JOURNAL OF CHEMICAL PHYSICS
VOLUME 117, NUMBER 2
8 JULY 2002
Transport diffusion of liquid water and methanol through membranes
Qinxin Zhanga)
Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
Jie Zheng
Department of Chemical Engineering, University of Washington, Seattle, Washington 98195
Abhijit Shevadeb)
Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
Luzheng Zhang
Department of Chemical Engineering, University of Washington, Seattle, Washington 98195
Stevin H. Gehrke
Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
Grant S. Heffelfinger
Computational Biology and Materials Technology Department, Sandia National Laboratories, Albuquerque,
New Mexico 87185
Shaoyi Jiangc)
Department of Chemical Engineering, University of Washington, Seattle, Washington 98195
共Received 11 January 2002; accepted 12 April 2002兲
In this work, we carried out dual-control-volume grand canonical molecular dynamics simulations
of the transport diffusion of liquid water and methanol to vacuum under a fixed chemical potential
gradient through a slit pore consisting of Au共111兲 surfaces covered by ⫺CH3 or ⫺OH terminated
self-assembled monolayers 共SAMs兲. Methanol and water are selected as model fluid molecules
because water represents a strongly polar molecule while methanol is intermediate between
nonpolar and strongly polar molecules. Surface hydrophobicity is adjusted by varying the terminal
group of ⫺CH3 共hydrophobic兲 or ⫺OH 共hydrophilic兲 of SAMs. We observed for the first time from
simulations the convex and concave interfaces of fluids transporting across the slit pores. Results
show that the characteristics of the interfaces are determined by the interactions between fluid
molecules and surfaces. The objective of this work is to provide a fundamental understanding of
how these interactions affect transport diffusion. © 2002 American Institute of Physics.
关DOI: 10.1063/1.1483297兴
I. INTRODUCTION
and charge-based transport selectivity for the separation of
radioactive and hazardous metal cations.5 Of the two categories of diffusion, transport diffusion is more important than
self-diffusion from both practical and theoretical points of
view.6
With the development of the dual-control-volume grand
canonical molecular dynamics 共DCV-GCMD兲 simulation
technique,7–9 transport diffusion has been simulated extensively in connection with membrane separation.6 –12 Many
new processes emerge in the recent years for liquid separation. However, all DCV-GCMD simulations almost exclusively deal with simple gases or gaseous mixtures. For membrane separation, the entrance effect of fluids into pores plays
an important role in mass transfer and separation process.
However, controlled volumes in DCV-GCMD simulations
are very often placed inside confined regions so that the entrance effect of fluids is neglected. Furthermore, final composition is unknown in membrane separation. However, final
composition in the sink 共CV2 in Fig. 1兲 has to be specified in
current DCV-GCMD simulations.
In this work, we performed DCV-GCMD simulations of
the transport diffusion of liquid water and methanol to
Membrane separation of mixtures is currently a subject
of great interest.1 Molecular-level understanding of the interactions between complex adsorbate molecules and surfaces
plays a critical role in membrane separation. Such interactions are governed by a number of parameters, such as fluid–
fluid interactions 共e.g., relative contribution from dispersion
and hydrogen bonding兲, solid–fluid interactions 共e.g., hydrophilic or hydrophobic nature of the surface兲, pore geometries
共e.g., shape and size兲, and operating conditions 共e.g., temperature and pressure兲. For designing an appropriate membrane for a separation process, it is important to determine
and control the surface properties of the membrane. Several
examples show the effect of surface properties on membrane
separation. They include chemical transport selectivity for
the separation of organic mixtures or aqueous solutions2– 4
a兲
Current address: Department of Chemical Engineering, University of Notre
Dame, IN 46556.
b兲
Current address: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109.
c兲
Author to whom correspondence should be addressed.
0021-9606/2002/117(2)/808/11/$19.00
808
© 2002 American Institute of Physics
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J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
Transport of water and methanol through membranes
809
FIG. 1. Schematic of a DCV-GCMD simulation cell.
vacuum under a chemical potential gradient through a slit
pore consisting of Au共111兲 surfaces covered by ⫺CH3 or
⫺OH terminated self-assembled monolayers 共SAMs兲. The
simulation resembles a pervaporation 共PV兲 separation process, in which components of a liquid feed permeate through
a membrane and evaporate into the downstream at different
rates. Pervaporation separation has emerged as an economical and simple alternative to many organic/organic separation
applications. This process is especially attractive in azeotropic and close boiling point separation applications, such as
benzene/cyclohexane,13 or water/ethanol.14 Unlike distillation processes, the separation mechanism in PV is not based
on the relative volatility of the components, but on the difference in sorption and diffusion properties of the feed substances in the membrane.13,14
A few molecular dynamics 共MD兲 simulations were attempted to investigate the diffusion and solubility of small
molecules through pervaporation membranes, such as amorphous polymers. Tamai et al.16 reported MD simulations of
the diffusion process of methane, water, and ethanol in poly共dimethyl
siloxane兲
共PDMS兲
and
polyethylene.
