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Concentration dependence of water self-diffusion
coefficients in dilute glycerol–water binary and
glycerol–water–sodium chloride ternary solutions and
the insights from hydrogen bonds
a
a
a
a
Cong Chen , Wei Zhong Li , Yong Chen Song , Lin Dong Weng & Ning Zhang
a
a
Key Laboratory of Ocean Energy Utilization and Energy Conservation of the Ministry of
Education, Dalian University of Technology, Dalian 116024, P.R. China
Accepted author version posted online: 18 Nov 2011.Version of record first published: 08
Dec 2011.
To cite this article: Cong Chen, Wei Zhong Li, Yong Chen Song, Lin Dong Weng & Ning Zhang (2012): Concentration
dependence of water self-diffusion coefficients in dilute glycerol–water binary and glycerol–water–sodium chloride ternary
solutions and the insights from hydrogen bonds, Molecular Physics: An International Journal at the Interface Between
Chemistry and Physics, 110:5, 283-291
To link to this article: http://dx.doi.org/10.1080/00268976.2011.641602
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Molecular Physics
Vol. 110, No. 5, 10 March 2012, 283–291
RESEARCH ARTICLE
Concentration dependence of water self-diffusion coefficients in dilute glycerol–water binary
and glycerol–water–sodium chloride ternary solutions and the insights from hydrogen bonds
Cong Chen*, Wei Zhong Li, Yong Chen Song, Lin Dong Weng and Ning Zhang
Key Laboratory of Ocean Energy Utilization and Energy Conservation of the Ministry of Education,
Dalian University of Technology, Dalian 116024, P.R. China
Downloaded by [University of Sydney] at 18:51 21 November 2012
(Received 23 September 2011; final version received 11 November 2011)
Water self-diffusion coefficients for glycerol–water binary and glycerol–water–sodium chloride ternary solutions
at low glucose concentrations have been predicted using the mean square displacements method. It was found
that the water self-diffusion coefficient decreases as the glycerol concentration increases. The reasons for the
decrease have been analysed from the viewpoint of the hydrogen bonds.
Keywords: molecular dynamics simulation; glycerol; diffusion coefficient; hydrogen bond
1. Introduction
Glycerol is common and can be used as a cryoprotective agent (CPA) [1,2], a solvent [3–6] and as biomass
[7–9]. Glycerol has been the subject of numerous
studies, both experimentally and numerically. The
structure [10], thermal behavior [11], acoustic dissipation [12], density [12,13], dielectric relaxation [14–16],
aging and solidification [17], spatial and temporal
heterogeneity [18], vitrification [19], the thermal expansion coefficient [13] and the shear viscosity [13,20] of
glycerol in liquid, supercooled or glassy states have
been studied experimentally. The influence of the
hydrophilic surface and geometrical confinement on
the structure, hydrogen-bond lifetime, and rotational
and translational molecular dynamics have been
analysed by the molecular dynamics simulation
(MDS) of liquid glycerol confined in a realistic model
of a cylindrical silica nanopore [21]. The structure and
dynamic properties of liquid glycerol have been studied
by MDS [22] and density functional calculations [23].
The structure and kinetics [24,25], pressure effects [26],
intermolecular ordering [27] and short-range order [28]
of the hydrogen bonding have been investigated
using MDS.
