Structure of aqueous electrolyte solutions near a hydrophobic surface
The structure of aqueous solutions of 1:1 salts (KCl, NaCl, KF, and CsI) near a hydrophobic surface is analysed using the angle-dependent integral equation theory. Water molecules are taken to be hard spheres imbedded with multipolar moments including terms up to octupole order, and hard spherical i...
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| Cite this: | Structure of aqueous electrolyte solutions near a hydrophobic surface / M. Kinoshita // Condensed Matter Physics. — 2007. — Т. 10, № 3(51). — С. 387-396. — Бібліогр.: 28 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1187042025-02-09T21:38:39Z Structure of aqueous electrolyte solutions near a hydrophobic surface Структура водних розчинiв електролiтiв поблизу гiдрофобної поверхнi Kinoshita, M. The structure of aqueous solutions of 1:1 salts (KCl, NaCl, KF, and CsI) near a hydrophobic surface is analysed using the angle-dependent integral equation theory. Water molecules are taken to be hard spheres imbedded with multipolar moments including terms up to octupole order, and hard spherical ions are immersed in this model water. The many-body interactions associated with molecular polarizability are treated at the self-consistent mean field level. The effects of cationic and anionic sizes and salt concentration in the bulk are discussed in detail. As the salt concentration increases, the layer of water molecules next to the surface becomes denser but its orientational order remains almost unchanged. The concentration of each ion at the surface can be drastically different from that in the bulk. As a striking example, at sufficiently low salt concentrations, the concentration of I⁻ is about 500 times higher than that of F⁻ at the surface. Структура водних розчинiв 1:1 солей (KCl, NaCl, KF, i CsI) поблизу гiдрофобної поверхнi аналiзується в рамках теорiї i орiєнтовно залежних iнтегральних рiвнянь. Молекули води розглядаються як твердi сфери з вставленими мультипольними моментами включно до октупольного момента. Твердi сферичнi iони помiщенi в цю модель води. Багаточастинковi взаємодiї, обумовленi молекулярною поляризованiстю, трактуються на рiвнi самоузгодженого середнього поля. Детально обговорюються ефекти катiонних та анiонних розмiрiв i концентрацiй солi в об’ємi . Iз зростанням концентрацiї солi шари молекул води бiля поверхнi стають густiшими, але їх орiєнтацiйний порядок залишається майже незмiнним. Концентрацiя кожного з iонiв бiля поверхнi може бути суттєво iншою, нiж в об’ємi. Як вражаючий приклад, при достатньо низьких концентрацiях солi, концентрацiя I⁻ бiля поверхнi майже в 500 раз вища, нiж концентрацiя F⁻. The author wishes to express his sincere thanks to Prof. G. N. Patey and Dr. D. R. B´erard for many fruitful discussions. This work was supported by Grants-in-Aid for Scientific Research on Priority Areas (No. 15076203) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and by the Next Generation Super Computing Project, Nanoscience Program, MEXT, Japan. 2007 Article Structure of aqueous electrolyte solutions near a hydrophobic surface / M. Kinoshita // Condensed Matter Physics. — 2007. — Т. 10, № 3(51). — С. 387-396. — Бібліогр.: 28 назв. — англ. 1607-324X PACS: 61.20.Gy, 61.20.Qg, 61.25.Em DOI:10.5488/CMP.10.3.387 https://nasplib.isofts.kiev.ua/handle/123456789/118704 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
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The structure of aqueous solutions of 1:1 salts (KCl, NaCl, KF, and CsI) near a hydrophobic surface is analysed using the angle-dependent integral equation theory. Water molecules are taken to be hard spheres imbedded with multipolar moments including terms up to octupole order, and hard spherical ions are immersed
in this model water. The many-body interactions associated with molecular polarizability are treated at the self-consistent mean field level. The effects of cationic and anionic sizes and salt concentration in the bulk are discussed in detail. As the salt concentration increases, the layer of water molecules next to the surface becomes denser but its orientational order remains almost unchanged. The concentration of each ion
at the surface can be drastically different from that in the bulk. As a striking example, at sufficiently low salt concentrations, the concentration of I⁻ is about 500 times higher than that of F⁻ at the surface. |
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Kinoshita, M. |
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Kinoshita, M. Structure of aqueous electrolyte solutions near a hydrophobic surface Condensed Matter Physics |
| author_facet |
Kinoshita, M. |
| author_sort |
Kinoshita, M. |
