Supporting Information

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1 Supporting Information Interface-Induced Affinity Sieving in Nanoporous Graphenes for Liquid-Phase Mixtures Yanan Hou, Zhijun Xu, Xiaoning Yang * State Key Laboratory of Material-Orientated Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing Tech University, Nanjing , China Department of Polymer Science, University of Akron, Akron, Ohio 44325, United States * Corresponding author Yangxia@njtech.edu.cn. Methods MD simulations: In the current study, both nonequilibrium and equilibrium simulations were carried out. Detailed information on the simulation systems were listed in the Supporting Information Table S1. 1

2 In the non-equilibrium MD simulations, ethanol-water mixtures were placed on the feed side, while the permeate side was initially in the vacuum. Periodic boundary conditions were applied in the x-y plane to maintain a continuous 2D membrane. Reflective boundary condition was applied at z=-65å. A rigid graphene piston was initially placed at z=62.7å. The simulation systems were firstly equilibrated in the NVT ensemble for at least 2 ns at K. After equilibration, the prescribed external pressure was applied on the piston. Each non-equilibrium simulation was performed for additional ns. To generate the desired external pressure ( P ), the applied force (f) was exerted on each carbon atom of the piston based on f P A/ n, 1 where A is the area of the piston and n refers to the total number of carbon atoms of the piston. In particular, when solution was placed on both sides of graphene membrane, the pressure-driven flow of molecules across nanopores was simulated in the systems with two pistons placed on the ends of the solutions. After equilibration, the desired pressure along the negative z direction was produced by exerting external force on the pistons. The carbon atoms in the piston were also treated as the uncharged L-J sphere, 2 which is the same as that for graphene membranes in our works. In order to weaken the adsorption of ethanol and water molecules onto the piston, in the non-equilibrium permeation simulation, the L-J interaction parameters ( ) between atoms in the two species and carbon atoms in piston were reduced by 50 times. In the equilibrium simulations, ethanol-water mixtures were placed on both sides of the nanoporous graphene. The period boundary conditions were applied in all directions. MD simulations were run for 12 ns and the last 8ns being used for data analysis. The Nose-Hoover thermostat 3,4 was used to maintain the temperature at K. A time-step of 1.0 fs was selected and data were collected every 1 ps for analysis. 2

3 Potential of mean force (PMF) calculation. The potential of mean force (PMF) was calculated along the z-axis in the system with the ethanol-water mixture (mole fraction of 0.5) on both sides of nanoporous graphene. The PMF of a moving molecule (ethanol or water) across the nanopore z 0 z 0 at the position z was obtained by W ( z) W ( z ) f ( z) dz, where W z ) is the reference value and it was chosen to be zero at z =20 Å in this work, f (z) is the mean total force acting on the ( 0 target molecule. As the nanoporous graphene was located at z =0, the z also referred to the distance of the moving molecule from the pore center. To produce the PMF profile, a series of constrained MD simulations were conducted with the target molecule moving from 20Å to -20Å with the increments of 1Å along the negative z-axis. In particular, the moving increments were 0.5Å from 6Å to -6Å to produce the accurate force. In each simulation, the center of mass of the moving molecule was kept fixed with the permission of absolutely free rotation to obtain average constraint force at accurate position, while the other molecules were completely free throughout the simulation course. All simulations were conducted for 10ns, with the last 6ns being collected for data analysis. The electron density computations. The electron density for nanoporous graphene membranes, ethanol, and water were computed using the Amsterdam Density Functional (ADF) program. 5 The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was employed for calculations within the generalized gradient approximation (GGA). The period boundary conditions were applied in all directions. After geometry optimization, electron density was obtained. 3

4 Table S1 Details of simulated systems systems graphene membrane ethanol mole fraction in feed in feed N ethanol / N water in permeate simulation box size (Å 3 ) P12-P /1050 0/ / /0 1050/ non-equilibrium P / / /923 0/ / /4331 0/4331 equilibrium P12-P / / /0 1334/0 4

5 Figure S1. The penetration numbers of ethanol and water molecules in the mixture with ethanol mole fraction of 0.5 passing through individual graphene nanopore under different pressures. For larger pores, the time-dependent penetration profile shows a decreasing slope under higher pressures. This phenomenon is possibly due to the rapid decrease of molecular number on the feed side in the present system with limited simulation scale. 5

6 Figure S2. Two additional simulations for the permeation performance of the P14 membrane at a pressure of 300 MPa with the permeate site in the vacuum and the feed side in two different initial conditions. (a) In the feed side, the initial configuration of mixture was not in the equilibrium state, but in the random mixing state; (b) In the feed side, water molecules were initially placed close to the graphene membrane surface and ethanol molecules were placed far away from the surface. From the two simulations, ethanol always has obvious higher permeation number than water. The results strongly confirm the preferentially selective pore penetration of ethanol over water in nanoporous graphene membrane regardless of the initial mixing state of ethanol-water mixture. 6

