THE JOURNAL OF CHEMICAL PHYSICS 122, 154707 共2005兲
The effects of confinement on the behavior of water molecules
between parallel Au plates of „001… planes
Shin-Pon Jua兲
Department of Mechanical and Electro-Mechanical Engineering; Center for Nanoscience & Nanotechnology,
National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China
Jee-Gong Changb兲
National Center for High-Performance Computing, No. 21, Nan-Ke 3rd Road, Hsin-Shi, Tainan, Taiwan,
Republic of China
Jenn-Sen Linc兲
Department of Mechanical Engineering, National United University, Maio-Li 360, Taiwan,
Republic of China
Yong-Sheng Lin
Department of Mechanical and Electro-Mechanical Engineering; Center for Nanoscience & Nanotechnology,
National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China
共Received 10 December 2004; accepted 1 February 2005; published online 18 April 2005兲
Molecular dynamics simulation is utilized to investigate the behavior of water molecules confined
between two Au plates of 共001兲 planes separated by gaps of 24.48, 16.32, 12.24, 11.22, and 10.20
Å. The simulation results indicate that the arrangements of the water molecules are dependent on the
gap size. For the largest gap size, adsorption of the Au surface creates two permanent water layers
in the vicinity of each Au plate. Furthermore, in this case, the gap size is sufficiently large to permit
the formation of a central region within which the water molecules are randomly oriented in a
similar manner to bulk water molecules. The results indicate that the orientation of the first water
layer directly absorbed by the plate surface does not change as the gap size between the two Au
plates is reduced. However, the orientations of the O–H bonds in the second water layer parallel to
the surface rearrange to form hydrogen bonds between the water layers as the separation between
the plates is decreased. Finally, an inspection of the variation of the self-diffusion coefficients with
the gap size suggests that the difference between the dynamic properties of the water molecules in
the z direction and the x-y plane decreases as the distance between the two Au plates increases.
© 2005 American Institute of Physics. 关DOI: 10.1063/1.1878552兴
I. INTRODUCTION
The behavior of confined water has attracted intensive
research interest since confined water molecules play an important role in many fields.1–5 For example, in the biological
systems of a restricted cell,1,2 confined water molecules can
stabilize the biological macromolecules. In the field of nanotribology, confined water molecules can act as a lubricant
between two solid surfaces. The viscosity of water and the
frictional properties of the liquid-solid system are strongly
influenced by the thickness of the confined water film.3–5
These particular material properties, whose characteristics
are determined by the space occupied by the confined water,
have been measured by various experimental methods, including x-ray scattering,1 quasielastic and inelastic neutron
scattering,2 scanning force microscopy,2 and surface force
balancing.4 The experimental results have revealed that the
structure and dynamic properties of water molecules confined in a small space are different from those of their bulk
a兲
Author to whom all the correspondence should be addressed. Electronic
mail: [email protected]
b兲
Electronic mail: [email protected]
c兲
Electronic mail: [email protected]
0021-9606/2005/122共15兲/154707/5/$22.50
water counterparts. Investigating molecular behavior using
direct methods is difficult due to the very small characteristic
scales involved. Consequently, numerical methods are generally adopted as a means of developing a deeper insight into
the experimentally observed results. Molecular dynamics
共MD兲 simulation is a powerful tool facilitating the investigation of molecular behavior at the atomic level. Using this
technique, Gordillo and Martí performed a series of investigations to clarify the effects of nanotube confinement and
temperature on the behavior of water molecules.6–8 Their
results revealed that water molecules confined in carbon
nanotubes experience a destruction of the hydrogen bonding
network, which leads to a reduction in the average number of
hydrogen bonds formed between the water molecules. This
confinement effect was observed to exist even when the water molecules were in a supercritical condition. Furthermore,
it was found that the hydrogen bonding network is also damaged by increasing temperature. As a result, the diffusion
ability of the water molecules is enhanced as the temperature
increases. Brovchenko et al. employed MD simulations to
investigate the properties of water molecules in nanopores at
an ambient temperature of 300 K and a pressure of 1 bar.9
Two values of the Lennard-Jones parameter ␧ were chosen,
122, 154707-1
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154707-2
J. Chem. Phys. 122, 154707 共2005兲
Ju et al.
