Molecular dynamics simulations of sodium chloride solutions in
water–dimethyl sulphoxide mixtures: Potentials of mean force and solvation
structures
Ashok K. Das and B. L. Tembe
Citation: J. Chem. Phys. 111, 7526 (1999); doi: 10.1063/1.480079
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 111, NUMBER 16
22 OCTOBER 1999
Molecular dynamics simulations of sodium chloride solutions
in water–dimethyl sulphoxide mixtures: Potentials of mean force
and solvation structures
Ashok K. Das and B. L. Tembea)
Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai, 400 076, India
共Received 7 December 1998; accepted 19 July 1999兲
Five solutions of sodium chloride in mixtures of water and dimethyl sulphoxide 共DMSO兲 have been
simulated using the conventional molecular dynamics technique. The potentials of mean force
共PMFs兲 of the sodium chloride ion pair in the presence of the five water–DMSO mixtures with
DMSO mole fractions (x DMSO) of 0.10, 0.21, 0.35, 0.48 and 0.91 have been computed. The derived
PMFs have been confirmed by the long time dynamical ion-pair trajectories. The solvation
structures of the ions in the presence of these mixtures have been analyzed using the ion-solvent
radial distribution functions and the corresponding integration numbers. It has been found that the
Na⫹ ion is always preferentially solvated by the water molecules in all the water–DMSO solvent
mixtures. The Cl⫺ ion is slightly preferred by the DMSO molecules in these mixed solvents.
© 1999 American Institute of Physics. 关S0021-9606共99兲51038-6兴
I. INTRODUCTION
decisive results for electrolyte solutions in water–methanol
mixtures.14 Computer simulation gives an opportunity to distinguish between the properties of each subsystem in the
solution and to follow the effects of each component of the
system. In the water–formamide mixture, both the Na⫹ cation and Cl⫺ anion are preferentially solvated by formamide
even if small amounts of formamide are present in the mixed
solvent.12
The solvent mixtures of water and DMSO have special
importance because of their unique physical and chemical
properties.15,16 With respect to the chemical properties, the
formation of water–DMSO mixtures is exothermic with the
magnitude of the heat of mixing showing a strong negative
deviation from ideality.17 The other macroscopic properties
such as density,18 viscosity,18 refractive index,18 dielectric
permittivity19,20 and surface tension21 show positive deviations from ideality. An aqueous solution of DMSO with
x DMSO ⬵ 0.25 has a freezing point ⫺70 °C in comparison to
the pure constituents 共0 °C for water and ⫹18.6 °C for
DMSO兲.22 These solvent mixtures show maximum deviations from ideal behavior in the DMSO mole fraction range
of 0.20–0.45. There is no general agreement about the
mechanism by which the two solvents interact to account for
these macroscopic deviations.23 However, it has been well
established that the water–DMSO hydrogen bond is much
stronger than the water–water hydrogen bond,8 which has
been accepted to be one of the major reasons for the deviations in macroscopic properties. The associative properties of
DMSO responsible for the nonidealities in water–DMSO
mixtures are also found in its associations with polarizable
nonionic and ionic substances.15,16 The existence of strongly
hydrogen bonded one DMSO-2 water aggregates have also
been proved through molecular dynamical simulations of
these solvent mixtures.9 In order to probe this associative
character of DMSO and its influence on ion solvation, we
have studied the solvation of the Na⫹ – Cl⫺ ion pair in the
The solvation of sodium chloride and other electrolytes
in several one component solvents has been a subject of detailed investigations, both theoretically and through simulations, for a considerably long time.1 Molecular dynamical
共MD兲 simulation studies on NaCl in the presence of model
polar solvents,2 water,3–5 methanol,6 and dimethyl sulphoxide 共DMSO兲7 have been reported. These studies cover many
aspects of the NaCl solvation in the respective solvents including the evaluation of the potential of mean force 共PMF兲,
analysis of the solvation structure and dynamics, computation of solvent friction kernels, calculation of transmission
coefficients across the PMF barriers and orientational distributions of the solvent molecules around the ions. The solvent
mixtures like water–methanol, water–acetone and water–
ammonia have been simulated by Ferrario et al.8 Similarly,
the water–DMSO mixture has been simulated by Vaisman
and Berkowitz9 and also by Luzar and Chandler.10 Interestingly, the simulations of NaCl solutions in solvent mixtures
are being reported only recently. The solvation of a single
Na⫹ ion and a single Cl⫺ ion in the presence of mixed solvents like water–methanol11 and water–formamide12 has
been reported in the recent past. Monte Carlo simulations
and neutron diffraction studies on a peptide forming system
CuCl2 –NaCl–H2 O have appeared recently.13
The phenomenon of preferential solvation of NaCl in the
water–methanol mixtures has been addressed by Hawlicka
and Wojcik.11 For the Na⫹ ion, the preferential solvation by
methanol decreases with increasing methanol mole fraction
and it vanishes at x methanol⫽0.9. The opposite behavior has
been noticed for the Cl⫺ ion. The most direct insight into the
structure of solutions is expected from x-ray and neutron
diffraction experiments. But these techniques do not provide
a兲
Electronic mail: [email protected]
0021-9606/99/111(16)/7526/11/$15.00
7526
© 1999 American Institute of Physics
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J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
NaCl solutions in water-dimethyl sulphoxide mixtures
TABLE I. Characteristics of the Na⫹ – Cl⫺ PMF in water and in DMSO.
Location of
Magnitude of
First
First
Second Dissociation Association
Solvent minimum maximum minimum
barrier
barrier Reference
a
Water
Waterb
DMSO
a
2.7 Å
2.9 Å
2.6 Å
3.5 Å
3.7 Å
4.9 Å
5.0 Å
5.0 Å
7.2 Å
5.6 k BT
2.8 k BT
28.7 k BT
3.2 k BT
3.7 k BT
1.9 k BT
3,4
5
7
TABLE II. Compositions of the water–DMSO mixtures. Solvent 1
⬅ DMSO; solvent 2 ⬅ water; x i⬅ mole fraction of solvent i; n i⬅ number
of molecules of solvent i in the cubic simulation cell of edge length L; ␳
⬅ density at 298 K; ⑀ ⬅ dielectric constant.
Composition
x1
x2
n1
n2
L
共Å兲
␳a
(gm ml⫺1 )
⑀b
3
2
1
5
4
0.10
0.21
0.35
0.48
0.91
0.90
0.79
0.65
0.52
0.09
25
53
88
120
228
225
197
162
130
22
21.228
22.784
24.764
26.066
30.211
1.0425
1.0725
1.0927
1.0983
1.0965
77.50
74.85
69.97
65.01
49.56
TIPS2 model.