There is also an enormous amount of literature
related to the investigation of glycerol solutions. The
speed of sound and the densities of mixtures of glycerol
with several alkanols (methanol, ethanol and
2-propanol) have been measured over the entire
composition range at 20 C [29]. Dielectric relaxation
spectroscopy has been utilized for the quantitative
*Corresponding author. Email: congchen@dlut.edu.cn
ISSN 0026–8976 print/ISSN 1362–3028 online
ß 2012 Taylor & Francis
http://dx.doi.org/10.1080/00268976.2011.641602
http://www.tandfonline.com
characterization of the antiplasticization of glassy
trehalose by glycerol [30]. The influence of glycerol
on the structure and thermal stability of lysozyme has
been studied by dynamic light scattering and circular
dichroism [31]. The liquid associated structure of
urea–glycerol mixtures has been investigated by dielectric spectroscopy [32]. The thermal stability [33],
viscosity [34–36], water activity and mobility [37],
Stokes–Einstein relation [38], space and time scaling
[39], relaxation dynamics [40], dielectric properties [41],
excess chemical potentials and entropies [37,42], supercooling [43], ice crystallization [44–47] and the glass
transition [48–51] of glycerol–water mixtures have been
studied experimentally. The effects of the level of
theory, basis set and solvation on strongly intramolecularly hydrogen-bonded glycerol–water binary systems have been analysed using computational potential
energy surfaces [52]. Temperature and concentration
effects on hydrogen-bonding abilities [53], the nature
of the hydrogen bonds of water molecules [54] and the
hydrogen-bonding network structure and kinetics [55]
in glycerol–water mixtures have been researched using
MDS [53,55] or attenuated total reflection infrared
spectroscopy [54]. The hydrogen-bonding structure
and kinetics has also been related to the cryoprotective
properties of glycerol–water mixtures [56]. The glycerol–water–sodium chloride ternary phase diagram has
been measured [57], extended [58] and synthesized
using binary phase diagrams [59]. Kinematic viscosities
and water activities of glycerol–water–sodium chloride
ternary solutions have been measured and
their relationships have been established [60].
Downloaded by [University of Sydney] at 18:51 21 November 2012
284
C. Chen et al.
Hydrogen-bonding
characteristics
in
glycerol–
water–sodium chloride ternary systems with different
concentrations have been studied [61] and, based on
hydrogen-bonding analysis, a relationship between the
melting temperature and the ratio of acceptor to donor
number for water/glycerol molecules has been established [62].
The diffusion coefficient of a solute moving
through a solvent is usually related to the shear
viscosity of the solvent by the Stokes–Einstein equation. When the solute is smaller than the solvent, the
Stokes–Einstein equation breaks down because of the
breakdown of the assumption inherent in the Stokes
drag equation. For solutions with attractive solute–
solvent interactions, take hydrogen bonds for example,
the interactions between the solute and solvent will
affect the friction coefficient, retard the motion of
solute molecules and lower the diffusion coefficient
[63–66]. The diffusion coefficients of pure glycerol have
been measured by the pulsed NMR technique at
different temperatures and a breakdown of the
Stokes–Einstein equation has been reported [67]. It
has been pointed out that the diffusion of glycerol
molecules decreases with decreasing temperature as its
viscosity increases in a manner simply described by the
Stokes–Einstein equation until the glass transition
occurs [38]. The diffusion coefficients of glycerol in
glycerol–water mixtures ranging from 0 to 93%
(weight percent) have been measured using an interferometric microdiffusion apparatus [68]. Mutual
diffusion coefficients and glycerol self-diffusion coefficients in glycerol aqueous solutions have been measured by the Taylor dispersion and Gouy
interferometric techniques [69]. Mutual diffusion
coefficients in glycerol–water binary mixtures have
been predicted using a holographic technique [70]. In
glycerol aqueous solutions, as a water molecule is
smaller than a glycerol molecule and hydrogen bonds
are present, it could be reasonably expected that the
water diffusion coefficient in glycerol deviates from the
values predicted by the Stokes–Einstein equation.
Water self-diffusion coefficients with glycerol mole
fractions above 0.13 at 25 C have been measured [69].
However, water self-diffusion coefficients for dilute
glycerol–water binary and glycerol–water–sodium
chloride ternary solutions are lacking and the role of
hydrogen bonds in the concentration dependence of
water self-diffusion coefficients is open to question.
MDS has been used to study diffusion coefficients
and the validity of predicted diffusion coefficients
strongly dependent on the force field used, especially
for water molecules [71]. The SPC/E water model [72]
gives a good prediction of water diffusion coefficients
compared with experiment values [71]. Using MDS,
the hydrogen-bonding network and kinetics can easily
be investigated [61], therefore MDS is a good choice
for the study of the effects of hydrogen bonds on water
diffusion. In the present work, MDS has been used to
study dilute glycerol–water and glycerol–water–sodium
chloride ternary solutions with different concentrations
using the SPC/E water model. Water self-diffusion
coefficients in dilute glycerol–water and glycerol–
water–sodium chloride ternary solutions have been
predicted and the concentration dependence of the
water self-diffusion coefficients was analysed from the
viewpoint of hydrogen bonds.
The rest of the paper is organized as follows.
