Ion-Gated Gas Separation through Porous Graphene

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Online Supporting Information for: Ion-Gated Gas Separation through Porous Graphene Ziqi Tian, Shannon M. Mahurin, Sheng Dai,*,, and De-en Jiang *, Department of Chemistry, University of California, Riverside, California 92521, United States Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996, United States *Corresponding authors: dais@ornl.gov; djiang@ucr.edu Table of Contents 1. Computational details 2. Pore-size modulation by the anion as reflected by the pore-anion distance 3. Gas permeation through the IL/graphene composite membranes of different pore sizes 4. Gas permeation through the [emim]bf 4 monolayer without the graphene layer 5. Effect of ionic liquid thickness on gas permeation 6. Force field parameters 7. References 1. Computational details Classical molecular dynamics (CMD) simulations were performed with the LAMMPS package 1 in the canonical (NVT) ensemble with two-dimensional periodic boundary condition (PBC) in xy directions. The porous graphene was fixed in the box, with dimensions of 49.2 Å by 42.6 Å in x and y directions, respectively. Forty ionic liquid pairs were coated above the surface in the case of a monolayer. Fifty gas molecules were placed in the gas phase above the ionic liquid layer on the feed side of the bichamber setup. The initial height of the feed-side chamber was adjusted to make the initial gas pressure at 10 atm, determined by the Peng Robinson equation. A vacuum layer was added on the other side of the porous graphene in the bi-chamber setup as the permeate side, with a thickness of 90 Å. During simulation, the size of the simulation box was fixed. The non-polarizable OPLS-AA type force field 2 was employed for the ionic liquids. Lennard- Jones parameters for the [emim] cation and all parameters for the BF 4 - and PF 6 - anions were from Liu et al. 3 The parameters for the bonded terms of the [emim] cation were from Borodin. 4 The partial atomic charges for the [emim] cation were obtained by fitting to the electrostatic potential at the B3LYP/6-31g(d) level from the RESP method of the Merz Kollman scheme. This set of parameters for [emim][bf 4 ] and [emim][pf 6 ] could well reproduce their bulk dynamic properties, as shown in our previous work. 5 The atomic charges of porous graphene were obtained based on DFT-derived electrostatic potential, also known as the Repeating Electrostatic Potential Extracted Atomic charges (REPEAT) method. 6 Regarding the Lennard-Jones terms for the carbon atoms in the graphene layer, we chose 0.086 kcal/mol for ε and 3.4 Å for σ as recommended, 7-8 while ε of 0.015 kcal/mol and σ of 2.45 Å were used for the terminating hydrogen atoms around the graphene pore rim. For CO 2 and N 2, three-site models were adopted, 9, 10 as our previous simulation. 11 All-atom model was used for methane. 2 Lennard-Jones potential terms were evaluated via the Lorentz-Berthelot mixing rule with a cutoff of 12 Å. S1

To calculate the long-range electrostatic interaction in the 2D periodic simulation cell, we used the 3D Particle-Particle-Particle-Mesh (PPPM) method with a slab correction for our main simulation runs. In the z-direction, a fictitious empty volume was inserted between the 2D slabs to correct the interslab dipolar interactions. Since the PPPM method is time-consuming for the periodic 2D system, 12 we also used a much faster truncation method for our parallel runs to obtain statistics on gas permeance, whereby a cutoff of 15 Å was used for the electrostatic interactions. Our tests showed that these two methods give very similar gas permeation data for the same system. All the data reported in this work were averaged over 20 parallel simulations from various initial velocity distributions. For each simulation, at the beginning, the ionic liquid layer was heated up to 1000 K for 1 ns and quenched to 300 K in 1 ns, to disperse the ionic liquid on porous graphene evenly. In most cases, ionic liquid formed a uniform layer, covering all the nanopores. After ionic liquid coating, 25 ns simulation was carried out in NVT ensemble. Temperature of ionic liquid and gas were kept at 300 K 13, 14 with the Nose-Hoover algorithm. 2. Pore-size modulation by the anion as reflected by the pore-anion distance Figure S1. Probability distribution of the distance from the pore center to the center of the closest BF 4 - anion for the [emim][bf 4 ]/6.0-Å-porous-graphene system (Figure 1c in the main text): with and without the CO 2 gas (w/o gas). S2

3. Gas permeation through the IL/graphene composite membranes of different pore sizes Figure S2. (a) A larger graphene pore of 9.6 Å in size; (b) a smaller graphene pore of 4.2 Å in size; (c) permeation of CO 2 and CH 4 through the [emim][bf 4 ]/9.6-Å-porous-graphene system. 4. Gas permeation through the [emim][bf 4 ] monolayer without the graphene layer Figure S3. Comparison of CO 2 and CH 4 permeation through a hypothetical unsupported ionic liquid layer at the same simulation conditions used in Figure 4 in the text. The centers of mass for both cations and anions are fixed to prevent the collapse of the membrane. S3

