Measurements of electric double layer between electrolyte-glass interface
by evanescent wave light illumination
by
Y. Kazoe(1) and Y. Sato(2)
Department of System Design Engineering
Faculty of Science and Technology, Keio University
Hiyoshi 3–14–1, Kohoku-ku, Yokohama, 223–8522, JAPAN
(1)
E-Mail : kazoe@mh.sd.keio.ac.jp
(2)
E-Mail : yohei@sd.keio.ac.jp
ABSTRACT
A novel measurement technique using large-area evanescent wave light illumination and fluorescent dye has been
devised to investigate the spatial and temporal structure of electric double layer (EDL) in the vicinity of the surface of
microchannel. A laser beam was directed to a hexagonal prism and refracted through the prism at an angle of incidence
of 76.5°, undergoing total internal reflection at an interface between an electrolyte and the surface of silica cover glass.
The evanescent wave was generated with the characteristic penetration depth of 88 nm, which directly penetrates into
the EDL. An illumination area of 6.85 mm × 2.6 mm was obtained to measure the two-dimensional distribution of EDL
in the junction area of T-shaped microchannel. The fluorescent intensity from Alexa Fluor 546, which produces the
negative ions in a HEPES buffer at constant pH of 7.2, was detected by a cooled CCD camera attached to a microscope.
A spatial resolution of 5 µm × 5 µm was achieved by using a 10× objective lens. Calibration curves, as shown in figure
I, depicting the relationship between the fluorescent intensity and the EDL thickness, i.e., the Debye length, was
prepared and showed that the fluorescent intensity was decreased with increasing values of the Debye length. Using this
relationship, the spatial distribution of EDL in electroosmotic flow was obtained, as illustrated in figure II. It can be
concluded that the spatial distribution of EDL thickness is dependent on the molecular diffusion of K+.
x [µm]
Fluorescent intensity [a.u.]
0
1.4
0
5
10
15
20
25
30 [nm]
100
1.2
200
1.0
0.8
(x, y) = (215, 180)
(x, y) = (215, 185)
(x, y) = (215, 415)
(x, y) = (215, 425)
(x, y) = (215, 430)
0.6
0.4
0.2
0.0
0
10
20
30
40
0
Debye length [nm]
Figure I. Calibration curves between the
fluorescent intensity and the Debye length.
Calibration locations indicate the pixel coordinate
of CCD camera.
200
y [µm]
400
Figure II. Spatial distribution of the EDL thickness, i.e., Debye
length, in the junction area of T-shaped microchannel. A 0.1 mM
HEPES buffer was injected into the left-hand side inlet, while a
7mM HEPES buffer was injected into the right-hand side inlet.
The applied electric field was 300 V.
1
1. INTRODUCTION
Micro- and nanotechnologies will be expected to microminiaturize the present large medical equipments, e.g., artificial
dialysis and plasma exchange equipments, bringing about drastic changes in our lives. These technologies will be based
upon the development of a micro- and nanoscale multiphase flow system that is comprised of liquids as continuous
phase and molecules, protein, submicron particles, etc. as dispersed phase. In this novel system, analyzing, chemical
reaction, migration (Devasenathipathy et al. 2003), mixing (Johnson et al. 2002) and separation (Giddings et al. 1989,
Andrew et al. 1999) will be innovatively synthesized. Small fluid sample volumes are handled by a force on the liquid,
which is generally exerted by an external electric field. This transport mechanism is well known as electromomotic flow
(EOF), in which the motion of ions is induced. Quantitative measurements of EOF structure will advance our
understanding, because the accurate control of EOF is a key issue of development of the microminiaturized and
integrated system. Experimental efforts using caged fluorescent dye (Paul et al. 1998, Ross et al. 2001) have showed
the velocity distribution of EOF in capillaries and microchannels, however, the influence of charged dye on velocity
measurements has been vaguely discussed. Sato et al. (2002) investigated the three-dimensional structure of EOF in an
I-shaped microchannel by using micron-resolution particle image velocimetry. Oddy and Santiago (2004) measured the
electroosmotic mobility, i.e., the proportionality factor between the electroosmotic velocity and the local electric field,
of a microchannel by using submicron fluorescent particles whose displacements were systematically changed by
alternating current and direct current applied electric fields. The above-mentioned measurement studies, however,
remain restricted to a spatial resolution on the order of a few µm.
From a viewpoint of nanoscale, as a net charge close to the solid surface of a microchannel is created, an electric force
can be used to drive a flow. In general, the positive ions are spontaneously attracted to the immobilized negative surface
charges by electrostatic forces and stay in the vicinity of the surface, that is, the electric double layer (EDL) is formed.
