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difference.1, 2, 911 The key to a NEMD simulation of a NFprocess is a mean of imposing different constant pressureson the two sides of the NF membrane. In our previous study,we reported a NEMD simulation system derived by Huang9and Takaba10 to study the transport phenomena of pressuredrivenwater flow through CNT membranes under NF operatingconditions.12, 13Real NF membranes are generally made from syntheticpolymers. The membrane structure (pore size, numberof pores, and membrane thickness) and the polymer characteristics(functional groups, electric charge, hydrophilicity/hydrophobicity, etc.) can both affect membrane performance.The interaction between solution and polymeric NFmembrane is one of the most important factors determiningmembrane separation and transport performance. In ourprevious work, the effect of membrane structure on watertransport through CNT membranes was investigated.12 Thiswork investigates the effect of water-CNT membrane interactionson modified CNT membrane performance with different0021-9606/2013/138(12)/124701/9/$30.00 138, 124701-1 2013 American Institute ofPhysicsThis article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http:

124701-3 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)shown in Eqs. (3) and (4), respectively,Rmin(ij ) = Rmin(ii) + Rmin(jj)2, (3)e(ij ) =ve(ii) e(jj) (4)indicating that the Rmin(ij) is an arithmetic mean and the e(ij) isa geometric mean.Two series of modified CNT membranes are producedfirst by varying the carbon atom Lennard-Jones well-depthvalues (e(CC)), and second by setting the atomic charges on

CNT carbon atoms (patterns of balanced positive and negativecharges are placed on the CNT). These modificationsaffect the interactions between water molecules and the CNTmembrane. NEMD simulations are carried out for unmodifiedand modified CNT membranes to analyze the NF transportphenomenon of pressure-driven water flow in terms of waterflow rate and density and velocity (in z direction) distributionsalong both radiNonequilibrium molecular dynamics simulation of pressure-driven water transportthrough modified CNT membranesLuying Wang, Randall S. Dumont, and James M. DicksonCitation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685

View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHow fast does water flow in carbon nanotubes?J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at lowpressurea)

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J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada(Received 21 December 2012; accepted 13 February 2013; published online 22 March2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigat

e the effectof water-membrane interactions on the transport properties of pressure-driven water flow passingthroatomic charges of atoms i and j; e0 is the electricconstant with a value of 8.854 10-12 C2/(N m2); and rij isthe distance between atoms i and j. The Lorentz-Berelot combiningrules19 and sulfateremoval from seawater. In addition, NF has been appliedin other industries: pulp and paper effluent treatment in thepapermaking industry, removal of dyes and other coloringagents in the textile industry, concentration of intermediatesand antibiotics in the pharmaceutical industry.8 In view of the

a)Author to whom correspondence should be addressed. Electronic mail:dickson@mcmaster.ca.growing industrial applications of NF, the transport mechanismof NF is examined using MD simulation with the goalof improving the understanding of the types of membranesbest suited for NF processes.To understand the microscopic dynamics properties ofthe NF process with MD simulation, nonequilibrium moleculardynamic (NEMD) simulations must be used becausepressure-driven fluid flow corresponds to a nonequilibriumconditions. NEMD is a valuable tool to study fluidflow through nanoscale channels, induced by a pressureNF worldwide have increased primarily in the water treatment

industry,7 such as water softening, organics removal,radium and heavy metal removal from wastewater;an help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013AmericanInstis several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.

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The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairse(ij )Rmin(ij )rij12-2Rmin(ij )rij6//scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-2 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)membrane characteristics. Although the solution-membraneinteractions in a real NF process are more complicated thanthe water-CNT interactions, this work provides fundamentalinformation how membrane characteristics affect membraneperformance.The modified CNT membranes have the same membrane

structure (pore size and membrane thickness) as the unmodifiedCNT membrane; only the van der Waals interactionsand electrostatic interactions between water molecules andCNT membranes are altered. Transport through the unmodifiedCNT membrane and modified CNT membranes is comparedto establish the role of the water-CNT interactions in determiningobserved transport properties. This work highlightsa unique advantage of MD simulationthe water-membraneinteraction can be adjusted to reveal the effect on the NF transport.The unmodified and modified CNT membranes in thispaper can be considered as functionalized CNTs or models ofsimplified NF membranes at operating conditions consistentwith real NF systems.

II. SIMULATION METHODSThe system model in Cartesian coordinates is shownin Fig. 1. The system consists of two graphene sheets actingas moveable walls, two water reservoirs, and the CNTmembrane model. The moveable walls and the membranemodel are 4 nm 4 nm in the x, y plane. The thickness andthe pore size of the CNT membrane is determined by the(12, 12) typ124701-3 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)shown in Eqs. (3) and (4), respectively,Rmin(ij ) = Rmin(ii) + Rmin(jj)2, (3)

e(ij ) =ve(ii) e(jj) (4)indicating that the Rmin(ij) is an arithmetic mean and the e(ij) isa geometric mean.Two series of modified CNT membranes are producedfirst by varying the carbon atom Lennard-Jones well-depthvalues (e(CC)), and second by setting the atomic charges onCNT carbon atoms (patterns of balanced positive and negativecharges are placed on the CNT). These modifications

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affect the inteMolecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada(Received 21 December 2012; accepted 13 February 2013; published online 22 March2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effectof water-membrane interactions on the transport properties of pressure-driven wa

ter flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between watermolecules and the CNT membranes. The unmodified and modified CNT membranes are models ofsimplified nanofiltration (NF) membranes at operating conditions consistent withreal NF systems.All NEMD simulare used to calculate the interaction terms forthe Lennard-Jones parameters between two different speciesof atoms i and j; the definition functions of Rmin(ij) and e(ij) areThis article is copyrighted as indicated in the article. Reuse of AIP content is

subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53tute of Physics. [http://dx.doi.org/10.1063/1.4794685]I. INTRODUCTIONMolecular dynamics (MD) simulation provides a dynamicview of microscopic systems. Water flow throughnanoscale channels, driven by external fields, is critical tomany phenomenafor example, biological channels, drugdelivery, membrane separations, fuel cells, and novel nanofluidicapplications (nanopumps, nanosyringes, nanosensors,etc.). In recent years, MD simulations have been used tostudy water flow driven by external fields such as pressure

difference,13 osmotic pressure difference,4, 5 and electricfield.6Nanofiltration (NF) is a common membrane separationprocess driven by a pressure difference between the two sidesof the NF membrane, where a concentrated stream on the highpressure side passes through the NF membrane and becomesa purified stream on the low pressure side. Applications ofNF worldwide have increased primarily in the water treatmentindustry,7 such as water softening, organics removal,radium and heavy metal removal from wastewater;lar and

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intramolecular interactions. The intermolecular potential energy(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairse(ij )Rmin(ij )rij12-2Rmin(ij )rij6124701-3 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)shown in Eqs. (3) and (4), respectively,Rmin(ij ) = Rmin(ii) + Rmin(jj)2

