A Tunable, Strain-Controlled Nanoporous MoS 2 Filter for Water Desalination

Transcription

1 Supporting Information A Tunable, Strain-Controlled Nanoporous MoS 2 Filter for Water Desalination Weifeng Li 1, Yanmei Yang 1, Jeffrey K. Weber 2, Gang Zhang* 3, Ruhong Zhou* 1,2,4 1. School for Radiological and Interdisciplinary Sciences (RAD-X) and Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Soochow University, Suzhou, China, Computational Biological Center, IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA 3. Institute of High Performance Computing, A*STAR, Singapore, Department of Chemistry, Columbia University, New York, NY 10027, USA * (G.Z.) zhangg@ihpc.a-star.edu.sg; (R.H. Z.) ruhong@us.ibm.com

2 1. Two Chloride Translocation Events Observed Over the Course of Piston-Driven Simulations For our water flow simulations, we obtained 35 trajectories in total (5 strain cases, each under 7 piston pressures). In the extreme case of the 12%-strained MoS 2 filter, two Cl - translocation events were observed (one each under piston pressures of 10 MPa and 100 MPa). As illustrated in Fig. S1, the z-coordinates of the two Cl - ions pass through the MoS 2 filter at 23.3 ns (under 10 MPa) and 29.2 ns (under 100 MPa) after binding near the nanopore center for a short while. It bears emphasizing that the saltwater region contains 30 Cl - ions; the occurrence of only one translocation event in each case still suggests this nanoporous MoS 2 filter has good salt filtering capabilities. Figure S1. The z-coordinates of the Cl - ions that have successfully passed through the MoS 2 filter under 10 MPa and 100 MPa, respectively. The MoS 2 nanopore center is at z = 0; translocation points are highlighted by red arrows. 2. Gate Size and Deformation under Pressure We have measured two aspects of the deformations of the nanopore under applied RO pressure: (i) the change of nanopore radius (deformation inside the MoS 2 pore); and (ii) the deviation of membrane surface in the water flow direction (deformation of the surface, dz, defined as the deviation in the z direction of Mo atoms at the nanopore edge from the idealized flat surface). The definitions are illustrated in Fig. S2a. First, the gate opening is mostly dependent on the strain strength. As demonstrated in the Fig. S2b, the radius of nanopore is almost linearly dependent on the strain strength, from 0.34 nm (free MoS 2 ) to 0.47 nm (12% strained MoS 2 ). Secondly, the applied RO pressure will slightly enlarge both the pore radius (increase ~0.001nm under 12% strain) and dz (less than 0.001nm) as shown in Fig. S2c and S2d. Moreover, the dz reaches a plateau after about 40 MPa under the current settings. For industrial applications, the typical operating RO pressure is usually several MPa, which is at the lower end in our simulations. Thus, the pressure effect on the nanopore structure is mostly negligible.

3 Figure S2. (a) Definitions of the pore radius and structure deformation in the water flow direction (dz) due to the pressure; (b) the pore radius with respect to strain; (c) pore radius of MoS 2 under 12% strain with respect to piston pressure and (d) deformation of MoS 2 under 12% strain in the water flow direction with respect to piston pressure. 3. Calculation of 2D-Projected Water Flux The calculation of 2D-projected water flux illustrated in Fig. 3 in the main text is comprised of 3 steps: 1) The water molecules that passed through the MoS 2 filter were identified. 2) The coordinates of the water molecules in step 1 were monitored, and (x, y) coordinates were tabulated when each water molecule was at its closest position in relation to the nanopore center. 3) The 2D distribution of the (x, y) coordinates was calculated and plotted. 4. Umbrella Sampling Simulation for Potential of Mean Force Profiling In order to probe the filtration mechanism of nanoporous MoS 2, we calculated potential of mean force profiles for water or salt ions passing through the MoS 2 nanopore with an umbrella sampling method. 1-3 For the present system, the z-component of the distance between a molecule and the center of geometry (COG) of the nanopore was selected as the principle collective variable. The value was sampled from -1.0 nm (sea water side) to 1.0 nm (pure water side) with a window resolution of 0.1 nm. In order to enhance the sampling efficiency, the x and y components of the distance were constrained in a range of dx <0.5 and dy <0.5, as implemented with PLUMED code. 4 This sampling space is illustrated by the red box in Fig. S3. A force constant of 2000 kj mol -1 nm -2 was applied for each sampling point. At each distance, the system was first equilibrated for 1 ns followed by a 10 ns data-productive simulation. Analogous equilibrium PMFs