Flexible SPC model.
b
a
presence of five selected water–DMSO mixtures with
x DMSO⫽0.10, 0.21, 0.35, 0.48 and 0.91. The choice of the
sodium and chloride ions is because of their importance in
chemistry and biochemistry.24,25
The PMF for the Na⫹ and Cl⫺ ion pair in pure water has
been reported by Berkowitz et al.,3 and by Karim and
McCammon4 using the umbrella sampling technique and
also by Guardia, Rey, and Padro5 using the constrained MD
simulations. These two sets of results differ only slightly
with respect to the location of the contact ion pair 共CIP兲
minimum, the transition state 共TS兲 maximum, the solvent
separated ion pair 共SSIP兲 minimum and also with respect to
the magnitudes of dissociation and association barriers. The
differences arise largely because of the different interaction
potential models used by these authors. While Berkowitz
et al.3 and Karim and McCammon4 have used the TIPS2
model for water, Guardia, Rey, and Padro5 have used the
flexible SPC model for water.
The ion–ion PMF for the Na⫹ and Cl⫺ ion pair in pure
DMSO has been reported by Madhusoodanan and Tembe7
using the constrained MD simulations. Table I collects the
main characteristics of the ion–ion PMF for the Na⫹ and
Cl⫺ ion pair in these two solvents and the ion–ion PMF in
the two solvents is shown in Fig. 1.
To our knowledge, ion-solvent interactions for this most
commonly used electrolyte 共i.e., Na⫹ Cl⫺ ) has not been re-
7527
Reference 18.
References 19 and 20.
b
ported in mixed solvents such as water–DMSO. In order to
explore the nature of the solvation of the ion pair in these
mixed solvents with extreme nonideality we have derived the
ion–ion PMF at five selected compositions, which we report
here. Significantly, in all the compositions studied, the short
distance stable minimum 共characteristic of the formation of a
CIP兲 is not observed.
These studies will yield a comparison of the nature of
the PMFs and the solvation structures of the ions in the presence of the mixed solvents of different compositions. The
preferential solvation of the Na⫹ and Cl⫺ ions in these
mixed solvents and the orientational distributions of the solvent molecules around a moving ion pair during its transformation from one solvated configuration into another may be
revealed through these studies.
II. THE MODELS AND THE METHOD
The details of the methodology have been given in the
earlier papers. The five systems for which the Na⫹ – Cl⫺
ion–ion PMF have been derived contain the two ions in the
presence of the five selected solvent compositions of the
water–DMSO mixture. The relevant details of the chosen
solvent mixtures are given in Table II.
A. The interaction potentials
The present work considers the interactions between the
ions, DMSO and water molecules to be composed of pairwise additive potential functions between the sites. For details, the reader may refer to our earlier work7 and the references cited.26–32 In all the five mixture compositions
considered here, water–water interactions are taken to be
those of the SPC model of water due to Berendsen et al.33
For the DMSO–DMSO interactions, the potential function
used by other authors9,10,32 has been chosen. The ion–ion
direct potential between the Na⫹ and Cl⫺ ions is taken to be
that of the Huggins–Mayer form31
U i j共 r 兲⫽
⫹
⫺
FIG. 1. The potentials of mean force W共r兲 for the Na – Cl ion pair in units
of k BT in DMSO and water as a function of the ion–ion separation.
冉 冊
q iq j
r
Cij
⫹B i j exp ⫺
⫺ 6 ,
r
␳ij
r
共1兲
where q i is the charge on the ith ion at a distance r from the
jth ion and B, C, and ␳ are parameters. The site–site ionsolvent and solvent–solvent potential is represented as
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7528
J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
A. K. Das and B. L. Tembe
TABLE III. Site–site potential parameters.
Salt
Na⫹ –Cl⫺
B i j /共kJ兲
2.01⫻10⫺19
␳ i j /Å
0.317
C i j /共kJ/ Å6 )
1.12⫻10⫺21
Solvent
Water
Site
O
H
⑀ /共kJ mol⫺1 )
0.6502
0.0
␴ /共Å兲
3.156
0.0
q/e a
⫺0.82
⫹0.41
Solvent
DMSO
Site
S
O
CH3
⑀/共kJ mol⫺1 )
0.844 03
0.275 86
0.668 52
␴/共Å兲
3.56
2.94
3.60
q/e a
⫹0.139
⫺0.459
⫹0.160
a
The term e is the magnitude of the electronic charge.
U ␣␤ 共 r 兲 ⫽
q ␣ q ␤ A ␣␤ C ␣␤
⫹ 12 ⫺ 6 ,
r
r
r
共2兲
where ␣ and ␤ denote a pair of interaction sites on different
molecules, r is the site-site separation, q ␣ is a point charge
located at site ␣ . The terms A ␣␤ and C ␣␤ are given by
A ␣␤ ⫽4␧ ␣␤ 共 ␴ ␣␤ 兲 12,
共3a兲
C ␣␤ ⫽4␧ ␣␤ 共 ␴ ␣␤ 兲 6 ,
共3b兲
where ⑀ ␣␤ and ␴ ␣␤ are the energy and distance parameters in
the Lennard-Jones potential. The cross interactions have
been obtained by using the Lorentz–Berthelot rules34
␴ ␣␤ ⫽ 21 共 ␴ ␣␣ ⫹ ␴ ␤␤ 兲 ,
共4a兲
␧ ␣␤ ⫽ 共 ␧ ␣␣ ␧ ␤␤ 兲 1/2.
共4b兲
The various potential parameters in Eqs. 共1兲 and 共2兲 used in
this work are presented in Table III.
The choice of the intersolvent potential is consistent with
the usual combining rules used in the statistical mechanics of
mixtures34,35 and with the independent determination of the
intermolecular DMSO—DMSO, water–water, ion-DMSO
and ion-water potentials. Earlier MD simulation studies on
solvent mixtures performed by Ferrario et al.8 proved that
such choice of the intersolvent potential is reasonably accurate for simulating water–methanol, water–acetone and
water–ammonia mixtures.
B. Preparation of the solvent mixtures
The starting solvent configurations for the five compositions of the mixtures have been chosen according to the
specifications given in Table II. In all the compositions, the
Na⫹ and Cl⫺ ions have been placed at the center of the cubic
simulation box. For placing the solvent molecules into the
simulation box, the following three procedures have been
adopted.
