Supporting Information for: Physics Behind the Water Transport through Nanoporous Graphene and Boron Nitride Ludovic Garnier, Anthony Szymczyk, Patrice Malfreyt, and Aziz Ghoufi, Institut de Physique de Rennes, IPR, UMR CNRS 6251, 263 Avenue du Général Leclerc, 35042 Rennes, France, Institut des Sciences Chimiques de Rennes, CNRS, UMR 6226, Université de Rennes 1, 263 Avenue du Général Leclerc, 35042 Rennes, France, Institut de Chimie de Clermont-Ferrand, ICCF, UMR CNRS 6296, BP 10448, F-63000 Clermont-Ferrand, France, and Institut de Physique de Rennes, IPR, UMR CNRS 6251, 263 Avenue du Général Leclerc, 35042 Rennes, France E-mail: aziz.ghoufi@univ-rennes1.fr To whom correspondence should be addressed Institut de Physique de Rennes, IPR, UMR CNRS 6251, 263 Avenue du Général Leclerc, 35042 Rennes, France Institut des Sciences Chimiques de Rennes, CNRS, UMR 6226, Université de Rennes 1, 263 Avenue du Général Leclerc, 35042 Rennes, France Institut de Chimie de Clermont-Ferrand, ICCF, UMR CNRS 6296, BP 10448, F-63000 Clermont- Ferrand, France Institut de Physique de Rennes, IPR, UMR CNRS 6251, 263 Avenue du Général Leclerc, 35042 Rennes, France 1
Computational Method and Force Field Graphene was described from a full Lennard-Jones potential developed by Werder et al. 1 while boron nitride was modeled by considering the partial charges on B and N. 2 Lennard-Jones and partial charges are given in Table S1. Both surfaces were considered as rigid. Water was modeled by using the non-polarizable rigid TIP4P/2005 model. 3 TAB. S1: Lennard-Jones parameters and partial charges of graphene (Cg) and boron nitride (N and B). σ (Å) ɛ (kj mol 1 ) q Cg 3.3997 0.3594056 - B 3.453 0.3971 +0.35 N 3.365 0.6060-0.35 As shown in Figure S1 equilibrium molecular dynamics (EMD) simulations consisted in graphene (416 atoms) or boron nitride (416 atoms) membranes located at z = 0 Å and surrounded by two water reservoirs. The dimensions of the simulation box are reported in Table S1. The solid/liquid interface was along the z direction. EMD simulations were carried out with DL_POLY package (version 4.0) 4 using the velocity-verlet algorithm 5 in the NpAT statistical ensemble where N is the particle number, p the pressure, A the surface area and T the temperature. Working in the NpAT ensemble was possible by using an anisotropic barostat such that the pressure was kept constant according to the normal of the interface i.e. the z direction. The Berendsen thermostat and barostat 6 with a relaxation time of τ t = 0.5 ps and τ p = 0.5 ps, respectively, were considered. Periodic boundary conditions were applied in the three directions. MD simulations were performed in the canonical ensemble at T=300 K and p= 1 bar. MD simulations were performed using a time step of 0.001 ps to sample 10 ns (acquisition phase) after a 10 ns equilibration. Electrostatic interactions were truncated at 12 Å and calculated by using the Ewald sum method with a precision of 10 6. Short range interactions were modeled by using a Lennard-Jones potential with a cutoff of 12 Å. Lennard-Jones interactions between the solid frameworks and water molecules were taken into account by means of the Lorentz-Berthelot mixing rule. Statistical errors were estimated using the block 2
average method. FIG. S1: Initial configuration for EMD of water/bn interface. TAB. S2: Dimensions of simulation box and number of water molecules. L z (Å) L x (Å) L y (Å) N(water) Cg, n s =1 91.36 31.929 34.32 3200 Cg z z, n s =1 92.00 34.032 31.93 3200 Cg, n s =2 94.81 31.929 34.32 3200 Cg, n s =3 97.65 31.929 34.32 3200 Cg, n s =4 100.91 31.929 34.32 3200 Cg, n s =5 103.99 31.929 34.32 3200 Cg, n s =6 108.12 31.929 34.32 3200 BN, n s =1 95.59 31.307 33.26 3200 BN, n s =1 98.99 31.307 33.26 3200 BN, n s =1 101.74 31.307 33.26 3200 BN, n s =1 104.51 31.307 33.26 3200 BN, n s =1 108.28 31.307 33.26 3200 BN, n s =1 111.05 31.307 33.26 3200 Water transport through nanoporous membranes was evaluated by carving a nanopore of diameter 7 Å in graphene and boron nitride sheets(see Figure S2). Few carbon atoms have been removed and hydrogen atoms have been added to keep the usual valence of carbon. For graphene partial charge of carbon and hydrogen atoms have been taken in. 7 For BN partial charges were calculated from first principles calculations. Details of 3