The EOF structure is governed by the formation of EDL, because the electromigration of ions in the EDL induces the
ion drag on the rest of liquid in a microchannel. Thus the spatial and temporal formation of EDL will extend our
knowledge for designing multifunctional microchannels and suppressing the loss in transport, such as hydrodynamic
dispersion is minimized and residence-time broadening is avoided. However, it is impossible to measure the EDL
thickness using a far-field optical system, because the EDL thickness is on the order of 10−100 nm, i.e., less than the
wavelength of conventional laser system. The evanescent wave generated by total internal reflection at a refractive
index surface has the ability to penetrate into the EDL, since the evanescent wave decays exponentially with the
distance from the interface, with a characteristic penetration depth of 10−100 nm. Past experiments (Preive et al. 1990,
Flicker et al. 1993, Tanimoto et al. 1999) have involved in investigations of the electrostatic interaction between
particles whose diameter is on the order of 1−10 µm and glass surface by using total internal reflection microscopy
(TIRM). These experiments, however, have been carried out in a stationary fluid, which means that the outcome from
these studies is hardly applied to EOF. Moreover, particle behavior in EOF may cause much controversy, because the
influence of forces acting on particles, e.g., a lift force due to velocity gradients near the surface or an electric force, on
electrokinetic phenomena is not negligible. It is noted that direct measurements of EDL thickness should avoid
confusing influences.
One of the promising techniques is an optical measurement utilizing fluorescent dye that ionizes in buffer solutions. The
negative ions from fluorescent dye in an electrolyte move away from the surface, so that the fluorescent intensity
absorbed by the evanescent wave is directly related to the EDL thickness. Figure 1 illustrates a schematic of the EDL
next to a negatively charged solid surface and the exponential distribution of evanescent wave intensity, Ieva. Lower the
ion concentration in a buffer solution is, thicker the EDL becomes, which is identical to the low fluorescent intensity
detected by a CCD camera, as shown in figure 1(a). A change in the ion concentration near the surface, which is caused
by application of the electric field, chemical reaction or transport and separation of protein, can be monitored by
detecting the fluorescent intensity. Therefore one can obtain the two-dimensional distribution of EDL in time series by a
fluorescent imaging technique (Sato et al. 2003) using the relationship between the fluorescent intensity and the EDL
thickness.
The objectives of the present study are to establish a large-area evanescent wave light illumination technique utilizing
2
(a) thick EDL
(b) thin EDL
(c)
z
Negative ion from
fluorescent dye
Evanescent wave
Negative ion from
fluorescent dye
Buffer
solution
Buffer
solution
Glass
Glass
Total internal reflection
Evanescent wave
0
Ieva
Total internal reflection
Figure 1. Schematic of (a) thick and (b) thin electric double layer illuminated by the evanescent wave, and (c) the
exponential distribution of evanescent wave.
fluorescent dye with a depth-wise spatial resolution of a few nm and to investigate the two-dimensional structure of
EDL between the electrolyte and the wall surface of microchannel in time series. In a conventional TIRM system, as a
laser beam is introduced into a 60× or 100× magnification, oil immersion objective lens, the illumination spot size at the
interface results in the circular spot in diameter of ca. 40 µm. In general the width of microchannel used in microfluidic
devices has the range 50−500 µm, so that an optical system generating a large illumination area is strongly required to
investigate the EDL distribution in the whole width of microchannel. In the present study, a laser beam is directly
introduced into a prism and the reflection occurs in a silica cover glass of 1 mm thickness, realizing an elliptical
illumination area of 6.85 mm × 2.6 mm. Measurements are performed in a T-shaped microchannel, in which a flow is
driven by pressure or the electric field. Calibration curves, which transforms the distribution of fluorescent intensity
captured by a CCD camera into the distribution of EDL thickness, are prepared by varying the concentration of
potassium chloride, i.e., KCl, which produces the positive ions in a HEPES buffer. Important conclusions obtained in
the present study enable us to control the ions in nanoscale, which are not yet fully understood, in order to create the
microminiaturized innovative system.
2. MEASUREMENT TECHNIQUE AND EXPERIMENTAL SETUP
2.1 Principle of Evanescent Wave Light Illumination
When a laser beam is incident on an interface separating two transparent media of different refractive indices, the light
is partially reflected back into the first medium and partially transmitted into the second medium, as shown in figure 2.