H1 „Hetero1…: Keeping the two ions at the center of the
box, n 1 DMSO molecules are placed around them. This
makes up the box size up to L 1 . This central box of DMSO
is then covered by n 2 water molecules in the form of a
sheath, to make up the full box length of L. 共For example, in
composition 1, n 1 ⫽88, L 1 ⫽21.8 Å, n 2 ⫽162, L⫽24.564 Å;
in composition 2, n 1 ⫽53, L 1 ⫽18.4 Å, n 2 ⫽197, L⫽22.784
Å and so on兲.
H2 „Hetero2…: Similar to H1, here n 2 molecules of water surround the ions in the inner box up to a box size of L 2 .
This water box is then covered by n 1 DMSO molecules as a
sheath, up to the net box length of L. 共For example, in composition 1, n 2 ⫽162, L 2 ⫽16.9 Å, n 1 ⫽88, L⫽24.564 Å; in
composition 2, n 2 ⫽197, L 2 ⫽18.1 Å, n 1 ⫽53, L⫽22.784 Å
and so on兲.
R „Random…: For the random configuration, two equilibrated solvent boxes are taken; one of which contains 254
DMSO molecules in a cubic box of edge length 31.039 Å
and the other which contains 300 water molecules in a cubic
box of edge length 20.77 Å. From the DMSO box, n 1 molecules are picked up at random. Then for these n 1 DMSO
molecules, we have located the water molecules with
S共DMSO兲–O共water兲 distance less than ⬃2.5 Å and deleted
these water molecules from the water box. Out of the remaining water molecules, only n 2 are retained for preparing
the mixture, and the rest are deleted. Finally, the n 1 DMSO
molecules and the n 2 water molecules are placed into the
simulation box along with the Na⫹ and Cl⫺ ions at the center
of the box.
In all these three procedures, about 1000 Monte Carlo
moves are performed in order to eliminate any site-site close
contacts. In the case of H2 and R, the system reaches equilibrium 共tested with the constancy of the total energy of the
system兲34 within 10 ps of MD simulation at 298 K. On the
other hand, H1 共with DMSO molecules forming an inner
sheath to the ions兲 takes a considerably long time 共more than
50 ps兲 to reach equilibrium. This is because of the presence
of the very deep potential minimum 共depth of 28.7 k BT)
existing in the PMF of the Na⫹ – Cl⫺ in DMSO at a short
interionic separation 共2.6 Å兲. However, the equilibration of
H1 can be achieved faster by increasing the temperature of
the system gradually followed by slow cooling to 298 K.
All these three strategies have been tested for giving the
identical PMF for the Na⫹ – Cl⫺ ion pair in all five mixture
compositions.
C. Details of the simulations
In order to simulate the ion pair dynamics in the presence of the mixed solvents we have used the constrained MD
methodology36 in all the simulations. The method requires
the MD simulation of the system consisting of the ions and
the solvent molecules in which not only the intrasolvent
atom–atom or site–site separations are held constant, but
also the ion–ion separation is kept fixed. This was achieved
by using the SHAKE algorithm.37 The short range interactions were truncated using a spherical cutoff with half the
box length as the cutoff radius. The long range interactions
were computed using the reaction field technique.35 The
equations of motion were solved numerically using the Verlet algorithm38 using a time step of 0.5 fs.
For the system consisting of two ions 共A,B兲 and N solvent molecules, the force due to the solute–solvent interactions, acting along the interionic axis is evaluated as39
⌬F 共 r,t 兲 ⫽ ␮
冋
册
F AS共 r,t 兲 F BS共 r,t 兲
⫺
•r̂,
mA
mB
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共5兲
J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
NaCl solutions in water-dimethyl sulphoxide mixtures
7529
where F AS(r,t) and F BS(r,t) are the total forces on the solute particles A and B due to the solvent molecules; m A and
m B are the individual masses of the ions; ␮ is the reduced
mass of the ion pair and r̂ is the unit vector along the AB
direction. The ⌬F(r,t) values are calculated at each time
step and then averaged over the whole simulation. The total
mean force between the ions is the sum of the direct 共bare兲
ion–ion force, F d(r) and the solvent contribution, ⌬F(r).
That is
F 共 r 兲 ⫽F d 共 r 兲 ⫹⌬F 共 r 兲 ,
共6兲
where ⌬F(r)⬅⬍⌬F(r,t)⬎, the angular brackets denoting
an ensemble average. The potential of mean force, W共r兲, of
the ion pair in the presence of the solvent can then be calculated as39
W 共 r 兲 ⫽⫺
冕
F 共 r 兲 dr⫽W 共 r 0 兲 ⫺
冕
r
r0
F 共 r 兲 dr.
共7兲
The choice of W(r 0 ) is required to be done in such a way
that the calculated mean force potential matches the macroscopic Coulombic potential at long distances
W共 r0兲⫽
q iq j
,
r 0␧
共8兲
where q i is the charge on the ith ion and ⑀ is the dielectric
constant of the solvent. The experimental values of the dielectric constants19,20 have been given in Table II. We have
found that the ion–ion PMFs for the solvent compositions
studied are not sensitive to the choice of r 0 if r 0 is greater
than 8.0 Å.
Interionic separations 共r兲 from 2.0 to 9.0 Å with increments of 0.2 Å were considered for the estimation of the
PMFs. This constitutes a series of 36 MD simulations for
each of the solvent compositions. Several initial configurations were generated for a given interionic separation. In
each case after an initial equilibration period of 20 ps, the
ion–ion separation was increased and/or decreased to cover
the whole range of distances. For each value of r, the system
was further equilibrated for 20 ps which was followed by a
production period ranging from 60 to 80 ps, during which the
ion-solvent mean force ⌬F(r) was computed. We have determined the errors in ⌬F(r) by repeating the production
runs over several initial solvent configurations. Typical values of the standard deviations of ⌬F(r) range from about 5
k BT 共at smaller r between 2.6 and 4.0 Å兲 to about 1 k BT 共at
longer r兲.