| title |
Structure of aqueous electrolyte solutions near a hydrophobic surface |
| title_short |
Structure of aqueous electrolyte solutions near a hydrophobic surface |
| title_full |
Structure of aqueous electrolyte solutions near a hydrophobic surface |
| title_fullStr |
Structure of aqueous electrolyte solutions near a hydrophobic surface |
| title_full_unstemmed |
Structure of aqueous electrolyte solutions near a hydrophobic surface |
| title_sort |
structure of aqueous electrolyte solutions near a hydrophobic surface |
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Інститут фізики конденсованих систем НАН України |
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2007 |
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https://nasplib.isofts.kiev.ua/handle/123456789/118704 |
| citation_txt |
Structure of aqueous electrolyte solutions near a hydrophobic surface / M. Kinoshita // Condensed Matter Physics. — 2007. — Т. 10, № 3(51). — С. 387-396. — Бібліогр.: 28 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT kinoshitam structureofaqueouselectrolytesolutionsnearahydrophobicsurface AT kinoshitam strukturavodnihrozčinivelektrolitivpoblizugidrofobnoípoverhni |
| first_indexed |
2025-12-01T01:52:58Z |
| last_indexed |
2025-12-01T01:52:58Z |
| _version_ |
1850268955916107776 |
| fulltext |
Condensed Matter Physics 2007, Vol. 10, No 3(51), pp. 387–396
Structure of aqueous electrolyte solutions near a
hydrophobic surface
M.Kinoshita
Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611–0011, Japan
Received May 5, 2007
The structure of aqueous solutions of 1:1 salts (KCl, NaCl, KF, and CsI) near a hydrophobic surface is anal-
ysed using the angle-dependent integral equation theory. Water molecules are taken to be hard spheres
imbedded with multipolar moments including terms up to octupole order, and hard spherical ions are im-
mersed in this model water. The many-body interactions associated with molecular polarizability are treated
at the self-consistent mean field level. The effects of cationic and anionic sizes and salt concentration in the
bulk are discussed in detail. As the salt concentration increases, the layer of water molecules next to the
surface becomes denser but its orientational order remains almost unchanged. The concentration of each ion
at the surface can be drastically different from that in the bulk. As a striking example, at sufficiently low salt
concentrations, the concentration of I− is about 500 times higher than that of F− at the surface.
Key words: water, electrolyte solution, hydrophobic surface, multipolar moment, integral equation theory
PACS: 61.20.Gy, 61.20.Qg, 61.25.Em
1. Introduction
The aqueous electrolyte solution is an essential constituent of a system in a variety of fields such
as solution chemistry, electrochemistry, biophysics, biochemistry, and colloidal science. Above all,
the elucidation of the structure and properties of the solution at surfaces has been a central issue for
decades. The solution at an extended, structureless hydrophobic surface is the most fundamental
example to be investigated in the first stage, and the product of the investigation should provide
basic information and important physical insights. Nevertheless, even for this simple system our
microscopic understanding is not complete.
At present, computer simulations including water molecules and ions at finite concentration are
problematic. Such simulations are usually performed by confining a fixed number of ions and water
molecules between two plates, and there is no reliable way of estimating the bulk equilibrium
concentration of ions. Grand Canonical Monte Carlo calculations could solve this problem but
such calculations would be impractical [1]. This difficulty in computer simulations may be a major
reason for the slow progress of our studies on aqueous electrolyte solutions at surfaces.
The integral equation theory does not suffer from the drawbacks found in computer simulati-
ons mentioned above. However, it is not straightforward to implement the analyses because of the
presence of water molecules. The water-water and water-ion correlations are dependent not only
on the distance between centers of the particles but also on the particle orientations. Treating the
orientational correlations in an explicit manner is crucially important in analyses on the dielectric
properties of aqueous electrolyte solutions [2]. Incorporating the effects of molecular polarizability
is a nontrivial task. The water-surface correlations are also dependent on the orientations of wa-
ter molecules. Further, the severe numerical instability is often encountered in solving the basic
equations once the ionic concentration becomes finite.
