Anal. Chem. 2001, 73, 2366-2368

Technical Notes

A High-Performance and Simplified Quasi-Elastic
Laser Scattering Method Using Homodyne
Detection in Beam Divergence
Isao Tsuyumoto* and Hiroshi Uchikawa

Department of Environmental Systems Engineering, Kanazawa Institute of Technology, 7-1 Ohgigaoka,
Nonoichi, Ishikawa 921-8501, JapanWe devise the new principle of the quasi-elastic laser
scattering (QELS) method using a homodyne detection
technique in a beam divergence and successfully facilitate
the equipment. The QELS method is a unique technique
for the noncontact and time-resolved study of surface
tension at liquid surfaces and liquid/liquid interfaces. The
conventional QELS method requires a precise opticalalignment using a local oscillator such as a diffraction
grating, and the determination of the surface tension
accompanies much difficulty because of the low S/N ratioof the power spectra. Our new principle allows highperformance QELS measurements by only a simple alignment of a downsized experimental setup. The power
spectra are obtained with 50-100 times higher S/N ratios
than the conventional ones. The power spectra are analyzed by a new theory, and the calculated surface tensions
agree with the literature values. The accuracy of thesurface tension measurements using the QELS method
is substantially improved.
Surface tension measurements provide much information on
surfactant dynamics at liquid surfaces and liquid/liquid interfaces.
Common industrial processes such as washing, printing, andcoating are closely related to the adsorption of surfactants, andsurface tension measurements are widely used for quality control,
research, and development in various industries. The measurements are also helpful for fundamental studies in view of theinterfacial thermodynamics, properties, and structures. A numberof methods for surface tension measurements such as theWilhelmy method, the Du Noüy method, the spinning drop
method have been reported so far,1 but these methods bring aboutmechanical perturbation and are not suitable for time-resolved
measurements. Katyl and Ingard reported a quasi-elastic laser
scattering from liquid surfaces by capillary waves (ripplons), which
are spontaneously generated at liquid surfaces.2 Several researchers reported that the QELS method is an appropriate method forsurface tension measurements, indicating that the surface tensions(1) Mingins, J.; Taylor, J. A. G.; Pethica, B. A.; Jackson, C. M.; Yue, B. Y. T. J.
Chem. Soc., Faraday Trans. 1 1982, 78, 323.
(2) Katyl, R. H.; Ingard, U. Phys. Rev. Lett. 1968, 20, 248.

2366 Analytical Chemistry, Vol. 73, No. 10, May 15, 2001

calculated from the capillary wave frequencies agreed with theother methods.3-5 Tsuyumoto and co-workers have fabricated theconventional QELS measurement system based on a laser
heterodyne apparatus6 using a diffraction grating as a local
oscillator and have reported on the dynamics of mass transfer ofsurfactants at the water/nitrobenzene interface.7-11 However,many experimental difficulties arose in the measurements, e.g.,
the detection of the signal from the capillary waves was very
difficult because of the extremely small amplitude of the waves(∼10 nm), and the determination of the surface tensions included
accidental errors due to the low S/N ratio of the observed power
spectra. In this study, to improve the QELS method, we devise ahomodyne detection technique using a beam divergence insteadof heterodyne detection using the diffraction grating. We present
here the measurement results of standard samples and discuss
the advantages of the new homodyne QELS method.
PRINCIPLE
The principles of the conventional and the new homodyne
QELS methods are shown in Figure 1a and b, respectively. A
thermally generated spontaneous density fluctuation occurs at theliquid surface. The surface tension acts as a restoring force on
the fluctuation, and it excites a surface tension wave, which iscalled a capillary wave or ripplon. The capillary waves occurringon liquid surfaces have various wavelengths, and each frequency
is dependent on each wavelength. This makes it essential to selecta capillary wave with a certain wavelength to determine thedispersion relation of the waves. The QELS methods measure the(3) Sakai, K.; Tanaka, H.; Takagi, K. Jpn. J. Appl. Phys. 1990, 29, L2247.
(4) Sauer, B. B.; Chen, Y. L.; Zografi, G.; Yu, H. Langmuir 1988, 4, 111.
(5) Sano, M.; Kawaguchi, M.; Chen, Y.-L.; Skarlupka, R. J.; Cheng, T.; Zografi,G.; Yu, H. Rev. Sci. Instrum. 1986, 57, 1158.
(6) Härd, S.; Hamnerius, Y.; Nilsson, O. J. Appl. Phys. 1976, 47, 2433.
(7) Uchiyama, Y.; Tsuyumoto, I.; Kitamori, T.; Sawada, T. J. Phys. Chem. B
1999, 103, 4663.
(8) Uchiyama, Y.; Kitamori, T.; Sawada, T.; Tsuyumoto, I. Langmuir 2000,16, 6597.
(9) Uchiyama, Y.; Fujinami, M.; Sawada, T.; Tsuyumoto, I. J. Phys. Chem. B
2000, 104, 4699.
(10) Zhang, Z. H.; Tsuyumoto, I.; Kitamori, T.; Sawada, T. J. Phys. Chem. B 1998,102, 10284.
(11) Zhang, Z. H.; Tsuyumoto, I.; Takahashi, S.; Kitamori, T.; Sawada, T. J. Phys.
Chem. A 1997, 101, 4163.
10.1021/ac001338e CCC: $20.00© 2001 American Chemical Society
Published on Web 04/05/2001

