. Generally speaking, as the extent of reaction increases, the viscosity increases but only very slightly. This result is consistent with what has been observed experimentally for other AHA ILs; the viscosity of these materials is insensitive to the extent of reaction with CO2 . Anion Effects The effect of the anion on the viscosity was investigated. The computed viscosities of AHA ILs with the [P2222 ]+ cation at the reaction extents of 0%, 50% and 100% are plotted in

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Figure 5 for five different AHAs. As can be observed, the anion effects on viscosity are quite small. With the exception of the fully reacted systems, all AHA ILs with the [P2222 ]+ cation showed almost the same viscosity. We believe this is due to the fact that their molecular structures and sizes are similar. When all the anions are reacted with CO2 , however, there are slight differences in viscosities, with [P2222 ][pyrr] exhibiting a consistently lower viscosity than the other ILs. This may be due to the fact that the [pyrr] anion binds CO2 more strongly than the other anions, and so it has the most compact planar shape, a feature known to enhance dynamics. 34 Cation Effects To achieve higher CO2 separation performance, lower viscosity is preferable. However, as shown in the previous section, the viscosities are similar for all AHA ILs with similar anion structures. Therefore, to design AHA ILs with lower viscosity, modification of the cation is considered. Tsunashima and Sugiya studied experimentally the cation effects on viscosity of unreactive ILs and found that triethyl(methoxymethyl)phosphonium bis(trifluoromethylsulfonyl)imide ([P222(1o1) ][TFSI]) had extremely low viscosity. 33 In the present study, [P222(1o1) ]+ was paired with AHA anions and their viscosities were calculated. The effect of the cation was investigated by comparing the computed viscosity of [P2222 ][pyrr] and [P222(1o1) ][pyrr] in Figure 6. At all the extents of the reaction, the viscosity of [P222(1o1) ][pyrr] is always lower than that of [P2222 ][pyrr]. The same results were obtained at other extents of reaction and in all other AHA IL systems (results not shown). Zhou et al. reported that flexibility of methoxyalkyl groups may increase ion mobility and therefore decrease viscosity. 61 Experimentally, it is difficult to confirm this effect. However, mobility of a given species can be calculated by tracking the movement of ions in the MD simulation. Therefore, the enhancement of the ion mobility was investigated by directly calculating the ion mobility. The ion mobility was calculated as the mean square displacement

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(MSD)

− − MSD(t) = [→ r i (t) − → r i (0)]2

(7)

− where → r i (t) is the position of the center of mass (COM) of the ion i at time t. In the MSD calculations, the first 1 ns of the trajectory was ignored due to the non-equilibrium region and averaged MSDs were calculated from three independent 10 ns trajectories. The averaged MSDs of [P2222 ][pyrr] and [P222(1o1) ][pyrr] at the reaction extents of 0%, 50% and 100% are plotted in Figure 7. Error bars in Figure 7 represent the standard deviation among the independent trajectories. In Figure 7, MSDs of the anions are larger than those of the cations. This is likely because of the smaller molecular size of the anions, and the fact that they are mostly planar. 34 The same phenomenon is observed in the comparison of [pyrr]– and reacted [pyrr−CO2 ]– anions. In Figure 7 (b), the MSD of the larger [pyrr−CO2 ]– anions is smaller than that of the unreacted [pyrr]– . It is interesting to notice that the MSD of [P222(1o1) ]+ is larger than that of [P2222 ]+ . This result suggests that the methoxymethyl group on the phosphonium cations does indeed induce greater cation mobility and thus lower viscosity.

Expected Performance As described in the discussion above, [P222(1o1) ][pyrr] was found to have the greatest CO2 binding energy and the lowest viscosity among the AHA ILs investigated in this study. In order to compare the performance of [P222(1o1) ][pyrr]-FTM with existing FTMs, the CO2 permeability of [P222(1o1) ][pyrr]-FTM was studied. The CO2 permeation through the membrane can be divided into three steps, CO2 absorption by carriers on the feed side, diffusion of the CO2 -carrier complexes and CO2 desorption on the permeate side. The rate-determining step of the CO2 permeation through the TSIL-FTMs is the diffusion step. 24 Therefore, CO2 permeability of AHA IL-FTMs, RCO2 , can be predicted by estimating the diffusion rate of 21




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CO2 -carrier complexes. RCO2 =

ǫ Ccom,f − Ccom,p Dcom τ PCO2 ,f − PCO2 ,p

(8)

Here, ǫ and τ are the dimensionless porosity and tortuosity, which were 0.5 and 1.2, respectively. Dcom (m2 s−1 ), Ccom (mol m−3 ) and PCO2 (kPa) are the diffusion coefficient of the CO2 complexes in the ILs, the concentrations of CO2 complex near the surface of the membrane and CO2 partial pressure, and the subscripts f and p represent the membrane feed side and permeate side, respectively. Dcom was estimated by using the Wilke-Chang equation 64