Cares must be taken in choosing a water model when ions are included in water. In the multipo-
lar model for water [2,3], the multipolar moments of a water molecule experimentally determined [4]
are used. When ions are included, the water-ion electrostatic interaction potentials are accurately
expressed by the dipole-ion, quadrupole-ion, and octupole-ion interactions. The SPC/E model [5],
c© M.Kinoshita 387
M.Kinoshita
which is the most popular water model, is nearly optimized in computer simulations so that only
the structure and properties of pure water can be reproduced. It is not definite if the water-ion
electrostatic interaction potentials can be accurately described with the SPC/E model due to the
potential impertinence of its multipolar moments.
In these 20 years, a great progress has been made in constructing the angle-dependent integral
equation theories combined with the multipolar water model for aqueous electrolyte solutions in
the bulk and at surfaces and in developing the robust numerical solution algorithms [2,3,6–22].
The inclusion of the octupole moment is essential because anions are more strongly hydrated
than cations even when they share the same size and this effect can well be reproduced only by
including the octupole moment. It is much easier to include ions in water at infinite dilution, and
there are only several works [8,9,13,17,20] dealing with aqueous electrolyte solutions where the ionic
concentration is finite. In most of these works only the dipole moment and the quadrupole moment
with tetrahedral symmetry are considered. The only exception is found in our earlier work [20] on
the solutions near a simplified metal surface. In this article, we are concerned with the structure of
the solutions near a hydrophobic surface for which the water-surface and ion-surface interactions
are much weaker and the hydration properties of the ions are crucially important.
Here we consider aqueous solutions of 1:1 salts (KCl, NaCl, KF, and CsI): electrolyte solutions
with ions of varying size, K+, Na+, Cs+, F−, Cl−, and I−. Water molecules are taken to be hard
spheres imbedded with multipolar moments including terms up to octupole order [3], and hard
spherical ions are immersed in this model water. The model solutions near a hydrophobic surface
are studied by analysing the density profiles of cations, anions, and water molecules and the water
orientational structure. The angle-dependent reference hypernetted-chain integral equation theory
[2,3,6–22] is employed. The many-body interactions associated with molecular polarizability are
treated at the self-consistent mean field level [2,3]. The numerical solution of the basic equations
is performed using our robust, highly efficient algorithms [10,11,14–18,20–22]. The major concern
is to examine the effects due to cationic and anionic sizes and salt concentration in the bulk. We
are interested in quantitative aspects of the conclusions as well as in qualitative arguments.
2. Model
A water molecule is modeled as a hard sphere of diameter dS = 0.28 nm in which a point dipole,
quadrupole, and octupole are embedded [3]. Hard spherical cations and anions with diameters d+
and d−, respectively, are immersed in water. The diameters of the ionic species (Na+, K+, Cs+, F−,
Cl−, and I−), which are determined from x-ray electron density measurements [2,23], are collected
in table 1. Since water molecules have C2v symmetry, the dipole, quadrupole, and octupole moments
have, respectively, 1, 2, and 2 mutually independent components [2].
Table 1. Diameters of hard spherical ions (i = +,−).
Ion di/dS
Na+ 0.84
K+ 1.08
Cs+ 1.28
F− 0.84
Cl− 1.16
I− 1.44
The influence of molecular polarizability of water is included by employing the self-consistent
mean field (SCMF) theory [2,3]. At the SCMF level the many-body induced interactions are reduced
to pairwise additive potentials involving an effective dipole moment. The effective dipole moment
thus determined is about 1.43 times larger than the bare gas-phase dipole moment. The values of the
multipole moments used in the calculations are given elsewhere [20]. The dielectric constant of pure
388
Solutions near a hydrophobic surface
water predicted by the reference hypernetted-chain (RHNC) integral equation theory combined
with the present model is 85.6 which is larger than the experimental value only by ∼10%.