i.e., −1.93 and −4.62 kcal/ mol, to represent the weaker and
stronger interactions, respectively, between water and the
nanopores. The results demonstrated that a stronger waterpore interaction prompts the formation of two prominent water layers in the vicinity of the pore surface. Gallo et al.
adopted a MD simulation approach to investigate the behavior of water molecules confined in a silica pore of 2 nm
radius under various water density and temperature conditions. In a series of studies, the effects of water density and
system temperature on the hydrogen bond network and water
molecule arrangement in the silica pore were thoroughly
investigated.10–12 The numerical results revealed that the local arrangement of the water molecules in silica pores is
dependent on the density of water. Furthermore, it was
shown that a strong interaction between the water molecules
and the pore induces a distortion of the hydrogen network. In
the high water density case, two distinct regimes are formed,
i.e., near the pore surface and in the central region of the
pore, respectively. The static and dynamic properties of the
water molecules in these two regions are significantly different. Conversely, in the lower density case, only a surface
absorbed layer exists and an anomalous diffusion is identified in the vicinity of the pore. Liu also employed MD simulations to inspect the behavior of water confined at low density in nanopores.13 Inhomogeneity was identified along the
axial and radial directions. The axial diffusivity was found to
be approximately four to ten times larger than the diffusivity
along the radial direction. In addition to these investigations
of water molecules confined in nanopores, the behavior of
water molecules confined in nanoscale gaps has also been
observed using MD simulation. Zangi and Mark found that
the arrangement of water molecules is strongly dependent on
the thickness of the gap between two parallel plates under
ambient conditions.14,15 The numerical results indicated that
for a constant number of water molecules confined within the
nanoscale gap, continuously decreasing the separation distance between the two plates from 1.14 to 0.85 nm, 0.85 to
0.57 nm, and 0.57 to 0.41 results in the formation of threelayered, two-layered, and one-layered water structures, respectively. It is observed that the lateral diffusion coefficient
drops in the one-layered and two-layered water structure regions because of the formation of a monolayer ice and a
bilayer ice at some specific thicknesses of gaps.
From the discussions above, it is clear that MD simulation provides a powerful technique for investigating fundamental molecular behaviors at an atomic level. Accordingly,
the present study utilizes MD simulations to investigate the
behavior of water molecules confined in nanoscale gaps at a
constant density of 0.973 g / cm3 and a constant temperature
of 400 K. Specifically, this study investigates the arrangement of water molecules by considering the density concentration profiles of the oxygen and hydrogen atoms, the average number of H-bonds per water molecule 共nHB兲, and the
orientation factor s共z兲. The self-diffusion coefficients of the
water molecules along the z direction and the x-y plane are
also examined in order to explore the dynamic properties of
the confined water molecules along the directions parallel
and normal to the two plates.
FIG. 1. Schematic diagram of side view of simulation model.
II. SIMULATION MODEL
Figure 1 presents a schematic diagram of the water molecules confined between two parallel Au 共001兲 plates. Each
plate is composed of a seven-layered structure with each
layer comprising a total of 450 Au atoms. It is noted that the
upper and lower Au layers are fixed in order to prevent the
system from moving in a disorderly manner during the simulation. Furthermore, periodic boundary conditions are imposed in the x and y directions.
The present simulations consider various atomic interactions, i.e., interactions between the Au atoms, interactions
between the water molecules, O–H bonding and H–O–H
bending intramolecular interactions within individual water
molecules, and interactions between the Au atoms and the
water molecules. The atomic interactions between the Au
atoms are modeled using the many-body, tight-binding potential method.16,17 Meanwhile, the intermolecular and intramolecular interactions of the H2O molecules and the interactions between the H2O molecules and the Au atoms are
modeled using the flexible 3-centered 共F3C兲 water model18
and the Spohr potential 共as modified by Dou et al.兲 共Refs.