III. RESULTS AND DISCUSSION
A. The solvent contributions to the mean force
The mean force F共r兲 on the Na⫹ and Cl⫺ ions in the
presence of the five mixed solvents 共whose compositions are
indicated on the curves兲 are displayed in Fig. 2 together with
the direct F d(r) contribution. Similar results were obtained
for the Na⫹ - Cl⫺ ion pair in model polar solvents by Ciccotti
et al,36 in pure water by Guardia, Rey, and Padro5 and in
pure DMSO by Madhusoodanan and Tembe.7 The sign of
⌬F(r) 关which is F(r)⫺F d (r) and is not shown in the graph兴
is positive for all the mixed solvent compositions. Positive
FIG. 2. Ion–ion total mean force F共r兲 on the Na⫹ – Cl⫺ ion pair in units of
k BT/Å in the presence of the five water–DMSO mixed solvents as a function of the interionic separation 共r兲. The mole fraction of DMSO (x DMSO) is
indicated on each curve and the successive curves are shifted by 60 units.
The F共r兲⫽0 line is shown on each curve. The direct ion–ion force F d(r) is
shown by dotted lines.
⌬F(r) was also observed in the case of pure water5 as well
as in pure DMSO7 at all the interionic separations. This implies that for a system of charged particles 共i.e., ions兲 in the
presence of polar solvents, the characteristics of ⌬F(r) are
the manifestations of the electrostatic forces on the ions
which are dictated by the equilibrium solvent configurations
at that particular interionic separation. From the nature of the
F共r兲 in all the solvent compositions, it is evident that the
contributions of the solvent forces are important for values of
r up to 8.0 Å. The repulsive character of F共r兲 关which is due
to ⌬F(r)] in all the solvent compositions can be understood
by the fact that the polar mixed solvent assists in separating
the oppositely charged Na⫹ and Cl⫺ ions. Total mean force
F共r兲 on the ions has the composite effect of two contributions, namely, the bare attractive ion–ion force F d (r) and the
repulsive ion-solvent force ⌬F(r). These two are of opposite signs for all ion–ion separations greater than 2.3 Å;
hence the resulting F共r兲 may be sensitive to the choice of the
ion–ion (U i j ), ion-solvent and solvent–solvent (U ␣␤ ) interaction potentials which are responsible for the magnitude as
well as the sign of F d (r) and ⌬F(r), respectively. This
needs further investigation.
From the curves in Fig. 2, it can be seen that the solvent
contributions ⌬F(r) differ only at small ion–ion separations.
A shallow minimum in ⌬F(r) or F共r兲 near 3.0 Å is observed
in the first three compositions. A local maximum is noticed
only for x DMSO⫽0.21 at r Na⫹ ⫺Cl⫺ ⫽6.6 Å. A small barrier in
⌬F(r) is observed between 4.0 and 5.5 Å in all the compositions. In the first three compositions, F共r兲 rises significantly
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7530
J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
A. K. Das and B. L. Tembe
TABLE IV. Characteristics of the Na⫹ – Cl⫺ PMF in water–DMSO mixtures.
FIG. 3. Na⫹ – Cl⫺ potentials of mean force 共PMFs兲 W共r兲, as a function of
the ion–ion separation 共r兲 in the presence of the five water–DMSO mixed
solvents. The mole fraction of DMSO (x DMSO) is indicated on each curve
and the successive curves are shifted by 20 units. The W共r兲⫽0 line is shown
on each curve.
above zero between 3.5 to 5.0 Å and this leads to their corresponding PMFs to be above zero for r⬍4.0 Å 共Fig. 3兲. For
x DMSO⫽0.48 and 0.91, the F共r兲s are flatter in the region 3.0
Å⬍r⬍5.0 Å and hence the corresponding PMFs are below
zero in the distance range 3.0 Å⬍r⬍5.0 Å. Beyond about 8.0
Å, the ⌬F(r) decays to small magnitude for all the solvent
compositions. However, for composition with x DMSO⫽0.21,
the appearance of a small barrier in ⌬F(r) at around 6.6 Å is
a significant characteristic of the mixed solvent at x DMSO
⫽0.21.
B. The potentials of mean force
The ion–ion PMFs, W共r兲s, for the five solvent compositions have been obtained by direct integration of the total
force, F共r兲, according to Eq. 共7兲, taking r 0 ⫽8.0 Å, and satisfying Eq. 共8兲. These are displayed in Fig. 3 for the five
solvent compositions. From these figures it is evident that the
first short-distance minimum in the Na⫹ – Cl⫺ PMF seen in
pure water 共at 2.9 Å兲 and in pure DMSO 共at 2.6 Å兲 does not
appear in any of the mixture compositions. The mixture
compositions with x DMSO⫽0.10, 0.21 and 0.35 show narrow
shoulder regions between 3.0 and 4.0 Å very near the CIP
configurations observed in the pure solvents. The characteristics of the Na⫹ – Cl⫺ PMFs in the presence of the mixed
solvents are given in Table IV.
All these observations point to the fact that none of the
solvent mixtures permit the Na⫹ and Cl⫺ ions to remain
‘‘intimate’’ within a short ion–ion distance corresponding to
the CIP in the pure solvents. In pure water, the ions can exist
both as a CIP and as a SSIP with an equilibrium constant of
7.7 at 298 K for the CIP ⇔ SSIP equilibrium.5 The corre-
x DMSO
First
minimum
共Å兲
Depth
(k BT)
First
maximum
共Å兲
Height
(k BT)
Second
minimum
共Å兲
Depth
(k BT)
0.10
0.21
0.35
0.48
0.91
4.6⫾0.7
5.0⫾0.5
5.0⫾0.5
5.0⫾0.7
4.4⫾0.6
⫺14.0⫾5.0
⫺10.0⫾3.0
⫺9.0⫾3.0
⫺13.0⫾3.0
⫺18.0⫾5.0
¯
6.6
¯
¯
¯
¯
⫺3.5⫾1.0
¯
¯
¯
¯
7.0
¯
¯
¯
¯
⫺5.5⫾1.0
¯
¯
¯
sponding value of the equilibrium constant is much less, 1.5
⫻10⫺8 at 298 K in pure DMSO, in which the CIP configuration 共with a potential depth of 28.7 k BT) is much more
stable than the SSIP.7 These features do not get reproduced
by any of the solvent mixtures considered here. The presence
of broad SSIP minima as well as a shallow barrier for
x DMSO⫽0.21 allow for the possibilities for several low barrier transitions40,41 between various arrangements of the molecules of the solvent mixtures at different ion-pair separations.