A hard sphere macroparticle of diameter dM = 30dS is immersed at infinite dilution in the model
aqueous electrolyte solutions. It interacts with water molecules and ions through the hard-sphere
potentials and acts as a hydrophobic macroparticle. It has been shown that the size of 30dS is large
enough to mimic an extended surface [21,22]. The reason for employing hard-sphere repulsions is
that the distance between particles and the distance between the surface and a particle can clearly
be defined. The surface corrugation is neglected in the present model. However, it has been shown
that the corrugation has remarkably little effect on the water structure near the surface [24], and
this is probably true for the structure of aqueous electrolyte solutions.
Hereafter, the subscripts “S”, “+”, “–”, and “M” denote “solvent (water)”, “cations”, “anions”,
and “macroparticle”, respectively. We consider 0.25M KCl, NaCl, KF, and CsI solutions. For KCl
solutions two more concentrations, 0.00M (at the infinite dilution limit) and 3.00M, are also tested.
The number densities of water molecules, cations, and anions in each solution are determined from
the experimental solution density at 298 K and 1 atm [25,26].
3. Theory
The Ornstein-Zernike (OZ) equation for the mixture comprising water molecules, cations, an-
ions, and macroparticles can be written as [17]
ηαβ(12) =
{
1/(8π2)
}
∑
γ
ργ
∫
cαγ(13){ηγβ(32) + cγβ(32)}d(3), (1a)
ηαβ(12) = hαβ(12) − cαβ(12), α, β = S,+,−,M, (1b)
where h and c are the total and direct correlation functions, respectively, (ij) represents (rij , Ωi,
Ωj), rij is the vector connecting the centers of particles i and j, Ωi denotes the three Euler angles
describing the orientation of particle i,
∫
d(3) represents integration over all position and angular
coordinates of particle 3, and ρ is the number density. The closure equation is expressed by [17]
cαβ(12) =
∫
∞
r
[hαβ(12)∂{wαβ(12) − bαβ(12)}/∂r] dr − uαβ(12)/(kBT ) + bαβ(12), (2a)
wαβ(12) = −ηαβ(12) + uαβ(12)/(kBT ), (2b)
where u is the pair potential, b is the bridge function, r is the distance between the centers of two
particles, kB is the Boltzmann constant, and T is the absolute temperature.
Since the macroparticles are present at infinite dilution (ρM = 0), the calculation process can
be split into two steps [17]:
(i) Solve equations (1) and (2) for the aqueous electrolyte solution comprising water molecules,
cations, and anions. Calculate the correlation functions, XSS, XS+, XS−, X++, X+−, and
X−− (X = h, c).
(ii) Solve equations (1) and (2) for the aqueous electrolyte solution near a macroparticle using the
correlation functions obtained in step (i) as input data. Calculate the correlation functions,
XMS, XM+, and XM−.
For the numerical solution of equations (1) and (2), the pair potentials and correlation functions
are expanded in a basis set of rotational invariants, and the basic equations are reformulated in
terms of the projections Xmnl
µν (r) occurring in the rotational-invariant expansion of X [2,3,6–22].
The expansion considered for nmax 64 gives sufficiently accurate results for uncharged surfaces.
More details are described in earlier papers. The quantities we mainly analyse are the reduced
density profiles g000
MS00
, g000
M+00
, and g000
M−00
(g = h−1) which are denoted simply by gMS, gM+, and
gM−, respectively. We also analyse the water orientational order at contact with the surface using
389
M.Kinoshita
the probability density functions p(θ) where θ is the angle with respect to the surface normal (into
the aqueous solution) of either the molecular dipole (θµ) or an OH bond (θOH).
In the RHNC theory, the reference bridge functions are incorporated in the closure equations.
The reference system in step (i) is a mixture of hard spheres of diameters dS, d+, and d− (the
number densities are ρS, ρ+, and ρ−, respectively), and that for step (ii) is a hard macrosphere of
diameter dM immersed in the hard-sphere mixture. In the present study, the particle-particle bridge
functions needed in step (i) are estimated using the procedure developed by Lee and Levesque [27],
and the macrosphere-particle bridge functions required in step (ii) are calculated in accordance
with the method given by Henderson and Plischke [28].
A sufficiently long range rL is divided into N grid points (rm = mδr,m = 0, 1, . . . , N − 1; δr =
rL/N) and the projections for the pair potentials and correlation functions are represented by
their values on these points. N and δr are set at 4096 and 0.01 dS, respectively. The very large
set of stiff, nonlinear simultaneous equations is solved using the robust, highly efficient algorithms
developed by Kinoshita and coworkers [10,11,14–18,20–22].
