Ion-Gated Gas Separation through Porous Graphene

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1 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: 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 kcal/mol for ε and 3.4 Å for σ as recommended, 7-8 while ε of 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

2 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 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

4 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 O N 2 N Center of Mass CH 4 C H 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

5 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) C (sp3; off the ring) N H (-CH 3 ) H (-CH 2 -) H (on the ring) Anions B P F 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 H-Cm C-N Cm-N H-C Cc-N Cc-Cc H-Cc B-F P-F Angle K θ θ 0 / H-Cm-C H-Cm-H Cm-C-N H-C-N C-N-Cc S5

6 Cc-N-Cc Cc-Cc-N H-Cc-N H-Cc-Cc N-Cc-N H-Cm-N F-B-F F-P-F /180.0 Dihedral Kφ d n N-Cc-N-Cc N-Cc-N-Cm H-Cc-N-Cc H-Cc-N-Cm Cc-Cc-N-Cc Cc-Cc-N-Cm N-Cc-Cc-H N-Cc-Cc-N H-Cc-Cc-H N-C-Cm-H H-C-Cm-H H-Cm-N-Cc Improper Kφ d n N-N-Cc-H Cc-N-Cc-H Cc-Cc-N-C Porous graphene Table S3. Lennard-Jones parameters for C and H atoms on the porous graphene ε / kcal/mol σ / Å C H 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 H H H H H H H H H H H S6

7 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C S7

8 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C S8

9 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C S9

10 C C C C C C C C C C C C C C C C C C C C C C C References (1) Plimpton, S. J. Comput. Phys. 1995, 117, (2) Jorgensen, W. L.; Maxwell, D. S.; TiradoRives, J. J. Am. Chem. Soc. 1996, 118, (3) Liu, Z. P.; Huang, S. P.; Wang, W. C. J. Phys. Chem. B 2004, 108, (4) Borodin, O. J. Phys. Chem. B 2009, 113, (5) Babarao, R.; Dai, S.; Jiang, D. E. J. Phys. Chem. B 2011, 115, (6) Campana, C.; Mussard, B.; Woo, T. K. J. Chem. Theory Comput. 2009, 5, (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, (9) Murthy, C. S.; Singer, K.; Klein, M. L.; Mcdonald, I. R. Mol. Phys. 1980, 41, (10) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, (11) Liu, H. J.; Dai, S.; Jiang, D. E. Nanoscale 2013, 5, (12) Yeh, I. C.; Berkowitz, M. L. J. Chem. Phys. 1999, 111, (13) Nose, S. J. Chem. Phys. 1984, 81, (14) Hoover, W. G. Phys. Rev. A 1985, 31, S10

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