Solvation response of polar liquid mixtures: Water-dimethylsulfoxide
Daniel Laria and Munir S. Skaf
Citation: The Journal of Chemical Physics 111, 300 (1999); doi: 10.1063/1.479290
View online: http://dx.doi.org/10.1063/1.479290
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 111, NUMBER 1
1 JULY 1999
Solvation response of polar liquid mixtures: Water-dimethylsulfoxide
Daniel Laria
Unidad Actividad Quı́mica, Comisión Nacional de Energia Atómica, Av. del Libertador 8250, (1429)
Capital Federal, Argentina and Departamento de Quı́mica Inorgánica, Analı́tica y Quı́mica Fı́sica
and INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón II,
(1428) Capital Federal, Argentina
Munir S. Skaf
Instituto de Quı́mica, Universidade Estadual de Campinas, Cx. P. 6154, Campinas-SP, 13083-970, Brazil
~Received 25 February 1999; accepted 7 April 1999!
The solvation dynamics following the instantaneous creation of a positive or negative electronic
charge in a previously neutral solute immersed in different water-dimethyl sulfoxide ~DMSO!
mixtures, spanning the entire composition range, is analyzed by molecular dynamics simulations.
The solvation responses are strongly dependent on the sign of the solute charge, being considerably
faster in the presence of cations for all mixtures considered. In terms of the composition
dependence, the mixtures’ solvation response to the creation of the anion departs substantially from
the pure solvents’, whereas for the cation, the mixtures’ responses are close to those exhibited by
pure DMSO. In the case of anions, the mixture overall solvation time, defined as the time integral
of the nonequilibrium response, can be as large as ten times the solvation time in pure DMSO, the
slowest of the two cosolvents. The DMSO contribution to the mixtures’ solvation response may
present an intriguing negative branch in the rotational-diffusion regime which persists for times
much longer than the time scales typically found in other polar liquids and mixtures. This negative
portion is nearly cancelled by an equally long-lasting positive contribution from water, resulting in
a fast-decaying, total response curve which is typical of many polar liquid environments. This
behavior is rationalized in terms of the time evolution of the first solvation shell around each type
of solute. © 1999 American Institute of Physics. @S0021-9606~99!51325-1#
I. INTRODUCTION
shifts in polar/nonpolar mixtures. Time-resolved fluorescence experiments have also been performed in polar mixtures containing water/methanol10 and acetonitrile/benzonitrile.11 All experiments show significant modifications in
the characteristic times describing the dynamics as the relative concentrations of the components’ changes.
From the theoretical point of view, Chandra et al.12 have
developed an analytical formalism to describe dynamics of
solvation in binary mixtures of dipolar spheres based on generalized hydrodynamics complemented with the mean
spherical model. An extension of the theoretical treatment
that incorporates a microscopic picture has been proposed
too.13 More recently, Patey and collaborators have performed
molecular dynamics ~MD! simulations14 complemented by a
time-dependent density functional study15 to investigate solvation dynamics in similar mixtures. One of the important
conclusions that can be drawn from these papers is that the
responses of the dipolar mixtures investigated involve an initial step associated with electrostriction followed by a second, much slower process, during which changes in the composition of the first solvation shells take place. Yet, although
these conclusions seem to be fairly general, there are still
some open questions as whether results from their simplified
picture of embedded point dipoles in Lennard-Jones spheres
may be fully valid for real mixtures. It is thus desirable to
elucidate the behavior of the solvation response of different
mixed solvents modeled by a Hamiltonian that incorporates a
higher degree of detail in the description of the geometries
The dynamical characteristics of solvation in simple polar environments is now sufficiently well characterized.1–6 At
a microscopic level, the clearest manifestations of the solvation response are reflected in the gradual modifications that
take place in the solvent density fields in the close vicinity of
a probe following a sudden change in its electronic distribution. The gross features of this relaxation normally involve
well-differentiated temporal regimes: the first one, which accounts for a significant portion of the total response, takes
place on a time scale of the order of a hundred femtoseconds
and involves mostly fast, Gaussian rotations, followed by
small amplitude librations of the individual solvent molecules. Such librational oscillations are much more prominent in hydrogen ~H!-bonding than in nonprotic solvents.7 In
addition, there is a subsequent, somewhat slower, diffusional
regime during which there is a global reorganization of the
spatial arrangement of the solvent around the modified solute
species. The latter changes require typical times of the order
of picoseconds.
The consideration of the solvation responses of polar
mixtures represents the natural extension of the previously
described phenomena. However, despite the wide variety of
simple polar fluids that has been studied, information about
the dynamical response of more complex mixtures is still
somewhat scarce. Hallidy et al.8 and Cichos et al.9 have performed time-resolved spectroscopy to determine the Stokes
0021-9606/99/111(1)/300/10/$15.00
300
© 1999 American Institute of Physics
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
and charge distributions of the molecules beyond the simplified Stockmayer fluid picture. In this context, MD simulations have been reported by Ladanyi and Skaf on the solvation dynamics following a charge exchange between the sites
of a diatomic solute immersed in methanol-water
mixtures.16–18 In particular, it was shown that the formation
of solute–solvent H-bonds may be an important slow step in
the solvation dynamics in these systems and that, depending
on the solute size, the solvation response of the mixture may
present nontrivial trends with composition.
In the present paper we investigate the solvation dynamics in mixtures of water and dimethylsulfoxide ~DMSO!.