In Section 2, the computation details for MDS, water
self-diffusion coefficients and hydrogen bonds are
presented. The results for the water self-diffusion
coefficients and insights from the hydrogen bonds are
summarized in Section 3. The conclusions and outlooks are presented in Section 4.
2. Methods
2.1. Simulation details
The molecular dynamics simulation package NAMD
[73] was used to carry out MDS in the present study.
The force field employed by Reiling et al. [74] was used
to describe the interactions of glycerol. Standard
techniques for periodic boundary conditions and
neighborhood lists were applied. The neighborhood
lists distance was 13.5 Å and lists were updated every
10 time steps with a time step of 2 fs. The non-bonded
interactions were truncated using a switching function
between 10.0 and 12.0 Å. Initial velocities were
generated randomly from a Gaussian distribution.
Coulombic interactions were computed using the
particle mesh Ewald (PME) method [75] with a grid
spacing of about 1.0 Å. The PME interpolation order
was cubic and the direct sum tolerance was 106. The
SHAKE algorithm [76] was used to fix the water
molecule geometry and covalent bonds between hydrogen and the heavy atoms. The multiple time step
integration technique r-RESPA [77] was adopted. The
number of time steps between full electrostatic evaluations was two and the number of time steps between
non-bonded evaluations was one. The long- and
short-range electrostatic forces were split using a
continuous shifting function between 10.0 and 12.0 Å.
All simulations were performed in the NPT ensemble.
The pressure was set to 1.0 bar and the temperature
was maintained at 300 K. The coupling methods for
pressure and temperature were the same as in other
studies [53,55].
Downloaded by [University of Sydney] at 18:51 21 November 2012
Molecular Physics
The simulation systems were constructed from a
water box with a density of 1 g cm3. Different
numbers of glycerol molecules were randomly added
to the water box to construct different simulation
boxes with desired glycerol concentrations. Different
numbers of ions (the same numbers of Naþ and Cl)
were added to the glycerol/water boxes at random
positions. In the present study, six glycerol–water
binary simulation boxes were constructed and the
numbers of glycerol molecules (water molecules) were
70 (2223), 100 (1908), 130 (1571), 140 (1391), 160
(1185) and 170 (1105), respectively. The glycerol mole
fractions of these six glycerol–water binary solutions
were 0.03, 0.05, 0.08, 0.09, 0.12 and 0.13.
Correspondingly, six glycerol–water–sodium chloride
ternary simulation boxes were constructed. The numbers of water molecules (ions) in the six ternary
solutions were 2211 (12), 1898 (10), 1560 (8), 1383
(8), 1179 (6) and 1099 (6), respectively. The number of
glycerol molecules was the same as that in the glycerol–
water binary solution from which the ternary solution
was constructed. The numbers of ions were quite small
and their effects on the glycerol concentration were
negligible. In total, 12 boxes were simulated for a 1-ns
equilibration and then another 1-ns production run
was generated to analyse solution structure and kinetics. It should be noted that several results produced
with these simulation trajectories have been published
elsewhere [55,61,62].
2.2. Diffusion coefficients
Diffusion coefficients can be expressed as a function of
the velocity autocorrelation function or mean square
displacement (MSD). In the present study, mean
square displacement has been used to calculate the
diffusion coefficient,
*
+
Nm
X
1
D ¼ lim
½rj ðtÞ rj ð0Þ2 ,
ð1Þ
t!1 6Nm t
j¼1
where D is the diffusion coefficient, Nm the total
number of atoms, t the time and rj(t) is the true
displacement vector of the jth atom at time t.
285
Figure 1. MSDs of one water molecule (the average values
over all water molecules) as a function of simulation time for
glycerol–water binary solutions. The figures are glycerol
mole fractions. Between each two points there are 50 data
points that have been omitted for clarity.
Figure 2. MSDs of one water molecule (the average values
over all water molecules) as a function of simulation time for
glycerol–water–sodium chloride ternary solutions. The figures are glycerol mole fractions. Between each two points
there are 50 data points that have been omitted for clarity.
angle was selected according to its distribution, and the
cut-offs for intermolecular hydrogen bonds were
selected as 30 . For details, see Ref. [55].