Snell’s law gives the angle of refraction, θr, as
sin θ r =
n1
sin θi .
n2
where θi is the angle of incidence, n1 and n2 are the refractive indices of the first medium and the second medium,
respectively. When the light is internally reflected, i.e., n1 > n2, θr is always larger than θi. Thus an increase in θi results
in θr = 90°. When θi is larger than the critical angle of incidence, θc, defined as
θ c = sin −1
n2 ,
n1
the light is totally reflected at the interface. The evanescent wave intensity, Ieva, decays exponentially with the distance,
z, from the interface, defined as
⎛ z
I eva ( z ) = I eva (0) exp ⎜ −
⎜ zp
⎝
⎞
⎟⎟ ,
⎠
where Ieva(0) is the evanescent wave intensity at the interface and zp is the characteristic penetration depth of the
evanescent wave, which is given by
3
(a)
(b)
Inlet
Inlet
Y
n1
Refracted
beam
Interface
400 µm
Z
Y
400 µm
Cover glass
Incident
beam
θi
50 µm
X
1 mm
n2
PDMS
200 µm
θr
Reflected
beam
Outlet
Figure 2. Schematic of internal
reflection at an interface
separating two media of different
refractive indices (n1 > n2).
Figure 3. (a) Top and (b) cross-sectional views of the
T-shaped microchannel
Mirror unit
Iris diaphragm, 2.8 mm
Optics
Microchannel
Prism
Microscope objective lens
×10, NA 0.5
Filter block
Optical fiber
Nd:YAG laser 532 nm
Objective lens ×10
Mercury lamp
Cooled CCD camera
656 × 494 pixels, 12 bit
Figure 4. Schematic of the measurement system.
zp =
λ
4π
n12
,
sin 2 θ i − n22
where λ is the laser wavelength in a vacuum. In the present experiments, zp is calculated to be 88 nm considering the
refractive index of a silica cover glass, n1 = 1.461, and a buffer solution, n2 = 1.336, a laser wavelength of λ = 532 nm
and an angle of incidence of θi = 76.5°.
2.2 Microchannel
Figure 3 shows a schematic diagram of a T-shaped microchannel consisting of a 5 mm poly(dimethylsiloxane) (PDMS)
chip and a ∅50 mm diameter silica cover glass plate. The thickness of the cover glass was determined to be 1 mm by
considering the distance between each illumination area and the working distance of objective lens. The PDMS chip
was fabricated by using soft lithography. The hydraulic diameter of the channel for the horizontal arm section is 89 µm.
2.3 Experimental Apparatus
A schematic of the present optical measurement system is given in figure 4. A 12-bit cooled CCD camera (Hamamatsu
Photonics, K.K., C4880-80) with a 656 × 494 array was mounted on an inverted microscope (Nikon Corp., TE2000U).
A laser beam from a continuous Nd:YAG laser (Laser Quantum, Ltd.) operating at a wavelength of 532 nm and a power
4
(a)
Top view
Laser beam
Microchannel
PDMS
Cross-sectional
view
6.5°
25°
θi
Silica cover glass
Index matching oil
Al + MgF2
20°
Borosilicate prism
(not in scale)
(b)
Top view
Microchannel
PDMS
Cross-sectional
view
Silica cover glass
10× objective lens
(not in scale)
Evanescent wave intensity [a.u.]
Figure 5. Schematic illustration of evanescent wave light illumination (a) near the prism and (b) in the measurement
area. The size of elliptical illumination area is 6.85 mm × 2.6 mm.
Table 1. Properties of Alexa Fluor 546
1.0
Chemical structure
0.8
H3C
0.6
H
N
SO3 -
SO3 O
H
N+
H3C
CH3
CH3
0.4
CH3 Cl
O
COH CH3
O
Cl
0.2
N
0.0
0
100
200
300
400
500
O
C (CH2)5NH
C CH2S
O
O
O
Distance from surface [nm]
Molecular weight
Absorption wavelength* [nm]
Emission wavelength* [nm]
Figure 6. The evanescent wave intensity, Ieva,
against the distance from the surface, z. The angle
of incidence is θi = 76.5°.
Cl
Na +
1079.39
554
571
*Peak value
of 2 W was directed into a hexagonal prism made of borosilicate glass through an optical fiber, optics, an iris diaphragm
and a mirror. This mirror was attached to a rotating stage that permits control of the angle of incidence. Fluorescence
from the dye was collected through a 10× magnification objective lens (Nikon Corp.) with a numerical aperture of 0.5
and an emission filter transmitting wavelengths longer than 605 nm onto the CCD pixel sheet. The size of the CCD
pixel sheet along with the objective lens used in the present study corresponded to a measurement area of 652 µm × 489
µm in the object plane. The exposure time and frame interval of the CCD camera were 36 ms and 37 ms, respectively.