19–21兲, respectively.
This study focuses specifically on the influence of the
gap size between two parallel plates on the behavior of the
confined water molecules. Hence, the remaining simulation
conditions, such as the water density 共0.973 g / cm3兲 and the
system temperature 共400 K兲, are assumed to be constant. The
scaling method22,23 is used to scale the temperature of the
water molecules and the Au atoms to an equilibrium temperature of 400 K during the simulation. The multiple time
step method23,24 and the Verlet algorithm22,23,25 are employed
to calculate the trajectories of the atoms. A small time step of
0.1 fs is used when simulating the fast motions associated
with the bonding and bending of the water molecules. However, a larger time step of 1 fs is adopted when simulating all
other motions.
III. RESULTS AND DISCUSSION
The statistical data presented in Figs. 2 and 3 are
sampled from the system over a time period of 10 ps following the completion of a relaxation process of duration 30 ps.
Figure 2 presents the local reduced density distributions
of the hydrogen and oxygen atoms, and the variation of the
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Water molecules between parallel Au plates
J. Chem. Phys. 122, 154707 共2005兲
FIG. 2. Distributions of oxygen and hydrogen densities, orientation factor s共z兲, and average hydrogen bond number per water molecule nHB for water
molecules confined in nanoscale gaps of size 共a兲 24.48 Å, 共b兲 16.32 Å, 共c兲 12.24 Å, 共d兲 11.22 Å, and 共e兲 10.20 Å.
O–H bond orientation factor s共z兲 along the vertical direction.
The value of the bond orientation factor is given by26
s共z兲 = 1.5 具cos2 ␪典 − 0.5,
where ␪ is the angle between the O–H bond and the direction
normal to the plate 共i.e., the z direction兲. The bracketed term
expresses the average over the number of O–H bonds and
time steps in the MD simulation. Values of s共z兲 = −0.5, 0.0,
and 1.0 denote that the O–H bonds are oriented parallel to
the plates, randomly, and normally to the plates, respectively.
To develop a clearer understanding of the local hydrogen
bonding of the water molecules, Fig. 2 also shows the variation in the average number of H-bonds per water molecule
nHB with increasing distance from the bottom Au plate. In
determining the value of nHB, the present study adopts the
geometric criterion6,7 that a hydrogen bond will be formed if
the distances between two oxygen atoms and the oxygen and
hydrogen atoms of a pair of water molecules are less than the
first minimum18 of the F3C O–O radial distribution function
共3.4 Å兲 and the F3C O–H radial distribution 共2.4 Å兲.18 In
addition, this study specifies that the angle between the O–O
and O–H directions must be less than 30°. In order to investigate the influence of the confined thickness on the water
molecule arrangement, Figs. 2共a兲–2共e兲 present the oxygen
and hydrogen reduced density profiles, the bond orientation
factor profile, s共z兲, and the nHB profile for gap sizes of 24.48,
16.32, 12.24, 11.22, and 10.20 Å. In these figures, the left
vertical axis indicates the reduced density 共␳local / ␳bulk兲 and
nHB, while the right vertical axis indicates the value of the
orientation factor s共z兲. The horizontal axis indicates the distance from the bottom of the lower plate. It should be noted
that Figs. 2共a兲–2共e兲 adopt different horizontal axis scales in
order to show more clearly the variations of these curves for
the different cases.
Figure 2共a兲 presents the results for the largest gap size of
24.48 Å. It is observed that three oxygen and hydrogen reduced density peaks are formed in the vicinities of both
plates. The prominent nature of the first peak indicates that
the water layer is adsorbed directly by the plate surface. The
interaction between the plate and the water molecules becomes weaker as the interatomic distance increases, and
hence the values of the second and third peaks are reduced.