Figure 1. Measurement principles of the QELS methods. (a) The
conventional heterodyne technique using a diffraction grating and (b)the new homodyne technique utilizing a beam divergence.

capillary wave frequency of a selected wavelength, and the surface
tension is calculated from the relationship between the frequency
and the wavelength. The two principles are different in thetechnique for selecting the wavelength and for measuring thefrequency.
(a) The Conventional Heterodyne QELS. A brief outline ofthe principle of the conventional method based on Figure 1afollows. The incident beam normal to the surface is quasielastically scattered by the capillary wave with a Doppler shift at
an angle determined by the following equation:

K tan θ ) k(1)where K and k are the wavenumbers of the incident beam andthe capillary wave, respectively. Thus, the wavenumber k of thecapillary wave is obtained by giving θ. To adjust the angle θ, atransmitting diffraction grating was arranged in front of the cell.
The angle θ is determined by the following equation using thespacing d and the order n of the diffraction grating,d sin θ ) nλ(2)where λ is the wavelength of the laser beam. From eqs 1 and 2,
the wavenumber k and the wavelength Λ of the observed capillary
wave are obtained.
The capillary wave frequency is detected by an optical
heterodyne technique, which uses a diffracted beam as a locallight. The incident laser beam (F Hz: F ) c/λ) is quasi-elasticallyscattered by the capillary wave (f Hz) at the liquid surface. The
scattered beam is accompanied by a Doppler shift, and its
frequency becomes F ( f Hz. The scattered beam (F ( f Hz) isoptically mixed with the diffracted beam (F Hz) from thediffraction grating to generate an optical beat in the mixed light.
The beat frequency (f Hz) obtained here is the same as theDoppler shift, i.e., the capillary wave frequency.
In the measurement, by locating a photodiode at the nthdiffraction spot, the power spectrum of the capillary wave withthe wavelength calculated from eqs 1 and 2 is obtained. The S/Nratio of the power spectrum depends on the beat intensity in themixed light, and the beat intensity is proportional to the productof the electric field intensities of the scattered light and thediffracted light. The intensity of the diffracted light is not morethan 5% of the light source, and the observed scattered light isonly a small portion (∼1%) of the expedient light scattered in theshape of concentric circles. These result in the low S/N ratio of
the spectra, and a precise optical alignment is necessary becauseof the experimental difficulties in detecting the signals.
(b) The New Homodyne QELS. To improve the disadvantages of the conventional QELS method, we devised a principle
using homodyne detection technique in a beam divergence asshown in Figure 1b. A laser beam with a continuous intensity
distribution in the divergence is incident normal to the surface.
The light intensity has a maximum at the center of the irradiatedspot and decreases monotonically with the distance from thecenter. Because of the divergence, the angle of incidence varies
as a function of the distance from the center. The strongest partof the beam is incident exactly normal to the surface, and its
transmitted light is used as a local light (F Hz). The surroundingparts of the beam are incident obliquely and are scattered almost
nondirectionally by capillary waves of various wavelengths. Someparts of the light are scattered exactly normal to the surface witha scattering angle of θ and are mixed with the local light togenerate an optical beat. By locating a photodiode at the strongest
part of the transmitted light, the optical beat between the local
light and the scattered light is observed in a power spectrum.
Because of the continuous spatial distribution of the incident beam,
the scattered beam generating the optical beat consists of multiple
scattering angles. The scattering angle that generates the greatest
signal intensity can be determined from the angle of the beam
divergence and it gives the wavelength of the observed capillary
wave as follows. The relationship between this wavelength andthe observed peak frequency gives a surface tension.
The electric field intensity of the incident beam at a distanceof r from the center is expressed by the following equation,

E(r) ∝ exp(-r2/a2)(3)

where a is the spot radius whose intensity is 1/e2 of the center.
While the electric field intensity E(r) decreases monotonically withincreasing r, the scattering area of the same scattering angle θincreases in proportion to a circle with radius r, i.e., 2πr. Thus,
the electric field intensity generated by all the scattered light at
a distance of r from the center is approximately expressed by thefollowing equation,

E(r) ∝ 2πr exp(-r2/a2)(4)