Images were captured with a frame grabber (Coreco Inc., IC-PIC) for further postprocessing and analysis. To reduce
pixel error, an average per 5 × 5 pixels was performed to obtain a luminous value. This resulted in a spatial resolution of
5 µm × 5 µm.
A schematic of evanescent wave light illumination is illustrated in figure 5. One side of the hexagonal prism was coated
by aluminum and magnesium fluoride, which results in a reflectance of 85%. The prism was attached to the silica cover
glass with index matching oil. The laser beam was focused at an angle of incidence of 6.5° onto the prism and refracted
through the prism at an angle of incidence of θi = 76.5°, undergoing total internal refection at the interface. A 1 mm
5
thickness silica cover glass was selected considering the working distance of objective lens of 1.2 mm and a laser beam
diameter of 2.6 mm, which yields an elliptical illumination area of 6.85 mm × 2.6 mm and the distance between each
area of 7.46 mm. The actual illumination used in the present experiments is the third total internal reflection of the laser
beam.
Figure 6 shows the exponential distribution of evanescent wave intensity calculated by using the characteristic
penetration depth of 89 nm. The EDL thickness has the range 1−30 nm in the present experiments, thus the evanescent
wave intensity is sufficient to illuminate the fluorescent dye.
2.4 Properties of Fluorescent Dye and Buffer Solution
The Alexa Fluor 546 (Molecular Probes, Inc.) was selected as the fluorescent dye, and its chemical structure and optical
properties are compiled in table 1. The monovalent positive ion, Na+, is produced in a buffer solution. The lifetime
fluorescent emission is extremely short, i.e., 4.0 ns.
A working fluid is composed of a 5 mM HEPES buffer at pH = 7.2 (Beyon and Easterby 1996), in which a 10 µM
Alexa Fluor 546 was dissolved. KCl with the concentration range 0.1−7 mM was added to the fluid to change the
positive ion concentration. The Na+ concentration ionized from the fluorescent dye is 10µM and the proton, H+,
concentration in the HEPES buffer results in 63 nM, so that the K+ concentration is representative of the positive ion
concentration in the solution, which mainly forms the EDL at the interface.
2.5 Fluorescence Imaging Technique
A fluorescence imaging technique used in the present study was developed by Sato et al. (2003). The fluorescent
intensity, If, irradiated by the excitation intensity, Ie, is given by Walker (1987)
I f (λe ) = α I e (λe )Cdye ,
where λe is the excitation wavelength, α is the coefficient determined by the quantum yield and the molar absorption
coefficient, and Cdye is the concentration of fluorescent dye. At a constant temperature, the fluorescent intensity near the
interface excited by the evanescent wave can be transformed into
I f ( z ) = β I eva ( z )c( z ) ,
where β is the coefficient, Ieva is the evanescent wave intensity, c is the ion concentration near the surface and z is the
distance from the surface. In the present experiments, the depth-of-field of the 10× magnification objective lens (NA =
0.5) is calculated to be 1.1 µm taking into account the emission wavelength of Alexa Fluor 546 of 569 nm, which is
larger than the characteristic penetration depth of 89 nm. Thus the fluorescent intensity detected by the CCD camera is
written as
If =γc,
where γ is the coefficient determined by the evanescent wave intensity. The fluorescent intensity depends on the
excitation intensity, so that this factor must be kept constant to avoid measurement errors. Therefore the fluorescent
intensity at a reference ion concentration, cref, was measured in a closed cell in order to avoid measurement errors
associated with the illumination distribution of evanescent wave. Using the ratio of the measurement values to those at
the reference concentration, the following relation is obtained:
If
I ref
=
c .
cref
3. RESULTS AND DISCUSSION
3.1 Relationship between Fluorescent Intensity and EDL Thickness
Prior to investigations of the relationship between the fluorescent intensity excited by the evanescent wave and the EDL
6
Fluorescent intensity [a.u.]
Fluorescent intensity [a.u.]
1.4
1.2
(x, y) = (215, 180)
(x, y) = (215, 185)
(x, y) = (215, 415)
(x, y) = (215, 425)
(x, y) = (215, 430)
1.0
0.8
1.4
1.2
1.0
0.8
(x, y) = (215, 180)
(x, y) = (215, 185)
(x, y) = (215, 415)
(x, y) = (215, 425)
(x, y) = (215, 430)
0.6
0.4
0.2
0.0
0
1
2
3
4
5
6
7
8
0
10
KCl concentration [mM]
30
40
Debye length [nm]
Figure 7. Calibration curves obtained after correction
using a reference value at 0.5 mM. Calibration locations
indicate the pixel coordinate of CCD camera.
