Self archive of H. Torii, J. Chem. Phys. 127 (5), 054508 (2007)

Scheme of detecting microscopic inhomogeneity in binary liquid mixtures utilizing
resonantly coupled vibrational modes
Hajime Torii a)
Department of Chemistry, School of Education, Shizuoka University,
836 Ohya, Shizuoka 422-8529, Japana) Telephone and Fax: +81-54-238-4624; E-mail: torii@ed.shizuoka.ac.jp.

Influence of microscopic inhomogeneity in binary liquid mixtures on their vibrational spectra is studied
by doing calculations on a model liquid system. The concentration dependence of the noncoincidence
effect (NCE), which is a feature of vibrational bands related to intermolecular resonant coupling ofvibrational modes, is analyzed. It is suggested that observation of convex behavior of the NCEs for thevibrational bands of both species, especially that of the less polar species, in a binary liquid mixture is anindication of the occurrence of microscopic inhomogeneity.

the molecular dynamics (MD) simulation and othertheoretical methods.16–19 While small-angle x-ray
and neutron scattering measurements lead toestimates of the Debye correlation lengths of liquidmoremolecularly
detailed
structures,7–9
information is derived by the large-angle x-ray andneutron diffractions, the vibrational and NMR
spectroscopic methods, and the computational andtheoretical methods. However, for example in thecase of the methanol/water binary liquid mixture,
there is a contradiction among the results of thestudies utilizing these methods; no signature of
microscopic inhomogeneity has been found in the
low-frequency Raman spectrum,20 as also
supported by x-ray diffraction21 and thermodynamic studies,1 but the occurrence of substantial
molecular segregation has been suggested in aneutron diffraction study.22 In this sense, further
methodological development is preferable toobtain clearer knowledge on the intermolecularinteractions and liquid structures.
In the previous studies on the vibrational
spectra in the 4000–700 cm-1 region focusing on
the microscopic inhomogeneity of binary liquid
mixtures,12,13 vibrational frequency shifts inducedby the surrounding molecules have been analyzed.
Based on the classification of the effects ofintermolecular interactions on the vibrational
spectra introduced in our previous study,23–26 thisquantity is classified as diagonal, meaning that it

I. INTRODUCTION
Microscopic structural ordering in binary
liquid mixtures is a fundamental problem in liquidstate chemistry and physics, for better
understanding of intermolecular interactions and,in particular, of molecular self organization on the
microscopic scale. Sometimes this problem has
been discussed in relation to thermodynamic
properties. It is known that the thermodynamic
properties of many real liquid mixtures deviate
more or less from those of ideal mixtures,1 andsome of those deviations are referred to asanomalous. Based on the Kirkwood–Buff theory,2,3
those anomalous thermodynamic properties are
related4 to microscopic inhomogeneity (ormicroheterogeneity5) of liquid structures, whichmeans preferential solvation by the molecules ofthe same species within a length scale of a multipleof molecular diameters in binary liquid mixtures,6
originating from molecular self association ofmoderate strength (not at all weak, but not sostrong to lead to macroscopic phase separation). In
some recent studies, the intermolecularinteractions and the liquid structures are more
directly analyzed by using the small- andlarge-angle x-ray and neutron scattering
methods,7–11 the vibrational [infrared (IR) and
Raman], dielectric, and nuclear magnetic
resonance (NMR) spectroscopic methods,12–17 and1

