JOURNAL OF CHEMICAL PHYSICSVOLUME 111, NUMBER 20

22 NOVEMBER 1999

Generation and observation of GHz ultrasonic waves on liquid surfaces
and a liquid/liquid interface by transient reflecting grating method
Sachiyo Ikeda, Kenji Katayama,a) Takayuki Tanaka, and Tsuguo Sawadab)
Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University ofTokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Isao Tsuyumoto
Department of Environmental Systems Engineering, Kanazawa Institute of Technology, 7-1 Ohgigaoka,
Nonoichi, Ishikawa 921-8501, Japan

Akira Harata
Department of Molecular and Material Sciences, Graduate School of Engineering Sciences, Kyushu
University, Kasugakoen 6-1, Kasuga-shi, Fukuoka 816-8580, Japan

共Received 5 April 1999; accepted 31 August 1999兲
We optically generated and observed GHz ultrasonic waves on liquid surfaces and a liquid/liquidinterface for the first time using the transient reflecting grating 共TRG兲 method. Four kinds ofsamples were used for measurement of the surfaces; two types of black ink, an aqueous solution of
crystal violet 共CV aq solution兲 and ethanol aqueous solutions of CV. A cyclohexane/CV aq solution
interface was used for measurement of the liquid/liquid interface. The 0.7 GHz and 0.6 GHz
ultrasonic waves were generated on the liquid surfaces and the liquid/liquid interface, respectively.
These ultrasonic waves resemble longitudinal acoustic waves partly localized at the surface, andthey cause surface displacement. The amplitudes of TRG signals from surfaces of the CV mixed
solvent solutions were found to be greatly affected by both the viscosity and surface tension. This
result indicated the viscosity and interface tension must be considered as perturbations in the elastic
theory. The strong dependence on interface tension showed the high selectivity of the TRG signals
for the interface. © 1999 American Institute of Physics. 关S0021-9606共99兲70244-8兴

INTRODUCTION

nomena of bulk molecules such as molecular dynamics oftranslation, vibration, and rotation, solute–solvent effect, andisomerization have been discussed using many methods. Ultrasonic spectroscopy is one method to investigate themechanism of the absorption or the relaxation of the ultrasonic waves in a substance using a spectrum of the soundvelocity or the absorption coefficient vs the frequency of theultrasonic waves. For liquid samples, ultrasonic waves with afrequency between the MHz and GHz region are mainly
used. The dissociation reaction of micelles and monomers ina surfactant solution and the local rotational dynamics ofpolymer chains in a polymer solution have been investigatedwith this method.12–14 Furthermore, the hydration number ofions in an electrolyte solution has been determined from theadiabatic compressibility obtained by measuring sound velocity in the solution.15–17 Thus, we focus on the applicationof this method to liquid surfaces and liquid/liquid interfaces.
Therefore, techniques to induce and observe ultrasonicwaves on liquid surfaces and liquid/liquid interfaces with thefrequency from the MHz to GHz region are highly desirable.
Waves on a liquid surface have been investigated for along time, beginning more than two hundred years ago froman interest in the waves at sea. Early casual interest gaveaway to serious studies in the 1960s which used mechanicalmethods. Mann and Hansen18 induced and observed waves
using a ripple generator and ripple transducer, while Davies
and Vose19 induced waves with an electromagnetic vibrator
and observed them stroboscopically. Still in the 1960s Lu-

Liquid surfaces have attracted much attention because
they play important roles in basic processes in various fields
of science and technology, e.g., evaporation, condensation,energy transfer, mass transfer, and photoionization.1–3 However, experimental research on liquid surfaces is still in an
early stage because it is difficult to measure them.4 Microscopic clarifications of the structures, roughness, properties
such as elasticity, viscosity, and interface tension, andsolute–solvent interaction of the liquid surface and theliquid/liquid interface are highly desirable. The static structures of liquid surfaces have been proposed based on resultsfrom second harmonic generation and sum frequency
generation,5–7 but the dynamic processes on liquid surfaces
are still unknown. As a method to investigate and analyze thecollective molecular dynamics on liquid surfaces, the quasielastic laser scattering method has been reported.8–11 It allows the measurement of capillary waves on liquid surfaces
and liquid/liquid interfaces with a frequency up to the MHz
region. However, it is still insufficient to observe fast phenomena of intra- and intermolecules around liquid surfaces
and liquid/liquid interfaces. Although much effort has been
made, there still remain many fundamental problems to beclarified.
As for solute molecules in bulk solution, the fast pheElectronic mail: katayama@laser.t.u-tokyo.ac.jp; Fax: ⫹81-3-5841-6037.
Author to whom all correspondence should be addressed.