2.3. Hydrogen-bond definition
3. Results and discussion
In the present study, hydrogen bonds were defined
using geometrical criteria on the basis of the O H
distance and the H–O O angle. The cut-off of the
O H distance (2.4 Å) was selected from the position
of the first minimum of the intermolecular O–H radial
distribution functions. The cut-off of the H–O O
3.1. Water self-diffusion coefficients
The mean square displacements of water molecules as a
function of simulation time in glycerol–water binary
and glycerol–water–sodium chloride ternary solutions
were calculated and are illustrated in Figures 1 and 2,
respectively. It can be seen that, for such systems,
286
C. Chen et al.
Table 1. Diffusion coefficients of water molecules in glycerol–water binary and glycerol–water–sodium chloride ternary
solutions. Mean square displacements have been linearly fitted with simulation time t when t is longer than 2 ps. The standard
errors and correlation coefficients R arising from the linear regression are also listed. xg is the glycerol mole fraction. D is the
water self-diffusion coefficient.
Binary
xg
Downloaded by [University of Sydney] at 18:51 21 November 2012
0
0.03
0.05
0.08
0.09
0.12
0.13
Ternary
D (109 m2 s1)
Standard error (1010 m2 s1)
R
D (109 m2 s1)
Standard error (1010 m2 s1)
R
2.212
1.597
1.360
1.162
1.133
0.938
0.844
0.002
0.019
0.008
0.009
0.005
0.011
0.005
0.999
0.999
0.999
0.999
0.999
0.999
0.999
2.212
1.492
1.300
1.109
1.015
1.026
0.863
0.002
0.005
0.004
0.008
0.010
0.004
0.009
0.999
0.999
0.999
0.999
0.999
0.999
0.999
the difference between the mean square displacements
seems to lie in their early time behavior rather than in
the long time dynamics. In fact, above 2 ps, the MSDs
are roughly shifted along the y axis without presenting
a significant difference in their slope. Above 2 ps, the
order of MSDs is consistent with that of glycerol mole
fractions.
The MSDs of water molecules have been linearly
fitted with simulation time t when t is larger than 2 ps
and the results are summarized in Table 1. The
diffusion coefficient of pure water has also been
calculated for comparison. The predicted water
diffusion
coefficient
in
the
present
study
(2.212 109 m2 s1) agrees well with experimental
results [78] (2.272 109 m2 s1). As summarized in
Table 1, the water self-diffusion coefficients decrease
when the glycerol mole fraction increases. Water
diffusion is slowed by 27.80% when the glycerol mole
fraction increases from 0 to 0.03. When the glycerol
mole fraction increases further from 0.03 to 0.13,
the water self-diffusion coefficient decreases by 47.15%
from 1.597 to 0.844. When the glycerol mole fraction is
0.13, the water self-diffusion coefficient is reduced by
more than 60% compared with pure water. The
decrease of water self-diffusion coefficients as the
glycerol mole fraction increases has also been reported
by other researchers [69].
3.2. Insights from hydrogen bonds
The sharp slowing of water diffusion has also been
found in other aqueous solutions and it has been
pointed out that the slowing of water dynamics stems
from the increasing number of hydrogen bonds [66]. In
glycerol aqueous solutions, hydrogen bonds form and,
for water molecules, the maximum number of
hydrogen bonds per molecule is five [55]. Hydrogen
bonds affect the diffusion of water, and water diffusion
in a solvent with which it can hydrogen bond is slower
than that in a solvent with which it cannot form
hydrogen bonds when the viscosity of the solvents are
the same [63]. For water molecules with different
numbers of hydrogen bonds, the diffusion may be
different. Because of the frequent forming and breaking of hydrogen bonds [55,61], it is difficult to predict
the diffusion coefficients of water molecules with a
certain number of hydrogen bonds. However, the effect
of hydrogen bonds on water self-diffusion coefficients
can be analysed according to the mean number of
hydrogen bonds at each concentration.
Hydrogen bonds for water molecules can be
classified into two types, namely hydrogen bonds
between glycerol and water molecules (type I) and
hydrogen bonds between water molecules (type II).
The mean numbers of hydrogen bonds (types I and II)
per water molecule have been calculated and are
illustrated in Figure 3 as a function of glycerol mole
fraction. For comparison, the results for binary and
ternary solutions are summarized in the same figure.