Self archive of H. Torii, J. Chem. Phys. 127 (5), 054508 (2007)

is a property of individual molecules affected bytheir local environment, such as dielectric reaction
field and hydrogen bonding. However, there isanother category of phenomena originating froman off-diagonal property of molecular vibrations,meaning that it is related to direct intermolecular
coupling of vibrational modes. The noncoincidence effect (NCE), which is the phenomenon
that the frequency positions of the IR, isotropic
Raman, and anisotropic Raman components of avibrational band do not coincide,23–31 belongs tothis category. This effect is seen in liquid systems
as well as in biomolecules with repeat units,32,33
and is most clearly recognized in the resonant case,where the intrinsic frequencies of the coupledmodes are sufficiently close to each other ascompared with the magnitude of the coupling. As aresult, in binary liquid mixtures, this effectoriginates almost exclusively from the vibrational
couplings between molecules of the same species,and diminishes even upon dilution with an
isotopically substituted species, for example, upondilution of acetone-12C=O with acetone-13C=O.31
Its concentration dependence is affected by detailsof liquid structural changes, such as the anisotropy
in the liquid structural changes in methanol/CCl4.30
In this sense, analysis of this effect is expected tobeusefulalso to detect microscopic
inhomogeneity of liquid structures as a property
related to the distances and relative orientations of
the molecules of the same species.
In the present work, this point is studied bydoing calculations on a model liquid system. The
effect of preferential solvation on vibrational bandprofiles is examined by isolating it from those ofother factors of liquid structures. It is shown that anonlinear convex behavior of the concentration
dependence of the NCEs of the vibrational bandsof both species (not only one of those species) in abinary liquid mixture is an indication of theoccurrence of microscopic inhomogeneity.
Distinction with the nonlinear concentration
dependence of the NCEs arising from polarity
difference is discussed.

II.
MODEL
PROCEDURE

ANDCOMPUTATIONAL

The model liquid system adopted in the present
work consists of polar spherical particles
interacting with each other by the Lennard-Jonesand dipole–dipole interactions (Stockmayer
fluid),34 with a one-dimensional oscillator (representing a vibrational degree of freedom) having avibrational transition dipole and a Raman tensor
being buried in each particle.35 Denoting thecoordinate (weighted by the square root of the
reduced mass) of the mth particle’s oscillator as qm,
its vibrational transition dipole and Raman tensor
are expressed within the harmonic approximationas (∂μm/∂qm) <1m| qm |0m> and (∂αm/∂qm) <1m| qm|0m>, respectively, where |0m> and |1m> are theground and one-quantum excited states of thisoscillator. While the Lennard-Jones anddipole–dipole interaction parameters wereassumed to be the same for all the particles (ε =150 K, σ = 4.2 Å, and μ* ≡ μ(εσ3)1/2 = 2.5),35 two
sets of parameters (force constants, etc.) wereassumed for the vibrational modes to model thetwo species in binary liquid mixture, and wereassigned according to specified mole fractions.
Specific values of the parameters assumed in thepresent calculation are summarized in Table I.
Ensembles of liquid structures of a 512-particle
system, with respect to the locations andorientations of the particles, were generated by theMonte Carlo method.36 Two thermodynamic states,(T*, ρ*) = (2.0, 0.9) and (4.0, 0.45) (called state A
and B hereafter),35 where T* (≡ T/ε) and ρ* (≡ρσ3)
are the reduced temperature and density, wereconsidered as examples. To simulate preferential
solvation in this binary liquid mixture, virtual
energy of self association (VESA), which is aseparate energy scale and operates between themolecules of the same species within the firstsolvation layer, was introduced in the assignmentof the parameters of vibrational modes, andensembles of the assignments were generated by
the Monte Carlo method on the basis of the sum of
this virtual energy. In other words, simulations of
the liquid structures were carried out in two steps:2

Self archive of H. Torii, J. Chem. Phys. 127 (5), 054508 (2007)

TABLE I. Values of the parameters of vibrational modes assumed in the present calculation.
=============================================================
Species 1
Species 2——————————————————————————————————
force constant (mdyn Å-1 amu-1)aaverageb
1.7
1.1
c
0.017
0.011
standard deviation
1.5
1.21|∂μm/∂qm| (D Å-1 amu-1/2)d1.0
1.0(∂αm/∂qm)zz (arbitrary unit)e=============================================================aWeighted by the inverse of the mass.
Corresponding to the uncoupled vibrational frequencies of 1698.6 and 1366.4 cm-1.
Gaussian distribution is assumed.
The direction of ∂μm/∂qm is parallel to the permanent dipole of each particle.
The form of ∂αm/∂qm is assumed to be axially symmetric, only its zz component being nonzero,
where z axis is taken to be parallel to the permanent and transition dipoles.