a兲b兲

0021-9606/99/111(20)/9393/5/$15.00

9393© 1999 American Institute of Physics

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J. Chem. Phys., Vol. 111, No. 20, 22 November 1999

cassen first discussed longitudinal waves, and Sohl et al.20
developed an apparatus to investigate longitudinal waves byintroducing an electrocapillarity method. This technique wasfollowed by Miyano21 and the waves were induced by electric fields and observed with a laser beam. Hajiloo22 generated waves on liquid surfaces by a laser beam and this technique was easily extended to liquid/liquid interfaces as well.
However, these techniques were not able to generate surface
waves with a frequency between the MHz and GHz region.
To measure ultrasonic waves with such a high frequency
on solid surfaces and at solid/liquid interfaces, we and otherfew groups have developed a transient reflecting grating
共TRG兲 technique.23–26 Fayer and co-workers27,28 and Nelson
and co-workers28 presented detailed theoretical analysis of
the method. This technique was used to generate and detect
GHz surface acoustic waves successfully. Elastic and thermal properties of thin films and multilayer thin films were
estimated by this technique.29–33 Some chemical or physicalapplications were also made for measurements of ultrafast
carrier dynamics.34–38 This method has advantages of providing noncontact, nondestructive, and interface-selective
measurements, and high temporal resolution. Moreover, it
can be applied to various types of samples because it utilizes
nonradiative relaxation processes.
Therefore, as we have demonstrated on solid surfaces
and solid/liquid interfaces, the optical generation and observation of GHz ultrasonic waves will be a powerful tool for
an investigation of liquid surfaces and liquid/liquid interfaces.
In this study, we apply the TRG method to the liquidsurfaces and the liquid/liquid interface and to investigate thepossible use as a technique to generate ultrasonic waves on
liquid surfaces and at liquid/liquid interfaces.
PRINCIPLE

The TRG method uses optical interference fringes on
surfaces.22–33 Two temporally coincident laser pulses 共pump
pulses兲 with the same wavelength produce optical interference fringes on and under the sample surface. These opticalfringes cause spatial modulations of the refractive index andsurface displacement. Increases in photoexcited species andin temperature are the main causes of the refractive index
modulation. The modulation of the surface displacement iscaused by thermal expansion. All these modulations work as
a transient reflecting grating 共TRG兲 which causes a third
pulse beam 共probe beam兲 to be diffracted. A TRG is considered as a corrugated grating superimposed on the reflectivity
grating. For convenience, a TRG is classified into three
types; a population grating formed by the density distributionof photoexcited species, a thermal grating formed by thetemperature distribution resulting from nonradiative relaxation and heat generation, and an acoustic grating formed bythermal expansion that generally generates counterpropagating surface acoustic waves for solids. For liquids, the acoustic grating is due to a longitudinal acoustic wave localized at
the interface. Both the spacing and direction of the grating
are optically controllable. The optical fringe spacing ⌳ isgiven by

FIG. 1. The optical arrangement to observe the liquid surfaces and theliquid/liquid interface.