These mixtures present several interesting physicochemical
properties due to the strong associative character of the interactions between water and DMSO molecules. A wealth of
experimental data19–27 and several computer simulations25,27,28 indicate that stable water-DMSO hydrogen ~H!bonded aggregates are responsible for these mixtures’ unusual behavior. From the dynamical point of view, both the
translational and rotational motions, as indicated by independent experimental techniques, including NMR22,23 and dielectric relaxation,24 as well as MD simulations,25,27,28 seem
to be strongly coupled and considerably slower than the pure
liquids at compositions between 30% and 50% mole of
DMSO. This behavior is markedly in contrast with that exhibited by other associating mixtures such water–methanol,
water–ammonia, and water–acetone.29 We consider here the
solvation dynamics following the creation of a positive or
negative charge on a previously neutral monoatomic spherical solute immersed in water-DMSO mixtures spanning the
entire composition range. The description of ionic states in
polar mixtures necessarily leads to the consideration of selective or preferential solvation.30,31 Although there is direct
experimental information about NMR chemical shift and ultraviolet ~UV! maximum shifts in solutions containing H2O,
DMSO, and ionic species,32,33 there seems to be no simple
criterion that would allow one to establish a general trend of
a preferential ionic solvation by either solvent. While I2,
1
1
NO2
3 , and Cs are preferentially solvated by DMSO, Li is
preferentially solvated by water. The conclusion that would
emerge from the experimental evidence is that the enhancement or depletion of the local density of a particular solvent
around an ionic solute is the result of a complex interplay
between specific characteristics of the solute–solvent and
solvent–solvent interactions, combined with the particular
composition of the mixture that is being considered. Thus, in
order to gain insight about the underlying mechanisms of the
solvation dynamics, we have performed a detailed analysis
of the time relaxation of different solute–solvent couplings
along with the concomitant evolution of the different solvent
densities that follow the instantaneous ionization of an originally neutral solute. We considered both the generation of
positively and negatively charged solutes in an attempt to
detect fundamental differences, if any, in the solvation dynamics that might be associated with the type of ion created.
In addition, we have also explored the predictive power from
linear response theory.
The rest of the paper is organized as follows: in Sec. II
we provide details of the model and the methodology em-
Solvation dynamics in water-DMSO mixtures
301
ployed. Results from nonequilibrium relaxation simulations
are shown in Sec. III. Section IV includes a microscopical
analysis of the solvation process in different mixtures. Concluding remarks are found in Sec. V.
II. MODEL
The systems under investigation were composed by a
single solute dissolved in different mixtures of water ~W!
and dimethyl sulfoxide @ ~CH3!2SO# . For H2O, we adopted
the three-site SPCE model developed by Berendsen et al.34
The molecule has three interaction sites held at the fixed
distances: d O-H51 and d H-H51.633 Å. DMSO was modeled
by the P2 potential of Luzar and Chandler, which is also a
rigid interaction site model comprising two CH3, S, and
ODMSO units, with the following intramolecular distances25:
d S-C51.80, d S-O51.53, d S-CH351.80, and d CH32CH3
52.704 Å. The angles among the constituents were set to:
u CSO597°248 , u CSO5106°458 . The molecular dipole moments are m H2O52.35 and m DMSO54.48 D.
The solvent potential energy was considered a sum of
pair interactions
V s5
v~ i, j ! ,
(
i, j
~1!
where v (i, j) represents the interaction between the i-th and
j-th molecule,
v~ i, j ! 5
lj
coul
@v ag
~ u rai 2rgj u ! 1 v ag
~ u rai 2rgj u !# ,
(
ag
lj
v ag
~ r ! 54 e ag
coul
v ag
~ r !5
FS D S D G
s ag
r
12
2
s ag
r
~2!
6
,
z az ge 2
.
r
~3!
~4!
In the previous equations, rai denotes the position of the a-th
site in the i-th molecule, i5H2O, and DMSO and e represent
the electron charge. Solute–solvent interactions V is were
also modeled using a standard ~6–12! Lennard-Jones term
plus a Coulombic tail,
V is 5
u ais ~ u ri 2raj u ! ,
(
j, a
with
u ais ~ r ! 54 e a
~5!
FS D S D G
sa
r
12
2
sa
r
6
1
z iz ae 2
;
r
~6!
ri and z i identify the position and charge of the solute, respectively. Three different types of solute, hereafter referred
to as Cl, Cl1, and Cl2, were investigated with z i 50, 11,
21, respectively. For all cases, the solute–solvent length and
energy parameters, s a and e a , were identical and corresponded to those for the chloride ion.35 Full details of the
different intermolecular potential parameters are given in
Table I.
We investigated three H2O-DMSO mixtures at T
5298 K with DMSO molar fractions x DMSO50.25, 0.5, and
0.75. In addition, we also performed a few test runs for
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
D. Laria and M. S. Skaf
TABLE I. Parameters for the potentials. ~The usual geometrical and arithmetic means were used to determine the s and e parameters for the cross
interactions.!
Site
s ~Å!
e /k B ~K!
Charge ~e!
OW
H
S
ODMSO
CH3
Cl6
3.17
0.00
3.40
2.80
3.80
4.33
78.48
0.000
120.0
35.99
147.9
53.31
20.8476
0.4238
0.139
20.459
0.160
61.0
x DMSO50.1 and for the pure solvents as well. The simulated
systems contained approximately 220 molecules and the densities were set to the experimental values at 1 atm.19 Two
sets of simulations were performed: The first one consisted
of typically 1–2 ns canonical runs36 using a time step of 1 fs.