4. Results and discussion
The calculations are performed for 0.25M KCl, NaCl, KF, and CsI solutions. For KCl solutions
two more concentrations, 0.00M (at the infinite dilution limit) and 3.00M, are also tested. The
probability density functions p(θOH) and p(θµ) next to the hydrophobic surface are plotted in
figures 1 and 2, respectively. They are shown for 0.00M and 3.00M KCl solutions. The reduced
Figure 1. The probability density functions
p(θOH) next to the surface for 0.00M and
3.00M KCl solutions.
Figure 2. The probability density functions
p(θµ) next to the surface for 0.00M and 3.00M
KCl solutions.
density profiles of water molecules near the surface are shown for 0.00M, 0.25M, and 3.00M KCl
solutions in figure 3 and for 0.25M NaCl and CsI solutions in figure 4 (dM2 = dM/2). The reduced
density profiles of cations and anions for 0.25M solutions are shown in figures 5–8. The oscillatory
behavior of the curves in figures 3–8 is ascribed to the adoption of a molecular model for water.
The values of the reduced density profiles of cations, anions, and water molecules at contact with
the surface are summarized in table 2 for all the solutions tested.
390
Solutions near a hydrophobic surface
Table 2. Values of reduced density profiles of cations, anions, and water molecules at contact
with the surface.
Salt Solution gM+,Contact gM−,Contact gMS,Contact
0.00M KCl 0.1260 0.1863 1.5480
0.25M KCl 0.2788 0.5237 1.6448
3.00M KCl 0.6282 1.0926 2.3899
0.25M NaCl 0.0226 0.5694 1.6585
0.25M KF 0.2539 0.0090 1.6515
0.25M CsI 1.6425 4.7153 1.6428
Figure 3. Reduced density profiles of water
molecules for 0.00M, 0.25M, and 3.00M KCl
solutions.
Figure 4. Reduced density profiles of water
molecules for 0.25M NaCl and CsI solutions.
4.1. Orientational structure of water
The probability density functions for pure water near the hydrophobic surface are identical to
those for 0.00M KCl solution shown in figures 1 and 2. The function p(θOH) in figure 1 indicates
that at the contact with the surface is a dominant contribution from water molecules oriented with
one OH bond directed into the surface: The local maxima occur at θOH ∼ 71◦ and 180◦ [21,22].
This feature is also reflected in p(θµ) plotted in figure 2 where it has a local maximum at θµ ∼ 55◦
and a remnant of a local maximum at θµ ∼ 125◦ [21,22]. At the same time, p(θµ) indicates a
preference for dipoles inclined into the aqueous solution rather than toward the surface. This trend
of p(θµ) is considerably stronger than that reported by Torrie and Patey [12] who employed the
Lee-Levesque (L-L) procedure [26] for the macrosphere-particle bridge functions as well. However,
it should be noted that the L-L procedure gives pathological bridge functions when it is extended
to such a large sphere immersed in small spheres [21]. The orientational order next to the surface
persists until the salt concentration becomes as high as 3.00M.
4.2. Density profile of water molecules
The reduced density profile of water molecules for pure water near the hydrophobic surface is
identical to that for 0.00M KCl solution shown in figure 3. When a hydrophobic surface intrudes
into water, it is impossible to maintain the hydrogen bonds as in the bulk and the loss of the bonds
391
M.Kinoshita
Figure 5. Reduced density profiles of ions for
0.25M KCl solution (i=+,–).
Figure 6. Reduced density profiles of ions for
0.25M NaCl solution (i=+,–).
is unavoidable. The loss is kept minimal by taking special orientations relative to the surface
described above. In any case, the water molecules at contact are unfavorable, so the number of
such molecules needs to be decreased. This dewetting effect competes with the entropic excluded-
volume effect (or equivalently, the so-called packing force) causing the formation of a much denser
layer near the surface as found in the hard-sphere solvent. Despite the dewetting effect, the contact
value of the reduced density profile gMS,Contact is higher than unity and the layer in the immediate
vicinity of the surface is slightly denser than the bulk, which implies that the packing force still
dominates.