⌳⫽␭/2 sin ␪ ,共1兲

where ␭ is the optical wavelength and 2␪ is the incident
angle of the pump pulses. Thus, ⌳ is tunable over a range
from sub-␮m to more than 100 ␮m with a visible laser
source.
EXPERIMENTThe experimental setup of the TRG system was the sameas described previously,31–33 except for the arrangement toobserve liquid surfaces and liquid/liquid interfaces 共Fig. 1兲.
A mirror was placed between the lenses and the liquidsample on the stages, and consequently both pump and probe
pulses were incident on the liquid surface and the liquid/
liquid interface. A mode-locked Q-switched Nd:YAG laser
共Quantronix, model 416兲 was used as a light source. The
pulse train wavelength was 532 nm with a repetition rate of
1 kHz and a pulsewidth of 80 ps in full-width at halfmaximum. The pulse was separated into pump and probe
pulses using a partial reflective mirror. The pump beam wasfurther divided into two beams by a half-mirror. The twopump pulses were crossed and irradiated onto the same spotof the sample surface so as to coincide in time to form aninterference pattern. The probe pulse was irradiated at thecenter of the spot after passing through a computercontrolled optical delay line. The reflecting diffracted light
was monitored with a photomultiplier 共PMT兲 connected to a
flexible light guide, whose entrance was placed at one of thefirst order reflecting diffraction spots. The output signal fromthe PMT was gated and averaged over one millisecond witha boxcar integrator before an analog-to-digital transformation for computer storage. The spot diameters of the pumpand probe beams were 60 ␮m and 40 ␮m, respectively. The
fringe spacing was typically 2.3–2.4 ␮m. The intensity ofthe pump and probe pulse was less than 3, 0.1 ␮J/pulse,
respectively.
We used four liquid samples for measurements of thesurfaces: black ink 1, ‘‘art pen ink’’ 共Rotring, Art.R598
317兲; black ink 2, ‘‘drawing ink’’共Rotring, Art.R591. 017兲;
an aqueous solution of crystal violet 共CV; Kanto ChemicalCo., Inc.: special grade兲; and CV ethanol aqueous solutions.
Thin layer chromatography showed that the first threesamples were a colloidal solution, a mixed-dye aqueous solution, and a single-dye aqueous solution, respectively. A
cyclohexane 共Kanto Chemical Co., Inc.; special grade兲/CV
aq solution interface was used for measurement of the liquid/
liquid interface. All the reagents were used as purchased

J. Chem. Phys., Vol. 111, No. 20, 22 November 1999

GHz ultrasonic waves on liquid surfaces

9395

TABLE I. The experimental frequencies of the vibrations f ac and the attenuation time constants ␶ ac of the two TRG signals obtained by fitting formula
共1兲, and the velocity V ac calculated as the product of f ac and the fringe
spacing ⌳.

FIG. 2. 共a兲, 共b兲, and 共c兲 are the TRG signals from the surfaces of the CV
aqueous solution 共36 mM兲, and black inks 2, and 1, respectively. Pump
power, 2.9 ␮J/pulse. Grating spacing, 2.3 ␮m.

without further purification. The two black inks were diluted
by purified water 共from a Millipore Milli-Q system兲 and solutions were prepared in the range of 10–100 %w/w. The CV
aq solutions were prepared in the range of 4.4–36 mM. The
CV ethanol aqueous solutions were prepared at 10 mM andthose solvents were prepared by mixing ethanol into purified
water with ratios of 100%, 50%, 20%, 5%, and 0%. The
optical absorption length of these samples was in the range
of 5–10 ␮m. About 5 ml of these samples were added to a
glass measurement cell which had a depth of 1 cm. As forthe liquid/liquid interface, about 5 ml of 10 mM CV aq
solution were added before the addition of the same volume
of cyclohexane to the solution.
RESULTS AND DISCUSSION

The TRG signals from the surface of black ink 1, 2, andCV aq solution are shown in Fig. 2. The signal of black ink
1 has neither sharp peaks nor vibrations, but rather a gentle
slope after the maximum value. Signals of black ink 2 andthe CV aq solution have the largest and the sharpest firstpeak, and both show vibrations. This is the first observationof TRG signals with vibrations from liquid surfaces, which
are very similar to those from solid surfaces.
In order to analyze these signals, we introduced the formula below, which was derived from the empirical equation
for solid surfaces,39
S 共 t 兲 ⫽A 关 exp共 ⫺t/ ␶ th兲 ⫺r exp共 ⫺t/ ␶ ac兲 cos共 2 ␲ f act 兲兴 2
⫹A el exp共 ⫺2t/ ␶ el兲 ,共2兲

where A and A el are constants, r is the ratio of the acoustic
effect to the thermal effect of each contribution to grating
amplitude. ␶ th , ␶ ac , and ␶ el are attenuation time constants forthe temperature, the acoustic wave, and the excited species,
respectively. f ac is the frequency of the vibrations.
We calculated f ac and ␶ ac of two TRG signals from black
ink 2 and the CV aq solution by fitting with formula 共1兲, and
we also calculated each ultrasonic velocity V ac as the productof f ac and the fringe spacing ⌳. These results are summarized in Table I. Both values of V ac seem to be a little larger
than that of the sound velocity in bulk water 共1.48 km/s兲 at