, (3)e(ij ) =ve(ii) e(jj) (4)indicating that the Rmin(ij) is an arithmetic mean and the e(ij) isa geometric mean.Two series of ractions between water molecules and the CNTmembrane. NEMD simulations are carried out for unmodifiedand modified CNT membranes to analyze the NF transportphenomenon of pressure-driven water flow in terms of waterflow rate and density and velocity (in z direction) distributionsalong both radiNonequilibrium molecular dynamics simulation of pressure-driven water transport

through modified CNT membranesLuying Wang, Randall S. Dumont, and James M. DicksonCitation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHow fast does water flow in carbon nanotubes?J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at low

pressurea)J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313

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Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada(Received 21 December 2012; accepted 13 February 2013; published online 22 March2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effectof water-membrane interactions on the transport properties of pressure-driven water flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between water

molecules and the CNT membranes. The unmodified and modified CNT membranes are models ofsimplified nanofiltration (NF) membranes at operating conditions consistent withreal NF systems.All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K),constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The waterflow rate, density, and velocity (in flow direction) distributions are obtainedby analyzing the NEMDsimulation results to compare transport through the modified and unmodified CNTmembranes. Thepressure-driven water flow through CNT membranes is from 11 to 21 times faster t

han predicted bythe Navier-Stokes equations. For water passing through the modified membrane with stronger vander Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities.These investigations show the effect of water-CNT membrane interactions on watertransport underNF operating conditions. This work can help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013American(Received 21 December 2012; accepted 13 February 2013; published online22 March 2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigat

e the effectof water-membrane interactions on the transport properties of pressure-driven water flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between watermolecules and the CNT membranes. The unmodified and modified CNT membranes are models ofsimplified nanofiltration (NF) membranes at operating conditions consistent with

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real NF systems.All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K),constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The waterflow rate, density, and velocity (in flow direction) distributions are obtainedby analyzing the NEMDsimulation results to compare transport through the modified and unmodified CNTmembranes. Thepressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted bythe Navier-Stokes equations. For water passing through the modified membrane with stronger vander Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities.These investigations show the effect of water-CNT membrane interactions on watertransport underNF operating conditions. This work can help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013AmericanInstis several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy(also called long-range potential energy) includes the

Lennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairse(ij )Rmin(ij )rij12

-2Rmin(ij )rij6e CNT, which has a 6.0 nm length and 0.643nm internal radius.1, 14 The top and bottom water reservoirs,connected by the CNT membrane model, provide the sourceand sink of the water flow passing through the membrane,along the z direction. External force is applied on each carbonatom of the moveable walls to produce 8.1 MPa pressureFIG. 1. Perspective snapshots of the simulation systems produced by VMDpackage at the beginning status of MD simulations (adapted from the figurein Ref. 12). Shown is the beginning empty CNT membrane model connecting

two liquid filled reservoirs, and the two graphene sheets acted as the movablewalls where the force ft or fb is applied on each carbon atom of the top orbottom wall. Carbon atoms in green, hydrogen atoms in white, and oxygenatoms in red.on the top water reservoir and 0.1 MPa on the bottom waterreservoir to give a pressure difference of 8.0 MPa. We usea simulated pressure difference across the CNT membranethat is somewhat higher than typical NF systems (usuallyless than 3 MPa pressure difference) as this higher pressuredifference reduces the (still large) CPU time needed for the

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simulations.An equilibrium MD simulation, in an isothermal-isobaric(NPT) ensemble, is carried out first to energy-minimize andequilibrate the system; and then a NEMD simulation is carriedout to simulate the pressure-driven water flow throughthe CNT membrane. Each simulation is at 300 K, and takesabout 14 CPU days for 1.0 ns of simulation (the length ofeach NEMD simulation is from over 100 ns to about 250 ns).The detailed simulation methodology (force field parameters,integration algorithm, periodic boundary conditions, etc.)and simulation procedures are the same as in our previouswork.12All MD simulations are performed using NAMD(NAnoscale Molecular Dynamics) package15 and VMD(Visual Molecular Dynamics) package16 in the CHARMM(Chemistry at HARvard Molecular Mechanics)17 force field.The water molecule is represented by the modified flexibleTIP3P (transferable intermolecular potential three-point) watermodel. Unlike the original rigid TIP3P model in whichthe van der Waals force is only set on the oxygen atom, theTIP3P water model in NAMD package is a flexible modeland is modified additionally to include Lennard-Jones parametersfor the hydrogen atoms.18 The use of a flexible watermodel here requires more calculations during a MD simulation

but produces a more accurate representation of thewater molecule needed in this work. The CHARMM forcefield includes several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairs

e(ij )Rmin(ij )rij12-2Rmin(ij )rij6,(1)

Eelect =nonbonded atom pairsqiqj4pe0rij, (2)where e(ij) is the Lennard-Jones well-depth between atoms iand j and Rmin(ij) is the distance at the Lennard-Jones minimuminteraction energy between atoms i and j; qi and qj arethe partialNonequilibrium molecular dynamics simulation of pressure-driven water

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transport

of water-membrane interactions on the transport properties of pressure-driven water flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between watermolecules and the CNT membranes. The unmodified and modified CNT membranes are models ofsimplified nanofiltration (NF) membranes at operating conditions consistent withreal NF systems.All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K),constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The waterflow rate, density, and velocity (in flow direction) distributions are obtainedby analyzing the NEMDsimulation results to compare transport through the modified and unmodified CNTmembranes. Thepressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted bythe Navier-Stokes equations. For water passing through the modified membrane with stronger van

der Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities.These investigations show the effect of water-CNT membrane interactions on watertransport underNF operating conditions. This work can help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013AmericanInstitute of Physics. [http://dx.doi.org/10.1063/1.4794685]I. INTRODUCTIONMolecular dynamics (MD) simulation provides a dynamicview of microscopic systems. Water flow throughnanoscale channels, driven by external fields, is critical to

many phenomenafor example, biological channels, drugdelivery, membrane separations, fuel cells, and novel nanofluidicapplications (nanopumps, nanosyringes, nanosensors,etc.). In recent years, MD simulations have been used tostudy water flow driven by external fields such as pressuredifference,13 osmotic pressure difference,4, 5 and electricfield.6Nanofiltration (NF) is a common membrane separationprocess driven by a pressure difference between the two sidesof the NF membrane, where a concentrated stream on the highpressure side passes through the NF membrane and becomesa purified stream on the low pressure side. Applications ofNF worldwide have increased primarily in the water treatment

industry,7 such as water softening, organics removal,radium and heavy metal removal from wastewater; and sulfateremoval from seawater. In addition, NF has been appliedin other industries: pulp and paper effluent treatment in thepapermaking industry, removal of dyes and other coloringagents in the textile industry, concentration of intermediatesand antibiotics in the pharmaceutical industry.8 In view of thea)Author to whom correspondence should be addressed. Electronic mail:dickson@mcmaster.ca.growing industrial applications of NF, the transport mechanism

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of NF is examined using MD simulation with the goalof improving the understanding of the types of membranesbest suited for NF processes.To understand the microscopic dynamics properties ofthe NF process with MD simulation, nonequilibrium moleculardynamic (NEMD) simulations must be used becausepressure-driven fluid flow corresponds to a nonequilibriumconditions. NEMD is athrough modified CNT membranesLuying Wang, Randall S. Dumont, and James M. DicksonCitation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHow fast does water flow in carbon nanotubes?J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at lowpressurea)J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236

Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranes

Luying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada(Received 21 December 2012; accepted 13 February 2013; published online 22 March2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effecttransport through CNT membranes was investigated.12 Thiswork investigates the effect of water-CNT membrane interactionson modified CNT membrane performance with different0021-9606/2013/138(12)/124701/9/$30.00 138, 124701-1 2013 American Institute of

PhysicsThis article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-2 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)membrane characteristics. Although the solution-membraneinteractions in a real NF process are more complicated thanthe water-CNT interactions, this work provides fundamentalinformation how membrane characteristics affect membrane