The first two peaks are clearly more pronounced than the
third. This implies that two plane water layers are formed
close to each Au surface. Moreover, the reduced densities of
the oxygen and hydrogen atoms in the region between the
two third peaks are close to 1, which implies that a bulk
water arrangement exists in this region. Meanwhile, it is apparent that the variation of the orientation factor s共z兲 complements the variation of the oxygen density, i.e., the peaks and
valleys of the s共z兲 profile correspond to the valleys and peaks
of the oxygen density profile. The values of the first and
second valleys of the s共z兲 profile are ⬇−0.45 and −0.30,
respectively. Accordingly, it can be surmised that most of the
O–H bonds within the first and second water layers lie parallel to the plate surface and form a flat hydrogen network.
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154707-4
Ju et al.
Moreover, the first and second peaks of the s共z兲 profile imply
that the O–H bonds between the water layers rotate from the
horizontal direction to form hydrogen bonds with the nearest
water layer. The hydrogen atoms of these O–H bonds point
toward the nearest water layer with the result that the hydrogen density is less than the oxygen density in the water layers, but is greater than the oxygen density in the region between the water layers. The high water molecule density in
the first water layer increases the average number of hydrogen bonds nHB to its maximum value in this layer. In other
words, the water molecules within the first layer have the
strongest hydrogen bonding. Since most O–H bonds in the
first water layer are oriented parallel to the Au surface, the
stronger hydrogen bonding is generated primarily by the
plane hydrogen bonding network. From Fig. 2共a兲, it can be
seen that the value of nHB decreases between the first two
water layers. There are very few water molecules in this
region, and hence the water molecules which do exist have a
reduced opportunity to form hydrogen bonds with other water molecules in this region. In other words, these particular
water molecules lose the opportunity to form hydrogen
bonds in the x-y plane, and hence the value of nHB decreases
rapidly. Since the water molecules in the randomly oriented
region do not actually interact with the Au plates, the differences in the water molecule arrangements between the randomly oriented region and the water layer region are attributed most feasibly to the simple presence of the Au plates.
Consequently, increasing the thickness of the nanoscale gap
between the two plates simply leads to an increase in the
thickness of the randomly oriented region and the water density in this region is much closer to the average density of
0.973 g / cm3. However, the density distribution of the water
layers will not change because of the strong adsorption of Au
plates.
In Fig. 2共b兲, the thickness between the two plates is reduced to 16.32 Å. The density, orientation factor, and hydrogen bond profiles of the first two water layers are similar to
those observed in the previous case. However, for the reduced gap size considered in this figure, insufficient space
exists to permit either the formation of a third peak or a
randomly oriented region. Hence, a single water layer is
formed in the central region. Consequently, five water layers
are apparent in the figure rather than the six layers shown in
the previous case. Each layer is connected with its nearest
water layer by hydrogen bonding with the observation of the
peaks of s共z兲 between water layers, which implies that most
O–H bonds are almost normal to Au plates, so the hydrogen
density is larger than oxygen density between water layers.
The value of nHB between the second water layer and the
central layer increases because water molecules in this region
have the opportunity to form hydrogen bonds with the upper
and lower water layers in addition to other water molecules
in the same region.
Figure 2共c兲 illustrates the profiles of the oxygen and hydrogen densities, together with those of s共z兲 and nHB for a
reduced gap size of 12.24 Å. The central water layer visible
in the previous case 共gap size 16.32 Å兲 is no longer apparent,
and hence just four distinct oxygen layers are formed. Due to
the stronger adsorption of the first water layer, the distribu-
J. Chem. Phys. 122, 154707 共2005兲
tion of the oxygen and hydrogen atom densities in this particular layer are similar to those of the larger gap size cases.