The second one corresponded to nonequilibrium relaxations
whose initial conditions were taken from the previous canonical runs, separated by 5 ps intervals to provide sufficient
statistical independence between them. For asymmetric mixtures, special care was taken in performing simulation experiments during sufficiently long periods to guarantee stable
equilibrium values. At t50, the Nosé thermostat was
switched off, the electric charge of the solute was set to 61,
and all velocities were randomized according to the Boltzmann distribution. From these initial conditions, we monitored different parameters relevant to the solvation relaxation
of the different environments during typical time periods of 3
ps. The MD integration was performed using the Verlet
algorithm.37 Constraints due to intramolecular distances in
the solvents were treated with the SHAKE algorithm.38 The
long-range Coulomb forces were handled using Ewald sums
techniques.37 For systems electrically non-neutral, the presence of a uniform neutralizing background was assumed.
III. NONEQUILIBRIUM RELAXATIONS
The starting point of our analysis will be the investigation of the nonequilibrium response of different environments to the instantaneous generation of positive and negative unit charges in an initially electrically neutral solute.
The model reactions we are interested in can be described
schematically as follows:
Cl→Cl1,
Cl→Cl2.
~7!
The usual route to characterize the dynamics of the surrounding that follows a sudden change in the electrical state of a
solute is through the total nonequilibrium response function
S~ t !5
^ V c ~ t ! 2V c ~ ` ! & ne
,
^ V c ~ 0 ! 2V c ~ ` ! & ne
~8!
where V c (t) represents the electrical potential at the solute
site at time t and ^ ... & ne denotes a sampling over a distribution of nonequilibrium initial conditions.39
Results for the overall response for cationic and anionic
solute species are shown in Fig. 1, where we present curves
for mixtures and for the pure solvents as well. From a quali-
FIG. 1. Nonequilibrium solvation response for different water-DMSO mixtures; the top and bottom panels correspond to Cl→Cl2 and Cl→Cl1 processes, respectively. x DMSO50.0 ~solid lines!; x DMSO50.25 ~dotted lines!;
x DMSO50.5 ~dot-dashed lines!; x DMSO50.75 ~short-dashed lines!; x DMSO
51.0 ~long-dashed lines!.
tative point of view, the behaviors of S(t) for the pure solvents H2O and DMSO are those typically found in most
liquid polar environments: a markedly dual behavior characterized by an initial fast decay that accounts for a large fraction of the total response, followed by a much slower branch
at large t, normally ascribed to diffusional motion. Yet, the
responses of H2O and DMSO are not identical and present
distinctive features worth mentioning. The two most evident
are: ~i! the overall nonequilibrium response of DMSO looks
somewhat slower than that of water and ~ii! the absence of
any high-frequency component in the DMSO response at
early stages. In the water response, these oscillations are the
reflection of small amplitude, librational motions that, due to
the relative small magnitude of the water principal moments
of inertia, occur in the time scale of the order of a few tens of
femtoseconds. Given the much larger magnitude of any of
the DMSO moments of inertia, it is not surprising that these
oscillations are not prominent in its response. Still, note that
this oscillatory portion of the water relaxation for the case of
cations represents a larger fraction of the total response ~almost 80%! and persists for periods of '300 fs, while for
anions, the fraction of the relaxation accomplished in the
initial portion is somewhat smaller, '55%, and lasts for a
shorter period of about 100 fs. A possible explanation for
these differences could be found in the characteristics of the
anion–solvent coupling—dominated basically by hydrogen
bonds—whose strength and strong directionality might induce a quicker damping of the initial oscillatory motions.
Considering now the case of mixtures, the characteristics
of the responses to anionic and cationic species are well differentiated. For negatively charged solutes, the overall solvation responses of all mixtures are much slower than those of
the pure solvents. A reasonable estimate for the characteristic
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Solvation dynamics in water-DMSO mixtures
303
TABLE II. Solvation parameters for H2O-DMSO mixtures.
t s ~ps!
x DMSO
Cl2
1.00
0.75
0.50
0.25
0.00
0.33
3.3
3.1
1.2
0.17
Cl1
t H2O ~ps!
Cl2
Cl2
0.50
0.56
0.35
0.75
0.11
27.0
11.0
1.9
0.17
118.9
159.7
189.5
211.3
237.9
times involved in the relaxation can normally be obtained
from t s , the overall solvation response time defined as
t s5
E
`
0
~9!
S ~ t ! dt.
Results for t s are displayed in Table II. Interestingly, for
anions, t s presents a nonmonotonic behavior and attains
maximum values for DMSO concentrated solutions. In passing, we also remark that the addition of very small proportions of DMSO to pure water also generates important
changes in overall response: we have found that the response
of solutions with only x DMSO50.1 is more than three times
slower than that of pure water. The composition dependence
of the mixtures’ responses to the generation of a positive ion
shown in the bottom panel of Fig. 1 is not so marked, and
there is a clear distinction between the fast decay of pure
water and the rest of the environments, which in all cases
present a behavior much more comparable to that of pure
DMSO.
For the case of mixtures, the global response of the solvent can be decomposed into contributions from the individual responses of the components of the mixture, namely
S ~ t ! 5DV WS W1DV DMSOS DMSO ,
~10!
b eV c
DV H2O
Cl1
Cl2
2204.1
2189.4
2171.7
2149.1
2118.3
0.00
0.54
0.77
0.87
1.00
Cl1
DV DMSO
Cl2
Cl1
0.00
0.15
0.42
0.79
1.00
1.00
0.46
0.23
0.13
0.00
1.00
0.85
0.58
0.21
0.00
and present negative relaxation branches with characteristic
times sufficiently long such that, in the scale of the figure,
the curves seem to have reached practically plateau values.