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performance.The modified CNT membranes have the same membranestructure (pore size and membrane thickness) as the unmodifiedCNT membrane; only the van der Waals interactionsand electrostatic interactions between water molecules andCNT membranes are altered. Transport through the unmodifiedCNT membrane and modified CNT membranes is comparedto establish the role of the water-CNT interactions in determiningobserved transport properties. This work highlightsa unique advantage of MD simulationthe water-membraneinteraction can be adjusted to reveal the effect on the NF transport.The unmodified and modified CNT membranes in thispaper can be considered as functionalized CNTs or models ofsimplified NF membranes at operating conditions consistentwith real NF systems.II. SIMULATION METHODSThe system model in Cartesian coordinates is shownin Fig. 1. The system consists of two graphene sheets actingas moveable walls, two water reservoirs, and the CNTmembrane model. The moveable walls and the membranemodel are 4 nm 4 nm in the x, y plane. The thickness andthe pore size of the CNT membrane is determined by the(12, 12) type CNT, which has a 6.0 nm length and 0.643nm internal radius.1, 14 The top and bottom water reservoirs,

connected by the CNT membrane model, provide the sourceand sink of the water flow passing through the membrane,along the z direction. External force is applied on each carbonatom of the moveable walls to produce 8.1 MPa pressureFIG. 1. Perspective snapshots of the simulation systems produced by VMDpackage at the beginning status of MD simulations (adapted from the figurein Ref. 12). Shown is the beginning empty CNT membrane model connectingtwo liquid filled reservoirs, and the two graphene sheets acted as the movablewalls where the force ft or fb is applied on each carbon atom of the top orbottom wall. Carbon atoms in green, hydrogen atoms in white, and oxygenatoms in red.on the top water reservoir and 0.1 MPa on the bottom waterreservoir to give a pressure difference of 8.0 MPa. We use

a simulated pressure difference across the CNT membranethat is somewhat higher than typical NF systems (usuallyless than 3 MPa pressure difference) as this higher pressuredifference reduces the (still large) CPU time needed for thesimulations.An equilibrium MD simulation, in an isothermal-isobaric(NPT) ensemble, is carried out first to energy-minimize andequilibrate the system; and then a NEMD simulation is carriedout to simulate the pressure-driven water flow throughthe CNT membrane. Each simulation is at 300 K, and takesabout 14 CPU days for 1.0 ns of simulation (the length ofeach NEMD simulation is from over 100 ns to about 250 ns).The detailed simulation methodology (force field parameters,

integration algorithm, periodic boundary conditions, etc.)and simulation procedures are the same as in our previouswork.12All MD simulations are performed using NAMD(NAnoscale Molecular Dynamics) package15 and VMD(Visual Molecular Dynamics) package16 in the CHARMM(Chemistry at HARvard Molecular Mechanics)17 force field.The water molecule is represented by the modified flexibleTIP3P (transferable intermolecular potential three-point) watermodel. Unlike the original rigid TIP3P model in which

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the van der Waals force is only set on the oxygen atom, theTIP3P water model in NAMD package is a flexible modeland is modified additionally to include Lennard-Jones parametersfor the hydrogen atoms.18 The use of a flexible watermodel here requires more calculations during a MD simulationbut produces a more accurate representation of thewater molecule needed in this work. The CHARMM forcefield includes several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairse(ij )Rmin(ij )rij12-2

Rmin(ij )rij6Nonequilibrium molecular dynamics simulation of pressure-driven water transportthrough modified CNT membranesLuying Wang, Randall S. Dumont, and James M. DicksonCitation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP Publishing

Articles you may be interested inHow fast does water flow in carbon nanotubes?J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at lowpressurea)J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313

Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)

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papermaking industry, removal of dyes and other coloringagents in the textile industry, concentration of intermediatesand antibiotics in the pharmaceutical industry.8 In view of thea)Author to whom correspondence should be addressed. Electronic mail:dickson@mcmaster.ca.growing industrial applications of NF, the transport mechanismof NF is examined using MD simulation with the goalof improving the understanding of the types of membranesbest suited for NF processes.To understand the microscopic dynamics properties ofthe NF process with MD simulation, nonequilibrium moleculardynamic (NEMD) simulations must be used becausepressure-driven fluid flow corresponds to a nonequilibriumconditions. NEMD is a valuable tool to study fluidflow through nanoscale channels, induced by a pressuredifference.1, 2, 911 The key to a NEMD simulation of a NFprocess is a mean of imposing different constant pressureson the two sides of the NF membrane. In our previous study,we reported a NEMD simulation system derived by Huang9and Takaba10 to study the transport phenomena of pressuredrivenwater flow through CNT membranes under NF operatingconditions.12, 13Real NF membranes are generally made from syntheticpolymers. The membrane structure (pore size, number

of pores, and membrane thickness) and the polymer characteristics(functional groups, electric charge, hydrophilicity/hydrophobicity, etc.) can both affect membrane performance.The interaction between solution and polymeric NFmembrane is one of the most important factors determiningmembrane separation and transport performance. In ourprevious work, the effect of membrane structure on watertransport through CNT membranes was investigated.12 Thiswork investigates the effect of water-CNT membrane interactionson modified CNT membrane performance with different0021-9606/2013/138(12)/124701/9/$30.00 138, 124701-1 2013 American Institute ofPhysicsThis article is copyrighted as indicated in the article. Reuse of AIP content is

subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-2 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)membrane characteristics. Although the solution-membraneinteractions in a real NF process are more complicated thanthe water-CNT interactions, this work provides fundamentalinformation how membrane characteristics affect membraneperformance.The modified CNT membranes have the same membranestructure (pore size and membrane thickness) as the unmodifiedCNT membrane; only the van der Waals interactionsand electrostatic interactions between water molecules and

CNT membranes are altered. Transport through the unmodifiedCNT membrane and modified CNT membranes is comparedto establish the role of the water-CNT interactions in determiningobserved transport properties. This work highlightsa unique advantage of MD simulationthe water-membraneinteraction can be adjusted to reveal the effect on the NF transport.The unmodified and modified CNT membranes in thispaper can be considered as functionalized CNTs or models ofsimplified NF membranes at operating conditions consistentwith real NF systems.

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II. SIMULATION METHODSThe system model in Cartesian coordinates is shownin Fig. 1. The system consists of two graphene sheets actingas moveable walls, two water reservoirs, and the CNTmembrane model. The moveable walls and the membranemodel are 4 nm 4 nm in the x, y plane. The thickness andthe pore size of the CNT membrane is determined by the(12, 12) type CNT, which has a 6.0 nm length and 0.643nm internal radius.1, 14 The top and bottom water reservoirs,connected by the CNT membrane model, provide the sourceand sink of the water flow passing through the membrane,along the z direction. External force is applied on each carbonatom of the moveable walls to produce 8.1 MPa pressureFIG. 1. Perspective snapshots of the simulation systems produced by VMDpackage at the beginning status of MD simulations (adapted from the figurein Ref. 12). Shown is the beginning empty CNT membrane model connectingtwo liquid filled reservoirs, and the two graphene sheets acted as the movablewalls where the force ft or fb is applied on each carbon atom of the top orbottom wall. Carbon atoms in green, hydrogen atoms in white, and oxygenatoms in red.on the top water reservoir and 0.1 MPa on the bottom waterreservoir to give a pressure difference of 8.0 MPa. We usea simulated pressure difference across the CNT membranethat is somewhat higher than typical NF systems (usually

less than 3 MPa pressure difference) as this higher pressuredifference reduces the (still large) CPU time needed for thesimulations.An equilibrium MD simulation, in an isothermal-isobaric(NPT) ensemble, is carried out first to energy-minimize andequilibrate the system; and then a NEMD simulation is carriedout to simulate the pressure-driven water flow throughthe CNT membrane. Each simulation is at 300 K, and takesabout 14 CPU days for 1.0 ns of simulation (the length ofeach NEMD simulation is from over 100 ns to about 250 ns).The detailed simulation methodology (force field parameters,integration algorithm, periodic boundary conditions, etc.)and simulation procedures are the same as in our previous

work.12All MD simulations are performed using NAMD(NAnoscale Molecular Dynamics) package15 and VMD(Visual Molecular Dynamics) package16 in the CHARMM(Chemistry at HARvard Molecular Mechanics)17 force field.The water molecule is represented by the modified flexibleTIP3P (transferable intermolecular potential three-point) watermodel. Unlike the original rigid TIP3P model in whichthe van der Waals force is only set on the oxygen atom, theTIP3P water model in NAMD package is a flexible modeland is modified additionally to include Lennard-Jones parametersfor the hydrogen atoms.18 The use of a flexible watermodel here requires more calculations during a MD simulation

but produces a more accurate representation of thewater molecule needed in this work. The CHARMM forcefield includes several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):

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EVW =nonbonded atom pairse(ij )Rmin(ij )rij12-2Rmin(ij )rij6Nonequilibrium molecular dynamics simulation of pressure-driven water transportthrough modified CNT membranesLuying Wang, Randall S. Dumont, and James M. DicksonCitation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHow fast does water flow in carbon nanotubes?