As illustrated in Figure 3, in glycerol–water binary
and glycerol–water–sodium chloride ternary solutions,
the mean numbers of hydrogen bonds (all) per water
molecule decrease as the glycerol mole fraction
increases. A similar trend has been found for the
mean number of hydrogen bonds (type II) per water
molecule. However, the mean number of hydrogen
bonds (type I) increases as the glycerol mole fraction
increases. The different trends for hydrogen bonds
(types I and II) can explain the behavior of water selfdiffusion coefficients. Glycerol molecules diffuse at a
lower velocity (on the order of 1010 m2 s1) than water
molecules (on the order of 109 m2 s1) [68]. As the
glycerol mole fraction increases, the number of
Downloaded by [University of Sydney] at 18:51 21 November 2012
Molecular Physics
Figure 3. Mean numbers of hydrogen bonds (types I and II)
per water molecule nw as a function of glycerol mole fraction
in glycerol–water binary (lines) and glycerol–water–sodium
chloride ternary (symbols) solutions. The mean numbers of
hydrogen bonds were calculated by averaging 400 configuration files generated every 0.5 ps, corresponding to 200 ps of
the production run. For binary solutions: (1) the errors for
mean numbers of hydrogen bonds (all) per water molecule in
different simulation boxes (glycerol mole fraction from 0.03
to 0.13) are 0.02, 0.02, 0.02, 0.02, 0.03 and 0.03, respectively;
(2) the errors for the mean numbers of hydrogen bonds
(type II) per water molecule are the same as those in
simulation boxes with the same glycerol mole fractions; (3) as
for hydrogen bonds (type I), the errors are 0.004, 0.006,
0.008, 0.010, 0.015 and 0.011, respectively. For ternary
solutions: (1) the errors for mean numbers of hydrogen
bonds (all) per water molecule in different simulation boxes
(glycerol mole fraction from 0.03 to 0.13) are 0.06, 0.02, 0.02,
0.02, 0.02 and 0.02, respectively; (2) as for hydrogen bonds
(type I), the errors are 0.005, 0.005, 0.008, 0.009, 0.009 and
0.011, respectively; (3) the errors for mean numbers of
hydrogen bonds (type II) per water molecule are 0.06, 0.02,
0.02, 0.02, 0.02 and 0.03, respectively.
hydrogen bonds between water molecules decreases
and more and more water molecules form glycerol–
water hydrogen bonds. As a result, more and more
water molecules interact with glycerol molecules, which
move slower, leading to a slowing of the diffusion
velocity. Furthermore, as the glycerol mole fraction
increases, the lifetimes of the hydrogen bonds between
glycerol and water molecules increase [55,61]. This
further slows water self-diffusion because of the
stronger interaction between glycerol and water
molecules.
The above analysis is based on the overall average
of water molecules. In the present study, the glycerol
mole fractions are quite small and it is probable that
there are some kinds of water molecules that are only
involved in water–water hydrogen bonds. This kind of
water molecule does exist and the reduced numbers of
287
Figure 4. The ratio N/N0 as a function of glycerol mole
fraction in glycerol–water binary and glycerol–water–sodium
chloride ternary solutions. N is the number of water
molecules forming only water–water hydrogen bonds. N0 is
the total number of water molecules in different simulation
boxes.
water molecules forming only water–water hydrogen
bonds relative to the total number of water molecules
in simulation boxes have been calculated and are
shown in Figure 4. The percentages of water molecules
that are only involved in water–water hydrogen bonds
decrease sharply as the glycerol concentration increases
in both binary and ternary solutions. In glycerol–water
binary solutions, the percentage of water molecules
that form only water–water hydrogen bonds decreases
from 44% to 18% when the glycerol mole fraction
increases from 0.03 to 0.09. In glycerol–water–sodium
chloride ternary solutions, the percentage decreases
from 45% to 19%. In both binary and ternary
solutions, when the glycerol mole fraction is larger
than 0.09, the effect of the glycerol concentration
seems to be limited. The reason for this may be that, as
the glycerol mole fraction increases, the interaction
between glycerol molecules plays a more and more
important role.