Finally, also note that the initial drop exhibits a nonmonotonic concentration dependence, attaining minimum values
for mixtures close to the equimolar case.
The individual responses to the instantaneous generation
of positive solutes are shown in Fig. 3 and contrast sharply
with the results for anions. The individual responses of water
are in all cases slower than in the pure H2O. However, the
characteristic times exhibit a nonmonotonic dependence with
water concentration. Moreover, the plots of S DMSO(t) show
the usual exponential-like decay, except in the most dilute
solutions where the response exhibits the long time, negative, plateaulike behavior already described for the case of
anions.
The results that we have presented in the previous paragraphs show important qualitative differences and a wide
variety of time scales associated with global and individual
species solvent responses whose rationalization will require a
careful analysis of microscopical details of the dynamics of
solvation in terms of spatial and orientational correlations
that will be presented in the following section. It is important
to stress here that the overall solvation response time of the
where
S i~ t ! 5
^ V ic ~ t ! 2V ic ~ ` ! & ne
.
^ V ic ~ 0 ! 2V ic ~ ` ! & ne
~11!
In the previous equation, V ic (t) represents the contribution to
V c (t) from the i-th component of the mixture (i5W,
DMSO!. Similarly, DV i represents the fractional contribution of the same component to the total solvent–solute coupling gap,
DV i 5
V ic ~ 0 ! 2V ic ~ ` !
V c ~ 0 ! 2V c ~ ` !
.
~12!
Results for equilibrium values of V c and DV i are presented
in Table II.
Let us concentrate first on the individual responses for
anionic response shown in Fig. 2. Two important aspects of
these sets of curves should be remarked on: first, the individual response of water is progressively slower as its concentration decreases; estimates of the time scales involved in
these relaxations computed via t H2O , as shown in Eq. ~9!,
also appear in Table II. For water-diluted solutions this time
is approximately one order of magnitude larger than the global t s . Second, after a sharp initial drop lasting '250 fs, the
DMSO nonequilibrium responses for all mixtures cross zero
FIG. 2. Individual nonequilibrium solvation responses for anionic solutes.
Same labeling as Fig. 1.
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
D. Laria and M. S. Skaf
FIG. 3. Individual nonequilibrium solvation responses for cationic solutes.
Same labeling as Fig. 1.
mixture for both types of solute perturbation does not follow
the typical trend with composition as observed in both the
translational and rotational relaxations, which present
maxima between 30% and 50% DMSO, as mentioned in Sec.
I.
FIG. 4. Solute–solvent radial distribution functions for pure H2O and
DMSO.
IV. MICROSCOPIC ANALYSIS OF SOLVATION
A. Equilibrium structures
Before addressing the study of solvation in different
H2O-DMSO mixtures, and to gain some preliminary insight
about the results for mixtures that will follow, it will be
instructive to briefly present the basic aspects of ionic solvation in pure W and DMSO. Our description of the structural
aspects of solvation will be based on the analysis of different
solute–solvent radial distribution functions g a (r), defined
as,
r ag a~ r ! 5
1
4pr2
(j ^ d ~ u raj 2riu ! & ;
~13!
where r a is the density of the solvent site a. We start by
considering the spatial distributions of the pure solvents
around different solutes shown in Fig. 4. In Fig. 4~c! we
show results for a neutral solute. For water, the analysis is
straightforward: g O(r) and g H(r) present two main peaks
located at practically the same distance r max'4 Å containing
n OW'22 oxygen atoms and practically twice the number of
hydrogens, n H'52. These structural characteristics are the
typical ones found in aqueous solvation of noble gas like
particles40 and are indicative of straddled configurations of
the water molecules surrounding the solute, with their dipoles perpendicular to the radial direction. The solvation
structure of DMSO is characterized by two main peaks for
CH3 and S groups, located at r max54.12 and 5.26 Å, respec-
tively. The profile for g ODMSO(r) is too diffuse to clearly
identify a first solvation shell. The fact that the first peaks of
g CH3(r) and g S(r) contain approximately 12 atoms indicates
that only one methyl group per molecule lies in close contact
with the solute, while the remaining 12 methyl groups are
located approximately 2 Å farther away from the solute and
are accounted for by a much smaller hump in g CH3(r) located between 5.8 and 7.1 Å.
The solvation structures for ionic solutes contrast
sharply with those of neutral species. Results for the most
relevant g a (r) are shown in panels a and b of Fig. 4 for Cl2
and Cl1, respectively. The relevant feature in the Cl2-W
profiles is the presence of main peaks in g H(r) and g OW(r)
located at r max52.25 and 3.3 Å, respectively, representing
the clear fingerprint of about n W'7 water molecules, tightly
bound to the solute via linear hydrogen bonds. For DMSO,
the most prominent solute–solvent spatial correlations correspond to the CH3 groups. The main peak containing roughly
n CH3514 atoms presents a size similar to that of the OW and
is centered at r max'3.9 Å. The solvent structures around cationic species are characterized in both cases by oxygen
peaks. Note the unusually large disparity between the magnitude of the main peak of g ODMSO compared to that of g OW ,
which suggests a much larger degree of structuring from the
part of DMSO around the cationic species.
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Solvation dynamics in water-DMSO mixtures
305
FIG. 5. Solute–solvent radial distribution functions for Cl dissolved in different H2O-DMSO mixtures.