J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at lowpressurea)J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490

This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada(Received 21 December 2012; accepted 13 February 2013; published online 22 March

2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effectof water-membrane interactions on the transport properties of pressure-driven water flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between watermolecules and the CNT membranes. The unmodified and modified CNT membranes are m

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odels ofsimplified nanofiltration (NF) membranes at operating conditions consistent withreal NF systems.All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K),constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The waterflow rate, density, and velocity (in flow direction) distributions are obtainedby analyzing the NEMDsimulation results to compare transport through the modified and unmodified CNTmembranes. Thepressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted bythe Navier-Stokes equations. For water passing through the modified membrane with stronger vander Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities.These investigations show the effect of water-CNT membrane interactions on watertransport underNF operating conditions. This work can help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013AmericanInstitute of Physics. [http://dx.doi.org/10.1063/1.4794685]

I. INTRODUCTIONMolecular dynamics (MD) simulation provides a dynamicview of microscopic systems. Water flow throughnanoscale channels, driven by external fields, is critical tomany phenomenafor example, biological channels, drugdelivery, membrane separations, fuel cells, and novel nanofluidicapplications (nanopumps, nanosyringes, nanosensors,etc.). In recent years, MD simulations have been used tostudy water flow driven by external fields such as pressuredifference,13 osmotic pressure difference,4, 5 and electricfield.6Nanofiltration (NF) is a common membrane separationprocess driven by a pressure difference between the two sides

of the NF membrane, where a concentrated stream on the highpressure side passes through the NF membrane and becomesa purified stream on the low pressure side. Applications ofNF worldwide have increased primarily in the water treatmentindustry,7 such as water softening, organics removal,radium and heavy metal removal from wastewater; and sulfateremoval from seawater. In addition, NF has been appliedin other industries: pulp and paper effluent treatment in thepapermaking industry, removal of dyes and other coloringagents in the textile industry, concentration of intermediatesand antibiotics in the pharmaceutical industry.8 In view of thea)Author to whom correspondence should be addressed. Electronic mail:dickson@mcmaster.ca.

growing industrial applications of NF, the transport mechanismof NF is examined using MD simulation with the goalof improving the understanding of the types of membranesbest suited for NF processes.To understand the microscopic dynamics properties ofthe NF process with MD simulation, nonequilibrium moleculardynamic (NEMD) simulations must be used becausepressure-driven fluid flow corresponds to a nonequilibriumconditions. NEMD is a valuable tool to study fluidflow through nanoscale channels, induced by a pressure

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difference.1, 2, 911 The key to a NEMD simulation of a NFprocess is a mean of imposing different constant pressureson the two sides of the NF membrane. In our previous study,we reported a NEMD simulation system derived by Huang9and Takaba10 to study the transport phenomena of pressuredrivenwater flow through CNT membranes under NF operatingconditions.12, 13Real NF membranes are generally made from syntheticpolymers. The membrane structure (pore size, numberof pores, and membrane thickness) and the polymer characteristics(functional groups, electric charge, hydrophilicity/hydrophobicity, etc.) can both affect membrane performance.The interaction between solution and polymeric NFmembrane is one of the most important factors determiningmembrane separation and transport performance. In ourprevious work, the effect of membrane structure on watertransport through CNT membranes was investigated.12 Thiswork investigates the effect of water-CNT membrane interactionson modified CNT membrane performance with different0021-9606/2013/138(12)/124701/9/$30.00 138, 124701-1 2013 American Institute ofPhysicsThis article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3

On: Tue, 22 Apr 2014 06:16:53124701-2 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)membrane characteristics. Although the solution-membraneinteractions in a real NF process are more complicated thanthe water-CNT interactions, this work provides fundamentalinformation how membrane characteristics affect membraneperformance.The modified CNT membranes have the same membranestructure (pore size and membrane thickness) as the unmodifiedCNT membrane; only the van der Waals interactionsand electrostatic interactions between water molecules andCNT membranes are altered. Transport through the unmodifiedCNT membrane and modified CNT membranes is compared

to establish the role of the water-CNT interactions in determiningobserved transport properties. This work highlightsa unique advantage of MD simulationthe water-membraneinteraction can be adjusted to reveal the effect on the NF transport.The unmodified and modified CNT membranes in thispaper can be considered as functionalized CNTs or models ofsimplified NF membranes at operating conditions consistentwith real NF systems.II. SIMULATION METHODSThe system model in Cartesian coordinates is shownin Fig. 1. The system consists of two graphene sheets actingas moveable walls, two water reservoirs, and the CNTmembrane model. The moveable walls and the membrane

model are 4 nm 4 nm in the x, y plane. The thickness andthe pore size of the CNT membrane is determined by the(12, 12) type CNT, which has a 6.0 nm length and 0.643nm internal radius.1, 14 The top and bottom water reservoirs,connected by the CNT membrane model, provide the sourceand sink of the water flow passing through the membrane,along the z direction. External force is applied on each carbonatom of the moveable walls to produce 8.1 MPa pressureFIG. 1. Perspective snapshots of the simulation systems produced by VMDpackage at the beginning status of MD simulations (adapted from the figure

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in Ref. 12). Shown is the beginning empty CNT membrane model connectingtwo liquid filled reservoirs, and the two graphene sheets acted as the movablewalls where the force ft or fb is applied on each carbon atom of the top orbottom wall. Carbon atoms in green, hydrogen atoms in white, and oxygenatoms in red.on the top water reservoir and 0.1 MPa on the bottom waterreservoir to give a pressure difference of 8.0 MPa. We usea simulated pressure difference across the CNT membranethat is somewhat higher than typical NF systems (usuallyless than 3 MPa pressure difference) as this higher pressuredifference reduces the (still large) CPU time needed for thesimulations.An equilibrium MD simulation, in an isothermal-isobaric(NPT) ensemble, is carried out first to energy-minimize andequilibrate the system; and then a NEMD simulation is carriedout to simulate the pressure-driven water flow throughthe CNT membrane. Each simulation is at 300 K, and takesabout 14 CPU days for 1.0 ns of simulation (the length ofeach NEMD simulation is from over 100 ns to about 250 ns).The detailed simulation methodology (force field parameters,integration algorithm, periodic boundary conditions, etc.)and simulation procedures are the same as in our previouswork.12All MD simulations are performed using NAMD

(NAnoscale Molecular Dynamics) package15 and VMD(Visual Molecular Dynamics) package16 in the CHARMM(Chemistry at HARvard Molecular Mechanics)17 force field.The water molecule is represented by the modified flexibleTIP3P (transferable intermolecular potential three-point) watermodel. Unlike the original rigid TIP3P model in whichthe van der Waals force is only set on the oxygen atom, theTIP3P water model in NAMD package is a flexible modeland is modified additionally to include Lennard-Jones parametersfor the hydrogen atoms.18 TNonequilibrium molecular dynamics simulation of pressure-driven water transportthrough modified CNT membranesLuying Wang, Randall S. Dumont, and James M. Dickson

Citation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHow fast does water flow in carbon nanotubes?J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at lowpressurea)J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484

Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded t

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o IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada(Received 21 December 2012; accepted 13 February 2013; published online 22 March2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effectof water-membrane interactions on the transport properties of pressure-driven water flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between watermolecules and the CNT membranes. The unmodified and modified CNT membranes are models ofsimplified nanofiltration (NF) membranes at operating conditions consistent withreal NF systems.