b
c
d
e

tensor. TDC is known as the typical couplingmechanism for the vibrational modes exhibiting alarge magnitude of NCE, e.g., the C=O stretchingmodes of many carbonyl compounds (such asacetone and N,N-dimethylformamide), the O–H
and C–O stretching modes of methanol, the O–H
stretching mode of water, and the S=O stretchingmode of dimethyl sulfoxide. The normal modes ofthe liquid system were calculated by diagonalizing
the vibrational Hamiltonian constructed from theforce constants of individual oscillators (diagonalterms) and the vibrational couplings according to
the TDC mechanism (off-diagonal terms). The IR
and Raman spectra were calculated from thosenormal modes combined with the vibrationaltransition dipoles and the Raman tensors.23
The calculations described above were carriedout with our original programs on Hewlett–Packard zx6000 and other servers. Part of thecalculations was carried out on Altix 4700
computers at the Research Center for Computational Science of the National Institutes of Natural
Sciences at Okazaki.

locations and orientations of the particles were
determined by the real interaction energy(determined by ε, σ, and μ), and for each set(configuration) of those locations and orientationsof the particles, ensembles of the assignments ofthe molecular species were generated with aseparate energy scale. Since the locations andorientations of the particles were fixed in the latter
step, it is possible to examine the effect ofpreferential solvation on vibrational band profiles
separately from those of the translational androtational degrees of freedom of the liquid
structures. In the present calculation, a few valuesof VESA were assumed as described below insection III. In total, 2500 sets of liquid structures
were sampled for the calculation of the vibrational
spectrum for each value of VESA and at each mole
fraction.
The vibrational modes of different particles arecoupled by the transition dipole coupling (TDC)
mechanism,23–26,28–31,33 expressed as
Fmn = −∂μ∂μ m
⋅ Tmn ⋅ n
∂q n
∂q m

(m ≠ n)(1)where Tmn is the dipole interaction tensor between
the mth and nth particles, which is given asTmn =2
3rmn rmn − rmn
I
5
rmn

(2)

where rmn = rm – rn is the distance vector (of lengthrmn) between the particles, and I is a 3 × 3 unit3

Self archive of H. Torii, J. Chem. Phys. 127 (5), 054508 (2007)

III. RESULTS AND DISCUSSION
Radial distribution

3

As an example of the calculated radial
distribution functions, those calculated for state A
with VESA11 = –0.4 kT (operating between
molecules of species 1) at the mole fraction x1 =0.5 are shown in the upper part of Fig. 1. It is seenthat preferential solvation occurs between themolecules of the same species as a result of theL
VESA, so that the local mole fractions x11
andLLx 22 , where xmn is defined as the mole fraction of
species m in the surroundings (the first solvation
layer) of a molecule of species n,1 are larger thanthe (global) mole fractions x1 and x2 (= 0.5). In thiscase, microscopic inhomogeneity extends to thesecond solvation layer. The small steps of theradial distribution functions at r = 6.22 Å are theartifacts due to the modeling of preferential
solvation described above, but will be smoothedby defining the VESA as decreasing gradually as rincreases rather than vanishing suddenly at theboundary of the first solvation layer (r = 6.22 Å)
as in the present calculation. The IR and Raman
spectra calculated for this case are shown in thelower part of Fig. 1. In both the frequency regionsof the vibrations of species 1 (~1700 cm-1) andspecies 2 (~1360 cm-1), the isotropic Raman bandis lower in frequency than the IR and anisotropic
Raman bands (the NCE). At the same time, theisotropic Raman band profiles are noticeably
asymmetric. Both the NCE and the asymmetry of
the band profiles originate from the vibrational
couplings. Although the band asymmetry is also
informative of intermolecular interactions,37 only
the behavior of the NCE is discussed in the present
work. In the presence of band asymmetry, the peak
positions and the first moments are different. In
such a case, it is legitimate to evaluate the value ofNCE (defined as ν~NCE(aniso-iso) ≡ ν~aniso − ν~isoand ν~NCE(IR -iso) ≡ ν~IR − ν~iso ) on the basis of thefirst moments.38
The concentration dependencies of the relative
magnitudes of NCE and the local mole fractions
LLx11
and x 22
calculated for a few values of
VESA are shown in Fig. 2. The former quantity isdefined, for the vibrational band of each species,

