J. Phys. Chem. A 1997, 101, 4163-4166

4163

Monitoring of Molecular Collective Behavior at a Liquid/Liquid Interface by aTime-Resolved Quasi-Elastic Laser Scattering Method
Zhenhui Zhang, Isao Tsuyumoto, Satoshi Takahashi, Takehiko Kitamori, and Tsuguo Sawada*
Department of Applied Chemistry, School of Engineering, The UniVersity of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113, Japan
ReceiVed: December 9, 1996; In Final Form: March 10, 1997X

We monitored the change in the number density of cetyltrimethylammonium bromide (CTAB) molecules ata water/nitrobenzene (W/NB) liquid/liquid interface by a newly developed time-resolved quasi-elastic laser
scattering (QELS) method. The results are used to discuss the molecular collective behavior there. From
the time-courses after the injection of a CTAB solution beyond its critical micelle concentration (cmc), we
found an anomalous temporary increase of the number density of CTAB molecules at the interface, whichcannot be explained by a simple diffusion model. This suggests that the transfer of CTAB micelles acrossthe interface occurs in the following process: the collapse of micelles at the interface region; the oriented
adsorption of CTAB molecules onto the interface, forming a monolayer; and the desorption from the interface.
Thermodynamic evaluation results also support this model; that is, the equilibrium number density of CTAB
molecules at the interface follows the Langmuir adsorption isotherm obtained from our measurement, andthe adsorption energy calculated from the isotherm agrees well with the theoretical value of the micelles.

Introduction
The interface between two immiscible liquids is one of themost interesting and important areas of study, since transportphenomena across the interface are fundamental to understanding solvent extraction, chromatography, phase transfer catalysis,
biological membranes, etc. Although numerous experimental
studies and theoretical modelings have been done,1-3 there arestill some basic points to be clarified, e.g., the nature of thebarrier in mass transfer across the interface and the molecularinterface structure.
Experimental probes of structure have been done mainly by
spectroscopic techniques, which are advantageous for monitoring
the interface between two bulk phases because their measurements result in no mechanical perturbation. Second harmonic
generation (SHG) and sum frequency generation (SFG) techniques have been used to probe liquid/liquid interfaces and havethe potential to provide interface dynamic properties.4-13 These
techniques are suitable for the measurement of the orientationof adsorbed molecules at liquid/liquid interfaces, but they cannot
provide information on the behavior of the molecules in adisordered orientation. Neutron specular reflectivity measurements have been used to study the effect of surfactants on theroughness of oil/water interfaces.14 This method, however,requires too much time to allow its use in elucidating molecular
dynamic behavior. Therefore, these spectroscopic techniques
are not appropriate for the dynamic properties of the interfaces,
because they require too much time for measurement.
We have developed a quasi-elastic laser scattering (QELS)
method for monitoring the dynamics of liquid/liquid interfaces.15-17 The QELS method has an advantage over otherspectroscopic methods, owing to its improved time-resolution,that each power spectrum can be obtained in 1-3 s. The
method monitors the frequencies of capillary waves, which arespontaneously generated by thermal fluctuation at liquid/liquidinterfaces. Since the capillary wave frequency is a function ofinterfacial tension, and the change in the interfacial tension* To whom all correspondence should be addressed.
X Abstract published in AdVance ACS Abstracts, May 15, 1997.

S1089-5639(96)04016-9 CCC: $14.00

reflects the change in the number density of surfactant molecules
at the interface, the QELS method enables us to observe thedynamic change of liquid/liquid interfaces such as the formationof a lipid monolayer17 and the change in number density ofsurfactant molecules.
In this study, we focus on the molecular collective behaviorof surfactant molecules at a liquid/liquid interface. Since
amphiphilic surfactant molecules contain both a hydrophilic head
and a hydrophobic tail, they are expected to exhibit meaningful
behavior of the investigation of dynamic properties of liquid/
liquid interfaces. Moreover, interest in the behavior of
surfactants is growing because they play an increasingly
important role in various chemical and biological areas such as
the synthesis of inorganic materials, pharmaceuticals, anddetergents.18-20 Then we focus on elucidating the molecularcollective behavior in transfer across a liquid/liquid interface
by using the QELS method.
Here we present the results from monitoring the capillary
wave frequency at a liquid/liquid (W/NB: water/nitrobenzene)
interface by the QELS method when a cationic surfactant(CTAB: cetyltrimethylammonium bromide) solution was injected into the aqueous phase. An anomalous change of thecapillary wave frequency was observed when a CTAB solution
beyond the critical micelle concentration (cmc) was injected,
and we discuss a model for mass transfer dynamics across theinterface.
Experimental Section
Principle. The principle of the quasi-elastic laser scattering
method was described previously.15-17 A brief outline follows
here based on Figure 1. A thermally generated spontaneousdensity fluctuation occurs at the liquid/liquid interface. Theinterfacial tension acts as a restoring force on the fluctuation,and it excites an interfacial tension wave, which is called acapillary wave or ripplon. The incident beam normal to theinterface is quasi-elastically scattered by the capillary wave witha Doppler shift at an angle determined by the following equation:

K tan θ ) k© 1997 American Chemical Society(1)4164 J. Phys. Chem. A, Vol. 101, No. 23, 1997

Zhang et al.

Figure 1. Principle of the quasi-elastic laser scattering method.

where K and k are the wavenumbers of the incident beam andthe capillary wave, respectively. Thus, the wavenumber k ofthe capillary wave is obtained by giving θ.
We arranged a transmitting diffraction grating in front of thecell to adjust the angle θ.21 The angle θ is determined by thefollowing equation using the spacing d and the order n of thediffraction grating,d sin θ ) nλ(2)where λ is the wavelength of the laser beam.
From eqs 1 and 2, we obtain the wavenumber k and thewavelength Λ of the observed capillary wave:k ) 2πn/d(3)Λ ) d/n(4)

The capillary wave frequency is detected by an optical
heterodyne technique. The laser beam quasi-elastically scatteredby the capillary wave at the liquid/liquid interface is accompanied by a Doppler shift. The scattered beam is optically
mixed with the diffracted beam from the diffraction grating to
generate an optical heat in the mixed light. The beat frequency
obtained here is the same as the Doppler shift, i.e., the capillary
wave frequency. By selecting the order of the mixed diffracted
beam, we can change the wavelength of the observed capillary
wave according to eq 4.
The relationship between the capillary wave frequency f andthe interfacial tension γ is approximately expressed by Lamb’s
equations,22

f)

(

)

(5)

F ) Fw + Fo

(6)

1/2
1
γ
k3/2
2π Fw + Fo

where Fw is the density of the aqueous phase, Fo is the densityof the oil phase, and k is the wavenumber of the capillary wave.
The relationship between the interfacial tension γ and thenumber density Γ of a monolayer is approximately expressedby the following equation, as we have reported previously:16,17

γ ∝ 1/Γ

(7)

We employed this experimental relation instead of the conventional Gibbs equation because it is actually more suitable forour liquid/liquid interfacial system. Therefore, the number
density Γ of surfactant molecules can be monitored by measuring the capillary wave frequency f. Since the time-resolutionof the QELS method is 1-3 s, the method can provide great
insight into the collective motion of surfactant molecules at theinterface.

Figure 2. Schematic diagram of the experimental setup: NB,
nitrobenzene phase; W, water phase; S, microsyringe; T, glass tube;
PD, photodiode; AMP, preamplifier; FFT, FFT analyzer.