Mölle-Plathe15 investigated the diffusion of water in mixtures of water and poly共vinyl alcohol兲 共0–97%兲 using MD
simulations. Fritz and co-workers14 studied the transport of
water-ethanol mixtures in polydimethylsiloxane membranes.
All these studies dealt with the diffusion of liquids either
inside membranes or cross the interfaces between bulk liquids and membranes. However, none of their simulations
was performed under a fixed chemical potential 共or concentration兲 gradient encountered in pervaporation processes.
In our DCV-GCMD simulations, adsorption/desorption,
diffusion, and pore entrance effects encountered in a pervaporation separation process are all taken into account.
Methanol and water are selected as model fluid molecules
because water represents a strongly polar molecule while
methanol is intermediate between nonpolar and strongly polar molecules. Surface hydrophobicity is adjusted by varying
the terminal group of ⫺CH3 共hydrophobic兲 or ⫺OH 共hydro-
philic兲 of SAMs. Previous grand canonical ensemble Monte
Carlo 共GCMC兲 simulations showed different adsorption behaviors of hydrogen bonding mixtures on hydrophobic and
hydrophilic surfaces.18 As shown before, the adsorption of
water–methanol mixtures in slit activated carbon 共hydrophilic兲 pores occurs by continuous filling, while sharp capillary condensation is observed in graphite 共hydrophobic兲
pores.18 All of these results were from equilibrium studies. It
is desirable to investigate the transport behaviors of fluids
through membranes under a chemical potential gradient.
In this paper, we report results for pure liquids and we
will report simulation results for fluid mixtures in subsequent
papers. The ultimate goal of this work is to provide a fundamental understanding of how the interactions between fluid
molecules and surfaces affect transport diffusion and membrane separation so as to tailor the surface chemistry of a
pore for a specific separation task.
TABLE II. VDW parameters and charges for water, methanol, SAMs, and
gold.
Site
␴ 共nm兲
⑀ 共K兲
q 共e兲
O
H
0.31656
0.0
78.21
0.0
⫺0.82
0.41
CH3
O
H
0.3775
0.307
0.0
104.16
85.554
0.0
0.265
⫺0.7
0.435
CH3
CH2
Sd
S-Se
CH2 f
O3
H3
0.3905
0.3905
0.3550
0.4250
0.3905
0.3070
0.0
88.1
59.4
126.0
200.0
59.4
85.6
0.0
0.0
0.0
0.0
0.0
0.265
⫺0.70
0.435
Au
0.2655
529.28
0.0
a
H2O
CH3 OHb
SAMc
Aug
TABLE I. Geometries for water and methanol.
Water 共SPC model兲a
r 共H–O兲
␪ e (⬔H–O–H)
a
Reference 21.
Reference 22.
b
0.10 nm
109.47°
Methanol 共OPLS model兲b
r 共H–O兲
r (O–CH3)
␪ e (⬔H–O–CH3)
0.0945 nm
0.1430 nm
108.50°
a
Reference 21.
Reference 22.
c
References 23 and 24.
d
For the interactions between S and other atoms, except for S–S interactions.
e
For S–S interactions only.
f
First three active sites for the hydrophilic thiol.
g
Reference 28.
b
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810
Zhang et al.
J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
TABLE III. Valence parameters for SAMs.a
Bond 共fixed兲
S–CH2
CH2 – CH2
CH2 – CH3
CH2 – O
O–H
0.0945
r 共nm兲
0.1812
0.1530
0.1530
0.1430
Angle 关Eq. 共8兲兴
S–C–C
C–C–C
C–C–O
C–O–H
K ␪ (103 K/rad2兲
␪ e 共degree兲
62.5
114.4
62.5
109.5
62.5
108.0
62.5
108.5
Torsion 关Eq. 共9兲兴
C0
C1
C2
C3
C4
C5
1.116
-1.462
-1.578
0.368
3.156
3.788
X – C–C–X (103 K兲
a
Adapted from Refs. 23 and 24.