The packing force becomes stronger as the total packing fraction ηT of the aqueous electrolyte
solution increases for a salt species given. As the salt concentration increases, ηT becomes higher:
The values of ηT for 0.00M, 0.25M, and 3.00M KCl solutions are, respectively, 0.3831, 0.3854, and
0.4066. As observed in figure 4, with the increase in the salt concentration gMS,Contact certainly
increases and the layer in the immediate vicinity of the surface becomes denser.
For different species, the reduced density profile of water molecules is effected by the salt species
as well as by ηT. The values of ηT for 0.25M NaCl and CsI solutions are, respectively, 0.3852 and
0.3864. However, gMS,Contact is lower in the CsI solution. The reason for this is as follows. The
ions are much larger in the CsI solution and they are preferentially excluded from the bulk to the
surface (see figure 8) due to the weak hydration. This enrichment of ions leads to a less number of
water molecules in the immediate vicinity of the surface.
4.3. Effects of ionic sizes on density profiles of ions
For 0.25M solutions, there is a depletion of Na+, K+, F−, and Cl− near the hydrophobic surface
(see figures 5–7) because they are preferentially hydrated in the bulk. This is true even for K+
and Cl− which are larger than water molecules. In general, smaller ions are more depleted at a
hydrophobic surface. Though Na+ and F− share the same size, the depletion is more conspicuous
for F− (“gM+,Contact for Na+”/“gM−,Contact for F−”=2.51), which can well be reproduced only
by including the octupole moment of water molecules. By contrast, Cs+ and I− are considerably
enriched in the close vicinity of the surface (see figure 8) because they can only weakly be hydrated
and excluded from the bulk to the surface. In particular, gM−,Contact for I− well exceeds 4.
The difference between the curve for cations and that for anions in 0.25M KCl solution is
somewhat smaller than in 0.25M NaCl, KF, and CsI solutions. The size of Cl− is only slightly larger
than that of K+ and anions are more strongly hydrated, leading to almost the same strength of
392
Solutions near a hydrophobic surface
Figure 7. Reduced density profiles of ions for
0.25M KF solution (i=+,–).
Figure 8. Reduced density profiles of ions for
0.25M CsI solution (i=+,–).
the hydration followed by the small difference between the reduced density profiles of Cl− and K+.
4.4. Effects of salt concentration on density profiles of ion s
The reduced density profiles of K+ and Cl− are shown in figure 9 and figure 10, respectively.
Those for 0.00M, 0.25M, and 3.00M KCl solutions are compared in these figures. The profiles shift
upward at all separations as the salt concentration becomes higher. This is attributable mainly to
the packing force which becomes larger as the salt concentration increases and ηT becomes higher.
Figure 9. Reduced density profiles of K+
for 0.00M, 0.25M, and 3.00M KCl solutions
(i = +).
Figure 10. Reduced density profiles of Cl−
for 0.00M, 0.25M, and 3.00M KCl solutions
(i = −).
In 0.00M and 0.25M solutions, the ions (K+ and Cl−) are depleted near the surface. In 3.00M
393
M.Kinoshita
solution, the reduced density profile for K+ exceeds unity at some separations near the surface, but
a slight depletion occurs. On the other hand, a slight enrichment is observed for Cl− (gM−,Contact
is larger than unity) when the salt concentration reaches 3.00M.
4.5. Densities of ions at surfaces
The reduced density profiles of K+ for 0.25M KF and KCl solutions are compared in fig-
ure 11. They are not significantly different from each other. Likewise, those of Cl− for 0.25M
NaCl and KCl solutions are almost the same as shown in figure 12. Thus, at sufficiently low salt
concentrations (60.25M), the reduced density profile of an ionic species is not significantly ef-
fected by the other ionic species which are co-present. Hence, the following examples can be given:
gM+,Contact/gM−,Contact ∼ 180 for CsF and gM−,Contact/gM+,Contact ∼ 210 for NaI; and for the mix-
ture of KF and KI, “gM−,Contact for I−”/“gM−,Contact for F−”∼520. Even when the concentrations
of all ions are the same in the bulk, the concentration of an ionic species at the surface can be
drastically different from that of another ionic species.