However, some O–H bonds in the second water layer close
to the lower and upper Au plates, which originally lay flat in
Figs. 2共a兲 and 2共b兲, rearrange in this reduced gap size case to
form hydrogen bonds with the second oxygen layer close to
the upper and lower Au plates, respectively. This results in a
higher hydrogen density between the two second oxygen layers. Accordingly, compared to the cases shown in Figs. 2共a兲
and 2共b兲, a lower hydrogen density exists in the second layer
in the present case. Since a reduction in the gap size between
the two Au plates will significantly increase the repulsive
energy of the water molecules, the only way to increase the
attractive energy is to change the orientation of the O–H
bonds in the second water layers to form hydrogen bonds
between the two second oxygen layers.
Figure 2共d兲 shows the distributions of the oxygen and
hydrogen densities, and those of s共z兲 and nHB for the case of
a 11.22 Å gap size. It can be seen that there is insufficient
space between the two plates to form a second water layer,
and hence only the first and central water layers are evident.
An observation of the s共z兲 profile suggests that most water
molecules in the central layer lie flat and that some hydrogen
atoms form hydrogen bonds with the first water layers. As
shown in Fig. 2共e兲, which shows the case where the gap size
is further reduced to 10.2 Å, the hydrogen density decreases
in the central layer, but increases in the region between the
first water layer and the central layer. The O–H bond orientations of the water molecules in the central layer rearrange
themselves in order to form more hydrogen bonds with the
first water layer and to maintain a more stable structure as
the thickness between the two plates decreases. Consequently, the value of nHB in the central layer is smaller than
in the central layer of Fig. 2共d兲 since fewer hydrogen atoms
are in central layer.
Figure 3 presents the profiles of the self-diffusion coef-
FIG. 3. Profiles of self-diffusion coefficient in z direction and x-y plane.
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154707-5
J. Chem. Phys. 122, 154707 共2005兲
Water molecules between parallel Au plates
TABLE I. Correlation between gap size and average number of hydrogen bonds per water molecule.
Thickness 共Å兲
Average hydrogen bonds per water molecule
10.2
3.17
11.22
3.27
ficients along the z direction and in the x-y plane. Table I
shows the average hydrogen bonds per water molecule for
each gap size considered in Fig. 3 in order to understand the
influence of the gap size on the average hydrogen bond number. The values of the self-diffusion coefficients are obtained
from the Green–Kubo expression based on the integrated velocity autocorrelation. Other than the smallest gap size case
where all water molecules are strongly absorbed by the Au
plates leading to a lowest self-diffusion ability, it is clear that
the self-diffusion coefficient increases and the average hydrogen bonds per water molecule decrease as water molecule
forms fewer hydrogen bonds with its nearest neighbor water
molecules, and hence these water molecules have a greater
ability to diffuse in both the x-y plane and the z direction.
Moreover, the values of the self-diffusion coefficient in the
x-y plane are consistently larger than those in the z direction.
This observation indicates that the homogeneity evident in
bulk water does not exist in confined water. However, the
trend of the self-diffusion coefficient variation with gap size
presented in Fig. 3 suggests that the difference in the dynamic properties of the water molecules along the z direction
and the x-y plane decreases as the gap size between the two
parallel plates increases.
IV. CONCLUSIONS
This study has investigated the effect of the nanoscale
gap size between two parallel plates on the arrangement of
water molecules confined between the two plates. The
numerical results have demonstrated that the differences between the confined and bulk water structures can be attributed to the presence of the Au 共001兲 plates and to the confinement of the water molecules between these two plates.
For a large gap size, the adsorption of the Au plate creates
two prominent flat water layers in the proximity of each plate
surface and a region of randomly oriented water molecules
arranged in a similar manner to bulk water molecules in the
central area of the gap. There is no obvious confinement
effect on the water arrangement within the randomly oriented
region. However, as the gap size is reduced, the randomly
oriented region disappears and a significant confinement effect becomes apparent. For the case of a 16.32 Å gap size,
insufficient space exists between the two parallel plates to
permit the formation of either upper and lower third layers or
a randomly oriented region in the central area of the gap. In
this case, the confinement effect creates one central water
layer. As the gap size is further reduced to 12.24 Å, the water
molecules in the second water layer are influenced both by
12.24
3.28
16.32
3.18
20.4
3.14
24.48
3.11
32.64
3.07
36.72
3.07
40.8
3.06
the adsorption of the Au plate and by the confinement effect.