5. Effect of ionic liquid thickness on gas permeation Figure S4. Permeation of CO 2 and CH 4 through the [emim][bf 4 ]/6.0-Å-porous-graphene system for different thickness of the [emim][bf 4 ] ionic liquid (IL) layer. 6. Force field parameters 6.1 Gas molecules Table S1. Partial atomic charges and Lennard-Jones parameters for gas molecules ε / kcal/mol σ / Å q / e CO 2 C 0.0559 2.757 0.6512 O 0.1600 2.565-0.3256 N 2 N 0.0728 3.318-0.4048 Center of Mass 0 0 0.8096 CH 4 C 0.0664 3.500-0.2400 H 0.0300 2.500 0.0600 6.2 Ionic liquids The OPLS force field was used for the ionic liquids The non-bonded term includes the Lennard-Jones and the Columbic interaction; the bonded term is expressed below: E bonded = K b (R R 0 ) 2 + K θ (θ θ 0 ) 2 + K φ [1 + d cos(nφ)] 2 bonds angles dihedrals impropers S4

Scheme 1. Partial atomic charges on the [emim], BF 4, and PF 6 ions. Atoms are labelled for the bonded-term parameters. Table S2. Lennard-Jones parameters for the ionic liquids ε / kcal/mol σ / Å Emim C (sp2; on the ring) 0.0860 3.400 C (sp3; off the ring) 0.0110 3.400 N 0.1700 3.250 H (-CH 3 ) 0.0157 2.500 H (-CH 2 -) 0.0157 2.650 H (on the ring) 0.0150 2.450 Anions B 0.0950 3.581 P 0.2000 3.742 F 0.0610 3.118 Bonded terms for the emim, BF 4, and PF 6 ion (K R, K θ, Kφ all in kcal/mol) Bond K R R 0 / Å C-Cm 309.0 1.520 H-Cm 327.5 1.100 C-N 369.5 1.472 Cm-N 369.5 1.472 H-C 327.5 1.100 Cc-N 650.0 1.372 Cc-Cc 309.0 1.353 H-Cc 327.5 1.083 B-F 290.0 1.389 P-F 190.0 1.600 Angle K θ θ 0 / H-Cm-C 43.0 110.5 H-Cm-H 38.5 107.7 Cm-C-N 70.0 109.0 H-C-N 35.0 104.6 C-N-Cc 70.0 124.3 S5

Cc-N-Cc 70.0 109.6 Cc-Cc-N 72.0 106.7 H-Cc-N 35.0 122.7 H-Cc-Cc 36.0 130.6 N-Cc-N 70.0 111.4 H-Cm-N 35.0 108.3 F-B-F 49.9 109.5 F-P-F 80.0 90.0/180.0 Dihedral Kφ d n N-Cc-N-Cc 10.000-1 2 N-Cc-N-Cm 2.000-1 2 H-Cc-N-Cc 1.500-1 2 H-Cc-N-Cm 1.500-1 2 Cc-Cc-N-Cc 10.000-1 2 Cc-Cc-N-Cm 2.000-1 2 N-Cc-Cc-H 1.500-1 2 N-Cc-Cc-N 10.000-1 2 H-Cc-Cc-H 1.500-1 2 N-C-Cm-H 0.160 1 3 H-C-Cm-H 0.150 1 3 H-Cm-N-Cc 0.164 1 3 Improper Kφ d n N-N-Cc-H 1.1-1 2 Cc-N-Cc-H 1.1-1 2 Cc-Cc-N-C 2.0-1 2 6.3 Porous graphene Table S3. Lennard-Jones parameters for C and H atoms on the porous graphene ε / kcal/mol σ / Å C 0.0860 3.400 H 0.0150 2.450 Cartesian coordinates (Å) and partial atomic charges on the 6.0-Å porous graphene Rectangular unit cell: a=24.60 Å, b=21.30 Å q / e x y H 0.1480 9.490680 8.388491 H 0.1490 13.475880 7.446969 H 0.1490 16.285200 10.420645 H 0.1490 8.314800 12.299428 H 0.1490 11.124120 15.275234 H 0.1490 15.109320 14.333712 H 0.1490 11.124120 7.446969 H 0.1480 15.109320 8.388491 H 0.1490 8.314800 10.420645 H 0.1490 9.490680 14.333712 H 0.1490 13.475880 15.275234 H 0.1490 16.285200 12.299428 S6