Radial distribution functions
2

1

0
4

8

12

16

Distance / ÅIntensity

IR

Raman

iso.

aniso.

1740

1700

1660

1400

Wavenumber / cm

1360

1320

-1

FIG. 1. Radial distribution functions (upper part) andthe IR and Raman spectra (lower part) calculated forstate A with VESA11 = –0.4 kT (operating between
molecules of species 1) at the mole fraction x1 = 0.5,
taken as an example. In the upper part, g11(r), g22(r), andg12(r) (where gmn(r) is the function for the distances
between the molecules of species m and species n) are
shown in pink, purple, and light blue, respectively. The
function in the case of no preferential solvation isshown with a black broken line as a reference. In the
Raman spectra (bottom), the isotropic and anisotropic
components are shown in blue and green, respectively.

value of NCE ( ν~NCE(aniso-iso) or
NCE(IR -iso) ) at a specified mole fraction divided
by that of the neat liquid. In the case of nopreferential solvation, the relative magnitudes ofNCE depend linearly on the mole fraction.
However, as the preferential solvation is
introduced by VESA, the concentration dependencies of the relative magnitudes of NCE of both
species become convex, in the same way as thoseof the local mole fractions. As expected, thedeviation is largest at intermediate concentrations.
In the case of state A, the calculated behavior of
ν~NCE(IR -iso) is indistinguishable from that of
ν~NCE(aniso-iso) (overlapped in Fig. 2), and isalmost symmetric between the vibrational bands ofspecies 1 and 2. In the case of state B, however,the behavior of ν~NCE(IR -iso) and ν~NCE(aniso-iso)

as
ν~

4

the

Self archive of H. Torii, J. Chem. Phys. 127 (5), 054508 (2007)
state B

Microscopic inhomogeneity

Relative magnitude of NCE

state A1.00.8(e) VESA11= – 0.6 kT(a) VESA11= – 0.4 kT

0.6
0.4
0.2
0.0
1.0

0.8
0.6
0.4
0.2
0.0
0.0

0.8

Polarity difference

1.0

0.2

0.4

0.6

0.8

1.0 0.0

0.2

0.4

0.6

0.8

1.0

Mole fraction of species 1
Relative magnitude of NCE
and local mole fraction

0.6
0.4

(b) VESA11= – 0.3 kT(f) VESA11= – 0.4 kT(c) VESA11= – 0.2 kT(g) VESA11= – 0.2 kT(d) VESA11= 0.0(h) VESA11= 0.0

FIG. 3. Schematic drawings of the nonlinear
concentration dependencies of the relative magnitudesof NCE arising from microscopic inhomogeneity (left)
and polarity difference (right). The former is taken from
Fig. 2 (a). The latter is drawn on the basis of Logan’s
theory [Eq. (17) of Ref. 28], assuming that themagnitude square of the dipole moment of species 1 is
(as an example) twice as large as that of species 2.