II. POTENTIAL MODELS
A. Fluid–fluid potentials
Water and methanol are selected as fluid molecules. A
water molecule is described by the simple point charge
共SPC兲 potential model that contains three charge sites and
one Lennard-Jones 共LJ兲 site. A methanol molecule is described by the optimized potentials for liquid simulation
共OPLS兲 model. In these models, the fluid–fluid potential energy is described by site–site interactions:
E f f ⫽E Q ⫹E VDW ,
ma
E Q⫽
mb
兺兺
i⫽1 j⫽1
q iq j
na
nb
E VDW⫽
再
rij
兺兺
i⫽1 j⫽1
0
共1兲
共2兲
,
4⑀ij
冋冉 冊 冉 冊 册
␴ij
rij
12
⫺
␴ij
6
rij
r⭐r c
共3兲
MD simulations of quasi-2D systems and Monte Carlo simulations in both 3D and quasi-2D systems.20 For large systems, computation time scales approximately with N 共number of particles兲 in CMM 共Ref. 19兲 while with N 2 in the
conventional method. Equation 共3兲 represents the short-range
van der Waals 共VDW兲 interaction between sites i and j, and n
is the number of LJ sites per molecule. The potential parameters ␴ and ⑀ were taken from Berendsen et al.21 and Jorgensen et al.22 We truncate the LJ potential at a cutoff distance r c ⫽1.4 nm. The SPC potential results in nine
electrostatic interactions and one pair of LJ interaction between two oxygen sites for the water–water interaction. The
OPLS potential model for the methanol–methanol interaction has four LJ and nine electrostatic interactions. Geometries, VDW parameters, and charges for various molecules
are given in Tables I and II. The flux was calculated by
measuring the net movement of each component crossing a
given plane.
r⬎r c .
The long-range electrostatic interactions between charge
sites i and j of molecules a and b are described by Eq. 共2兲,
where m is the number of charge sites per molecule, r i j is the
interatomic distance between a pair of interacting sites i and
j, and q is the charge on a charge site.
Lack of symmetry in quasi-two-dimensional 共2D兲 confined systems makes it difficult to use the Ewald summation
method to account for long-range interactions. We have tried
to minimize this problem by using a large number of molecules and a half-box cutoff for long-range Coulombic interactions. Our previous study on the adsorption of the water–
methanol mixture in graphite pores showed that difference in
potential energy was only 0.5–0.7% between the 2D Ewald
sum and the half-box length cutoff techniques with comparable density profiles obtained using both these methods.
However, the 2D Ewald sum method17 is two orders of magnitude slower than the half-box length cutoff method.18
Recently, we implemented the cell multiple method19
共CMM兲 in MD simulations of 3D systems and extended to
J i⫽
RL
N LR
i ⫺N i
n steps⌬tA yz
共4兲
,
RL
where N LR
i and N i are the number of the fluid molecules of
component i moving from the left to the right and vice versa,
respectively, n steps is the number of MD steps, A yz is the area
of the yz plane, and ⌬t is the MD time step. We choose a
time step ⌬t⫽2.5 fs.
B. Surface potentials
The membrane is a slit pore consisting of two Au共111兲
surfaces covered by n-alkanethiol SAMs. The Au共111兲 surfaces are represented by discrete atoms. The surface properties of the pore are adjusted by varying the terminal group of
⫺CH3 共hydrophobic兲 or ⫺OH 共hydrophilic兲 of SAMs. The
chains of the SAMs 关 S共CH2兲8CH3 or S共CH2兲7OH] are described by the united-atom model of Hautman and Klein, and
co-workers.23,24 The total potential energy of a chain molecule contains valence (E val) and nonbonded (E nb) contributions
TABLE IV. Parameters for the chain–surface interactions.a
TABLE V. Configurational chemical potentials 共kJ/mol兲 in control volumes.
␴ i⫺Au 共nm兲
⑀ i⫺Au 共K兲
a
CH3
CH2
S
O
H
0.3495
71.948
0.3495
51.988
0.2565
2030.791
0.2855
212.853
0.0
0.0
Pure water
Pure methanol
␮ in CV1
␮ in CV2
⫺76.93
⫺70.86
⫺⬁
⫺⬁
From Ref. 27.
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J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
Transport of water and methanol through membranes
811
FIG. 2. Snapshots of water molecules diffusing through
a slit pore of size 2.113 nm covered by hydrophobic
SAMs/Au共111兲 under a chemical potential gradient at
298 K from t⫽0 to 550 ps.
E chain⫽E val⫹E nb ,
共5兲
where the bonded interactions consist of bond stretch
(E bond), bond-angle bend (E angle), and dihedral angle torsion
(E torsion) terms,
E val⫽E bond⫹E angle⫹E torsion ,
共6兲
while the nonbonded interactions consist of van der Waals
(E VDW) and electrostatic (E Q ) terms:
E nb⫽E VDW⫹E Q .