A rationale for the absence of the CIP in these mixtures
has been obtained by analyzing the solvent structures that
develop around the ion pair in these solvents. We observed
that in all these solvent mixtures, the water molecules remain
strongly bound to the ion pair at the SSIP minima, and one
molecule of water tends to be close to the ion pair along the
interionic axis. In Fig. 4, we present a typical solvent configuration around the Na⫹ and Cl⫺ ions for x DMSO⫽0.91 at
r Na⫹ – Cl⫺ ⫽5.0 Å. It is noticed that a water molecule is close
to the ion pair at a distance of about 3.0 Å from both the
ions. The strong bonding of the water molecules to form the
closest solvation shell even at this lowest water containing
mixture (x DMSO⫽0.91) dictates the formation of the SSIP
minima at a large ion–ion distance of r Na⫹ – Cl⫺ near 5.0 Å.
The contour plots of the O 共water兲 density profiles around
the Na⫹ and Cl⫺ ions described in our earlier work42 at
mixture compositions of x DMSO⫽0.21 and 0.35 also support
FIG. 4. A typical neighborhood of the Na⫹ – Cl⫺ ion pair in a water–DMSO
mixture of composition x DMSO ⫽0.91 for r Na⫹ – Cl⫺ ⫽5.0 Å. Notice the close
approach of a water molecule.
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J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
NaCl solutions in water-dimethyl sulphoxide mixtures
7531
the dominance of water molecules to form the SSIP minima
at an ion-ion distance of 5.0 Å in all the mixed solvents
considered here. The influence of DMSO to force the ion
pair to form a CIP is further reduced because of the strong
intersolvent water–DMSO hydrogen bond which is much
stronger than the water–water hydrogen bond.8 At the other
two compositions of x DMSO⫽0.10 and 0.48 we have noticed
a similar trend. This description will be further quantified in
a later section wherein we present the radial distribution
functions and the running coordination numbers between the
ions and the solvent sites. We shall now test these PMFs
using the dynamical trajectories of the ion pair.
C. Dynamical trajectories of the Naⴙ – Clⴚ ION PAIR
A second confirmation of the nature of the potentials of
mean force for the ion pair has been obtained by studying the
dynamical trajectories of the ion pair initiated at various ion–
ion separations. This is done by performing long MD simulations on the system by releasing the constraint on the ion
pair at time t⫽0, and then calculating the ion–ion separation
vector at each time step. For each of the mixture compositions we have selected several interionic separations 共in the
range of 2.6–9.0 Å兲 as the starting ion-ion distance and followed each of the ion-pair trajectories for short times 共5 ps兲
as well as for long times 共20 ps兲.
The trajectories starting with r Na⫹ – Cl⫺ of 2.6 to 5.0 Å for
all compositions settle at the broad SSIP minimum at 5.0
⫾0.8 Å in a very short time 共within 1 ps兲 and after this initial
period, the interionic distance remains near 5.0⫾0.8 Å for
well over 20 ps. Since these trajectories look similar beyond
2 ps and the average interionic distance does not change very
much beyond 2 ps, we show only a few distinctive trajectories initiated at short interionic separations in Fig. 5. One of
them is for the mixed solvent with x DMSO⫽0.10 and initiated
at r Na⫹ – Cl⫺ ⫽3.2 Å shown in Fig. 5共a兲. The ion–pair quickly
settles at a distance of 4.6⫾0.5 Å. The trajectories for compositions with x DMSO ⫽0.21, 0.35 and 0.48 initiated at a distance in the range r Na⫹ – Cl⫺ ⫽2.6– 5.0 Å also settle at an average value of r Na⫹ – Cl⫺ ⫽5.0⫾0.5 Å. The trajectories for
x DMSO⫽0.91 are shown in Figs. 5共b兲 and 5共c兲. The trajectory
initiated at r Na⫹ – Cl⫺ ⫽2.6 Å 关Fig. 5共b兲兴 settles at r Na⫹ – Cl⫺
⫽4.2⫾0.7 Å and the trajectory initiated at r Na⫹ – Cl⫺ ⫽3.4 Å
关Fig. 5共c兲兴 settles at r Na⫹ – Cl⫺ ⫽4.6⫾0.7 Å. Although an ion–
ion separation near 2.6 Å is expected to be a reasonably
sharp and long lived CIP configuration of the Na⫹ – Cl⫺ ion
pair 共which actually is, in the presence of pure DMSO兲,7 the
configuration is not stable in any of these mixtures and the
residence time of the ion pair in this region of the potential
well is much less (⬍1 ps). We have tested this finding with
several equilibrated solvent configurations at this distance.
The dynamical trajectories of Fig. 5 indicate that an ion pair
in these mixtures is a broad SSIP at a distance range of
4.2–5.8 Å.
Figure 6 displays the long time 共20 ps兲 trajectories of the
Na⫹ – Cl⫺ ion pair which are initiated at longer ion–ion
separations of ⭓7.0 Å, in the presence of the five solvent
mixtures. The diffusive nature of the ion pair trajectory in the
presence of the mixture with x DMSO⫽0.10 is clearly seen in
FIG. 5. Representative short time 共5 ps兲 trajectories of the Na⫹ – Cl⫺ ion
pair in water–DMSO mixed solvents of different compositions. 共a兲 x DMSO
⫽0.10 with starting r Na⫹ – Cl⫺ ⫽3.2 Å 共b兲 x DMSO ⫽0.91 with starting
r Na⫹ – Cl⫺ ⫽2.6 Å 共c兲 x DMSO ⫽0.91 with starting r Na⫹ – Cl⫺ ⫽3.4 Å.