Samplef ac(GHz)␶ ac(ns)

V ac(km/s)

Black ink 2
CV aq 共36 mM兲

0.705
0.687

2.75
3.37

1.62
1.57

20 °C. However, the discrepancies are within a reasonable
range because the densities of black ink 2 and CV aq solution are 0.993 g/cm3 , and 0.978 g/cm3 , respectively, and thesound velocity is proportional to the (density) ⫺1/2. Each attenuation time constant ␶ ac decreases with increasing viscosity 共black ink 2, 1.3 cP; CV aq, 0.93 cP兲. The frequency of
the TRG vibrations is much larger than that of a capillary
wave of the same wavelength, which is experimentally observed at 1.7–1.8 MHz.40 Therefore, we concluded that we
had generated and observed GHz ultrasonic waves on liquidsurfaces using the TRG method. Higher frequency vibrations
can be also easily generated because ⌳ is controllable bychanging the incident angle ␪.
As for the TRG signal from black ink 1, the reason why
this signal shows no vibrations is not clear. However, we canpresume that because of the unique behavior of carbon particles, something like a flow induced by heat from the carbon
particles diminishes the TRG oscillations.41
Here, we discuss how the TRG oscillations on liquidsurfaces are generated. Elastic theory shows that the surface
is deformed so as to satisfy the boundary condition when an
acoustic wave adjacent to the surface is generated.29,30,32,33
On the other hand, such an acoustic wave also causes modulation of the refractive index.27,28 Nelson and co-workers33
showed that the oscillations of TRG signals at the surface aremainly caused by the surface displacement modulation andnot by the refractive index modulation in the case of thesurface measurement. In addition to the report, we foundfrom diffraction theory considerations that the refractive index modulation was a minor component of the signal.31,42
Therefore, we can see that the TRG oscillations in the surface signal consist of the modulation of the surface deformation as the main component and that of the refractive index
as the minor component, both of which are induced byacoustic waves localized near the surface. The oscillating
signal contains information in the ⌳/2 region from the surface, that is, 1 ␮m in this case, because the acoustic waves
which causes the surface displacement are localized in thesurface region of the waves’ half-wavelength.43
We investigated the pump power dependence of the
TRG signals from surfaces of black ink 2 and CV aq solution. We examined the measured magnitude of the averageintensities of the first peaks of each signal. The results of theCV aq solution are shown in Fig. 3. The figure represented
that the TRG signals were proportional to the square of thepump power. According to the TRG theory on solid surfaces,
the surface displacement is directly proportional to the temperature change. In turn, the temperature change is directly
proportional to the pump power. Since diffracted light is

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Ikeda et al.

FIG. 3. The pump power dependence of the intensities of the TRG signals
from the surface of the CV aqueous solution 共20 mM兲. Grating spacing, 2.4
␮m. The pump power intensities of signals 共a兲, 共b兲, 共c兲, and 共d兲 are 1.1, 0.78,
0.39, and 0.26 ␮J/pulse, respectively. The averaged intensity of the TRG
signal from the surface of the CV solution is proportional to the square of
the pump power.

generally proportional to the square of surface displacement,
the TRG signal is proportional to the square of the pump
power. The agreement between the theory and this experimental result indicates that the TRG theory can be fundamentally applied to liquid surfaces just as with solid surfaces.
We consider what influences the signal amplitude, thatis, surface displacement. The surface displaces due to theapplied force to the surface. Referring to the elastic theory of
liquids44 and the theory of capillary waves,45 four forces areraised as the applied forces to the surface, that is, elastic
force, viscosity, surface tension and gravity. In this case,gravity can be negligible. Although mixture of solvents andaddition of solutes will cause other physical properties
changes, we can suppose that the influences are included in
the signal through these forces change. The viscosity andsurface tension dependence of the TRG signals from surfacesof the CV ethanol aqueous solutions was investigated. It is
well known that the viscosity and the surface tension are
greatly influenced by the portion of ethanol in water.46 The
relationship between the viscosity and surface tension of ethanol water mixtures at 25 °C is shown in Fig. 4共A兲. The
solvents were prepared by mixing ethanol into water at ratiosof 100%, 50%, 20%, 5%, and 0%. The CV solutions wereprepared at 10 mM with each solvent. The results are shownin Fig. 4共b兲. Amplitude of each signal is greatly affected. We
can suppose that the elastic force of the ethanol aqueous
solutions changes monotonically with the ethanol concentration because the sound velocity of the solution changes
monotonically. But the signal amplitude did not changemonotonically with the ethanol concentration. Therefore wecan see that the signal dependence is regarded due to theviscosity and/or surface tension, though it is not clear how
much each of them affects the TRG signal. Furthermore,
TRG signals were different in waveform at 0%, 5%, and100%, where the surface tension changes while the viscosity
is fairly constant. Though it is too much to say that thesesignals depends only on the surface tension, this dependence