共7兲
Since bond vibration is very fast, bond lengths between adjacent pseudoatoms are constrained using the RATTLE
algorithm25 with fixed bond lengths given in Table III. The
use of a dot product constraint26 could be more efficient than
a bond constraint for fixing internal angles used in this work.
E angle is described by a simple harmonic angle potential energy expression
E angle⫽ 21 K ␪ 共 ␪ ⫺ ␪ e 兲 2 ,
共8兲
with the equilibrium angle ␪ e and the force constant K ␪
given in Table III. Torsional potential E torsion is described by
a series expansion in the cosine of the dihedral angle ␸:
n
E torsion⫽
兺 C i cos 共 ␸ 兲 .
i
i⫽0
共9兲
The VDW potential in one chain or between two thiol
chains is described by the LJ 12-6 potential with a cutoff
distance of 1.4 nm as described in Eq. 共3兲. Electrostatic potentials described by Eq. 共2兲 are taken into account only for
the interactions between active sites located on CH2 , O, and
H in different chains for the hydrophilic thiol. Nonbonded
interactions 共VDW and Q兲 are not used between nearest
neighbors 共1-2 interactions兲 and next nearest neighbors 共1-3
interactions兲.
The chain–surface interaction is treated as the 12-3 cutoff potential to describe strong binding between thiolates and
Au共111兲 surfaces27 and the parameters are given in Table IV:
E chain⫺surface⫽2.117⑀
冋冉 冊 冉 冊 册
␴
r
12
⫺
␴
r
3
.
共10兲
The parameters are fit to give interaction energy with the
surface and the distance of the head group from the surface
comparable to those given by the continuum
approximation.23
C. Fluid–surface potentials
The interactions between fluids 共water and methanol兲
and surfaces 共SAMs/gold兲 were modeled with the cut-shifted
LJ 12-6 potential as described in Eq. 共3兲, where cutoff dis-
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812
J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
Zhang et al.
FIG. 3. Snapshots of water molecules diffusing through
a slit pore of size 2.113 nm covered by hydrophilic
SAMs/Au共111兲 under a chemical potential gradient at
298 K from t⫽0 to 550 ps.
tance was taken to be 1.4 nm. For the hydrophilic thiol,
electrostatic potentials E Q are taken into account for the interactions between fluid molecules and the last three atoms in
the chain. All LJ cross parameters were calculated using the
geometry combining rule ␴ i j ⫽ 冑␴ i ␴ j and ⑀ i j ⫽ 冑⑀ i ⑀ j . 23
III. SIMULATION METHODOLOGY
The DCV-GCMD method7 is designed to simulate transport diffusion and flow in the presence of a fixed chemical
potential gradient. The chemical potential of each species in
a control volume is fixed by inserting and deleting particles
共GCMC phase兲, while the dynamic motion of molecules in
the whole system is described by solving Newtonian equations of motion 共MD phase兲. In this work, the DCV-GCMD
technique is employed to study chemical-gradient-driven diffusion from liquid phase to vacuum. The simulation resembles a pervaporation process. The use of vacuum in the
sink eliminates the need to specify the final product composition of a mixture. This is particularly important for simulating membrane separation. The simulation system is shown
in Fig. 1. The dimensions of the simulation cell are 10.945
⫻4.326⫻5.60 nm. The membrane, i.e., a slit pore consisting
of two Au共111兲 surfaces covered by mixed SAMs, is placed
3.0 to 7.995 nm away. The length and width of the gold walls
are chosen to be an integral multiple 共e.g., 5 and 5兲 of the
corresponding dimensions of a SAM/gold cell 共0.999
⫻0.8652 nm兲. Thus, surface dimensions are approximately
4.995⫻4.326 nm with 100 n-alkanethiols adsorbed on each
surface. Gold atoms in each wall are arranged in three layers
with 300 gold atoms for each gold layer. The pore size between terminal groups of SAMs is about 2.113 nm. Typically, a simulation system contains about 3200 fluid molecules 共or 9600 adsorbate atoms兲 and 3800 adsorbent atoms
共including SAMs and gold兲. The flow direction is along the x
direction from the left 共liquid reservoir, CV1, placed from
0.5 to 1.5 nm兲 to the right 共vacuum sink, CV2, placed from
9.495 to 10.495 nm兲 control volumes. In each control volume, the chemical potential of each component is maintained
constant by GCMC simulations 共see Table V兲. The buffer
boxes of B1 and B2 allow one to investigate the entrance
effects while the buffer boxes of B3 and B4 are used to set
the control volumes in bulk environment. The simulation cell
is confined in the x direction by two hard walls, which are
located at the two ends of the cell along x direction. The
periodic boundary conditions and minimum image conventions are applied to y and z dimensions for fluid molecules in
the bulk, and only in the y direction for fluid molecules in the
confined region and SAMs.