Most of O–H bonds within the second flat hydrogen network
in the larger gap size case start to rearrange. More hydrogen
bonds are formed between the second layers in order to release some repulsive energy and to obtain a more stable arrangement. A similar confinement effect occurs in the central
water layer as the thickness of the nanoscale gap is decreased
from 11.22 Å to 10.2 Å. Finally, an inspection of the variation of the self-diffusion coefficient with the gap size suggests that the difference in the dynamic properties of the
water molecules in the z direction and the x-y plane decreases as the gap size between the two parallel plates increases.
ACKNOWLEDGMENT
The authors gratefully acknowledge the support provided to this research study by the National Science Council
of the Republic of China under Grant No. NSC 93-2212-E110-022.
M.-C. Bellissent-Funel, J. Mol. Liq. 78, 19 共1998兲.
M.-C. Bellissent-Funel, Eur. Phys. J. E 12, 83 共2003兲.
3
Y. Zhu and S. Granick, Phys. Rev. Lett. 87, 096104 共2001兲.
4
U. Raviv, S. Giasson, J. Frey, and J. Klein, J. Phys.: Condens. Matter 14,
9275 共2002兲.
5
A. Opitz, S. I.-U. Ahmed, J. A. Schaefer, and M. Scherge, Surf. Sci. 504,
199 共2002兲.
6
M. C. Gordillo and J. Martí, Chem. Phys. Lett. 329, 341 共2000兲.
7
M. C. Gordillo and J. Martí, Chem. Phys. Lett. 341, 250 共2001兲.
8
J. Martí and M. C. Gordillo, Phys. Rev. E 64, 021504 共2001兲.
9
I. V. Brovchenko, A. Geiger, and D. Paschek, Fluid Phase Equilib. 183184, 331 共2001兲.
10
P. Gallo, M. Rovere, and E. Spohr, Phys. Rev. Lett. 85, 4317 共2000兲.
11
P. Gallo, M. Rapinesi, and M. Rovere, J. Chem. Phys. 117, 369 共2002兲.
12
M. Rovere and P. Gallo, Eur. Phys. J. E 12, 77 共2003兲.
13
Y. C. Liu, Q. Wang, and L. H. Lu, Chem. Phys. Lett. 381, 210 共2003兲.
14
R. Zangi and A. E. Mark, Phys. Rev. Lett. 91, 025502 共2003兲.
15
R. Zangi and A. E. Mark, J. Chem. Phys. 119, 1694 共2003兲.
16
V. Rosato, M. Guillope, and B. Legrand, Philos. Mag. A 59, 321 共1989兲.
17
F. Cleri and V. Rosato, Phys. Rev. B 48, 22 共1993兲.
18
M. Levitt, M. Hirshberg, R. Sharon, K. E. Laidig, and V. Daggett, J. Phys.
Chem. B 101, 5051 共1997兲.
19
E. Spohr, J. Mol. Liq. 64, 91 共1995兲.
20
Y. Dou, L. V. Zhigilei, N. Winograd, and B. J. Garrison, J. Phys. Chem. A
105, 2748 共2001兲.
21
Y. Dou, N. Winograd, B. J. Garrison, and L. V. Zhigilei, J. Phys. Chem. B
107, 2362 共2003兲.
22
J. M. Haile, Molecular Dynamics Simulation 共Wiley, Canada, 1992兲.
23
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquid 共Clarendon, Oxford, 1991兲.
24
M. Tuckerman and B. J. Berne, J. Chem. Phys. 97, 1990 共1992兲.
25
D. Frenkel and B. Smit, Understanding Molecular Simulation 共Academic,
San Diego, 1996兲.
26
I. Bitsanis and G. Hadziioannou, J. Chem. Phys. 92, 3827 共1990兲.
1
2
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