C 0.0000 0.000000-0.002130 C -0.0010 1.230000 2.128010 C 0.0000 0.000000 1.420803 C 0.0010 1.230000 3.548813 C 0.0000 2.462460 0.000000 C -0.0020 3.692460 2.125880 C 0.0000 2.462460 1.420803 C 0.0020 3.690000 3.548813 C -0.0010 4.922460 0.000000 C -0.0020 6.154920 2.130140 C 0.0000 4.922460 1.420803 C 0.0080 6.154920 3.553074 C -0.0030 7.384920-0.002130 C 0.0050 8.612460 2.134400 C -0.0020 7.384920 1.422934 C -0.0060 8.614920 3.557334 C 0.0000 9.842460 0.000000 C -0.0060 11.070000 2.125880 C 0.0010 9.842460 1.420803 C 0.0150 11.070000 3.548813 C 0.0030 12.300000 0.000000 C -0.0060 13.530000 2.125880 C 0.0030 12.300000 1.420803 C 0.0150 13.530000 3.548813 C 0.0000 14.757540 0.000000 C 0.0050 15.987540 2.134400 C 0.0010 14.757540 1.420803 C -0.0060 15.985080 3.557334 C -0.0030 17.215080-0.002130 C -0.0030 18.445080 2.130140 C -0.0020 17.215080 1.422934 C 0.0080 18.445080 3.553074 C -0.0010 19.677540 0.000000 C -0.0020 20.907540 2.125880 C 0.0000 19.677540 1.420803 C 0.0020 20.910000 3.548813 C 0.0000 22.137540 0.000000 C -0.0010 23.370000 2.128010 C 0.0000 22.137540 1.420803 C 0.0010 23.370000 3.548813 C -0.0010 0.000000 4.256020 C -0.0010 1.227540 6.386160 C 0.0000 0.000000 5.678953 C 0.0010 1.227540 7.809093 C -0.0010 2.460000 4.256020 C 0.0020 3.685080 6.384030 C 0.0000 2.457540 5.676823 C -0.0020 3.680160 7.809093 C -0.0010 4.917540 4.258150 C 0.0120 6.145080 6.386160 C -0.0050 4.912620 5.674693 S7

C -0.0170 6.132780 7.800573 C -0.0080 7.382460 4.264540 C 0.0780 8.607540 6.415982 C -0.0170 7.380000 5.687474 C -0.3010 8.570640 7.804833 C -0.0180 9.844920 4.264540 C -0.3030 11.079840 6.358468 C 0.0810 9.864600 5.695994 C -0.0230 12.300000 4.245369 C -0.3030 13.520160 6.358468 C 0.1910 12.300000 5.668303 C -0.0180 14.755080 4.264540 C 0.0780 15.992460 6.415982 C 0.0810 14.735400 5.695994 C -0.3010 16.029360 7.804833 C -0.0080 17.217540 4.264540 C 0.0120 18.454920 6.386160 C -0.0170 17.220000 5.687474 C -0.0180 18.467220 7.800573 C -0.0010 19.682460 4.258150 C 0.0020 20.914920 6.384030 C -0.0060 19.687380 5.674693 C -0.0020 20.919840 7.809093 C -0.0010 22.140000 4.256020 C 0.0000 23.372460 6.386160 C 0.0000 22.142460 5.676823 C 0.0010 23.372460 7.809093 C -0.0010 0.000000 8.516300 C -0.0020 1.230000 10.650700 C 0.0000 0.000000 9.943494 C -0.0010 1.230000 12.071503 C -0.0020 2.457540 8.516300 C -0.0080 3.692460 10.644310 C 0.0080 2.464920 9.941363 C -0.0070 3.692460 12.077894 C 0.0080 4.912620 8.516300 C 0.0800 6.172140 10.633659 C -0.0150 4.920000 9.937103 C 0.0800 6.172140 12.088545 C 0.1890 7.365240 8.509909 C -0.3020 7.348020 9.915802 C 0.1890 17.234760 8.509909 C 0.0800 18.427860 10.633659 C -0.3020 17.251980 9.915802 C 0.0800 18.427860 12.088545 C 0.0080 19.687380 8.516300 C -0.0080 20.907540 10.644310 C -0.0150 19.680000 9.937103 C -0.0070 20.907540 12.077894 C -0.0020 22.142460 8.516300 C -0.0020 23.370000 10.650700 S8