FIG. 4. 共A兲 The relationship between the viscosity and the surface tensionof ethanol–water mixtures. The percentages above the circles are the volume ratio of ethanol. 共B兲 The TRG signals from the surfaces of the CV
ethanol aqueous solutions 共10 mM兲. Grating spacing, 2.4 ␮m. Pump power,
1.8 ␮J/pulse. The ratios of ethanol in the solution 共a兲, 共b兲, 共c兲, 共d兲, and 共e兲
are 100%, 50% 20%, 5%, and 0%, respectively.

implies the high selectivity of the TRG signals for the interface. For more exact analysis, we must solve the elastic
equation including viscosity and surface tension as perturbations, and we are now in progress. In addition to the viscosity
and surface tension, we suppose that the absorption of theacoustic wave by solutes will affect the signal waveform formeasurements at the specified wavelength. The information
will give some information on the solute–solvent interaction
at the surface or interface.
As shown in Fig. 3, the first peak of the TRG signal
splits as the intensity of the pump power decreases. As
shown in Fig. 4共B兲, the first sharp peak of the signal diminishes as the ratios of ethanol in the solvents of the CV solutions change. These peaks seem to reflect the dynamics ofthe relaxation of the electronically photoexcited state of CV
molecules on the surface. Thus, it would be possible toclarify this dynamics and to investigate the solute–solvent
effect on the surfaces by applying a femtosecond pulsedlaser to the surface of the CV aqueous solution.
As for liquid/liquid interfaces, we also applied the TRG
method to the cyclohexane/CV aq solution interface. The
results are shown in Fig. 5. The signal at the liquid/liquidinterface shows oscillations like the liquid surfaces did. The
frequency of these oscillations was calculated as 0.6 GHz.
The pump power dependence of this signal was investigated.

J. Chem. Phys., Vol. 111, No. 20, 22 November 1999

GHz ultrasonic waves on liquid surfaces
5

FIG. 5. The TRG signal from the cyclohexane/CV aqueous solution 共10mM兲 interface. Grating spacing, 2.3 ␮m. Pump power, 0.23 ␮J/pulse. Probe
power, 0.035 ␮J/pulse.

The signal is proportional to the square of the pump power.
Thus, we conclude that we can generate and observe ultrasonic waves at the liquid/liquid interface as well as at liquidsurfaces.
As shown before, it is easy to generate ultrasonic waves
of various frequencies with the TRG method by changing theinterference fringe spacing. By analyzing the fringe spacing
dependence of the TRG signals, it is expected that we canapply the TRG method to ultrasonic measurements of interfaces and to ultrasonic spectroscopy in order to investigate
the relaxation phenomena of molecules at interfaces. It isalso expected that we can investigate fast phenomena on asurface and at a liquid/liquid interface microscopically, suchas the solute–solvent effect by using a femtosecond pulsedlaser.
CONCLUSIONS

The 0.7 GHz ultrasonic wave on liquid surfaces and 0.6
GHz ultrasonic wave at a liquid/liquid interface were successfully generated and observed using the TRG method forthe first time. These waves were considered to have a surface
displacement normal to the surface and were considered toinclude information about the surface region to a penetration
depth of 1 ␮m. It is expected that this method will be a
powerful tool to observe and analyze fast phenomena microscopically on liquid surfaces and liquid/liquid interfaces.
ACKNOWLEDGMENT

This work is supported by Grants-in-Aid for Specially
Promoted Research 共No. 07102004兲 from the Ministry of
Education of Japan.
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