FIG. 6. Selected solute–solvent radial distribution functions for Cl2 dissolved in different H2O-DMSO mixtures.
We now turn to the examination of solvation in mixtures. For a given solute, we have found that the qualitative
characteristics of g a (r) for all mixtures are quite similar.
Profiles of different g a (r) for a neutral solute are shown in
Fig. 5. Note that the three panels exhibit similar profiles. The
main peaks of the water oxygen and hydrogen sites are located at practically the same distance, r max'4 Å. This reveals that the presence of DMSO does not modify substantially the straddled configurations already mentioned. DMSO
spatial correlations around the solute are characterized by
two peaks: The closest to the solute corresponds to the CH3
groups, followed by a much broader peak corresponding to
approximately 9.2 S sites. The distribution of O sites remains
diffuse and featureless.
Similarly to the pure solvent cases, the spatial distributions around ionic species present important modifications
when they are compared to those corresponding to a neutral
solute. Most notably, the g a (r)’s exhibit higher and narrower peaks and the equilibrium positions of their maxima,
r max , shift toward smaller distances. Changes in the equilibrium distribution of water around anionic solutes are perhaps
the most evident ~see Fig. 6!. Note that the magnitude of the
main water peaks raises up monotonically as the DMSO concentration increases, revealing large fluctuations in the local
density away from their average bulk values. Moreover,
from the entries of Table III, one can see that these enhance-
ments become even more prominent the smaller the molar
fraction of W considered. On the other hand, DMSO-Cl2
spatial correlations are basically characterized by a much
more moderate main peak corresponding to CH3 groups with
no important features for S and ODMSO sites. A similar analysis performed for Cl1-solvent correlations ~Fig. 7! shows
that the magnitude of the relevant peaks corresponding to the
oxygen atom of both water and DMSO—OW and ODMSO,
respectively—are much more moderate and of similar size.
One important aspect associated with the distribution of the
oxygen atoms around the Cl1 ion is that this cation seems to
be preferentially surrounded by ODMSO. This is clearly due to
the higher electronegativity of ODMSO compared to OW,
which in turn is also related to the fact that DMSO is a
stronger H-bond acceptor than water.
The different results for solute–solvent spatial correlations that we have just presented show important modifications that take place in the overall solvation structures in
passing between the t50 and t5` scenarios, corresponding
to neutral and ionic solvation, respectively. It is reasonable to
anticipate that the dynamical response of the different environments to the instantaneous ionization of an initially neutral solute species will necessarily involve not only rotational
and translational motions of the individual molecules, but
also important changes in the composition of the local densities in the vicinity of the solute. We have shown that these
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
D. Laria and M. S. Skaf
TABLE III. Parameters for selected solute-site solvent radial distribution
functions.†
Solute
x DMSO
a
r max
a a (r max)
Cl
1.00
CH3
OW
CH3
OW
CH3
OW
CH3
OW
CH3
OW
CH3
OW
CH3
OW
CH3
OW
ODMSO
OW
ODMSO
OW
ODMSO
OW
ODMSO
OW
4.12
4.10
4.26
3.95
4.15
3.97
4.14
3.93
3.86
3.25
4.00
3.27
4.10
3.3
4.14
3.23
3.03
3.30
3.09
3.37
3.12
3.41
3.15
3.42
1.95
1.57
1.97
1.51
2.00
1.64
2.05
1.82
3.66
22.5
2.54
13.9
1.60
7.55
1.25
3.82
14.3
8.45
10.5
7.20
6.48
5.22
2.33
2.57
0.75
0.50
0.25
Cl2
0.00
1.00
0.75
0.50
0.25
Cl1
0.00
1.00
0.75
0.50
0.25
0.00
na
12.0
1.64
10.1
4.68
9.79
10.1
7.44
23.9
13.9
2.91
9.88
4.99
6.93
6.09
4.22
7.25
6.57
'2 †
5.08
'6 †
3.11
'10†
0.91
11.6
†
The profiles do not provide a clear boundary for the first solvation shell.
changes in concentration are far from being minor and they
will require considerable interdiffusion between the different
solvent species driven by the preferential solvation of a given
solute species by a particular solvent. As we shall see
shortly, many of the unusual aspects of the global and individual responses presented in the previous section will find a
reasonable explanation after examining microscopical details
of the time evolution of the local densities along the relaxation process.
B. Nonequilibrium solute–solvent spatial correlations
The first aspect that we will try to elucidate in this section is why the global and individual responses of the water
and DMSO that we have presented in previous sections are
qualitatively so different. We have seen that, depending on
the specific concentration and solute considered, the response of the different environments may exhibit time scales
with monotonic and nonmonotonic concentration dependence and individual solvent contributions exhibiting positive or negative long time relaxation branches. To start our
analysis, it will be convenient to define a new parameter,
N i (t), representing the population of a given solvent site i, at
time t contained within a spherical volume around the solute.
By fixing the volume, we tried to avoid problems related to
the gradual shrinkage and shift of the first solvation shells as
the relaxation evolves. For the sake of the present discussion,
the exact size of this volume is unimportant, provided it is
chosen sufficiently close to the solute to monitor changes in
the local concentration and, at the same time, contains a
meaningful number of solvent sites. Here, we arbitrarily
fixed the radii close to the position of the first minimum of
the corresponding g a (r) for ionic solutes.