Figure 11. Reduced density profiles of K+ for
0.25M KF and KCl solutions (i=+).
Figure 12. Reduced density profiles of Cl− for
0.25M NaCl and KCl solutions (i = − ).
5. Concluding remarks
The structure of 1:1 electrolyte solutions near an extended hydrophobic surface is analysed
using the angle-dependent RHNC theory combined with the multipolar model for water. The
many-body interactions associated with molecular polarizability are treated at the SCMF level.
Unlike the earlier works, the following two conditions are satisfied: (1) the ionic concentrations are
finite; and (2) multipolar moments having terms up to octupole order are included.
The layer of water molecules next to the surface is slightly denser than the bulk and becomes
progressively denser as the salt concentration increases. The orientational order of water molecules
at contact with the surface is characterized by a tendency of one OH bond directed into the surface
and a preference for dipoles inclined into the aqueous solution. This orientational order persists
until the salt concentration becomes as high as 3.00M.
The ions, Na+, K+, and F−, are preferably hydrated in the bulk, and there is a depletion
of these ions near the surface. The depletion is more conspicuous as the ionic size decreases and
the hydration becomes stronger. Anions are more strongly hydrated than cations even when they
share the same size: Though the sizes of Na+ and F− are the same, the latter is more depleted.
394
Solutions near a hydrophobic surface
By contrast, Cs+ and I− are considerably enriched near the surface because they are just weakly
hydrated and excluded from the bulk to the surface. As for Cl−, they are depleted near the surface
at low concentrations in the bulk but slightly enriched at high concentrations. Overall, the strength
of the hydration in the bulk follows the order, F− > Na+ � K+ ∼Cl− � Cs+ > I−.
Even when the concentrations of all ions are the same in the bulk, the concentration of
an ionic species at the surface can be drastically different from that of another ionic species.
For example, at sufficiently low salt concentrations (60.25M), gM+,Contact/gM−,Contact ∼180 for
CsF and gM−,Contact/gM+,Contact ∼210 for NaI. For the mixture of KF and KI, “gM−,Contact for
I−”/“gM−,Contact for F−”∼520.
6. Acknowledgements
The author wishes to express his sincere thanks to Prof. G. N. Patey and Dr. D. R. Bérard
for many fruitful discussions. This work was supported by Grants-in-Aid for Scientific Research
on Priority Areas (No. 15076203) from the Ministry of Education, Culture, Sports, Science and
Technology of Japan and by the Next Generation Super Computing Project, Nanoscience Program,
MEXT, Japan.
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M.Kinoshita
Структура водних розчинiв електролiтiв поблизу
гiдрофобної поверхнi
М.Кiношiта
Iнститут новiтньої енергетики, Унiверситет м. Кiото, Кiото 611–0011, Японiя
Отримано 5 травня 2007 р.
Структура водних розчинiв 1:1 солей (KCl, NaCl, KF, i CsI) поблизу гiдрофобної поверхнi аналiзу-
ється в рамках теорiї i орiєнтовно залежних iнтегральних рiвнянь. Молекули води розглядаються як
твердi сфери з вставленими мультипольними моментами включно до октупольного момента. Твердi
сферичнi iони помiщенi в цю модель води. Багаточастинковi взаємодiї, обумовленi молекулярною
поляризованiстю, трактуються на рiвнi самоузгодженого середнього поля. Детально обговорюю-
ться ефекти катiонних та анiонних розмiрiв i концентрацiй солi в об’ємi . Iз зростанням концентрацiї
солi шари молекул води бiля поверхнi стають густiшими, але їх орiєнтацiйний порядок залишається
майже незмiнним. Концентрацiя кожного з iонiв бiля поверхнi може бути суттєво iншою, нiж в об’ємi.
Як вражаючий приклад, при достатньо низьких концентрацiях солi, концентрацiя I− бiля поверхнi
майже в 500 раз вища, нiж концентрацiя F−.
Ключовi слова: розчин електролiту, гiдрофобна поверхня, мультипольний момент, теорiя
iнтегральних рiвнянь
PACS: 61.20.Gy, 61.20.Qg, 61.25.Em
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