Fig. 6共a兲. The ion pair settles at the SSIP minimum near 5.0
Å. The trajectory in Fig. 6共b兲 indicates that the ion pair in the
presence of the mixture with x DMSO⫽0.21 spends a very
long time at the less stable second SSIP minimum at
r Na⫹ – Cl⫺ ⫽7.0 Å. These results have been reconfirmed by 50
ps runs. The ion trajectories starting at shorter distances, viz.,
r Na⫹ – Cl⫺ ⫽2.6, 3.2, 4.8, and 5.4 Å 共not shown in the figures兲
also settle around the SSIP distance of 5.0 Å; but the trajectories starting at r Na⫹ – Cl⫺ ⫽7.0 Å or at a larger interionic
separation settle at around 7.0 Å, the location of the second
minimum in the ion–ion PMF in a mixture with x DMSO
⫽0.21. All trajectories starting at r Na⫹ – Cl⫺ ⫽6.6 Å for this
mixture have a finite nonzero probability of crossing to the
either side of this ⬃8 k BT barrier 共from the minimum on the
left兲. We have already reported the computation of the transmission coefficients 共whose value is 0.26⫾0.10) across this
PMF barrier.42 The solvation structures of the ion pair in the
presence of this mixed solvent with x DMSO⫽0.21 have also
been reported42 in this mixture composition. The ion pair at
x DMSO⫽0.35 settles at the SSIP minimum near 5.0⫾0.6 Å
关Fig. 6共c兲兴 within 5 ps and tends to remain oscillatory between r Na⫹ – Cl⫺ ⫽4.5 Å and 5.3 Å. The solvent mixture with
x DMSO⫽0.48 causes the ion pair to settle at the SSIP minimum at r Na⫹ – Cl⫺ ⫽5.0 Å within about 8 ps 关Fig. 6共d兲兴. In this
composition, the PMF is quite broad at the minimum and
covers a range of 4.5–6.0 Å. Thus the ion pair shows the
tendency to remain oscillatory between 5.0 and 6.0 Å. The
trajectory starting at 7.0 Å in the presence of the mixed solvent with x DMSO⫽0.91 settles slowly at the stable SSIP minimum at around 4.4⫾0.7 Å 关Fig. 6共e兲兴. Because of the presence of a flat deeply negative region in the PMF in the
presence of this solvent mixture 共with x DMSO⫽0.91) at a
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7532
J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
A. K. Das and B. L. Tembe
g i␣共 r 兲 ⫽
V
N ␣共 r 兲
•
,
N ␣ 4 ␲ r 2 ⌬r
共9兲
where N ␣ is the number of the ␣ th solvent site in volume V
of the simulation shell and N ␣ (r) is the number of such sites
in the spherical shell (r,r⫹⌬r) at a distance r from the ion
i. The running coordination number n i ␣ (r) is the integrated
intensity of the g i ␣ (r) function up to the distance r
n i ␣ 共 r 兲 ⫽4 ␲␳ ␣
FIG. 6. Representative long time 共20 ps兲 trajectories of the Na⫹ – Cl⫺ ion
pair in water–DMSO mixed solvents of different compositions. The starting
ion-ion separation in each case is ⭓7.0 Å. The mole fraction of DMSO x D
is shown on the graphs.
shorter ion-ion separation of near 4.5 Å, the long time trajectories approach shorter interionic separations. These trajectories in Figs. 5 and 6 also show the presence of a broad
SSIP minimum in the distance range of 4.2–5.8 Å in all five
compositions and a second SSIP minimum at r Na⫹ – Cl⫺
⫽7.0 Å for the composition with x DMSO⫽0.21. As the mole
fraction of DMSO is increased up to 0.91, the SSIP minimum appears to become deeper and broader and shifts to a
smaller r Na⫹ – Cl⫺ distance confirming the pattern seen in Fig.
3. The well depth also appears to be the least when x DMSO
⫽0.35. As we increase x DMSO beyond 0.91 to unity we expect the CIP to eventually appear 共the PMF is already large
and negative near 3.0 Å for x DMSO⫽0.91), but simulations
with very few molecules of one component, especially a hydrogen bonding solvent such as water, are extremely time
consuming.
D. The ion-solvent radial distribution functions
In order to analyze the local solvation structures around
the Na⫹ and Cl⫺ ions in the five mixed solvents, we have
computed the ion-solvent pair distribution functions, g i ␣ (r),
and the running coordination numbers n i ␣ (r). The ionsolvent pair distribution function g i ␣ (r) is the ratio of the
local density of the solvent site ␣ at a distance r from the ion
i and the bulk density ( ␳ ␣ ⫽N ␣ /V)
冕
r
0
g i ␣ 共 s 兲 s 2 ds.
共10兲
The ion-solvent radial distribution functions have been calculated for all the solvent mixtures. For the sake of comparison, the interionic separation has been chosen to be
r Na⫹ – Cl⫺ ⫽5.0– 5.4 Å for all the five mixed solvents. Figure 7
presents the ion-solvent radial distribution functions 共RDFs兲
for the Na⫹ ion and Fig. 8 presents the ion-solvent RDFs for
the Cl⫺ ion. In both of these figures, the ion-solvent RDFs
have been shown by shifting them vertically with respect to
x DMSO .
From the plots in Fig. 7 we see that the
Na⫹ – S 共DMSO兲, Na⫹ – O 共DMSO兲, Na⫹ – O 共water兲 and
Na⫹ – H 共water兲 RDFs do not exhibit any change in the position of the peak maxima, but the intensities of the peaks
change with the change in the solvent composition. The
Na⫹ – CH3 共DMSO兲 pair shows most pronounced variations
in the peak position and peak height with the change in the
composition. However, these variations are less intense 共with
intensities less than four units and these plots are not presented here兲. We observe that the lowest DMSO containing
mixture (x DMSO⫽0.10) has the maximum height for the
Na⫹ – S 共DMSO兲, Na⫹ – O 共DMSO兲, Na⫹ – CH3 共DMSO兲
pairs. Once the solvation shell forms, it does not readily
allow the other DMSO molecules to come closer to the Na⫹
ion. With the increase in the DMSO mole fraction the bulk
density increases, but the local DMSO density around the
Na⫹ ion does not increase correspondingly. Hence the peak
height decreases. Turning to the solvation shell formed by
the water molecules around the Na⫹ ion, we find that the
lowest water containing mixture (x DMSO⫽0.91) has the
maximum height for the Na⫹ – O 共water兲 and Na⫹ – H 共water兲 pairs. The heights of the RDF maxima for these pairs
decrease as the mole fraction of water increases. The order of
increasing water content in the solvent mixtures is x DMSO
⫽0.91⬍0.48⬍0.35⬍0.21⬍0.10. Like before, with the increase in the water mole fraction the bulk water density increases, but the local water density around the Na⫹ ion does
not increase proportionately. This makes the peak height decrease with increasing water content in the mixtures. It is
thus evident that the solvation shell around the Na⫹ ion consists of both water and DMSO molecules and the shell structure does not change in proportion to the changes in the
solvent composition.
We shall now discuss the ion-solvent RDFs for the Cl⫺
ion in the presence of the five mixed solvents. These are
displayed in the plots of Fig. 8. We see that the
Cl⫺ – S 共DMSO兲 and Cl⫺ – CH3 共DMSO兲 pairs do not exhibit
the formation of well defined DMSO coordination shells.
