2684

J. Phys. Chem. B 1998, 102, 2684-2687

Density Estimation of Liquid/Liquid Interfacial Regions Using a Quasi-Elastic Laser
Scattering Method
Isao Tsuyumoto, Naohei Noguchi, Takehiko Kitamori, and Tsuguo Sawada*
Department of Applied Chemistry, School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-8656, Japan
ReceiVed: September 12, 1997; In Final Form: December 31, 1997

We developed a quasi-elastic laser scattering method and applied it to the density estimation of liquid/liquid(alcohol/water, carboxylic acid/water) interfacial regions. The observed densities are smaller than the expectedvalues in most of the cases, indicating that the interfacial densities are smaller than the bulk phase densities.
Moreover, there is a marked tendency for the observed density to become smaller as the hydrophobic groupin the alcohol and carboxylic acid molecules becomes larger. The results are consistent with theoreticalpredictions using the molecular dynamics method. The interfacial structure is discussed in connection withthese results.

Introduction
The interface between two immiscible liquids is one of themost important systems of study in chemistry, since transportphenomena across the interface are fundamentally important forunderstanding processes such as solvent extraction, liquid
chromatography, phase-transfer catalysis, etc.1,2 Probing theliquid/liquid interface experimentally is more difficult than
examining liquid/gas interfaces because of the buried nature of
the interface, and theoretical approaches to the interface arecomplicated by the inhomogeneous environment. Much effort
has been made to overcome the difficulty in research on theliquid/liquid interface. In recent years, progress in bothexperimental techniques and computer simulation has contributed significantly to our understanding of the liquid/liquidinterface.
Nonlinear optical techniques such as second harmonic
generation (SHG) and sum frequency generation (SFG) are able
to probe the liquid/liquid interface as well as liquid/gas andliquid/solid interfaces.3-12 These techniques have been extensively used to study molecules in the interfacial region and haveprovided great insight into the molecular orientation at liquid/
liquid interfaces. Neutron specular reflectivity measurements
have been used to study oil/water interfacial roughness and thethickness of surfactant layers at oil/water interfaces.13 Fluorescence anisotropy decay measurements have provided dataon the relationship between the lateral diffusion coefficient andthe roughness of alkane/water interfaces.14,15 Infrared attenuatedtotal reflection spectroscopy has provided quantitative descriptions of the adsorption of surfactant at a liquid hydrocarbon/
water interface.16 Many useful methods have been developed
to probe liquid/liquid interfaces. However, only fragmental
information on the interface structure has been accumulated suchas orientation, roughness, etc.
On the other hand, a large number of theoretical studies on
the liquid/liquid interface by computer simulation have beenreported.17-25 Many of these reports have predicted the density
profile of liquid/liquid interfacial regions by the molecular
dynamics (MD) method. These predictions are based on* To whom correspondence should be addressed.

statistical mechanics and include assumptions on the molecularpotential in the simulated model. Mass density may be a typicalparameter standing for the structure. Therefore, experimental
approaches to the interfacial density are of great significance.
A number of researchers have investigated liquid surfaces
by measuring capillary waves generated thermally at liquidsurfaces.26-30 Since capillary waves reflect the fundamental
properties of the surface or interfacial region, much effort has
been made to observe them and to analyze their spectra. We
have developed a quasi-elastic laser scattering (QELS) method
for measuring the interfacial capillary waves. Owing to ourimprovement of its time resolution, we have successfully
monitored the dynamic changes of interfacial molecular number
density of surfactants and have thereby provided insight into
the interfacial mass transfer.31-34 Moreover, in the present study
we have applied the QELS method to the density estimation ofliquid/liquid interfacial regions. The purpose of this work is
to estimate the interfacial density from the capillary wave using
the QELS method. Since the density reflects the interfacial
structure as discussed above, it provides insight into themolecular structure of the liquid/liquid interface. We present
here our method and results for the density estimated fromcapillary wave frequencies in terms of macroscopic hydrodynamic theory.
Theoretical Background
Capillary waves occur spontaneously at liquid/gas or liquid/
liquid interfaces due to thermal fluctuation of the bulk phases.
The theoretical understanding of these waves is well establishedin hydrodynamics, and light scattering from the waves is widelyused to monitor the interfaces.35,36 Since the capillary wave
frequency is a function of five parameters (the interfacial tension
and the interfacial densities and viscosities of both phases), theinterfacial densities and viscosities can be estimated from thecapillary wave frequency in principle. Here we briefly present
the relevant theory for density measurements. We note thatthe following hydrodynamic theory assumes a macroscopic,
continuous medium at the interfacial region, although it isactually composed of molecules.
The thermally excited displacement ξ(r,t) of the free surface

S1089-5647(97)02995-7 CCC: $15.00 © 1998 American Chemical Society
Published on Web 03/25/1998