this calculation can be found elsewhere. 8 Pressure driven simulations were conducted by using a piston (graphene wall) on which a given pressure was applied. The force to be apply on the piston atoms was calculated from the relation F = P S/N p where P is the pressure difference, S the piston surface area and N p the piston atom number. Contrary to EMD simulations only one reservoir was filled with water molecules in the initial configuration, while the second reservoir was used to collect water molecules flowing through the nanoporous membrane. TAB. S1: Lennard-Jones parameters and partial charges of graphene (Cg) and nitride boron (N and B). CgH, BH, NH, HCg, HN, HB are labels of carbon, boron, nitrogen and hydrogen atoms at the nanopore edges. σ (Å) ɛ (kj mol 1 ) q Cg 3.3997 0.3594056 - CgH 2.9850 0.192464 - HCg 2.42 0.12593840 - B 3.453 0.3971 +0.35 BH 3.453 0.3971 +0.52 HB 2.42 0.12593840-0.15 N 3.365 0.6060-0.35 NH 3.365 0.6060-0.675 HN 2.42 0.12593840 0.305 4
FIG. S2: Initial configuration for pressure-driven MD simulations. Horizontal arrows indicate the force exerted on the piston. 5
Flexibility of graphene To ensure that the calculated surface tension was independent of the surface flexibility and helicity we performed additional MD simulations by considering a flexible graphene (Table S3). As shown in Figure S4 the profiles of surface tension were found to be very similar for the different systems, i.e. rigid-armchair, rigid-zig-zag and flexible-armchair. TAB. S3: Force Field parameters for flexible graphene. Harmonic form was used to take into account stretching (k r (r r 0 ) 2 ) and bending potential (k Φ (Φ Φ 0 ) 2 ) where k r and k Φ are the force constants, r 0 and Φ 0 the equilibrium values. Torsions were considered from V (1 + cos(nψ + δ)) where, V is a force constant, ψ the dihedral angle and δ the phase shift and n the multiplicity. k r (Å) r 0 (Å) C-C 2694.0 1.420 k Φ (kj mol 1 deg. 2 ) Φ 0 (deg.) C-C-C 446.0 120 V (kj mol 1) δ (deg.) n C-C-C-C 13.167 180 2 6
FIG. S3: Local surface tension of water close to a graphene surface for three models at 300K and 1 bar. 7
Surface Tension Calculation Surface tension (γ) was calculated by using the non-exponential method 9 which is based on the usual test-area methodology 10 where γ is expressed as γ = ( ) F with F A the free energy, A the surface area, N the number of molecules and V the volume. Let us note that the non-exponential method was recently developed with a rigorous theoretical background. 9,11,12 Thus, the non-exponential approach cannot be considered as an approximation of the usual exponential form (TA). Calculation of F by means of an explicit derivation which provides γ = ( ) U A N,V,T A N,V,T was performed where U is the configurational energy. This expression was approximated through a finite difference such that γ = ( ) U = ( ) U where U is the energy difference between two states A N,V,T A N,V,T of different surface areas ( A = A 1 A 0 where 0 stands for the reference state and 1 stands for the perturbed state). Thus, to maintain the volume constant the following anisotropic transformations were used L (1) x = L (0) x 1 ± ξ, L (1) y and L (1) z = L (0) z /(1 ± ξ) where ξ is the perturbation length as ξ 0 and L the box length. The area of a planar interface is A = 2L x L y and A = A [ (1 ± ξ) 1/2 1 ]. Therefore, the surface tension can be expressed as γ = ( ) F A N,V,T = lim ξ 0 ( (U (1) (r N ) U (0) (r N ) )) A 0 (1) where U (0) (r N ) and U (1) (r N ) are the configurational energies of the reference and perturbed states, r N and r N are the configurational space for both states, <... > 0 stands for that the average taken over the reference state. A local version of Eq. (1) can be obtained by assuming a decorrelation of the slabs 11 N γ(z k ) = lim ξ 0 N H(z ik ) i=1 j>i ( (u (1) z k (r ij ) u (0) ) z k (r ij )) A 0 (2) 8