4 (corresponding to a piston-removed system within which salt concentrations on both sides of the filter can quickly equalize) were calculated using an identical protocol, yielding the data presented in Fig. S4. Figure S3. Demonstration of the simulation model used for potential of mean force calcuations. The red box at center indicates the space in which water/na + /Cl - can travel under the umbrella sampling of the z-coordinate; metadynamics adds constraints in the x-y plane. The cross-section at right illustrates that sampling was conducted exclusively within the silhouette of the membrane nanopore with respect to the x- and y-directions. Figure S4. Equilibrium PMFs derived from piston-removed configurations of the MoS 2 nanopore system. Pore-edge sodium peaks and chloride wells similar to those observed in NPMFs (Fig. 4 in the main text) also appear at equilibrium; the basins/plateaus that emerge on the pure water side of the filter, of course, disappear when salt concentrations are allowed to equalize. 5. First-Principles Calculations First-principles calculations have been conducted in order to check the structural stability of the MoS 2 filter under strain. The calculations were conducted using the Vienna Ab initio Simulation Package (VASP). 5, 6 Projector-augmented-wave (PAW) potentials 7 were used to take into account the electron ion interactions, while the electron exchange-correlation interactions were treated using a generalized gradient approximation (GGA) 8 in the scheme of Perdew Burke Ernzerhof. A plane-wave cutoff of 500 ev was used for all the elements. In the z

5 direction of the model, a vacuum space of 20 Å was kept to avoid mirror interactions. For the strained structures, the x and y lattice vectors (the MoS 2 plane) were rescaled with a factor of 1.03, 1.06, 1.09, 1.12 and 1.15 to mimic the tensile strain effect. A k-point sampling of was used for the structure optimization. All atomic positions were fully optimized using a conjugate gradient algorithm until the change of the total energy became smaller than 0.01 mev and all the forces on each atom became less than 0.01 ev/å, which was sufficient to obtain relaxed structures in our previous study Figure S5. The structures of MoS 2 filters under tensile strains of (a) 12% and (b) 15%, taken from first-principles calculations. For (b), the Mo atoms at nanopore edge (and their coordination changes) are highlighted with red arrows. For the MoS 2 filter under 12% tensile strain, the topology of the nanopore is well maintained as shown in Fig. S5a. However, severe structural reorganization happened for the edge Mo atoms, as indicated by red arrows in Fig. S5b: the six edge Mo atoms form covalent bonds with adjcent S atoms and become 6-coordinated. Although such a structure is still capable of water desalination (in principle), formation of this motif is beyond the scope of classical molecular dynamics simulations (which cannot, in general, describe coordination changes). The MoS 2 filter under 15% strain has thus not been discussed in the main manuscript. References: 1. Torrie, G. M.; Valleau, J. P., Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling. J. Comput. Phys. 1977, 23, Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A., Multidimensional Free-Energy Calculations Using the Weighted Histogram Analysis Method. J. Comput. Chem. 1995, 16, Roux, B., The Calculation of the Potential of Mean Force Using Computer Simulations. Comput. Phys. Commun. 1995, 91, Bonomi, M.; Branduardi, D.; Bussi, G.; Camilloni, C.; Provasi, D.; Raiteri, P.; Donadio, D.; Marinelli, F.; Pietrucci, F.; Broglia, R. A., Plumed: A Portable Plugin for Free-Energy Calculations with Molecular Dynamics. Comput. Phys. Commun. 2009, 180, Kresse, G.; Furthmuller, J., Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, Kresse, G.; Furthmuller, J., Efficiency of Ab-Initio Total Energy Calculations for Metals and

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