Liquid/Liquid Interfacial Regions

J. Phys. Chem. B, Vol. 102, No. 15, 1998 2685

of a liquid from the equilibrium position normal to the surface
can be Fourier decomposed into a complete set of surface modesas∑k exp[ik‚r + Ωt]

ξ(r,t) ) ξ0(1)

The complex wave frequency ()i0ω0 - Γ) is related to k via adispersion relation.
For an inviscid liquid, Lamb’s equation is well-known as aclassical approximation for the dispersion relation37

f)

(

)

1/2
γ
1
k3/2
2π FU + FL

(2)

where f is the capillary wave frequency, γ the interfacial tension,
FU the density of the upper phase, FL the density of the lower
phase, and k the wavenumber of the capillary wave. Thisequation is valid for both liquid surfaces and liquid/liquidinterfaces. For capillary waves at a liquid surface, FU is regarded
as zero in eq 2. In this equation, only the normal componentof the interfacial tension is considered to act as a restoring force
on the thermally excited displacement (r,t). Although thisequation neglects the effect of surface viscosity, it gives a good
fit to the observed relation between the frequency and wavenumber of capillary waves at a liquid surface such as ethanol,
anisol, or water.29,38
For the surface of a low-viscosity liquid, Levich39 has derived
the following dispersion relation:

D(S ) ) (S + 1)2 + y - (2S +1)1/2 ) 0(3)where S ) Ω/2νk2 and y ) σ/4Fν2k. Here ν is the kinematic
viscosity (ν ) η/F, where η is the viscosity of the liquid). In
this equation, both the normal components of the surface tension
and the viscous stress contribute to the restoring force on thedisplacement (r,t). Based on this equation, a heterodyne power
spectrum of the capillary wave in the frequency domain becomesa Lorentzian profile centered at

ω0 ) 2πf ) |Im(Ω)|(4)

having the full width at half-maximum (fwhm)

π∆f ) |Re(Ω)|(5)

Under the condition that the effect of the viscosity is negligible,
eq 3 is simplified to

Figure 1. Schematic diagram of the experimental setup for the QELS
method. A glass cylinder with an optically flat bottom is immersed in
the alcohol phase to avoid the observation of surface capillary waves.

adopted this equation for the analysis of the liquid/liquidinterfacial spectra.
Experimental Section
Method. The principle of the QELS method has already been
described previously.33,34 In brief, an incident laser beam normal
to the interface is scattered quasi-elastically with a Doppler shiftby the capillary waves (Figure 1). The scattered beam is
optically mixed with a local beam produced by a diffraction
grating to generate an optical beat in the mixed light.42 The
obtained beat frequency is the Doppler shift, i.e., the capillary
wave frequency. The generated optical beat is measured by aphotodiode, and the signals are Fourier transformed by a digitalspectrum analyzer. In the present study, we observed capillary
waves having a wavelength of 1.1 × 10-2 cm.
Sample Preparation. 1-Hexanol, 1-heptanol, 1-octanol,
1-decanol, hexanoic acid, heptanoic acid, octanoic acid, andnonanoic acid (all analytical grade, Kanto Chemical Co.) wereused without further purification. Purified water from a
Millipore Milli-Q system was used. Liquid/liquid interfaces
were prepared by adding the alcohol or the carboxylic acid to
the water in a quartz cell. The samples were left for more than
48 h before measurement so that equilibrium is establishedbetween the two phases.
Results and Discussion

1 γ 1/2 3/2
k
f)
2π F

()

(6)

∆f ) 2νk2/π

(7)

and

Equation 6 is the same as Lamb’s classical approximation (2).
Since Levich’s eq 3 was derived only for a liquid surface,some researchers have extended the equation to a liquid/liquidinterface.40 Jon et al.41 have proposed the analysis of liquid/
liquid interfacial spectra using a dispersion relation similar toeq 3. In their case F is taken as the sum of the densities ofboth phases and as the sum of the viscosities of both phases,that is, F ) FL + FU and ν ) (ηL + ηU)/(FL + FU) are substituted
into eq 3. Here FL and FU are the densities of the lower andthe upper phases, and ηL and ηU the viscosities of the lower
and the upper phases, respectively. In the present study, weA typical power spectrum obtained by the QELS method isshown in Figure 2. The broad peak centered at 2.0 kHz is dueto the capillary wave at the 1-decanol/water interface having awavelength of 1.1 × 10-2 cm. The detected signals are
somewhat noisy because of the transmitting optical configuration
employed in the present study. The width of the spectrum isdetermined by the instrumental function as well as the interfacial
viscosity. The asymmetric shape of the spectrum is considered
to be intrinsic to the capillary waves of low frequencies, andfurther theoretical investigation is needed to elucidate the shape.
In the present case, only the peak frequency is used for the
analysis. Table 1 shows the peak frequencies of capillary waves
at each interface along with the number of carbon atoms.
The densities of the liquid/liquid interfacial regions are
estimated from the peak frequencies of capillary waves using
eq 3. By substituting the capillary wave frequency, thekinematic viscosity and the interfacial tension in the literature43,44

2686 J. Phys. Chem. B, Vol. 102, No. 15, 1998

Tsuyumoto et al.