7 Figure S3. The additional simulation using the P14 membrane at a pressure of 300 MPa with the permeate side in the state of pure ethanol, (a) the corresponding initial and final configuration of this simulation, (b) the penetration numbers of ethanol and water molecules passing through the P14 membrane. The relative high ethanol permeation is observed as compared with that in the systems with permeate side in the vacuum, possibly owing to the additional attractive force from the permeate side. 7

8 Figure S4. Permeation fluxes for individual nanoporous graphene membrane versus various pore areas. The pore area is defined as the total area of benzene ring units drilled out. The total permeation flux is roughly proportional to the pore area, consistent with previous work regarding water flow across nanopores. 6 Ethanol has obvious higher permeation flux than water, indicating that the nanopores are selectively permeable to ethanol. In the P22 membrane, the total crosssectional area available for molecule passage increases by about 16%, while ethanol permeation flux decreases by about 4%, as compared with the P19. This is mainly caused by the enhanced water permeation flux (higher by about 117%), which is likely to decrease the pore area available for ethanol passage. Although the total pore area available for molecular flow across the P24 is only larger by about 9% than the P22, the permeation flux of ethanol and water for the P24 is higher by about 39% and 70%, respectively. This probably suggests that the subcontinuum molecular flow transits to a continuum flow for the relatively large pore P24. 8

9 Figure S5. A comparison between the nanoporous graphenes investigated in this work and the existing membranes. In the graphene-based nanoporous membranes, the ethanol permeability is considerably higher compared to current pervaporation membranes, with the separation factor ranging from 2.7 to The data except nanoporous graphenes in the figure is adapted from the literature. 7,8 9

10 Figure S6. Time evolution of the z-axial positions of five ethanol (a) and water (b) molecules transport across P14 pore. Different molecules are displayed with different colors. The reference (z=0) corresponds to the location of nanoporous graphene membrane. Among all the ethanol molecules passed through nanopores, some stay a long time inside the surface layer while some go through the surface layer in a short time. Water molecules usually stay for a long time within the surface layer (z~7å) before passing through the nanopore. (c) Trajectory of one representative ethanol molecule as it moves to the graphene membrane and then permeates through the nanopore. The arrows indicate the ethanol migrates in that direction. The cyan plane represents the location of P14 membrane. 10

11 Figure S7. Distribution of the orientation of ethanol passing through the nanopores. Inset illustrates the definitions of α,β, and γ. As for the smallest nanopore P12, the peaks of the orientation of α and γ indicate that the ethanol molecules prefer to pass through the P12 in such orientations that the CH 3 -CH 2 bond points toward the graphene nanopore (~20 with respect to the surface normal) and OH bond points away from the nanopores (~50 with respect to the surface normal). As the pore size increases, the distribution of α tends to at ~60 and becomes wide while the peak values show a certain decrease. A similar tendency also can be found in the orientation changes of β and γ. 11

12 Figure S8. The density profiles of pure ethanol (left) and pure water (right) obtained within a cylinder of axis perpendicular to the graphene nanopores and diameter equal to the pore diameter. The reference (z=0) corresponds to the location of nanoporous graphene membrane. Both ethanol and water molecules can form obvious adsorption layer on the pore surface. 12

13 Figure S9. (a) Left: The initial configuration of simulation with water molecules close to the graphene membrane surface and ethanol molecules far away from the surface. Right: The final configuration of this simulation. (b) Density profiles of ethanol and water obtained within a cylinder of axis perpendicular to the graphene nanopores and diameter equal to the pore diameter after the system has reached equilibrium. The reference (z=0) corresponds to the position of the P14 membrane. (c) The interaction energy of graphene with ethanol and water over time during the simulation, respectively. The final equilibrium configuration and the density profile strongly suggest that ethanol molecules have stronger competitive adsorption ability and expel water molecules from the graphene surface by moving into the surface region. 13

14 Figure S10. The occupation number of molecules within different graphene nanopores as a function of simulation time, ethanol and water in equimolar mixture (a), pure ethanol (b). For nanopores P12 and P14, almost only a single ethanol molecule can be inside pore at a time while water appears occasionally. In the case of larger pores, two or three ethanol molecules are capable of simultaneously staying inside the pores and the number of water molecules varies frequently over time. Although the number of water within nanopore P24 has a maximal value of 5, the value is zero for most of the simulation time. 14

15 Figure S11. Planar density distribution of the center of mass of ethanol inside each graphene nanopore considered in this work. Only small density region is observed at the pore centers in the P12 and P14. As the pore size increases, the ethanol-density presents more decentralization in the nanopores and shows dependent on the pore shape, implying the effective pore area for ethanol transport are enlarged. 15

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