For the GCMC29 phase, we follow the prescription of
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J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
Transport of water and methanol through membranes
813
FIG. 4. Snapshots of methanol molecules diffusing
through a slit pore of size 2.113 nm covered by hydrophobic SAMs/Au共111兲 under a chemical potential gradient at 298 K from t⫽0 to 550 ps.
Adams,29 in which the simulation is run at constant B 共or
␮ con), V and T, where B is defined as
B i ⫽ ␤␮ con,i ⫹lnV,
共11兲
where ␮ con,i is the configurational chemical potential of
component i, and ␤ ⫽1/kT. The standard GCMC algorithm
consists of three types of trial. Each step of GCMC simulation consists of an attempted movement 共translation or rotation兲 of a molecule, taken in the usual Metropolis Monte
Carlo manner, or either an attempted insertion of a molecule
at a random coordinate or an attempted deletion of a randomly chosen molecule. For a binary mixture, it is possible
to use an additional type of trial, viz., changing the identity
of two species.10 This swap technique has been shown to
increase the speed of convergence and reduce the fluctuation
in particle number once equilibrium is reached.30,31 For a
translation or rotation move, a trial configuration is generated
by randomly choosing one molecule in the control volume
space and giving it either a uniform random displacement or
a rotation about a random axis. Maximum translational and
rotational parameters can be adjusted so that acceptance rate
for such trials is approximately 50%. The probability of an
attempt to move being accepted is
accept
⫽min†1,exp关 ⫺ ␤ ⌬E 共 r 兲兴 ‡,
P move/rotate
共12兲
where ⌬E(r) is the change in configuration energy. For a
creation attempt, position and orientation are chosen at random. The algorithm due to Marsagalia is used to ensure a
random orientation of the molecule for insertion trials.32 The
probability of a creation attempt being accepted is
accept
P creation
⫽min†1,exp关 ⫺ ␤ ⌬E 共 r 兲 ⫹B i 兴 / 共 N i ⫹1 兲 ‡,
共13兲
where ⌬E(r) is the change in configuration energy due to
the addition of one particle. Since the velocities of a particle
are needed in the MD phase, the velocities of each atom for
a newly created particle are assigned based on a Gaussian
distribution. The probability of a destruction being accepted
is
accept
⫽min†1,exp关 ⫺ ␤ ⌬E 共 r 兲 ⫺B i 兴 N i ‡,
P destruction
共14兲
where ⌬E(r) is the potential energy change due to the removal of one particle. The probability of molecular swap
from A to B being accepted is
冋
册
NA
accept
exp共 B B ⫺B A 兲 exp关 ⫺ ␤ ⌬E 共 r 兲兴 ,
⫽min 1,
P swapA→B
N B ⫹1
共15兲
where N A and N B are the current numbers of species A and B
in the same control volume, respectively. ⌬E(r) is the en-
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814
Zhang et al.
J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
FIG. 5. Snapshots of methanol molecules diffusing
through a slit pore of size 2.113 nm covered by hydrophilic SAMs/Au共111兲 under a chemical potential gradient at 298 K from t⫽0 to 550 ps.
ergy change due to particle swap. B A and B B are defined by
Eq. 共11兲. The acceptance probability of a swap from B to A is
given by Eq. 共15兲 with the subscripts A and B interchanged.
The attempts to swap A to B or B to A are kept the same to
maintain microscopic reversibility. Chemical potentials in
both control volumes are set in such a way that the source
contains liquid while the sink is under vacuum. Configurational chemical potentials used in the simulations are listed
in Table V. The initial configuration of liquid, such as water
or methanol, in the feed side is created by a separate GCMC
simulation in the bulk with dimensions of 2.6⫻4.326⫻5.60
nm. In the bulk simulation, periodic boundary conditions and
minimum image conventions are applied to all directions.
After GCMC trials, the MD phase will follow to move
all the molecules 共i.e., water, methanol, SAM chains, but not
gold atoms which are static in this work兲 in the simulation
box. We use the velocity Verlet algorithm to integrate the
equations of motion with a time step of 2.5 fs, and the
RATTLE algorithm to constrain the bonds of SAM chains and
the bonds and angles of water and methanol molecules.33 To
fix the angle of a water or methanol molecule, we constrain
the distance of H–H for water or H–CH3 for methanol. Temperature rescaling is applied to maintain the system at constant temperature. Since particles can flow out of CV1 into
the buffer zone and then the pore in MD simulations, the
number of particles in CV1 decreases and the chemical potential of fluids in CV1 changes accordingly. GCMC simulations are performed to maintain a fixed chemical potential. In
this work, an optimum value for n MC /n MD 共the ratio of stochastic to dynamics steps兲 of 80–150 is used to yield correct
bulk density for pure water and methanol, and to keep a
minimum computing time. All simulations were run up to 1
ns. Fluxes were calculated between 600 ps and 1 ns.