Apparatus. A schematic diagram of the experimental setup
is shown in Figure 2. The beam from a He-Ne laser with 10
mW power (Uniphase 1135P) is incident on the transmitting
diffraction grating having a spacing of 3.3 × 10-2 cm and passes
through the bottom of the sample cell. The cell is made ofquartz glass and has an optically flat bottom, which is indispensable to maintaining good reproducibility of the experimental
results. After passing through the sample, the diffracted beams
are mixed with the scattered light from the capillary wave, andone of them is selected by an aperture (1 mm φ) positioned in
front of a photodiode. The optical beat of the mixed light ismeasured by the photodiode (Hamamatsu Photonics S1290). The
signals are Fourier transformed and saved by a digital spectrum
analyzer (Takeda Riken TR9404). In the present study, the fifthorder diffracted beam was selected for the measurement. Thus,
the wavelength of the observed capillary wave was 6.6 × 10-3
cm according to eq 4.
Sample Preparation. A liquid/liquid interface was preparedby slowly adding 10 mL of purified water (from a Millipore
Milli-Q system) to 10 mL of nitrobenzene (Kanto ChemicalCo., Inc.; special grade; 99.5% purity) in the quartz cell. To
observe the collective motion of surfactant molecules, theinjection of a CTAB solution (0.5 mL; Kanto Chemical Co.,
Inc.; first grade) to the aqueous phase was carried out with amicrosyringe. The concentrations of the injected CTAB solution
were in the range 2-30 mM; the average concentrations of
CTAB in the aqueous phase after injection were in the range
0.1-1.5 mM. The cmc of a CTAB solution, beyond whichsurfactant molecules form micelles, is 1.3 mM at 25 °C. We
intended to study how the behavior of surfactant moleculeschanges around the cmc.
Results and Discussion
Typical power spectra for capillary waves excited at the
W/NB interface are shown in Figure 3: (a) without CTAB
molecules and (b) 10 s after the injection of a CTAB solution(0.5 mL, 10 mM) to the aqueous phase. The detected signals
are somewhat noisy, but the beats of the local beam and thescattered beam due to the capillary wave are seen in the spectra.
The peaks appearing around 10-13 kHz are the beat frequencies, i.e., the capillary wave frequencies, as we discussed
previously.16,17 The peak of the capillary wave frequency shifts
from 12.5 to 10.0 kHz on the injection of CTAB solution. Thisis due to the decrease in interfacial tension caused by theincreased number density of surfactant molecules at theinterface.

Monitoring of Molecular Collective Behavior

Figure 3. Power spectra for capillary waves excited at the W/NB
interface (a) without CTAB molecules and (b) 10 s after injection of a
CTAB solution (0.5 mL, 10 mM) into the water phase.

Figure 4. Capillary wave frequency vs time after injection of the
CTAB solutions (0.5 mL, 2-30 mM). The concentrations of theinjected solution (C) are shown, along with the average concentrations(Ceq) in the aqueous phase.

In order to examine the change in the number density ofsurfactant molecules at the interface in detail, we investigated
the time-course of the capillary wave frequency after the
injection of the CTAB solution into the aqueous phase. The
power spectrum was obtained every 3 s, and the capillary wave
frequencies after the injection of the CTAB solution (0.5 mL,
2-30 mM) are plotted as a function of time in Figure 4. From
Figures 3 and 4, it is apparent that the time-resolution (3 s) of
the present QELS method is sufficiently high to detect thechange in the number density of CTAB molecules at theinterface. In Figure 4, an anomalous temporary decrease incapillary wave frequency is observed when the CTAB solution
beyond the cmc was injected. The capillary wave frequency
decreases rapidly on injection, and after attaining its minimum
value, it increases gradually, as shown in Figure 4. The initialsudden change means an abrupt increase in the molecularnumber density at the interface.
When the injected concentration of CTAB is below the cmc,
the capillary wave frequencies gradually decrease, in otherwords, the molecular number density gradually increases. We
have explained this gradual change of molecular number density
using a diffusion model.23 The theoretical time-course of thenumber density of the surfactant molecules at the interface
calculated by assuming that surfactant molecules are transferred
only by diffusion from one phase to the other is in good
agreement with the observed one below the cmc. This diffusion
model, however, cannot explain the anomalous behavior beyond
the cmc. Therefore, it seemed natural to us to consider theadsorption of surfactant molecules onto the W/NB interface. In
short, the abrupt decrease in the capillary wave frequency canbe attributed to the adsorption of surfactant molecules onto the
W/NB interface from the W phase, while the gradual increase

J. Phys. Chem. A, Vol. 101, No. 23, 1997 4165

Figure 5. Capillary wave frequency vs CTAB average concentrationin the water phase.