The mean numbers of hydrogen bonds per molecule for water molecules forming only water–water
hydrogen bonds and water molecules forming
glycerol–water and water–water hydrogen bonds have
been calculated and the results for binary and ternary
solutions are summarized in Figure 5. From the
viewpoint of the mean number of hydrogen bonds,
the behavior of water molecules forming only water–
water hydrogen bonds and water molecules forming
glycerol–water and water–water hydrogen bonds is
quite similar. The uncertainties for water molecules
forming only water–water hydrogen bonds are larger
than those for water molecules forming glycerol–water
288
C. Chen et al.
3.3. Parameters affecting diffusion coefficient
calculation
3.3.1. Force field
Downloaded by [University of Sydney] at 18:51 21 November 2012
The force field used in a molecular dynamics simulation plays an important role in the credibility of the
results. The force field used in the present study has
been used in other studies [55,61]. The densities of
glycerol–water binary solutions have been estimated
based on the molecular dynamics simulation method
and the results agree well with the experimental values
[55]. For pure water, the percent error is 0.20%, for
pure glycerol solutions the percent error is 7.34%,
and for other glycerol concentrations the percent errors
are all less than 2.10%.
Figure 5. Mean numbers of hydrogen bonds per molecule nw
for water molecules forming only water–water hydrogen
bonds (squares) and water molecules forming glycerol–water
and water–water hydrogen bonds (circles) in glycerol–water
binary (dotted lines) and glycerol–water–sodium chloride
ternary (solid lines) solutions. The mean numbers of hydrogen bonds were calculated by averaging 400 configuration
files generated every 0.5 ps, corresponding to 200 ps of the
production run. For water molecules forming only
water–water hydrogen bonds, the errors for the mean
number of hydrogen bonds per water molecule in binary
(ternary) solutions are 0.03 (0.07), 0.04 (0.04), 0.07 (0.06),
0.07 (0.08), 0.10 (0.09) and 0.13 (0.13), respectively. For
water molecules forming glycerol–water and water–water
hydrogen bonds, the errors for the mean number of hydrogen
bonds per water molecule in binary (ternary) solutions are
0.03 (0.06), 0.02 (0.02), 0.02 (0.02), 0.03 (0.02), 0.03 (0.03)
and 0.03 (0.03), respectively.
and water–water hydrogen bonds. The differences
become larger as the glycerol mole fraction increases.
The reason for this is that the number of water
molecules forming only water–water hydrogen bonds
decreases as the glycerol mole fraction increases, as
illustrated in Figure 4. The mean numbers of hydrogen
bonds per molecule for water molecules forming only
water–water hydrogen bonds change with glycerol
concentration, but are smaller than those in pure
water. Although not involved in glycerol–water hydrogen bonds, the kind of water molecule forming only
water–water hydrogen bonds cannot be recognized as
‘free water’. The diffusion behavior is surely affected
by the glycerol molecules, but the effects may be
different from those for water molecules involved in
glycerol–water hydrogen bonds. However, the percentages of water molecules forming only water–water
hydrogen bonds are smaller than those of water
molecules involved with glycerol–water hydrogen
bonds. As a result, the diffusion behavior of water
molecules involved in glycerol–water hydrogen bonds
governs the overall water self-diffusion coefficients.
3.3.2. Cut-off, damping coefficient and periodic
boundary conditions
The cut-off values, damping coefficient and periodic
boundary conditions also affect the diffusion coefficient [79] and some authors have concluded that the
rigid models used in standard molecular dynamics
force fields have difficulties in reproducing the
observed temperature variations in conductivity data
[80]. The system size dependence of the diffusion
coefficient from molecular dynamics simulations with
periodic boundary conditions has been analysed and a
correction has been made [79]. However, the correction
is based on viscosity, which is missing for glycerol
aqueous solutions, and the prediction of viscosity may
cause other uncertainties [81]. A detailed analysis of the
parameters affecting diffusion coefficient prediction in
a molecular dynamics study is not the subject of the
present paper. The purpose of the present study is to
investigate the effect of solute molecules on water
diffusion coefficients, and the predicted water diffusion
coefficients agree well with reported experimental
results (see Section 3.1), therefore the effects of cutoff, damping coefficient and periodic boundary conditions have not been considered further.