where k is the index of the cylindrical slab, z k the radius of the cylindrical shell, u zk is the energy of the kth element, H(z ik ) is the Heaviside function with H(z ik ) = 1 for z i = z k and 0 otherwise and r ij is the distance between i and j molecules. Thus surface tension can be evaluated as γ = k γ(z k ) (3) We provide in Figure S5 the integration of the profile of water surface tension close to the surface of graphene and BN monolayers. FIG. S5: Integration of the profile of water surface tension close to the surface of graphene and BN monolayers at 300K and 1 bar. 9
Density and Hydrogen Bonds FIG. S6: Profiles of water density a) and hydrogen bond number per water molecule b) for both graphene and boron nitride monolayers (n=1) at 300 K and 1 bar. 10
Radial Distribution Functions FIG. S7: Radial distribution function (RDF) between the oxygen of water (Ow) and carbon of graphene (Cg) and nitrogen (N) and boron (B) of boron nitride. 11
Local Surface Tension FIG. S8: Local surface tension of water close to graphene for n=1 and n=2 at 300K and 1 bar obtained from MD simulations with only one water reservoir. 12
FIG. S9: Local surface tension of water close to the BN surface for n ranging from 1 to 6 at 300K and 1 bar. 13
FIG. S10: Local water surface tension (left axis) and its integration (right axis) close to the graphene and BN bilayers (n=2) at 300K and 1 bar. 14
FIG. S11: a) Water molecules filtered as a function of time where. b) Profile of water density close to graphene and BN monolayers (n=1) at 300K and 1 bar. References 1. Werder, T.; Walther, J.; Halicioglu, R.; Halicioglu, T.; Koumoutsakos, P. On the water-carbon interaction for use in molecular dynamics simulations of graphite and carbon nanotubes. J. Phys. Chem. B 2003, 107, 1345 1352. 2. Tocci, G.; Joly, L.; Michaelides, A. Friction of Water on Graphene and Hexagonal Boron Nitride from Ab Initio Methods: Very Different Slippage Despite Very Similar Interface Structures. Nano Lett. 2014, 14, 6872 6877. 3. Abascal, J. L. F.; Vega, C. A general purpose model for the condensed phases of water: TIP4P/2005. J. Chem. Phys. 2005, 123, 234505 234516. 4. Todorov, I.; Smith, W.; Trachenko, K.; Dove, M. DLPOLY3: new dimensions in molecular dynamics simulations via massive parallelism. J. Mater. Chem. 2006, 16, 1911 1918. 5. Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford, 1987. 15
6. Berendsen, H.; Postma, J.; van Gunsteren, W.; Dinola, A.; Haak, J. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984, 81, 3684 3690. 7. Cohen-Tanugi, D.; Grossman, D. Water Desalination across Nanoporous Graphene. Nano Lett. 2012, 12, 3602 3608. 8. Ghoufi, A.; Deschamps, J.; Maurin, G. Theoretical Hydrogen Cryostorage in Doped MIL-101(Cr) Metal Organic Frameworks. J. Phys. Chem. C 2012, 116, 10504 10509. 9. Ghoufi, A.; Malfreyt, P. Calculation of the surface tension and pressure components from a non-exponential perturbation method of the thermodynamic route. J. Chem. Phys. 2012, 136, 024104 024109. 10. Gloor, G.; Jackson, G.; Blas, F.; de Miguel, E. Test-area simulation method for the direct determination of the interfacial tension of systems with continuous or discontinuous potentials. J. Chem. Phys. 2005, 123, 134703 134721. 11. Ibergay, C.; Ghoufi, A.; Goujon, F.; Ungerer, P.; Boutin, A.; Rousseau, B.; Malfreyt, P. Molecular simulations of the n-alkane liquid-vapor interface: Interfacial properties and their long range corrections. Phys. Rev. E 2007, 75, 051602 051619. 12. Ghoufi, A.; Malfreyt, P. Local description of surface tension through thermodynamic and mechanical definitions. Mol. Sim. 2012, 39, 603 611. 16