In Fig. 8 we present results for the relaxations of the
FIG. 7. Selected solute–solvent radial distribution functions for Cl1 dissolved in different H2O-DMSO mixtures.
water population following the creation of an anionic solute
as they are reflected by the normalized nonequilibrium responses S Na (t), defined as
S Na ~ t ! 5
^ N a ~ t ! 2N a ~ ` ! & ne
,
^ N a ~ 0 ! 2N a ~ ` ! & ne
~14!
with a 5OW. In the same figure, we have also included results of S W(t) @Eq. ~1!#. For all mixtures, the similarities
between the decay rates of the population and solvation responses provide a clear indication of the diffusional character
of the long time portion of the water solvation response. The
slow long time tail of S W(t) reflects the gradual approach of
water molecules generating the ionic first solvation shell. A
rough estimate of the concentration dependence of this characteristic time can be obtained from the ratio
H O
ts 2 '
l
2
6D
,
~15!
where D represents the intradiffusion coefficient between
DMSO and W and l represents a length scale that should be
proportional to r 21/3
W . Although in this study we did not
attempt to compute D, a typical value for this quantity should
be of similar order to the diffusion coefficient of the individual solvents in an x DMSO50.5 mixture which are both of
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
FIG. 8. Nonequilibrium response for the population of OW atoms for different W-DMSO mixtures ~lines!. Also shown are results of the logarithm of
the nonequilirbium responses S W(t) shifted in the vertical axis by different
amounts to provide an adequate match between the two sets of curves ~lines
and symbols!. Solid lines and circles: x DMSO50.75; dotted line and boxes:
x DMSO50.50; dot-dashed line and triangles: x DMSO50.25; dashed line and
diamonds: x DMSO50.10.
the order of 42231021 Å 2 ps21. 28 Similarly, a crude estimate for l for the equimolar mixture should be '5 Å, yieldH O
ing t s 2 '10 ps, a value which is comparable to that shown
in Table II. We also remark that the characteristics of the
water relaxation following the creation of a positive charge
are similar to those found for a negative one.
The nonequilibrium dynamics of the first solvation shells
of DMSO can be better understood by inspecting the normalized relaxations N a (t)/N a (0) shown in Fig. 9. The profiles
present important qualitative changes when they are compared to their water counterparts. Note that for the Cl→Cl2
process, the sudden switch of the solute–solvent Coulomb
forces leads to an increase in population of CH3 groups and
a slight reduction of the ODMSO one. Moreover, due to this
sudden attraction, the CH3 populations during the first stages
of the relaxation are in all cases greater than their final limiting t5` values ~indicated by the arrows in Fig. 9!. The
picture that emerges from these considerations is that starting
at t50, the methyl groups that are initially in the closest
vicinity of the neutral solute are driven almost immediately
toward the newly created negative ion due to the strong
solute–solvent Coulomb attractive forces. This process involves little molecular reorientation due to the favorable initial arrangement of the CH3 around the neutral solute and
requires a time of about t in'200– 300 fs, after which the
population of CH3 seems to remain practically unchanged.
Of course, this process is followed by a subsequent much
slower relaxation involving the interchange of DMSO by
H2O molecules. This process is characterized by an interdifH O
fusive time scale t dif' t s 2 @ t in which should be roughly
3/2
proportional to r W . Actually, our simulation results indicate
that ^ N CH3(t53 ps) & ne are always larger than ^ N CH3(t
5`) & . Considering that the solvation response in polar environments is dominated by the contribution from the closest
solvation shell,41 the previous trend is accordant to
Solvation dynamics in water-DMSO mixtures
307
FIG. 9. Normalized nonequilibrium relaxation of the population of CH3
~empty symbols! and ODMSO ~solid symbols! for different W-DMSO mixtures. The top and bottom panels correspond to Cl→Cl2 and Cl→Cl1 processes, respectively. Dot-dashed lines and circles: x DMSO50.75; dashed
lines and boxes: x DMSO50.50; solid lines and triangles: x DMSO50.25. The
arrows indicate the limiting N(t5`)/N(0) values for each mixture.
^ V DMSO(t53 ps) & ne. ^ V DMSO(t5`) & . ^ V CH3(t50) & . Consequently, the negative branch in the decay of S DMSO(t)
shown in Fig. 2 is just the manifestation of the nonmonotonic
time dependence of ^ N CH3(t) & ne . A similar analysis performed on the individual responses for the instantaneous
generation of a positive charge showed in all cases a reduction in ^ N CH3(t) & ne and very little variations in
^ N ODMSO(t) & ne . However, while for x DMSO50.75 and 0.50,
^ N ODMSO(t53 ps) & ne have attained values close to their limiting t→` counterparts, for x DMSO50.25, ^ N ODMSO(t
53 ps) & ne is still much larger than ^ N ODMSO(`) & . Here again,
this behavior is consistent with the unique negative relaxation branch shown in the bottom panel of Fig. 3. At this
point, it is important to realize that even at the largest x DMSO
considered in this study, we found no evidence of a negative
relaxation branch in the total solvent response S(t). This fact
comes as a consequence of the disparity in the magnitude of
the individual weights DV i . The entries in Table II show
that the most important individual contributions for Cl2 are
always those of water, regardless of the particular composition of the mixture considered.