3.3.3. Curve fitting parameters
The water self-diffusion coefficients were estimated
from the slope of the linear part at long times of the
mean square displacements versus time plot. The initial
part of the line, which is influenced by inertial effects,
was not included in the calculation. It has been found
that, for simulations without velocity scaling, the
results are very similar for all the tested intervals,
even at 2–10 ps [71]. The water self-diffusion coefficients have been predicted in an interval of 2–15 ps and
the good agreement between predicted values and
Downloaded by [University of Sydney] at 18:51 21 November 2012
Molecular Physics
Figure 6. The average temperature as a function of simulation time for the glycerol–water binary solution with a
glycerol mole fraction of 0.08.
experimental results demonstrates the selection of the
interval.
3.3.4. Temperature fluctuations
In molecular dynamics simulations, the ensemble
temperature fluctuates around the setting value. The
departure strongly depends on the temperature coupling scheme. The coupling method for the temperature in the present study has been used extensively
[53,55]. For the glycerol–water binary and glycerol–
water–sodium chloride ternary solutions studied in the
present study, the average ensemble temperature was
300 2.39 K. For the glycerol–water binary solution
with a glycerol mole fraction of 0.08, the average
temperature as a function of simulation time is
illustrated in Figure 6. The water self-diffusion coefficient for the glycerol–water binary solution with a
glycerol mole fraction of 0.13 at 298 K was calculated
and the predicted value is 0.822 109 m2 s1. The
water self-diffusion coefficient decreases about
0.02 109 m2 s1 when the temperature decreases
2 K. It can be concluded that the effect of temperature
fluctuations on the water self-diffusion coefficients is
acceptable.
4. Conclusions
Molecular dynamics simulations have been performed
on dilute glycerol–water binary and glycerol–water–
sodium chloride ternary solutions at different concentrations. Water self-diffusion coefficients have been
predicted from the slope of the linear part of the
mean square displacement versus time plot.
289
The concentration dependence has been analysed.
It has been found that, as the glycerol mole fraction increases, the water self-diffusion coefficient
decreases.
The
concentration
dependence
of
water
self-diffusion coefficients was further investigated
from the viewpoint of hydrogen bonds. Water molecules can be classified into two types: (1) those forming
both glycerol–water hydrogen bonds and water–water
hydrogen bonds; and (2) those forming only water–
water hydrogen bonds. For water molecules of type
(1), as the glycerol mole fraction increases, the number
of hydrogen bonds between water molecules decreases
and more and more water molecules form glycerol–
water hydrogen bonds. As a result, more and more
water molecules interact with glycerol molecules, which
thus move slower, leading to a slowing of the diffusion
velocity. Furthermore, as the glycerol mole fraction
increases, the lifetimes of the hydrogen bonds between
glycerol and water molecules increase, which further
slows water self-diffusion because of the stronger
interaction between the glycerol and the water molecules. For water molecules of type (2), although they
are not involved in glycerol–water hydrogen bonds,
they are affected by glycerol molecules because the
mean numbers of hydrogen bonds per water molecule
are smaller than in pure water. Their diffusion behavior is affected by the glycerol molecules, but the effects
may be different from that for water molecules
involved in glycerol–water hydrogen bonds. However,
the percentages of water molecules forming only
water–water hydrogen bonds are smaller than for
water molecules involved in glycerol–water hydrogen
bonds. As a result, the diffusion behavior of water
molecules involved in glycerol–water hydrogen bonds
governs the overall water self-diffusion coefficients.
Recently, the importance of ion hydration effects
beyond the first hydration shell has been demonstrated
and the structure and dynamics of water molecules are
different from those in the bulk and exhibit specific ion
effects [82]. In glycerol–water–sodium chloride ternary
solutions, the sodium cation and the chlorine anion
both hydrate several water molecules. In the present
study, the water self-diffusion coefficients for binary
(salt-free) and ternary (with salt) solutions with the
same glycerol mole fraction seem to be different, but
are very similar. The differences are comparable to the
computation errors, so the differences may be attributed to the noise of the simulations, and the hydrogenbond analysis in Figures 3 and 5 demonstrate this. The
effects of ion hydration on water self-diffusion coefficients should be studied in solutions with larger salt
concentrations.
290
C. Chen et al.
Acknowledgements
This research was supported by the Fundamental Research
Funds for the Central Universities (DUT11NY01) and
NSFC’s Key Program project (50736001). We thank the
Computing Center of the Department of Energy and Power
Engineering of Dalian University of Technology for providing the parallel computing environment.
Downloaded by [University of Sydney] at 18:51 21 November 2012
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