0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4

molecular orientational effect on the magnitude of
NCE. However, these nonlinear dependencies are
distinguished from those arising from microscopic
inhomogeneity, as shown schematically in Fig. 3.
In the case of polarity difference, the behavior of
the NCE of the more polar species exhibits aconvex curvature, while that of the less polar
species exhibits a concave curvature.28 This means
that, when the NCEs of the vibrational bands ofboth species are observed, one of them shows aconvex curvature and the other shows a concave
curvature, as shown on the right-hand side of Fig.
3, which is drawn by assuming that the magnitude
square of the dipole moment of species 1 is (as an
example) twice as large as that of species 2 in Eq.
(17) of Ref. 28. This is distinguished from thesituation arising from microscopic inhomogeneity
shown on the left-hand side of Fig. 3, where theNCEs of the vibrational bands of both species
show convex curvatures.
In real binary liquid mixtures, the molecular
dipole moments of the two species are generally
different, so that the factors shown in both parts ofFig. 3 should be simultaneously taken into account.
It should be noted that only the molecularorientational effect arising from polarity difference(and no effect of microscopic inhomogeneity) is
involved in the behavior on the right-hand side ofFig. 3, as clearly recognized from the derivation of
Eq. (17) in Ref. 28, while only the effect of
microscopic inhomogeneity (and no effect ofpolarity difference) is involved in the behavior on

0.2
0.0
0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Mole fraction of species 1

FIG. 2. Concentration dependencies of the relative
magnitudes of NCE of the vibrational bands of speciesL
1 and 2 (color lines) and the local mole fractions x11
Land x22 (black broken lines) calculated for state A(left, a–d) and state B (right, e–h) with the values of
VESA specified in each part. For state B, the curves for
ν~NCE(IR -iso) (red) do not overlap with those of
ν~NCE(aniso -iso) (light blue), so that they are drawn
separately. The black dotted lines indicate linear
dependencies and are drawn as a reference.

of the vibrational bands of species 1 and 2 isnoticeably asymmetric, with the deviation from thelinear behavior being larger for the vibrationalband of species 1. This is probably because of therather low density (ρ*) of this state. Note that the
VESA is introduced only between the molecules of
species 1 in the present calculation. In spite of thisasymmetry, when the magnitude of VESA issufficiently large, the convex dependence of the
NCE is recognized for the vibrational band of
species 2 as well as that of species 1.
As predicted in a previous theoretical study
based on the mean spherical approximation ofliquid structures28 and confirmed experimentally,31
nonlinear dependencies of the relative magnitudesof NCE on the mole fraction are also seen whenthe molecules of the two species in a binary liquid
mixture have different polarities (i.e., different
magnitudes of dipole moments), because of the5Self archive of H. Torii, J. Chem. Phys. 127 (5), 054508 (2007)

the left-hand side of Fig. 3. In this sense, it isimportant to analyze the behavior of the NCEs of
the vibrational bands of both species in the liquid
mixture, especially that of the less polar species, todiscuss the extent of microscopic inhomogeneity.
Observation of convex behavior of the NCEs forthe vibrational bands of both species will be aclear indication of the occurrence of microscopic
inhomogeneity.

17

Acknowledgment

23

18
19

20

21

22

This study was supported by a Grant-in-Aid for
Scientific Research from the Ministry of Education,
Culture, Sports, Science, and Technology of Japan,
and by a grant from the Morino Foundation for
Molecular Science.