This indicates the diffusiveness of the DMSO solvation shell
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J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
NaCl solutions in water-dimethyl sulphoxide mixtures
7533
FIG. 7. The ion-solvent radial distribution functions for the Na⫹ ion in the presence of the mixed water–DMSO solvents with x DMSO⫽0.10, 0.21, 0.35, 0.48
and 0.91. For clarity, the functions for successive mole fractions 共which are shown on the curves兲 are shifted vertically upwards.
around the Cl⫺ ion. On the contrary, the Cl⫺ – O 共water兲 and
Cl⫺ – H 共water兲 pairs show the formation of wellcharacterized water solvation shells around this ion. The
Cl⫺ – H 共water兲 pair shows the formation of a second water
shell which changes with the change in the solvent composition. While the peak positions of the Cl⫺ – O 共water兲 and
Cl⫺ – H 共water兲 pairs do not change with mixture composition, their intensities change significantly. As has been observed in the case of Na⫹ ion, the intensity of the RDF
maximum is highest in the case of lowest water containing
mixture (x DMSO⫽0.91), and the intensity decreases when
mole fraction of water increases in the solvent. The explanation for this is similar to that given for the Na⫹ ion. Water
molecules form the solvation shell around the Cl⫺ ion in the
presence of all five solvent mixtures considered here, and
this solvation shell does not undergo significant changes
when the composition is altered. The bulk density of water in
the mixed solvents increases from x DMSO⫽0.91⬍0.48
⬍0.35⬍0.21⬍0.10, but the local density of water around
the ion does not change appreciably because of the presence
of DMSO molecules, which form strongly hydrogen bonded
networks in the mixtures.9,10
Figure 9 presents the running coordination numbers,
n i ␣ (r) for the Na⫹ ion and Fig. 10 presents the n i ␣ (r) for the
Cl⫺ ion. In both of these figures the n i ␣ (r) functions are
stacked vertically with respect to x DMSO . From the
Na⫹ – S 共DMSO兲 and Na⫹ – O 共DMSO兲 n i ␣ (r)s we see the
presence of only one DMSO molecule near the Na⫹ ion at
DMSO mole fraction x DMSO⫽0.10, which rises to two
DMSO molecules at x DMSO⫽0.48 and at the highest DMSO
mole fraction of x DMSO ⫽0.91 this number is about 2.5.
Similarly the Na⫹ – O 共water兲 and Na⫹ – H 共water兲 n i ␣ (r)s
FIG. 8. The ion-solvent radial distribution functions for the Cl⫺ ion in the presence of the mixed water–DMSO solvents with x DMSO⫽0.10, 0.21, 0.35, 0.48
and 0.91. For clarity, the functions for successive mole fractions 共which are shown on the curves兲 are shifted vertically upwards.
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7534
J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
A. K. Das and B. L. Tembe
FIG. 9. The running coordination numbers around the Na⫹ ion in the presence of the mixed water–DMSO solvents with x DMSO⫽0.10, 0.21, 0.35, 0.48 and
0.91. For clarity, the functions for successive mole fractions 共which are shown on the curves兲 are shifted vertically upwards.
show the presence of four water molecules at x DMSO⫽0.10
which decreases to three water molecules at x DMSO⫽0.48
and to two water molecules at x DMSO ⫽0.91. We observe a
concomitant increase in the magnitude of the n i ␣ (r) functions with the increase in the component mole fraction, since
these n i ␣ (r)s are always weighted with the bulk number density of the solvent site ␣ 关Eq. 共10兲兴. These observations suggest that the Na⫹ ion solvation shell is composed of five
molecules 共comprised of both DMSO and water molecules兲
in all the five solvent mixtures.
The running coordination numbers for the Cl⫺ ion have
been presented in Fig. 10. In the n i ␣ (r) plots of
Cl⫺ – S 共DMSO兲 and Cl⫺ – CH3 共DMSO兲 it is seen that the
closest DMSO coordination shell around the Cl⫺ ion is
formed by the CH3 groups, although the shell is not very
well characterized. We find that only at x DMSO⫽0.91, the
n i ␣ (r) for the Cl⫺ – CH3 pair shows a significant bending
indicating the presence of 4–5 DMSO molecules in the solvation shell. At the lower mole fractions of DMSO, this
number could not be ascertained precisely since the solvation
shell is diffusive 关absence of the horizontal portions in the
n i ␣ (r) plots兴. The n i ␣ (r)s for the Cl⫺ – O 共water兲 and
Cl⫺ – H 共water兲 pairs indicate the presence of 5–6 water molecules at x DMSO⫽0.10, about four water molecules at
x DMSO⫽0.48 and 2–3 water molecules at x DMSO⫽0.91.
Hence the Cl⫺ ion solvation shell in the five solvent mixtures
FIG. 10. The running coordination numbers around the Cl⫺ ion in the presence of the mixed water–DMSO solvents with x DMSO⫽0.10, 0.21, 0.35, 0.48 and
0.91. For clarity, the functions for successive mole fractions 共which are shown on the curves兲 are shifted vertically upwards.
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J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
NaCl solutions in water-dimethyl sulphoxide mixtures
7535
is composed of 7–8 molecules 共comprising of both DMSO
and water molecules兲.
E. Preferential solvation of the Naⴙ – Clⴚ ion pair
In order to examine the solvent preferences of the
Na⫹ – Cl⫺ ion pair in the presence of the five mixed water–
DMSO solvents, we have calculated the local mole fractions
loc
loc
of DMSO and x W
of water in the ion solvation shells as
xD
a function of the bulk solvent composition. These have been
calculated using the formula12
loc
xD
共 xD兲⫽
n iD 共 x D 兲
,
n iD 共 x D 兲 ⫹n iW 共 x D 兲
共11兲
loc
xW
共 xW兲⫽
n iW 共 x W 兲
,
n iW 共 x W 兲 ⫹n iD 共 x W 兲
共12兲
where n iD (x D ) is the coordination number of the DMSO
solvation shell of the ith ion and n iW (x D ) is the coordination
number of the water solvation shell of the ith ion at the
solvent composition x D . The DMSO mole fraction is
x D (⬅x DMSO) and the water mole fraction is x W (⬅x water).