All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K),constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The waterflow rate, density, and velocity (in flow direction) distributions are obtainedby analyzing the NEMDsimulation results to compare transport through the modified and unmodified CNTmembranes. Thepressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted bythe Navier-Stokes equations. For water passing through the modified membrane with stronger vander Waals or electrostatic interactions, the fast flow is reduced giving lower f

low rates and velocities.These investigations show the effect of water-CNT membrane interactions on watertransport underNF operating conditions. This work can help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013AmericanInstitute of Physics. [http://dx.doi.org/10.1063/1.4794685]I. INTRODUCTIONMolecular dynamics (MD) simulation provides a dynamicview of microscopic systems. Water flow throughnanoscale channels, driven by external fields, is critical tomany phenomenafor example, biological channels, drug

delivery, membrane separations, fuel cells, and novel nanofluidicapplications (nanopumps, nanosyringes, nanosensors,etc.). In recent years, MD simulations have been used tostudy water flow driven by external fields such as pressuredifference,13 osmotic pressure difference,4, 5 and electricfield.6Nanofiltration (NF) is a common membrane separationprocess driven by a pressure difference between the two sidesof the NF membrane, where a concentrated stream on the highpressure side passes through the NF membrane and becomes

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a purified stream on the low pressure side. Applications ofNF worldwide have increased primarily in the water treatmentindustry,7 such as water softening, organics removal,radium and heavy metal removal from wastewater; and sulfateremoval from seawater. In addition, NF has been appliedin other industries: pulp and paper effluent treatment in thepapermaking industry, removal of dyes and other coloringagents in the textile industry, concentration of intermediatesand antibiotics in the pharmaceutical industry.8 In view of thea)Author to whom correspondence should be addressed. Electronic mail:dickson@mcmaster.ca.growing industrial applications of NF, the transport mechanismof NF is examined using MD simulation with the goalof improving the understanding of the types of membranesbest suited for NF processes.To understand the microscopic dynamics properties ofthe NF process with MD simulation, nonequilibrium moleculardynamic (NEMD) simulations must be used becausepressure-driven fluid flow corresponds to a nonequilibriumconditions. NEMD is a valuable tool to study fluidflow through nanoscale channels, induced by a pressuredifference.1, 2, 911 The key to a NEMD simulation of a NFprocess is a mean of imposing different constant pressureson the two sides of the NF membrane. In our previous study,

we reported a NEMD simulation system derived by Huang9and Takaba10 to study the transport phenomena of pressuredrivenwater flow through CNT membranes under NF operatingconditions.12, 13Real NF membranes are generally made from syntheticpolymers. The membrane structure (pore size, numberof pores, and membrane thickness) and the polymer characteristics(functional groups, electric charge, hydrophilicity/hydrophobicity, etc.) can both affect membrane performance.The interaction between solution and polymeric NFmembrane is one of the most important factors determiningmembrane separation and transport performance. In ourprevious work, the effect of membrane structure on water

transport through CNT membranes was investigated.12 Thiswork investigates the effect of water-CNT membrane interactionson modified CNT membrane performance with different0021-9606/2013/138(12)/124701/9/$30.00 138, 124701-1 2013 American Institute ofPhysicsThis article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-2 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)membrane characteristics. Although the solution-membraneinteractions in a real NF process are more complicated thanthe water-CNT interactions, this work provides fundamental

information how membrane characteristics affect membraneperformance.The modified CNT membranes have the same membranestructure (pore size and membrane thickness) as the unmodifiedCNT membrane; only the van der Waals interactionsand electrostatic interactions between water molecules andCNT membranes are altered. Transport through the unmodifiedCNT membrane and modified CNT membranes is comparedto establish the role of the water-CNT interactions in determiningobserved transport properties. This work highlights

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a unique advantage of MD simulationthe water-membraneinteraction can be adjusted to reveal the effect on the NF transport.The unmodified and modified CNT membranes in thispaper can be considered as functionalized CNTs or models ofsimplified NF membranes at operating conditions consistentwith real NF systems.II. SIMULATION METHODSThe system model in Cartesian coordinates is shownin Fig. 1. The system consists of two graphene sheets actingas moveable walls, two water reservoirs, and the CNTmembrane model. The moveable walls and the membranemodel are 4 nm 4 nm in the x, y plane. The thickness andthe pore size of the CNT membrane is determined by the(12, 12) type CNT, which has a 6.0 nm length and 0.643nm internal radius.1, 14 The top and bottom water reservoirs,connected by the CNT membrane model, provide the sourceand sink of the water flow passing through the membrane,along the z direction. External force is applied on each carbonatom of the moveable walls to produce 8.1 MPa pressureFIG. 1. Perspective snapshots of the simulation systems produced by VMDpackage at the beginning status of MD simulations (adapted from the figurein Ref. 12). Shown is the beginning empty CNT membrane model connectingtwo liquid filled reservoirs, and the two graphene sheets acted as the movablewalls where the force ft or fb is applied on each carbon atom of the top or

bottom wall. Carbon atoms in green, hydrogen atoms in white, and oxygenatoms in red.on the top water reservoir and 0.1 MPa on the bottom waterreservoir to give a pressure difference of 8.0 MPa. We usea simulated pressure difference across the CNT membranethat is somewhat higher than typical NF systems (usuallyless than 3 MPa pressure difference) as this higher pressuredifference reduces the (still large) CPU time needed for thesimulations.An equilibrium MD simulation, in an isothermal-isobaric(NPT) ensemble, is carried out first to energy-minimize andequilibrate the system; and then a NEMD simulation is carriedout to simulate the pressure-driven water flow through

the CNT membrane. Each simulation is at 300 K, and takesabout 14 CPU days for 1.0 ns of simulation (the length ofeach NEMD simulation is from over 100 ns to about 250 ns).The detailed simulation methodology (force field parameters,integration algorithm, periodic boundary conditions, etc.)and simulation procedures are the same as in our previouswork.12All MD simulations are performed using NAMD(NAnoscale Molecular Dynamics) package15 and VMD(Visual Molecular Dynamics) package16 in the CHARMM(Chemistry at HARvard Molecular Mechanics)17 force field.The water molecule is represented by the modified flexibleTIP3P (transferable intermolecular potential three-point) water

model. Unlike the original rigid TIP3P model in whichthe van der Waals force is only set on the oxygen atom, theTIP3P water model in NAMD package is a flexible modeland is modified additionally to include Lennard-Jones parametersfor the hydrogen atoms.18 The use of a flexible watermodel here requires more calculations during a MD simulationbut produces a more accurate representation of thewater molecule needed in this work. The CHARMM forcefield includes several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy

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(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairse(ij )Rmin(ij )rij12-2Rmin(ij )rij6he use of a flexible watermodel here requires more calculations during a MD simulationbut produces a more accurate representation of thewater molecule needed in this work. The CHARMM forcefield includeNonequilibrium molecular dynamics simulation of pressure-driven wat

er transportthrough modified CNT membranesLuying Wang, Randall S. Dumont, and James M. DicksonCitation: The Journal of Chemical Physics 138, 124701 (2013); doi: 10.1063/1.4794685View online: http://dx.doi.org/10.1063/1.4794685View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/138/12?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inHow fast does water flow in carbon nanotubes?J. Chem. Phys. 138, 094701 (2013); 10.1063/1.4793396Nonequilibrium molecular dynamics simulation of water transport through carbon n

anotube membranes at lowpressurea)J. Chem. Phys. 137, 044102 (2012); 10.1063/1.4734484Molecular simulation of pressure-driven fluid flow in nanoporous membranesJ. Chem. Phys. 127, 054703 (2007); 10.1063/1.2749236Molecular dynamics simulations of transport and separation of carbon dioxidealkane mixtures in carbonnanoporesJ. Chem. Phys. 120, 8172 (2004); 10.1063/1.1688313Kinetic theory and molecular dynamics simulations of microscopic flowsPhys. Fluids 9, 3915 (1997); 10.1063/1.869490This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded t

o IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53THE JOURNAL OF CHEMICAL PHYSICS 138, 124701 (2013)Nonequilibrium molecular dynamics simulation of pressure-driven watertransport through modified CNT membranesLuying Wang,1 Randall S. Dumont,2 and James M. Dickson1,a)1Department of Chemical Engineering, McMaster University, Hamilton, Ontario L8S4L7, Canada2Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada

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(Received 21 December 2012; accepted 13 February 2013; published online 22 March2013)Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effectof water-membrane interactions on the transport properties of pressure-driven water flow passingthrough carbon nanotube (CNT) membranes. The CNT membrane is modified with different physicalproperties to alter the van der Waals interactions or the electrostatic interactions between watermolecules and the CNT membranes. The unmodified and modified CNT membranes are models ofsimplified nanofiltration (NF) membranes at operating conditions consistent withreal NF systems.All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K),constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The waterflow rate, density, and velocity (in flow direction) distributions are obtainedby analyzing the NEMDsimulation results to compare transport through the modified and unmodified CNTmembranes. Thepressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted by

the Navier-Stokes equations. For water passing through the modified membrane with stronger vander Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities.These investigations show the effect of water-CNT membrane interactions on watertransport underNF operating conditions. This work can help provide and improve the understanding of how thesemembrane characteristics affect membrane performance for real NF processes. 2013AmericanInstitute of Physics. [http://dx.doi.org/10.1063/1.4794685]I. INTRODUCTIONMolecular dynamics (MD) simulation provides a dynamic

view of microscopic systems. Water flow throughnanoscale channels, driven by external fields, is critical tomany phenomenafor example, biological channels, drugdelivery, membrane separations, fuel cells, and novel nanofluidicapplications (nanopumps, nanosyringes, nanosensors,etc.). In recent years, MD simulations have been used tostudy water flow driven by external fields such as pressuredifference,13 osmotic pressure difference,4, 5 and electricfield.6Nanofiltration (NF) is a common membrane separationprocess driven by a pressure difference between the two sidesof the NF membrane, where a concentrated stream on the highpressure side passes through the NF membrane and becomes

a purified stream on the low pressure side. Applications ofNF worldwide have increased primarily in the water treatmentindustry,7 such as water softening, organics removal,radium and heavy metal removal from wastewater; and sulfateremoval from seawater. In addition, NF has been appliedin other industries: pulp and paper effluent treatment in thepapermaking industry, removal of dyes and other coloringagents in the textile industry, concentration of intermediatesand antibiotics in the pharmaceutical industry.8 In view of thea)Author to whom correspondence should be addressed. Electronic mail:

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dickson@mcmaster.ca.growing industrial applications of NF, the transport mechanismof NF is examined using MD simulation with the goalof improving the understanding of the types of membranesbest suited for NF processes.To understand the microscopic dynamics properties ofthe NF process with MD simulation, nonequilibrium moleculardynamic (NEMD) simulations must be used becausepressure-driven fluid flow corresponds to a nonequilibriumconditions. NEMD is a valuable tool to study fluidflow through nanoscale channels, induced by a pressuredifference.1, 2, 911 The key to a NEMD simulation of a NFprocess is a mean of imposing different constant pressureson the two sides of the NF membrane. In our previous study,we reported a NEMD simulation system derived by Huang9and Takaba10 to study the transport phenomena of pressuredrivenwater flow through CNT membranes under NF operatingconditions.12, 13Real NF membranes are generally made from syntheticpolymers. The membrane structure (pore size, numberof pores, and membrane thickness) and the polymer characteristics(functional groups, electric charge, hydrophilicity/hydrophobicity, etc.) can both affect membrane performance.The interaction between solution and polymeric NF

membrane is one of the most important factors determiningmembrane separation and transport performance. In ourprevious work, the effect of membrane structure on watertransport through CNT membranes was investigated.12 Thiswork investigates the effect of water-CNT membrane interactionson modified CNT membrane performance with different0021-9606/2013/138(12)/124701/9/$30.00 138, 124701-1 2013 American Institute ofPhysicsThis article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-2 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)

membrane characteristics. Although the solution-membraneinteractions in a real NF process are more complicated thanthe water-CNT interactions, this work provides fundamentalinformation how membrane characteristics affect membraneperformance.The modified CNT membranes have the same membranestructure (pore size and membrane thickness) as the unmodifiedCNT membrane; only the van der Waals interactionsand electrostatic interactions between water molecules andCNT membranes are altered. Transport through the unmodifiedCNT membrane and modified CNT membranes is comparedto establish the role of the water-CNT interactions in determiningobserved transport properties. This work highlights

a unique advantage of MD simulationthe water-membraneinteraction can be adjusted to reveal the effect on the NF transport.The unmodified and modified CNT membranes in thispaper can be considered as functionalized CNTs or models ofsimplified NF membranes at operating conditions consistentwith real NF systems.II. SIMULATION METHODSThe system model in Cartesian coordinates is shownin Fig. 1. The system consists of two graphene sheets actingas moveable walls, two water reservoirs, and the CNT

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membrane model. The moveable walls and the membranemodel are 4 nm 4 nm in the x, y plane. The thickness andthe pore size of the CNT membrane is determined by the(12, 12) type CNT, which has a 6.0 nm length and 0.643nm internal radius.1, 14 The top and bottom water reservoirs,connected by the CNT membrane model, provide the sourceand sink of the water flow passing through the membrane,along the z direction. External force is applied on each carbonatom of the moveable walls to produce 8.1 MPa pressureFIG. 1. Perspective snapshots of the simulation systems produced by VMDpackage at the beginning status of MD simulations (adapted from the figurein Ref. 12). Shown is the beginning empty CNT membrane model connectingtwo liquid filled reservoirs, and the two graphene sheets acted as the movablewalls where the force ft or fb is applied on each carbon atom of the top orbottom wall. Carbon atoms in green, hydrogen atoms in white, and oxygenatoms in red.on the top water reservoir and 0.1 MPa on the bottom waterreservoir to give a pressure difference of 8.0 MPa. We usea simulated pressure difference across the CNT membranethat is somewhat higher than typical NF systems (usuallyless than 3 MPa pressure difference) as this higher pressuredifference reduces the (still large) CPU time needed for thesimulations.An equilibrium MD simulation, in an isothermal-isobaric

(NPT) ensemble, is carried out first to energy-minimize andequilibrate the system; and then a NEMD simulation is carriedout to simulate the pressure-driven water flow throughthe CNT membrane. Each simulation is at 300 K, and takesabout 14 CPU days for 1.0 ns of simulation (the length ofeach NEMD simulation is from over 100 ns to about 250 ns).The detailed simulation methodology (force field parameters,integration algorithm, periodic boundary conditions, etc.)and simulation procedures are the same as in our previouswork.12All MD simulations are performed using NAMD(NAnoscale Molecular Dynamics) package15 and VMD(Visual Molecular Dynamics) package16 in the CHARMM