The relative maximum of this equation corresponds to the peakfrequency of the power spectra, because the beat intensity isproportional to this electric field intensity. By differentiating eq
4, we find the maximum at r ) a /x2. This corresponds to thescattering angle of θ0 /x2, where θ0 is the beam divergence ofthe light source. By substituting the angle of θ0 /x2 into eq 1,
we can obtain the wavelength of the capillary wave corresponding
to the peak in the power spectrum. In the present study, the beam
divergence of the light source is 1 mrad, and thus the wavelengthof the observed capillary wave is calculated as 0.752 mm.
The surface tension γ is calculated from the relationshipbetween the capillary wave frequency f and the capillary wave
wavenumber k using Lamb’s equation,
Analytical Chemistry, Vol. 73, No. 10, May 15, 2001

2367

f ) (1/2π)(γ/F)1/2k3/2(5)where F is the density of the liquid and k is the wavenumber ofthe capillary wave.
EXPERIMENTAL SECTION
Apparatus. The experimental setup of the new homodyne
QELS method is shown in Figure 2. It is much facilitated anddownsized compared to the conventional one, because the beam
divergence is already inherent in a compact laser light source andthe diffraction grating is unnecessary. The beam from a diodepumped YAG laser (CrystaLaser, model GCL-025S, 532 nm, 25mW) is incident normal to the liquid surface after passing throughthe bottom of the sample cell. An aperture (1 mm diameter) is
located at the strongest part of the transmitted light, and theselected light is detected by a photodiode (Hamamatsu Photonics
S1290). Signals from the photodiode are Fourier transformed andsaved by a personal computer.
Reagents. Ethanol (Kanto Chemical Co., Inc.; special grade;99.5%), acetone (Kanto Chemical Co., Inc.; special grade; 99.5%),and distilled water were used as samples. Measurements wereperformed at 22 °C.
RESULTS AND DISCUSSION
A power spectrum for capillary waves at an ethanol surface isshown in Figure 3. The spectrum is obtained with 50-100 times
higher intensity and S/N ratio than the conventional methods inour previous papers.9-11 The peak appearing at 0.64 kHz is thebeat frequency, i.e., the capillary wave frequency with thewavelength of 0.752 mm, as we discussed above. The second,
third, and fourth harmonics are also observed around 1.4-2.6 kHz,
along with the fundamental wave at 0.64 kHz. The surface tension
was calculated from the fundamental capillary wave frequency of0.64 kHz. Substituting the frequency, the wavelength, and thedensity into eq 5, the surface tension of ethanol at 22 °C wascalculated as 21.8 mN/m. This is in agreement with the literature
value of 22.3 mN/m.12 As shown in Table 1, the peak frequenciesof the fundamental waves for acetone and water were observed
at 0.65 and 1.03 kHz, respectively. The calculated surface tensions
were also in agreement with the literature values. It was also
possible to observe the decrease in surface tensions in situ. Thepeaks of the water surface including the second and the third
harmonics shifted to smaller frequencies by addition of surfactant.
This indicates that the present QELS method can be also applied
to monitor molecular dynamics at liquid surfaces and liquid/liquidinterfaces.
The measurements were also performed with the reflectiontype configuration. The beam was incident nearly normal to thesurface and the photodiode was located at the strongest part of
the reflected light. The S/N ratios and the peak frequencies were
the same as those of the above transmission type. This showsthat the present QELS method can also observe opaque solutions
such as suspensions.
The present QELS method will be useful in the measurementsof high-temperature liquids such as fused silicon, whose surface(12) Jasper, J. J. J. Phys. Chem. Ref. Data 1972, 1, 841.

2368 Analytical Chemistry, Vol. 73, No. 10, May 15, 2001

Figure 2. Schematic view of the experiment setup of the new
homodyne QELS method: AMP, preamplifier; ADC, analog-digitalconverter; PC, personal computer.

Figure 3. A typical power spectrum for capillary waves at an ethanol
surface. The peak corresponding to the fundamental wavelength of0.752 mm is marked by an arrow.
Table 1. The Peak Frequency f, the Experimental
Surface Tension by the Present QELS Method γobs, andthe Reported Surface Tension γ lit.12

ethanolacetonedistilled waterf (kHz)γobs (mN/m)

γlit. (mN/m)

0.64
0.65
1.03

21.8
22.6
71.7

22.3
23.8
73.2

tension in the manufacturing process affects the quality of theproduct of semiconductor monocrystals. It will be also possible
to perform microscopic measurements of surface tension, because
the present principle applies to a beam convergence as well as
the beam divergence. By focusing the beam in the vicinity of thesurface, we can obtain the signal from microsurfaces such as in
the channels of µ-TAS (micro total analysis systems). We expectthat the present QELS method will contribute significantly to thedevelopment of microchemistry at liquid surfaces and liquid/liquidinterfaces. Moreover, the same principle using beam divergencecan be applied to the other laser scattering methods observing
the Doppler shift such as Doppler current meters and zeta
potentiometers. We also expect that the present principle will bringabout a tremendous ripple effect to laser spectroscopy.

Received for review November 15, 2000. AcceptedFebruary 5, 2001.
AC001338E