Equations 共11兲 and 共12兲 provide an opportunity to compare
the results with nuclear magnetic resonance 共NMR兲 data as
has been done in the case of the solvation of Na⫹ – Cl⫺ in the
presence of water formamide mixtures.12 Since the S atom of
DMSO and the O atom of water are located near the center
of mass of the corresponding solvent molecule, the coordination numbers n iD and the n iW are evaluated by integrating
the g iS(DMSO) (r) and g iO(water) (r) functions up to the first
minimum (r min). For the Na⫹ – S 共DMSO兲, Na⫹ O 共water兲,
Cl⫺ – S 共DMSO兲 and Cl⫺ – O 共water兲 pairs the r min values are
4.2, 2.8, 6.4, and 4.0 Å, respectively. Figure 11 shows the
loc
loc
and x W
functions for the Na⫹ and the Cl⫺
plots of the x D
loc
loc
ions. From the plots of x D and x W
for the Na⫹ ion we find
⫹
that the Na ion is preferentially solvated by water in the
mixed solvents with DMSO mole fraction x DMSO ⭓ 0.21.
The solvation of the Cl⫺ ion is preferred by DMSO in the
solvent compositions with x DMSO ⫽0.10 and 0.21.
IV. CONCLUSIONS
Constrained MD simulations have been performed on
the Na⫹ – Cl⫺ ion pair in the presence of five selected water–
DMSO mixtures with the mole fraction of DMSO, x DMSO
⫽0.10, 0.21, 0.35, 0.48 and 0.91. The derived potentials of
mean force for the ion pair do not show the existence of a
stable contact ion pair in any of the mixtures. The presence
of the pervasive solvent separated ion pairs in all these compositions has been demonstrated from the nature of the
PMFs. The derived PMFs have been tested by doing auxiliary MD simulations on the ion pair and generating the dynamical ion-ion trajectories of the pair. This was done by
releasing the constraint on the ion pair at time t⫽0, and
trailing the ions for a considerably long time (⬎20 ps).
Interestingly, the Na⫹ – Cl⫺ ion pair in pure water is seen to
exist both as a CIP and as a SSIP, with the SSIP configuration a little more stable than the CIP.5 The ion pair in pure
loc
FIG. 11. The local mole fractions x Dloc of DMSO and x W
of water in the Na⫹
⫺
and Cl ion solvation shells as functions of solvent composition (x D or x W ).
DMSO also exists in both the configurations, but the CIP
configuration in DMSO is much more stable than the SSIP
configuration.7
The solvent composition with x DMSO⫽0.10 has shown a
single well-defined SSIP minimum at r Na⫹ – Cl⫺ ⫽4.6 Å. The
mixture with x DMSO⫽0.21 shows two well-defined SSIP
minima at r Na⫹ – Cl⫺ ⫽5.0 and 7.0 Å. These SSIPs are separated by an activation barrier at r Na⫹ – Cl⫺ ⫽6.6 Å. We have
analyzed the solvation of the individual ions at these ion–ion
separations in an earlier paper and also calculated the transmission coefficients across the PMF barrier in this mixture
composition.42 The mixed solvent with x DMSO⫽0.35 exhibits
the presence of only one SSIP at r Na⫹ – Cl⫺ ⫽5.0 Å. The
fourth solvent mixture with x DMSO⫽0.48 shows the presence
of a SSIP well covering the range of r Na⫹ – Cl⫺ ⫽4.4– 5.1 Å.
The composition with higher DMSO content (x DMSO
⫽0.91) shows the presence an SSIP at r Na⫹ – Cl⫺ ⫽4.4 Å, but
the PMF has become significantly negative near r Na⫹ – Cl⫺
⫽3.0 Å.
The ion-solvent radial distribution functions for the
Na⫹ – Cl⫺ ion pair in the presence of the five mixed water–
DMSO solvents emphasize the formation of solvation shells
around each ion comprising of molecules of both the components of the solvent mixture. In all the five mixtures the
local solvation shells around the ions are strong and do not
show any changes in the RDF peak positions with the change
in the mixture composition. With respect to the change in
intensities of the RDF peaks, the lowest DMSO containing
mixture (x DMSO⫽0.10) has the maximum height for the
Na⫹ – S 共DMSO兲, Na⫹ – O 共DMSO兲 and Na⫹ – CH3 共DMSO兲
pairs. Similarly, the lowest water containing mixture
(x DMSO⫽0.91) has the maximum height for the Na⫹ –O 共water兲 and Na⫹ – H 共water兲 pairs. These are attributed to the fact
that the local density of the solvent site around the ion
changes very slowly in comparison with the bulk density of
the solvent. Similar arguments hold good for the decrease in
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7536
J. Chem. Phys., Vol. 111, No. 16, 22 October 1999
the peak heights in the Cl⫺ –O 共water兲 and Cl⫺ –H 共water兲
RDFs with increasing water content. The RDFs of the
Cl⫺ – S 共DMSO兲 and Cl⫺ – CH3 共DMSO兲 pairs do not show
the formation of well-defined DMSO coordination shell
around this ion.
The plots of the running coordination numbers show that
the Na⫹ ion has a total of five solvent molecules and the Cl⫺
ion has a total of 7–8 solvent molecules in the respective
solvation shells. The numbers of each component solvent
molecules vary as the solvent composition changes. For example, at x DMSO⫽0.10, one DMSO and four water molecules
constitute the Na⫹ ion solvation shell. At x DMSO⫽0.91, three
DMSO and two water molecules solvate the Na⫹ ion. Similarly, at x DMSO⫽0.10, the solvation shell of the Cl⫺ ion has
one DMSO and 5–6 water molecules. At x DMSO⫽0.91, this
ion is solvated by four DMSO and 2–3 water molecules.
In order to determine the solvent preferences of the Na⫹
and Cl⫺ ions in the mixed solvents, we have calculated the
local mole fractions around each ion. It is found that the Na⫹
ion prefers to be solvated by water in the mixed solvents
with DMSO mole fraction x DMSO⭓0.21. The Cl⫺ ion is
preferred by the DMSO component in the mixtures with
x DMSO ⫽0.10 and 0.21.
It would be of great interest to investigate the translational diffusion of the Na⫹ and Cl⫺ ions in the presence of
these strongly nonideal solvent mixtures. The influence of
the solvation shell 共where both the component solvent molecules are present兲 on the individual ionic mobilities is also
worth investigating. Such studies in the presence of nearly
ideal solvent mixtures 共like water–formamide兲12 are being
investigated by other groups. The dependence of the results
on the choice of the models used for the site–site potentials
also needs to be assessed in detail.
ACKNOWLEDGMENTS
We gratefully acknowledge the computational support
provided by the Department of Science and Technology,
Government of India, for this work. We also thank the referee for a critical reading of the manuscript and valuable
suggestions.
1
J. Hubbard and P. Wolynes, in The Chemical Physics of Ion Solvation,
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