(Chemistry at HARvard Molecular Mechanics)17 force field.The water molecule is represented by the modified flexibleTIP3P (transferable intermolecular potential three-point) watermodel. Unlike the original rigid TIP3P model in whichthe van der Waals force is only set on the oxygen atom, theTIP3P water model in NAMD package is a flexible modeland is modified additionally to include Lennard-Jones parametersfor the hydrogen atoms.18 The use of a flexible watermodel here requires more calculations during a MD simulationbut produces a more accurate representation of thewater molecule needed in this work. The CHARMM forcefield includes several terms representing intermolecular andintramolecular interactions. The intermolecular potential energy

(also called long-range potential energy) includes theLennard-Jones 612 potential and the Coulomb potential todescribe van der Waals and electrostatic interactions, respectively.The mathematical expressions of the Lennard-Jones612 type potential (EVW) and Coulomb potential (Eelect) areshown in Eqs. (1) and (2):EVW =nonbonded atom pairse(ij )

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Rmin(ij )rij12-2Rmin(ij )rij6al and flow directions.III. RESULTS AND DISCUSSIONThe theoretical flux and velocity in the z direction arecalculated using the Navier-Stokes equations for a cylindricalchannel (Eqs. (5) and (6)). Equation (5) is also called theHagen-Poiseuille equation, and we will simply refer to Eq. (6)as the Navier-Stokes equation:JW = LP P =r2p8? (Lz/AK)P,AK =p r2p

Amem=p r2pLx Ly,(5)vz = P4?Lzr2p- r2

, (6water reservoir. Average density and velocity values foreach section are obtained from effective collected trajectorydata of the NEMD simulation. The stream velocity of waterflow in the water reservoirs is too lowdue to the lowpressure differenceto determine with reasonable accuracythrough the NEMD simulation. Instead, the water velocity ineach reservoir is determined from the velocity of each movablewall, which is calculated by fitting the moved distance ofthe wall to a linear dependence on simulation time. The numberof water molecules passing through the membrane modelare counted every 50 ps and plotted as a function of the simulationtime. The slope of the linear profile (through the origin)

is the number flow rate. For each flow rate value, the estimatederror of the flow rate is represented by the standard error onthe slope with the assumption of uncorrelated data (a correlationtime shorter than 50 ps). An example of the error analysisfor the simulation flow rate is provided in our previouswork.12 The error analyses for density or velocity values areperformed by considering the integrated autocorrelation time,which is used to calculate the effective sample number of timecorrelated dat)where LP is the permeability coefficient of the water fluid, rp

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is the pore radius, ? is the viscosity of water at the operatingtemperature, Lz/AK is the ratio of the membrane effectivethickness to the membrane porosity, P is the pressure difference,and r is the radial position. The density and viscosityof water at 300 K are 1000 kg/m3 and 8.54 10-4 Pa s,respectively,20 and theoretical flux is converted to theoreticalflow rate in molecules/nsto compare with the simulationflow rate.The simulation water flow rate is defined as the numberflow rate (molecules/ns), which is calculated by the slope ofthe linear trend between the number of water molecules in thebottom reservoir and simulation time. To obtain the densityand velocity distributions along the radial direction, the poreis divided into ten annular sections evenly spaced in the radialdirection. The distributions along the flow direction arestudied by dividing the entire system evenly into ten sectionswith equal distance along the flow direction: four sections inthe top water reservoir, three in the CNT, and three in the bottoma (the numberof uncorrelated samples).21 Thestatistical error of each density or velocity data point is calculateddirectly from the standard deviation of the sampledmean using the number of uncorrelated samples as discussedpreviously.12A. The modified Lennard-Jones parameters

of the CNT membranesTo study the effect of van derWaals interactions betweenwater and the membrane with respect to the transport phenomenon,the Lennard-Jones parameters of carbon atoms inthe CNT model are modified. As listed in Table I, the welldepthparameter of the carbon atom is set as the well-depth parametervalue of a hydrogen (Case I) or oxygen (Case II) atomin the modified CNT models (corresponding to smaller andlarger well depths, respectively). The distance of the Lennard-Jones minimum interaction energy is kept at the same valuei.e., that of a carbon atom. The value of the well-depth parameterreflects the strength of the van der Waals interaction betweentwo atoms: a larger value means a stronger interaction.

The flow rate of eachns)of unmodified and modified CNT membranes. The results are based onmembrane simulations using the (12, 12) CNT, Lz: 6.0 nm; P: 8.0 MPa;T: 300 K. The statistical error for each flow rate data is less than 0.5%. H-Pequation refers to the Hagen-Poiseuille equation (Eq. (5)), and the values ofthe well-depth parameters (e(CC), e(HH), and e(OO)) are shown in Table I.frictionless CNT surface, (2) the quite narrow pore size, and(3) the relatively weak interactions between water moleculesand the CNT surface. However, water transport does dependon the interactions between water and the CNT: strong interactionsimpede flow, while weak interactions permit morerapid flow. As the interactions increase (from Case I, to unmodified,to Case II) the water flow rate decreases due to these

interactions.According to the Eqs. (1) and (3), the Lennard-Jones potentialenergy between the water molecules and the membranesurfaces depends on the square root of the well-depth parameterof the CNT membrane. Figure 3 illustrates the relationshipbetween the simulation flow rate and the water-membrane interaction,which is represented by the square root of the welldepthparameter of the unmodified and modified CNT membranes.Here, we see the inverse relationship between flowFIG. 3. Simulation flow rate (molecules/ns) as a function of the square root

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of the well-depth parameter. The data points are based on membrane simulationsusing the (12, 12) CNT, Lz: 6.0 nm; P: 8.0 MPa; T: 300 K. Thestatistical error for each data point is less than 0.5%. The solid line is thelinear trend based on the simulation results.FIG. 4. Effect of van der Waals interactions between water and membrane,represented by the w CNT membrane and the theoreticalflow rate are shown in Fig. 2. As previously seen,12 CNTmembranes exhibit much higher flow rate than theoretical values.Here, we see that the simulation flow rate decreases withincreasing CC well-depth. A continuum flow dominated bythe bulk properties can be described by the Hagen-Poiseuilleequation. However, water passing through a nanoscale CNTmembrane forms a non-continuum nanofluid flow. Transportof water through the CNT membrane is not governed by theHagen-Poiseuille equation due to (1) a smooth and nearlyTABLE I. The Lennard-Jones parameters of the unmodified and modifiedCNT membranes.Lennard-Jones Modified Modifiedparametersa Unmodified Case I Case IIemem (kcal/mol) 0.07 = e(CC) 0.046 = e(HH)b 0.1521 = e(OO)cRmin/2 (nm) 0.19924 0.19924 0.19924aThe values of the parameters are based on CHARMM force field.17

bSet to the well-depth parameter for hydrogen, e(HH); a smaller interaction.cSet to the well-depth parameter for oxygen, e(OO); a larger interaction.This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-4 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)FIG. 2. Bar chart of simulation and theoretical flow rates (molecules/ell-depthparameter of the Lennard-Jones potential (interactionincreasing from red , to black , to green ), on the density distributionsalong the radial direction: density values are averaged over thinannular sections in the pore at the indicated r values over the NEMD simulationat steady state water flow. The data points are based on membrane

simulations using the (12, 12) CNT, Lz: 6.0 nm; P: 8.0MPa; T: 300 K. Thestatistical error for each data point is less than 1%. The values of the welldepthparameters (e(CC), e(HH), and e(OO)) are shown in Table I. The solidlines are the trend curves based on the simulation results, and the dotted linesare the pore surface represented by the effective pore radius (0.643 nm).rate and well depth. With only three points, the details of thisrelationship are not clearonly that flow rate decreases withincreasing well depth. Clearly, stronger attraction of water tothe pore surface reduces the flow as expected.Figures 4 and 5 sho from leftto right: the water reservoir on the high pressure side, the pore of the CNTmembrane, and the water reservoir on the low pressure side.