We close this section with a brief comparison between
the mixtures’ nonequilibrium solvation responses S(t) and
those obtained from the linear response ~LR! theory, C(t), in
which the system is propagated in the presence of the neutral
solute. LR theory has been shown to describe poorly the
actual solvation response in some associating liquids42 and
mixtures.16 Given the somewhat unusual behavior of the solvation dynamics in the mixtures considered here and the fact
that LR underlies several theoretical descriptions of solvation
dynamics, it is interesting to see the predictive power of the
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308
J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
FIG. 10. Nonequilibrium and equilibrium time correlation functions for the
solvent electrical potential on different solutes. Solid lines: C(t) for Cl;
dotted lines: S(t) for Cl→Cl1 process; dashed lines: S(t) for Cl→Cl2 process.
LR theory for the systems under study. The sets S(t) ~for
both Cl→Cl2 and Cl→Cl1 perturbations! and C(t) solvation
responses are depicted in Fig. 10 for the mixed solvents. The
data show that for the DMSO-rich mixture (x DMSO50.75),
the LR solvation response C(t) ~solid line! is very close to
the nonequilibrium Cl→Cl1S(t) response ~dotted line!,
whereas at x DMSO50.25, C(t) is closer to S(t) for the
Cl→Cl2 process ~dashed line!. These results can be readily
rationalized considering that LR theory works well for pure
water41–43 and DMSO, and the fact that the cation is better
solvated by DMSO while the anion is preferentially solvated
by water, as discussed earlier. Thus at x DMSO50.75, the C(t)
response should approach S(t) following the creation of the
cation because this nonequilibrium response is DMSO-like.
Similarly, at x DMSO50.25, C(t) should approach S(t) for the
anion since the latter is waterlike. For the equimolar mixture,
LR predicts a solvation response intermediate between the
nonequilibirum data for the creation of the two types of ions.
V. CONCLUDING REMARKS
We have presented an MD study of the solvation dynamics in DMSO-water mixtures over the entire composition
range where the solute’s charge redistribution which usually
takes place in typical time-dependent Stokes shift experiments is represented by a simplified model consisting of the
sudden creation of a charge in a previously neutral LennardJones particle resembling a chlorine atom. The nonequilibrium response functions present a complex dependence with
composition and are strikingly distinct for the cation and
anion. For the creation of the cation, the total solvation response stays close to that obtained for pure DMSO for all
mixtures considered. It was shown that this results from the
preferential solvation of this cation by DMSO molecules.
The response following the creation of the anion, however, is
strongly influenced by composition, being roughly ten times
slower than pure DMSO for mixtures with x DMSO'0.75.
The composition dependence of the overall solvation response time for the anion presents no apparent similarity
D. Laria and M. S. Skaf
with the characteristic behavior of the relaxation parameters
of other dynamical processes of DMSO-water mixtures such
as the viscosity,19 self-diffusion coefficients,23,28 NMR rotational relaxation times,22,28 and dielectric relaxation.24 This
suggests that very specific interactions between the solute
and solvent molecules may be dominating the solvation dynamics in this case. Therefore, depending on the solute’s
perturbation, expectations on the overall behavior of the solvation response time with composition based on the dielectric relaxation and other available dynamical properties of
these mixtures would have been completely misleading even
on a qualitative level. This is markedly in contrast with the
situation one has in methanol–water mixtures, where the
trends with composition of the solvation response16 and dielectric relaxation times44 are similar.
An analysis of the total solvation responses in terms of
their separate contributions from water and DMSO shows
that, despite the common, fast-relaxing appearance of the
total responses, the individual contributions from each solvent species may present very slowly relaxing components in
the rotational-diffusion regime. The DMSO contribution
S DMSO(t) may present a long-lasting negative branch which
is compensated for by an equally long-lasting positive contribution from water S W(t). The time evolution of a suitable
response function devised to monitor the population of water
molecules in the vicinity of the solute indicates that the diffusion of water toward the newly created charged solute is an
important contributor to the slow component of S W(t). In
addition, the analysis of the nonequilibrium population of
DMSO molecules around the solute clearly shows that the
observed negative branches in the S DMSO(t) curves are associated with the fact that during some intermediate stages of
the solvation processes there is a population excess ~i.e., with
respect to the corresponding populations at t50 and t5`)
of specific solvent sites. In the case of the anion creation,
which at t5` is preferentially solvated by water, it seems
likely that the diffusion of water molecules toward the immediate vicinity of the charged solute is complicated by the
strongly hydrophilic oxygen atom of DMSO, such that stable
water-DMSO aggregates would have to be broken before
new associations between water molecules and the anion
~e.g., H-bonding! could be formed.
Our final comment is a word of caution about the risks
of making a straightforward interpretation of the time scales
that characterize the response of a given environment based
on a single relaxation time model @c.f. Eq. ~9!#. As we have
seen, S(t) is in reality, at least for the anion case, a weighted
sum of W and DMSO contributions with opposite signs.
Consequently, there may be important dynamical information about the individual relaxations of both solvents that
may remain hidden in the total response due to possible cancellation effects. Moreover, under these circumstances, one
could even start wondering about the convenience of adopting a new additional parameter, other than global coupling
V c (t), that could provide more insight about the characteristics of the dynamics.
Note added in proof. After this paper was submitted we
became aware of a work by Patey and collaborators on solvation dynamics in DMSO-water mixtures, which has some
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
overlap with the present work. We thank Professor Patey for
sending us a copy of their paper prior to publication.
ACKNOWLEDGMENTS
D.L. is a member of Carrera del Investigador Cientı́fico
del CONICET ~Argentina!. Partial economic suport from
Fundación Antorchas of Argentina is very much appreciated.
M.S. gratefully acknowledges financial support from the
Brazilian agencies FAPESP ~Grant No. 95/9508-7! and
CNPq.