IV. RESULTS AND DISCUSSION
In this work, we performed GCMD simulations to study
the transport diffusion of pure water and methanol molecules
through pores covered by hydrophobic or hydrophilic SAMs.
Snapshots for water and methanol molecules for both pores
at several time steps up to 550 ps are shown in Figs. 2–5
while Fig. 6 gives segment density profiles for various cases
at 550 ps. Snapshot and corresponding density profiles are
given in Fig. 7 for methanol molecules diffusing through
hydrophilic pores at 1 ns.
A. Pure water
We first investigated the transport diffusion of water
through a slit pore covered by hydrophobic SAMs under a
fixed chemical potential gradient 共see Table VI兲. As shown in
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J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
Transport of water and methanol through membranes
815
FIG. 6. Segment density profiles along the z direction for 共a兲 water-hydrophobic, 共b兲 water-hydrophobic, 共c兲 methanol-hydrophobic, and 共d兲 methanolhydrophobic surfaces. The dashed lines indicate the locations of SAM terminal groups.
Fig. 2, at the initial stage (t⫽0 ps兲, there is a 0.4 nm gap
between the bulk water and the slit pore. As simulation proceeds, water molecules diffuse from the bulk to the pore. In
the bulk phase, liquid water molecules are able to reorient
into energetically favorable configurations and produce
H-bonded networks. Since no polar groups are present on the
hydrophobic surfaces and water–surface intermolecular interactions are on average considerably less attractive than
water-water ones, the adsorption of water on the surfaces
will lead to a loss of some H bonds present in the bulk liquid.
Thus, water molecules prefer to stay in the bulk phase and
cannot wet the hydrophobic surfaces. This results in that water molecules retract from the walls inside the pore. As can
be seen in Fig. 2, there exists a gap 共⬃0.3 nm兲 between water
molecules inside the pore and the hydrophobic surfaces. Segment density profiles 共O, H, CH3, and OH兲 for liquid water
and methanol molecules along the z direction inside a slit
pore of H⫽2.113 nm are shown in Fig. 6. It is shown in Fig.
6共a兲 that O and H atoms cannot be observed beyond z⫽
⫾0.75 nm. Hummer et al. reported that water molecules entering a hydrophobic nanotube from the bulk lose hydrogen
bonds, but a fraction of lost energy could be recovered
through VDW interactions with the nanotube.34 This finding
is consistent with our simulation results except for SAM hydrophobic slit pores used in this work instead of nanotubes.
Since the LJ energy parameter for the CH3 group of SAMs
( ⑀ CH3⫽0.175 kcal mol⫺1兲 is larger than that for the O atom
of water ( ⑀ O⫽0.155 kcal mol⫺1兲, the hydrophobic surfaces
provide stronger repulsive force on water molecules near the
surfaces than that provided by their surrounding water mol-
FIG. 7. Methanol molecules diffusing through a slit pore of size 2.113 nm
covered by hydrophobic SAMs/Au共111兲 under a chemical potential gradient
at 298 K at t⫽1 ns. 共a兲 Snapshot, and 共b兲 distributions of the segments
( – CH3 and ⫺OH兲 along the z direction.
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816
Zhang et al.
J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
TABLE VI. Flux (104 mol/m2 s兲 for the transport diffusion of water and
methanol through pores covered by hydrophobic or hydrophilic SAMs.
Hydrophobic surfaces
Hydrophilic surfaces
0.0
3.27
30.77
5.75
Water
Methanol
ecules. As distance from the walls increases, VDW interactions between fluid water molecules and surfaces become
weaker and approach the weakest at the center between two
surfaces. Thus, liquid water forms a convex interface as water molecules flow through the pore. After 500 ps and up to 1
ns, water molecules remain in the same location as simulation proceeds. The transport behavior of fluids through pores
is determined by competing fluid–fluid and fluid–solid interactions. As shown in Fig. 2, at the beginning of the simulation, water molecules in the control volume are pushed first
into the mouth of the pore and then into the pore due to bulk
water pressure. However, as more water molecules enter the
pore, resistance from surface forces increased. Thus, when
resistant force from the hydrophobic surface has balanced
force exerted by water molecules due to pressure gradient,
water molecules are stuck inside the slit pore 共e.g., after 500
ps兲.