24

25
26

References

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8

9

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Y. Marcus, Solvent Mixtures (Marcel Dekker, New
York, 2002).
J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 19, 774(1951).
A. Ben-Naim, J. Chem. Phys. 67, 4884 (1977).
E. Matteoli, J. Mol. Liq. 79, 101 (1999).
E. v. Goldammer and H. G. Hertz, J. Phys. Chem. 74,
3734 (1970).
Y. Marcus and Y. Migron, J. Phys. Chem. 95, 400(1991).
K. Nishikawa, H. Hayashi, and T. Iijima, J. Phys.
Chem. 93, 6559 (1989).
T. Takamuku, M. Tabata, M. Kumamoto, A.
Yamaguchi, J. Nishimoto, H. Wakita, and T.
Yamaguchi, J. Phys. Chem. B 102, 8880 (1998).
K. Yoshida, T. Yamaguchi, T. Otomo, M. Nagao, H.
Seto, and T. Takeda, J. Mol. Liq. 119, 125 (2005).
M. Misawa, J. Phys. Soc. Jpn. 72, 185 (2003).
D. T. Bowron, J. L. Finney, and A. K. Soper, J. Phys.
Chem. B 102, 3551 (1998).
J. E. Bertie and Z. Lan, J. Phys. Chem. B 101, 4111
(1997).
J. R. Reimers and L. E. Hall, J. Am. Chem. Soc. 121,
3730 (1999).
K. Egashira and N. Nishi, J. Phys. Chem. B 102, 4054
(1998).
S. Schrödle, B. Fischer, H. Helm, and R. Buchner, J.
Phys. Chem. A 111, 2043 (2007)
D. S. Venables and C. A. Schmuttenmaer, J. Chem.
Phys. 113, 11222 (2000).

29

30

31

32

33
34

35
36

37

38

6

H. Kovacs and A. Laaksonen, J. Am. Chem. Soc. 113,5596 (1991).
R. D. Mountain, J. Phys. Chem. A 103, 10744 (1999).
K. Yoshida, T. Yamaguchi, A. Kovalenko, and F.
Hirata, J. Phys. Chem. B 106, 5042 (2002).
K. Yoshida and T. Yamaguchi, Z. Naturforsch. 56a,
529 (2001).
T. Takamuku, T. Yamaguchi, M. Asato, M.
Matsumoto, and N. Nishi, Z. Naturforsch. 55a, 513(2000).
S. Dixit, J. Crain, W. C. K. Poon, J. L. Finney, and A.
K. Soper, Nature 416, 829 (2002).
H. Torii, in Novel Approaches to the Structure andDynamics of Liquids: Experiments, Theories andSimulations; edited by J. Samios and V. A. Durov(Kluwer, Dordrecht, The Netherlands, 2004), pp.
343–360.
H. Torii, M. Musso, and M. G. Giorgini, J. Phys.
Chem. A 109, 7797 (2005).
H. Torii, J. Phys. Chem. A 110, 4822 (2006).
H. Torii, J. Phys. Chem. A 110, 9469 (2006).
G. Fini, P. Mirone, and B. Fortunato, J. Chem. Soc.
Faraday Trans. 2, 69, 1243 (1973).
D. E. Logan, Chem. Phys. 131, 199 (1989).
H. Torii and M. Tasumi, J. Chem. Phys. 99, 8459
(1993).
M. Musso, H. Torii, P. Ottaviani A. Asenbaum, and M.
G. Giorgini, J. Phys. Chem. A 106, 10152 (2002).
M. Musso, M. G. Giorgini, H. Torii, R. Dorka, D.
Schiel, A. Asenbaum, D. Keutel, and K.-L. Oehme, J.
Mol. Liq. 125, 115 (2006).
R. Schweitzer-Stenner, F. Eker, K. Griebenow, X. Cao,and L. A. Nafie, J. Am. Chem. Soc. 126, 2768 (2004).
H. Torii, J. Phys. Chem. B 111, 5434 (2007).
J.-P. Hansen and I. R. McDonald, Theory of Simple
Liquids (Academic Press, London, 1986).
H. Torii, J. Phys. Chem. A 108, 2103 (2004).
M. P. Allen and D. J. Tildesley, Computer Simulationof Liquids (Oxford University Press, Oxford, 1989).
M. Musso, H. Torii, M. G. Giorgini, and G. Döge, J.
Chem. Phys. 110, 10076 (1999).
M. Musso, M. G. Giorgini, G. Döge, and A.
Asenbaum, Mol. Phys. 92, 97 (1997).