P. F. Barbara and W. Jarzeba, Adv. Photochem. 15, 1 ~1990!.
B. Bagchi, Annu. Rev. Phys. Chem. 40, 115 ~1989!.
3
B. Bagchi and A. Chandra, Adv. Chem. Phys. 80, 1 ~1991!.
4
M. Maroncelli, J. Mol. Liq. 57, 57, 1 ~1993!.
5
M. Maroncelli, P. V. Kumar, A. Papazyan, M. L. Horng, S. J. Rosenthal,
and G. R. Fleming, in Ultrafast Reaction Dynamics and Solvent Effects,
edited by Y. Gaudel and P. J. Rossky ~American Institute of Physics, New
York, 1994!, pp. 310–333.
6
R. M. Stratt and M. Maroncelli, J. Phys. Chem. 100, 12981 ~1996!.
7
B. M. Ladanyi and M. S. Skaf, Annu. Rev. Phys. Chem. 44, 335 ~1993!.
8
A. Hallidy and M. R. Topp, J. Phys. Chem. 82, 2415 ~1978!.
9
F. Cichos, A. Willert, U. Rempel, and C. von Borczyskowski, J. Phys.
Chem. A 101, 8179 ~1997!.
10
G. W. Robinson, R. J. Robbins, G. R. Fleming, J. M. Morris, A. E.
Knight, and R. J. Morrison, J. Am. Chem. Soc. 100, 7145 ~1978!.
11
W. Jarzeba, G. C. Walker, A. E. Johnston, and P. F. Barbara, Chem. Phys.
152, 57 ~1991!.
12
A. Chandra and B. Bagchi, J. Chem. Phys. 94, 8367 ~1991!.
13
A. Chandra, Chem. Phys. Lett. 235, 133 ~1995!.
14
T. J. F. Day and G. N. Patey, J. Chem. Phys. 106, 2782 ~1997!
15
A. Yoshimori, T. J. F. Day, and G. N. Patey, J. Chem. Phys. 109, 3222
~1998!.
16
M. S. Skaf and B. M. Ladanyi, J. Phys. Chem. 100, 18258 ~1996!.
17
M. S. Skaf and B. M. Ladanyi, J. Mol. Struct.: THEOCHEM 335, 181
~1995!.
1
2
Solvation dynamics in water-DMSO mixtures
309
M. S. Skaf, I. A. Borin, and B. M. Ladanyi, Mol. Eng. 7, 457 ~1997!.
J. M. G. Cowie and P. M. Toporowski, Can. J. Chem. 39, 2240 ~1961!.
20
G. J. Safford, P. C. Shaffer, P. C. Leung, G. F. Doebbler, G. W. Brady,
and E. F. X. Lyden, J. Chem. Phys. 50, 2140 ~1969!.
21
T. Tokuhiro, L. Menafra, and H. H. Szmant, J. Chem. Phys. 61, 2275
~1974!.
22
B. C. Gordalla and M. D. Zeidler, Mol. Phys. 59, 817 ~1986!; 74, 975
~1991!.
23
K. J. Packer and D. J. Tomlinson, Trans. Faraday Soc. 67, 1302 ~1971!.
24
U. Kaatze, R. Pottel, and M. Schäfer, J. Phys. Chem. 93, 5623 ~1989!.
25
A. Luzar and D. Chandler, J. Chem. Phys. 98, 8160 ~1993!.
26
A. K. Soper and A. Luzar, J. Chem. Phys. 97, 1320 ~1992!.
27
A. K. Soper and A. Luzar, J. Phys. Chem. 100, 1357 ~1996!.
28
I. A. Borin and M. S. Skaf, Chem. Phys. Lett. 296, 125 ~1998!; J. Chem.
Phys. 110, 6214 ~1999!.
29
M. Ferrario, M. Haughney, I. MacDonald, and M. L. Klein, J. Chem.
Phys. 93, 5156 ~1990!.
30
Y. Marcus, Ion Solvation ~Wiley, Chichester, 1985!.
31
P. Suppan, J. Chem. Soc., Faraday Trans. 1 83, 495 ~1987!.
32
T. R. Stengle, Y. C. E. Pan, and C. H. Langford, J. Am. Chem. Soc. 94,
9037 ~1972!.
33
A. K. Covington and J. M. Thain, J. Chem. Soc., Faraday Trans. 1 83,
1879 ~1974!.
34
H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91,
6269 ~1987!
35
T. P. Straatsma and H. J. C. Berendsen, J. Chem. Phys. 89, 5876 ~1988!.
36
S. Nosé, Mol. Phys. 52, 255 ~1984!.
37
M. P. Allen and D. J. Tildesley, Computer Simulations of Liquids ~Clarendon, Oxford, 1987!.
38
J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comput. Phys. 23,
327 ~1977!.
39
See, for example, D. Chandler, Introduction to Modern Statistical Mechanics ~Oxford University Press, New York, 1987!.
40
M. Re and D. Laria, J. Phys. Chem. B 101, 10494 ~1997!.
41
M. Maroncelli and G. R. Fleming, J. Chem. Phys. 89, 5044 ~1988!.
42
T. Fonseca and B. M. Ladanyi, J. Phys. Chem. 95, 2116 ~1991!; J. Mol.
Liq. 60, 1 ~1993!.
43
J. Bader and D. Chandler, Chem. Phys. Lett. 157, 501 ~1989!.
44
B. M. Ladanyi and M. S. Skaf, J. Phys. Chem. 100, 1368 ~1996!.
18
19
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