Dcom = 7.4 × 10

−12

√

ψIL MIL T ηVcom 0.6

(9)

where the subscripts "IL" and "com" denote the unreacted IL and the reacted complex between the anion and CO2 , respectively. ψIL , MIL (g mol−1 ) and Vcom (cm3 mol−1 ) are the dimensionless association constant, molecular weight of the ionic liquid and the molecular volume of the complex between the anion and CO2 , respectively. In our calculation of [P222(1o1) ][pyrr], ψIL was 2, the same as that in previous calculations for [P4444 ][Gly] and [P4444 ][2 −CNpyrr], while Vcom was 122 cm3 mol−1 . 24 The computed viscosity of [P222(1o1) ][pyrr] was used here to estimate the CO2 permeability in [P222(1o1) ][pyrr]-FTM. The composition of the unreacted ILs and reacted ILs would be different at arbitrary position through the membrane but because the viscosity of the AHA ILs is insensitive to the composition, and given the fact that the pyrrolide anion is very reactive, the viscosity value of the 100% reacted system was used in the calculation. The temperature dependency of viscosity was calculated using the VFT equation. For the 100% reacted [P222(1o1) ][pyrr] system, the fitting results were found to be A = 1.24 ×10−3 mPa s K−0.5 , k = 800 K and T0 = 209 K. PCO2 ,p and Ccom,p are zero due to the experimental conditions in which the the permeate side of the membrane is swept with He gas. Ccom,f is calculated from the CO2 absorption 23



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isotherm

Ccom,f =

KH,CO2 PCO2 (Kcom CIL,0 + Kcom KH,CO2 PCO2 + 1) Kcom KH,CO2 PCO2 + 1

(10)

where KH,CO2 (mol m−3 kPa−1 ) and Kcom (m3 mol−1 ) are the Henry’s law constant of the CO2 physical absorption and the equilibrium constant of the AHA IL-CO2 complex formation reaction, respectively. Detailed derivation of Eqn (10) was reported in previous work. 24 KH,CO2 and Kcom at various temperatures were calculated from the following van’t Hoff relationships ∆HCO2 ∆SCO2 + RT R

(11)

∆Hcom ∆Scom + RT R

(12)

lnKH,CO2 = −

lnKcom = −

Computed reaction enthalpy of [pyrr]– was used here to estimate Ccom,f of [P222(1o1) ][pyrr]FTM. In this estimation, other thermodynamic constants including the Henry’s law constants and the reaction entropy are also needed but are not available for this system. The Henry’s law constants of [P4444 ][Gly] and [P2225 ][Gly] for N2 absorption were found to have similar values (0.29 and 0.27 mol m−3 kPa−1 at 313 K, respectively, and values at other temperatures are similar, too). 57 The entropy change of CO2 absorption is dominated by the entropy loss of the CO2 molecule upon changing from an ideal gas state to a liquid state, 65 so it is expected that the absorption of CO2 in most ILs shows similar entropy change. 31 Therefore, in the current work the experimental values of Henry’s law constant and the reaction entropy of [P4444 ][2 −CNpyrr] were used in the calculation. The calculated CO2 permeability of [P222(1o1) ][pyrr]-FTM and previous FTMs are shown in Figure 8. It is likely that the calculated CO2 permeability in [P222(1o1) ][pyrr]-FTM have certain errors due to the use of the Henry’s law constants and the reaction entropy of an24


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other IL. But it is believed that these errors are small and it is possible to compare these results with the results in other FTMs. As shown in Figure 8, the CO2 permeability in [P4444 ][2 −CNpyrr]-FTM decreases at high temperature because [P4444 ][2 −CNpyrr] does not absorb CO2 well due to its low reactivity at high temperatures. On the other hand, the CO2 permeability in [P222(1o1) ][pyrr]-FTM does not decrease because the reactivity is high even at high temperatures. The expected CO2 permeability in [P222(1o1) ][pyrr]-FTM is around 100,000 Barrers at 373 K which is about 100 times higher than that in [P4444 ][2 −CNpyrr]FTM. This high permeability is mainly due to the low viscosity of [P222(1o1) ]+ -based AHA ILs. In practice, however, the rate-determining step may change from pore diffusion step to the desorption step, especially at high temperature where the viscosity is low. In this case, the performance may be lower in the [P222(1o1) ][pyrr]-FTM system. In the case that the ratedetermining step is the desorption step, AHAs with lower reaction enthalpy are preferable in order to increase the desorption rate. If this is found to be the case, then the [pyrr]– anion, which has a reaction enthalpy of -99 kJ mol−1 , could be replaced by other AHAs that bind CO2 less strongly. For example, [pyra]– has a reaction enthalpy of -74 kJ mol−1 and a similar molar volume to [pyrr]– . It is therefore expected to have higher desorption rate.

Conclusion AHA ILs with high CO2 reactivity and low viscosity are expected to improve the CO2 separation performance of FTMs. In this study, several AHA ILs were studied for CO2 separative FTMs and their CO2 reactivity and viscosity were computed. [pyrr]– was found to have much higher CO2 reactivity than [2 −CNpyrr]– . AHA ILs with [P222(1o1) ]+ showed lower viscosity than the ones with [P2222 ]+ . Therefore, [P222(1o1) ][pyrr]-FTM is expected to show better performance than previous FTMs. The CO2 permeability was estimated based on the simulation results of [P222(1o1) ][pyrr]-FTM and better performance than previous ILFTMs was obtained. However, CO2 permeability in [P222(1o1) ][pyrr]-FTM can be lower than

25




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Acknowledgement The authors thank computational resources for the Center for Research Computing (CRC) at the University of Notre Dame, and the financial support of the Research Organization for Membrane and Film Technology, Japan. This experimental work was supported by the Japan Science and Technology Agency-Advanced Low Carbon Technology Research and Development Program (JST-ALCA). YZ and EM thank the support of the U.S. Department of Energy, Basic Energy Science, Joint Center for Energy Storage Research under contract no. DE-AC02-06CH11357.

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