C 0.0080 22.135080 9.941363 C -0.0010 23.370000 12.071503 C -0.0010 0.000000 12.778710 C 0.0010 1.227540 14.913110 C 0.0000 0.000000 14.205904 C -0.0030 1.227540 16.333914 C 0.0070 2.464920 12.780840 C -0.0040 3.680160 14.913110 C 0.0000 2.457540 14.203774 C 0.0020 3.685080 16.338174 C -0.0180 4.920000 12.785100 C -0.0230 6.132780 14.919501 C 0.0130 4.912620 14.203774 C 0.0150 6.145080 16.336044 C -0.3020 7.348020 12.804272 C -0.3040 8.570640 14.917370 C 0.1930 7.365240 14.212294 C 0.0800 8.607540 16.304092 C -0.3020 11.079840 16.363735 C -0.3020 13.520160 16.363735 C -0.3040 16.029360 14.917370 C 0.0800 15.992460 16.304092 C -0.3020 17.251980 12.804272 C -0.0230 18.467220 14.919501 C 0.1930 17.234760 14.212294 C 0.0150 18.454920 16.336044 C -0.0180 19.680000 12.785100 C -0.0040 20.919840 14.913110 C 0.0130 19.687380 14.203774 C 0.0020 20.914920 16.338174 C 0.0070 22.135080 12.780840 C 0.0010 23.372460 14.913110 C 0.0000 22.142460 14.203774 C -0.0030 23.372460 16.333914 C 0.0030 0.000000 17.041120 C -0.0010 1.230000 19.173390 C 0.0000 0.000000 18.466184 C 0.0000 1.230000 20.594194 C 0.0020 2.457540 17.045380 C -0.0010 3.690000 19.171260 C 0.0000 2.460000 18.464054 C 0.0000 3.692460 20.594194 C -0.0060 4.912620 17.045380 C 0.0060 6.154920 19.167000 C 0.0010 4.917540 18.464054 C -0.0010 6.154920 20.592063 C -0.0200 7.380000 17.032599 C -0.0100 8.614920 19.164870 C -0.0040 7.382460 18.457663 C 0.0080 8.612460 20.587803 C 0.0790 9.864600 17.026209 S9

C 0.0130 11.070000 19.173390 C -0.0160 9.844920 18.457663 C -0.0050 11.070000 20.596324 C 0.1900 12.300000 17.051771 C 0.0130 13.530000 19.173390 C -0.0220 12.300000 18.476834 C -0.0050 13.530000 20.596324 C 0.0790 14.735400 17.026209 C -0.0100 15.985080 19.164870 C -0.0160 14.755080 18.457663 C 0.0080 15.987540 20.587803 C -0.0200 17.220000 17.032599 C 0.0060 18.445080 19.167000 C -0.0040 17.217540 18.457663 C -0.0010 18.445080 20.592063 C -0.0060 19.687380 17.045380 C -0.0010 20.910000 19.171260 C 0.0010 19.682460 18.464054 C 0.0000 20.907540 20.594194 C 0.0020 22.142460 17.045380 C -0.0010 23.370000 19.173390 C 0.0000 22.140000 18.464054 C 0.0000 23.370000 20.594194 7. References (1) Plimpton, S. J. Comput. Phys. 1995, 117, 1-19. (2) Jorgensen, W. L.; Maxwell, D. S.; TiradoRives, J. J. Am. Chem. Soc. 1996, 118, 11225-11236. (3) Liu, Z. P.; Huang, S. P.; Wang, W. C. J. Phys. Chem. B 2004, 108, 12978-12989. (4) Borodin, O. J. Phys. Chem. B 2009, 113, 11463-11478. (5) Babarao, R.; Dai, S.; Jiang, D. E. J. Phys. Chem. B 2011, 115, 9789-9794. (6) Campana, C.; Mussard, B.; Woo, T. K. J. Chem. Theory Comput. 2009, 5, 2866-2878. (7) Sidorenkov, A. V.; Kolesnikova, S. V.; Saletsky, A. M. Eur Phys J B 2016, 89, 220. (8) Wang, J. M.; Cieplak, P.; Kollman, P. A. J. Comput. Chem. 2000, 21, 1049-1074. (9) Murthy, C. S.; Singer, K.; Klein, M. L.; Mcdonald, I. R. Mol. Phys. 1980, 41, 1387-1399. (10) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, 12021-12024. (11) Liu, H. J.; Dai, S.; Jiang, D. E. Nanoscale 2013, 5, 9984-9987. (12) Yeh, I. C.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, 3155-3162. (13) Nose, S. J. Chem. Phys. 1984, 81, 511-519. (14) Hoover, W. G. Phys. Rev. A 1985, 31, 1695-1697. S10

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