Figure 2. A typical power spectrum for the capillary wave at the
1-decanol/water interface.

TABLE 1: Peak Frequency (kHz) of the Capillary Wave at
Studied Water/Alcohol and Water/Carboxylic Acid
Interfaces at 25 °Ca
samplepeak freq

samplepeak freq

1-hexanol/water
1-heptanol/water
1-octanol/water
1-decanol/water

2.59
2.80
2.68
2.01

hexanoic acid/water
heptanoic acid/wateroctanoic acid /water
nonanoic acid /water

2.48
2.80
3.05
1.78

aThe wavelength of each capillary wave is 1.1 × 10-2 cm.

into the equation, we obtain the sum of the interfacial densitiesof the upper and lower phases.
The kinematic viscosity and the density should be determined
independently by nature. Some researchers have reported thesurface viscosity as determined from the width of the capillary
wave spectra.26,35,45,46 In the present study, however, theinstrumental function was undetermined because of the transmitting optical configuration employed for the observation of
the interface, and the width could not be used for the analysis.
Regarding the reported results, the interfacial viscosity wasdifficult to determine even for liquid surfaces, and Langevin26
has reported that a highly viscous surface region does not exist
on the water surface. Thus, we assume this result also applies
to water surfaces in the interfacial region and therefore that thekinematic viscosity of the interfacial region can be related tothe bulk phase viscosities as described above. In addition, thechange in viscosity hardly affects the capillary wave frequency
whereas the change in density strongly affects the frequency.
This suggests that the large deviation of the frequency fromthe theoretical value is owing to the change in density.
The experimentally estimated densities (F ) FL + FU of eq3) of the alcohol/water and carboxylic acid/water interfacial
regions are shown in Figure 3. These values are lower thanthe calculated bulk FL + FU values except for the hexanoic acid/water and heptanoic acid/water interfaces, and there is a marked
decrease in the interfacial density as the hydrophobic group of
the alcohol molecule becomes larger. While this difference
between the experimental and the calculated FL + FU values
may mean that the interfacial mass density is actually lower
than the bulk phases, it could also indicate that Levich’s
equation, which assumes a continuous medium at the interfacial
region, cannot be applied to microscopic interfacial regions.
However, a number of reports have indicated the validity of
Levich’s equation for liquid surfaces.26,29,46 By analogy, weinterpret our results assuming the validity of Levich’s equation
at liquid/liquid interfaces. We conclude that alcohol/waterinterfacial regions have smaller densities than the bulk phases
and that the hydrophobic groups in both alcohol and carboxylic
acid molecules cause some porosity in the interfacial regions.

Figure 3. Relationship between the total density (the sum of the upper
phase and the lower phase, FL + FU) and the number of carbon atoms
in the hydrophobic group. The experimentally estimated interfacial
densities are shown as 9 and 2 for alcohol and carboxylic acid,respectively. The calculated bulk phase densities are shown as 0 and
4 for alcohol and carboxylic acid, respectively.

Our results are consistent with these obtained from othertheoretical and experimental studies.47-49 Michael and Benjamin47 have reported MD simulations that show the density of
the water/1-nonane interface to be smaller than that of water/“spherical” nonane, and Benjamin48 has indicated that the total
density of the water/1-octanol interface is smaller than that of
the bulk phase. Moreover, Conboy49 et al. have observed asignificant degree of molecular ordering at alkane/water interfaces using the SHG method. It may be reasonable to thinkthat the alcohol molecules are also ordered at the liquid/liquidinterfacial region, directing a hydrophobic group to the alcohol
phase and a hydrophilic group to the water phase. Thus, wemight hypothesize from these results and say that the orientationof the hydrophobic group at the interfacial region causes theinterfacial porosity.
Our experimental results have been interpreted on the basisof the macroscopic continuous medium model of hydrodynamic
theory. In this model the two phases are separated discontinuously by a dividing line having no width, and the microscopic
interfacial region is also regarded as a continuous medium. Theinterfacial region, however, is actually composed of molecules,
and the two phases are considered to be mixed at the interfacial
region. For a more precise discussion on microscopic interfacial
regions, a molecular theoretical interpretation of capillary waves
based on statistical mechanics will be necessary. Such a theory
would make the QELS method a more powerful tool for the
study of liquid surfaces or liquid/liquid interfaces.
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