This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-5 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)For the axial direction, as shown in Fig. 5, the densityremains constant throughout the length of the pore for allthree well depths. However, the constant value is sensitiveto the well depth. If the carbon well depth is increased fromthat of hydrogen (Case I), to carbon (unmodified) and then

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to oxygen (Case II), the density in the pore increases whilethe bulk values in the reservoirs remain unchanged. Overallthe increase in density (in the pore) from hydrogen to carbonand hydrogen to oxygen well-depth parameters is about2 molecules/nm3 (6%) and 4 molecules/nm3 (13%), respectively.The density decrease on entering the pore for the unmodifiedcase (well depth of carbon) is due to the orderedstacking of water molecules in the pore compared to bulk solutionand is consistent with results found previously.12 ForCase I, the attraction of water to the membrane wall is less andthe water is more free to align with itself and obtain a densityslightly higher (about 3%) than bulk water. On the other hand,for Case II, the interaction of water with the wall is strongerand this apparently forces the water into closer aligned ringsin the pore (as evidenced in Fig. 4) and an even higherdensity than for the unmodified case (about 10% higher) isobtained.The radial velocity distribution for continuum flowthrough a cylindrical pore should have a parabolic profiledetermined by the Navier-Stokes equations. Figure 6 showsthe oscillatory velocity distributions along the radial directionobserved for pressure-driven water flow through these CNTmembranes. The velocity profiles obtained from the NEMDsimulations are higher than the theoretical values predicted

by the Navier-Stokes equations. The non-parabolic distributionof water velocity in the CNT membrane is explained inour previous work.12, 13 Figure 6 shows that Case I, with theleast interaction, has the highest velocity curves and Case II,with the highest interaction, has the lowest velocity curves.Overall, the velocity profiles increase in the order of decreas-FIG. 6. Effect of van der Waals interactions between water and membrane,represented by the well-depth parameter of the Lennard-Jones potential (interactionincreasing from red , to black , to green ), on the velocitydistributions (in z direction) as a function of radial position: velocity(in z direction) values are averaged over thin annular sections in the poreat the indicated r values over the NEMD simulation at steady state water

flow. The data points are based on membrane simulations using the (12, 12)CNT, Lz: 6.0 nm; P: 8.0MPa; T: 300 K. The statistical errors for most datapoints are less than 10%. N-S equation refers to the Navier-Stokes equation(Eq. (6)), and the values of the well-depth parameters (e(CC), e(HH), and e(OO))are shown in Table I. The solid lines are the trend curves based on the simulationresults, the dashed lines are the trends based on the Navier-Stokesequation, and the dotted lines are the pore surface represented by the effectivepore radius (0.643 nm).FIG. 7. Effect of van der Waals interactions between water and membrane,represented by tw the density distributions along theradial and axial directions, respectively, for the three CNTmembrane models. The radial distributions of density all exhibit

similar oscillatory waves, with low density in the porecenter and two pairs of symmetrical peaksindicating thatthere are two cylindrical rings of water molecules within thepore. The effect of increasing the CNT well-depth parameteris to shift the outer ring towards the pore surface and boththe inner and outer water rings become more well defined(sharper peaks).FIG. 5. Effect of van der Waals interactions between water and membrane,represented by the well-depth parameter of the Lennard-Jones potential (interaction

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increasing from red , to black , to green ), on the density distributionsalong the flow direction: density values are averaged over thin sectionsabout the indicated z values (cylindrical sections in the pore and cuboidsections in the water reservoirs) over the NEMD simulation at steady statewater flow. The data points are based on membrane simulations using the(12, 12) CNT, Lz: 6.0 nm; P: 8.0 MPa; T: 300 K. The statistical error foreach data point is less than 1%. The values of the well-depth parameters(e(CC), e(HH), and e(OO)) are shown in Table I. The solid lines are the trendcurves based on the simulation results. The dashed lines are the membraneboundaries along z direction separating the system in three partshe well-depth parameter of the Lennard-Jones potential (interactionincreasing from red , to black , to green ), on the velocitydistributions (in z direction) along the flow direction: velocity (in z direction)values are averaged over thin sections about the indicated z values (cylindricalsections in the pore and cuboid sections in the water reservoirs) over theNEMD simulation at steady state water flow. The data points are based onmembrane simulations using the (12, 12) CNT, Lz: 6.0 nm; P: 8.0 MPa; T:300 K. The statistical error for each data point is less than 10%. The values ofthe well-depth parameters (e(CC), e(HH), and e(OO)) are shown in Table I. Thesolid lines are the trend curves based on the simulation results. The dashedlines are the membrane boundaries along the z direction separating the systemin three parts from left to right: the water reservoir at high pressure side,the pore of the CNT membrane, and the water reservoir at low pressure side.

ing attraction to the membrane wall as would be expectedsince the lower water-membrane attraction allows the waterto move faster. The oscillatory shape of the velocity distributionis approximately consistent with the two rings of waterobserved in the density distribution (Fig. 4): a higher velocitysection nearwhole length of the tube to get each average radial result; averagingthe values over the whole radius for each axial section toget each flow-directional result). The almost constant resultsalong the tube in Figs. 5 and 7 show that the entrance/exiteffects are approximately insignificant here (also shown inSec. III B). Note that Nicholls et al.22 have reported thatthe entrance/exit effects can be significant in their studies of

This article is copyrighted as indicated in the article. Reuse of AIP content issubject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 27.48.137.3On: Tue, 22 Apr 2014 06:16:53124701-6 Wang, Dumont, and Dickson J. Chem. Phys. 138, 124701 (2013)water transport through (7,7) CNTs at a 200 MPa pressuredifference.B. The polarized CNT membranesIt has been shown that the delocalized p-electrons of theCNT carbon atoms can result in polarized CNTs,2326 withpositive and negative partial charges of the polarized CNTforming a pattern.27 Simplified charge distributions (as shownin Fig. 8) are proposed here: positive and negative partial

FIG. 8. Charge patterns of the unmodified and modified CNTs: (a) unmodifiedCNT, (b) unwrapped CNT of the ring polarized model, and (c) unwrappedCNT of the band polarized model. This figure illustrates the relativelocations of the neutral atoms in green, the positive atoms in orange, andthe negative atoms in blue. Transport is from left to right as indicated by thearrows on the z-axes.charges arranged in distinct patterns are set on the unmodifiedCNT to model a fictitious polarized CNT. Unlike the unmodifiedCNT membrane, the polarized CNT membrane can affectthe water through electrostatic interactions. The water transport

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properties of the unmodified and polarized CNT membranesare investigated to show the effect of electrostatic interactionson the transport properties.Two modified CNTs with different charge patterns(Fig. 8) are used to model the polarized CNT membranes.Each CNT has a total net charge of zero, with positive andnegative atomic charges on selected carbon atoms along thelength or circumference of the CNT. Figure 8(b) shows thering polarized CNT with ten alternating charged rings withequal magnitude along the length. Figure 8(c) shows the bandpolarized CNT with six alternating charged bands with equalmagnitude along the circumference. The atomic charges ofeach charged ring or band have the same magnitude, andthe adjacent positive and negati