is due to the desorption from the W/NB interface to the NB
phase.
Details can be added to the above outline by estimating themolecular number density of CTAB at the interface from Figure
4. Around the minimum frequency, both adsorption onto the
W/NB interface from the W phase and the desorption from theinterface to the NB phase are taking place as competing
processes. It is clear from Figure 4 that the former process ismuch faster than the latter one. Thus, at the minimum
frequency, it is reasonable to assume that the adsorption
equilibrium between the W phase and the W/NB interface isestablished and that the mass transfer from the W/NB interface
to the NB phase is negligible. On the basis of this assumption,
we estimated the molecular number density of CTAB at theinterface from the minimum value of the capillary wave
frequency in Figure 4.
The minimum value of the capillary wave frequency changes
with the average concentration of CTAB as shown in Figure 5.
Since the square of the capillary wave frequency is proportional
to the interfacial tension (eq 5), which is approximately inversely
proportional to the number density of surfactant molecules (eq7), the relationship between the number density of CTAB
molecules adsorbed onto the interface and the average concentration of CTAB in the W phase was obtained as shown in
Figure 6. The experimental data are in good agreement withthe calculated Langmuir adsorption isotherm, indicating that theadsorbed surfactant molecules are confined to a monomolecularlayer, and the affinity of each binding site for surfactant
molecules is the same. It is apparent from this result that the
CTAB molecules are adsorbed onto the interface as an orientedmonolayer. This is consistent with the experimental results by
the SFG measurements, which indicated that SDS (sodium
dodecyl sulfate) molecules are ordered at the D2O/CCl4 interface
as a monolayer.10 Therefore, we thought Figure 4 suggested
that the transfer of CTAB molecules across the interface occurs
via the following process (Figure 7): the collapse of micelles
at the interface region; the oriented adsorption of CTAB
molecules onto the interface, forming a monolayer; and thedesorption from the interface.
Then, to confirm this model, we made a thermodynamic
evaluation. The adsorption energy of the CTAB micelles onto
the interface is estimated at ca. -29.4 kJ/mol from theexperimental data in Figure 6 using the following equation,24

ln CCTAB ) (E - µCTAB°)/kT + ln x/(1 - x)(8)where CCTAB is the concentration of the CTAB (here, it isreasonable to use concentration instead of activity because theconcentration of CTAB is low enough), E is the adsorptionenergy, µCTAB° is the chemical potential of CTAB molecules
in a 1 M solution, and x is the occupancy of the adsorptionsite.

4166 J. Phys. Chem. A, Vol. 101, No. 23, 1997

Zhang et al.

Figure 6. Interface coverage by CTAB molecules vs CTAB average
concentration in the water phase. Experimental data are shown as
squares, and the calculated Langmuir adsorption isotherm is the solidline.

The theoretical adsorption energy of the CTAB micelles iscalculated as the difference between the adsorption energy of
CTAB molecules and the micelle formation energy. The
adsorption energy of the CTAB molecules from an aqueous
solution onto the interface is estimated at -51.4 kJ/mol fromthe free energy change ∆Gm°(-CH2-) when 1 mol of methylene groups (-CH2-) move from an aqueous solution to awater/oil interface,25∆Gm°(-CH2-) ) -RT ln k
) -3.42 kJ/mol

Figure 7. Schematic illustration of the collective motion of CTAB
molecules at the liquid/liquid interface and its vicinity: (a) C < cmc;(b) C > cmc.

molecules. On the other hand, new fundamental questions arise
from the present model. For example, what triggers the collapseof micelles? In what part of the interface region do the micelles
collapse? It is apparent that the micelles are affected by someof the properties of the interface before they collapse, and these
special interface properties must be closely associated withbehavior. The QELS method is a powerful tool for studying
molecular dynamics at liquid/liquid interfaces, and we can
expect it to be turned to answering these questions.
References and Notes(9)where R is the gas constant (8.31 J K-1 mol-1), T is thetemperature, and k is the adsorption parameter that appears inTroube’s rule.
The formation energy of the micelles is roughly estimatedas -26.4 kJ/mol using the following equation:∆Gm° ) RT ln XCMC

(10)

XCMC ) 18.02C0/1000F(11)

where C0 is the critical micelle concentration, and F is thedensity of the solution.26 The theoretical adsorption energy of
the CTAB micelles is estimated as -25.0 kJ/mol from thedifference between the theoretical adsorption energy of the
CTAB molecules (-51.4 kJ/mol) and the formation energy of
the CTAB micelles (-26.4 kJ/mol).
The experimental adsorption energy (-29.4 kJ/mol) calculated from the Langmuir isotherm is in agreement with thetheoretical adsorption energy of the CTAB micelles (-25.0 kJ/mol), and not with that of CTAB molecules (-51.4 kJ/mol).
This indicates that the CTAB micelles are in equilibrium withthe adsorbed CTAB molecules, and consequently, the CTAB
micelles collapse to molecules immediately before the adsorption
onto the interface. Therefore, we concluded that the above
thermodynamic investigation strongly supports the collective
behavior of the CTAB molecules described in Figure 7.
The dynamics of mass transfer across the liquid/liquidinterface can be observed by the time-resolved QELS method,
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