The orientation of molecules near a surface is of interest
since interactions between fluid molecules and surfaces determine relative molecular orientations. The order parameter
S was used to define orientation,
S⫽
3 具 cos2 ␪ 典 ⫺1
2
,
共16兲
where 具 ¯ 典 indicates ensemble average and ␪ is the angle
between the molecular dipole of water 共or the vector pointing
from carbon to oxygen in case of methanol兲 and the z axis
perpendicular to the wall.18 By definition, S⫽⫺0.5 if the
molecules lie parallel to the surface, S⫽0 if the molecules
are randomly oriented, and S⫽1 corresponds to molecules
orienting perpendicular to the surface. In the hydrophobic
pore, water molecules have the preferred orientation S
⫽⫺0.3 to the surfaces while water molecules remain randomly oriented in the rest of the pore space. Previously, we
reported18 that water and methanol molecules lied parallel
near graphite surfaces when rigid and flat graphite surfaces
were used in simulations. In our current simulations, due to
dynamic SAMs used, pore surfaces are rough. Rough surfaces affect the orientation of water molecules. Thus, water
molecules have preferred orientations, but are no longer all
parallel to the surfaces as in the case of hydrophobic graphite
surfaces observed before.18 During simulations, it was observed that the size of the slit pore fluctuated slightly due to
the motion of SAMs. SAMs tilt towards the flow direction
due to the pressure of liquid water and the chains of SAMs
are not as ordered as when flow is absent. However, the
( 冑3⫻ 冑3)R30° structure of sulfur/gold remains.
By contrast, water molecules form a concave interface
when they diffuse through a hydrophilic slit pore under a
fixed chemical potential gradient. The formation of the concave interface is due to the strongest attractive forces near
the walls between water molecules and surfaces. Unlike the
water-hydrophobic surface case, snapshots in Fig. 3 show
that water molecules have completely diffused through the
hydrophilic slit pore at 500 ps. Since water molecules near
the surfaces have a tendency to form hydrogen bonding with
the OH terminal groups of the SAMs, water molecules wet
the surfaces as shown in Fig. 3. As can be seen from Fig.
6共b兲, O 共⬃15兲 and H 共⬃45兲 atoms are in the contact layers
near the hydrophilic surfaces. The contact layers are clearly
distinguished from the interlayer. The numbers of O and H
atoms in the middle are about 60 and 120, respectively. Since
water molecules wet the hydrophilic surfaces and dynamic
SAMs are used, no preferred orientation toward the surfaces
is observed. As fluid molecules fill the pore, Figs. 3共g兲 and
3共h兲 show that the interface between the heading water molecules and the vacuum becomes flat since there is no drag
force acting on those water molecules from the hydrophilic
surfaces.
Flux is monitored at one yz plane in the middle of the
pore (x⫽5.498 nm兲 and calculated by the flux plane method
关Eq. 共4兲兴 between 600 ps and 1 ns. Invariance of the fluxes
with time indicates that the system reaches steady state. The
fluxes of water in the pores covered by hydrophobic and
hydrophilic SAMs are J hydrophobic⫽0 mol/m2 s and
J hydrophilic⫽30.77⫻104 mol/m2 s, respectively. Water molecules are stuck in the middle of the hydrophobic pore while
water molecules diffuse through the hydrophilic pore. These
results indicate that surface property significantly affects the
diffusion behavior of water molecules.
B. Pure methanol
Similar to water, the behavior of methanol molecules
diffusing through slit pores with hydrophobic and hydrophilic surfaces under a given chemical potential gradient are
shown in Figs. 4 and 5, respectively. For similar reasons as
discussed previously for water, the methanol–methanol interaction is stronger than that between methanol molecules and
surfaces for the hydrophobic pore. Hence, methanol molecules in the pore are kept away from the surfaces. A gap of
about 0.5 nm at z⫽⫾0.75 nm between methanol molecules
and surfaces as in the water-hydrophobic case can be seen in
Figs. 4 and 6共c兲. The surfaces provide a resistance to the flow
of methanol molecules. Since the resistant force becomes
weaker as it is away from the surfaces to the center of the
pore, methanol forms a convex interface in the pore as
methanol molecules flow through the pore. In fact, methanol
forms a similar interface to water, but with a less clear interface since methanol molecules are less polar. It is interesting
to observe that methanol molecules can escape from the convex interface and transport through the pore into the vacuum
region at the early stage of simulations. However, such phenomenon was not observed for water-hydrophobic pores.
The peaks of CH3 and OH in the segment density profiles
shown in Fig. 6共c兲 occur at z⫽⫾0.618 nm, indicating that
methanol molecules have preferred orientations at the hydrophobic surfaces. The corresponding 具 S 典 is about ⫺0.25.
These results are consistent with those of our previous work
on water confined between two graphite surfaces.18
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J. Chem. Phys., Vol. 117, No. 2, 8 July 2002
Methanol molecules form a concave interface as methanol molecules flow through the hydrophilic pore before 550
ps 共see Fig. 5兲. In this case, the surfaces provide an attractive
force to methanol molecules along the flow direction. As
shown in Fig. 6共d兲, CH3 and OH segments with random
orientation were adsorbed near the hydrophilic surfaces up to
550 ps. As the simulation was extended to 1 ns, it is interesting to observe that more methanol molecules were relaxed
and reoriented their OH segments toward the hydrophilic
surfaces to form contact layers near the surfaces, while remaining CH3 segments were pointed away from the surfaces.
In another word, the hydrophilic surfaces were modified by
oriented methanol molecules into new hydrophobic surfaces.
A gap of 0.13 nm between methanol molecule and new hydrophobic surfaces along the z direction can be seen in Fig.
7共a兲. The gap is much smaller than that observed in the
methanol-hydrophobic surface case 共⬃0.5 nm兲 since only
⬃113 CH3 groups located at z⫽⫾0.90 nm 共the first peak兲
shown in Fig. 7共b兲 are exposed in the new hydrophobic surface while 200 CH3 groups of SAMs in the methanolhydrophobic surface case.
The fluxes of methanol molecules diffusing through the
hydrophobic and hydrophilic SAM pores are J hydrophobic
⫽3.27⫻104 mol/m2 s and J hydrophilic⫽5.75⫻104 mol/m2 s,
respectively. Methanol molecules completely diffuse through
both pores. Results show that methanol molecules are easier
to diffuse through the hydrophilic pore than the hydrophobic
one. The same holds true for the diffusion of water molecules
through both pores. For the hydrophobic pore, results show
that methanol has a much higher flux than that of water due
to its stronger dispersion and weaker hydrogen bonding.
Thus, it should be possible to separate water and methanol
mixtures using the hydrophobic pore. We are investigating
the separation of water-methanol mixtures using SAMmodified pores. Bhanushali et al. reported that the flux of
solvents was dependent on molecular polarity. The molecule
with stronger polarity has higher flux for the hydrophilic
pores. But, for the hydrophobic pores, it is opposite. Our
simulation results are consistent with these experimental
ones.30 Hydrogen bonding plays a critical role in the adsorption of polar fluids and fluid mixtures 共e.g., water and methanol兲 on hydrophobic/hydrophilic surfaces. For nonpolar molecules, such as methane, adsorption is determined by
dispersion interactions. However, the adsorption of strongly
polar molecules, such as water, occurs by hydrogen bonding
onto surfaces. Methanol might be expected to show adsorption behavior between these extremes. By introducing the
methyl group to replace one H in the water molecule, the
polarity of the methanol molecule has been decreased. Our
previous simulation results show that the average numbers of
hydrogen bonds are 3.47 per water and 1.82 per methanol
molecule inside hydrophilic pores.18 The difference in polarity between water and methanol is mainly responsible for the
difference in their flow behavior in pore.
V. CONCLUSIONS
DCV-GCMD simulations were performed to study the
transport diffusion of liquid water and methanol to vacuum
through a slit pore consisting of two Au共111兲 surfaces cov-
Transport of water and methanol through membranes
817
ered by CH3 共hydrophobic兲 or OH 共hydrophilic兲 terminated
SAMs under a chemical potential gradient. The simulation is
equivalent to a pervaporation process. In our DCV-GCMD
simulations, adsorption/desorption, diffusion, and pore entrance effects were all taken into account. We observed for
the first time from simulations the convex and concave interfaces of fluids transporting across the slit pores under a
chemical potential gradient. The nature of the interfaces depends on the fluid–fluid and fluid–surface interactions. Water forms concave and convex interfaces in hydrophobic and
hydrophilic pores, respectively. Methanol with stronger dispersion and weaker hydrogen bonding forms the similar interfaces to water, but with less clear interfaces. Simulation
results show that methanol has a much higher flux than that
of water in the hydrophobic pore. Thus, it is expected that
the separation of water–methanol mixtures could occur in
hydrophobic pores.
It is interesting to observe that, for the methanolhydrophilic surface case, as simulation is extended to 1 ns,
one contact layer of methanol molecules is adsorbed on the
hydrophilic surface due to the formation of hydrogen bonds
between OH segments of methanol molecules and surfaces.
Remaining CH3 segments in this layer point away from the
surfaces. As a result, the hydrophilic pore is modified into a
new hydrophobic pore of a reduced pore size by methanol
molecules.
ACKNOWLEDGMENTS
The authors are grateful to the Department of Energy,
the University of Washington, and the National Science
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