Figure 8. Calibration curves between the fluorescent
intensity and the Debye length. Calibration locations
indicate the pixel coordinate of CCD camera.
0
x [µm]
20
0
5
10
15
20
25
30 [nm]
100
200
0
200
y [µm]
400
Figure 9. Two-dimensional distribution of Debye length in pressure-driven flow at the Reynolds number of 1.17×10−1.
thickness, calibration between the fluorescent intensity and the positive ion concentration was performed in a closed
cell. The noise influence was removed by subtracting the background intensity from captured images. An average per 5
× 5 pixels was performed by using 100 images.
Figure 7 shows calibration curves depicting the relationship between the fluorescent intensity from Alexa Fluor 546 and
the KCl concentration over the range 0.1−7 mM. Due to the influence of the excitation intensity at each location, each
calibration curve has a different profile. In order to reduce these influences, values at 0.5 mM were chosen as a
reference value.
Using these calibration curves, the relationship between the fluorescent intensity and the EDL thickness is directly
obtained, because the EDL thickness, a.k.a., the Debye length, λD, depends on the bulk ion concentration, c0, defined as
1
⎛ ε RT ⎞ 2
λD = ⎜ 2 2 ⎟ ,
⎝ 2 F z c0 ⎠
where ε is the permittivity of liquid, R is the gas constant, T is temperature, F is the Faraday constant and z is the charge
number of ion. Figure 8 shows the relationship between the fluorescent intensity and the Debye length, which was used
in a set of experiments.
3.2 Spatial Distribution of EDL in Pressure-Driven Flow
The two-dimensional distribution of Debye length in pressure-driven flow was measured by the present fluorescence
imaging technique. A 0.1 mM HEPES buffer was injected into the left-hand side inlet, while a 7 mM HEPES buffer was
7
0
0
x [µm]
(b) t = t0 + 375 ms
x [µm]
(a) t = t0 + 185 ms
100
200
100
200
0
200
y [µm]
400
0
200
y [µm]
400
(c) t = t0 + 555 ms
x [µm]
0
0
5
10
15
20
25
30 [nm]
100
200
0
200
y [µm]
400
Figure 10. Temporal evolution of two-dimensional distribution of Debye length in electroosmotic flow. Applying a 300 V
electric field was started at t0.
injected into the right-hand side inlet. Both streams are moved towards the junction area at the equal flow rate and
flowed downstream due to difference in height of the buffer surface between in inlets and outlet. The Reynolds number
based on a channel hydraulic diameter of 89 µm and a bulk velocity of 1,156 µm/s was 1.17×10−1.
The two-dimensional distribution of Debye length is exhibited in figure 9, which was obtained by using calibration
curves in figure 8. Theoretically the Debye length depends on the K+ concentration, thus it is obvious from figure 9 that
the concentration gradient of K+ in the junction area was induced by molecular diffusion, which means that the spatial
distribution of Debye length is completely dependent on K+ diffusion.
As pressure-driven flow has a parabolic flow pattern due to the non-slip condition, a K+ diffusion field has the
three-dimensional structure in the microchannel. It is observed that the gradient of Debye length in the y-direction
becomes slightly steep, therefore it can be concluded that the spatial structure of EDL is closely related to the K+
concentration near the wall surface.
3.3 Transient Process of EDL in Electroosmotic Flow
When a flow is driven by the electric field, a fluid velocity in a microchannel, u, is given by
u = upressure + uEOF ,
8
x [µm]
0
-80
-60
-40
-20
0 [mV]
100
200
0
200
y [µm]
400
Figure 11. Two-dimensional distribution of ζ-potential in electroosmotic flow at t = t0 + 375 ms. The applied electric
field was 300 V.
where upressure is a velocity of pressure-driven flow and uEOF is a velocity of EOF. EOF has generally a plug flow pattern
and at the wall surface upressure = 0, thus a fluid velocity in the vicinity of the surface is assumed to be uEOF, which affects
the change in K+ diffusion in the vicinity of the surface. In order to investigate the effect of K+ diffusion on the EDL
thickness, measurements of EOF were performed. Platinum electrodes were submerged in both inlets and outlet to drive
a flow by using a high voltage power supply (KEPCO, Model BOP 1000M).
Figure 10 shows two-dimensional distribution of the Debye length in time series in the junction area. A 300 V electric
field was applied to at t = t0. The gradient of Debye length in the y-direciton gradually becomes steep near the centerline
in figure 10(c) in comparison with figure 10(a).
Theoretically the EOF velocity, uEOF, is defined as
εζ E ,
uEOF = −
µ
Where ζ is the ζ-potential, E is the magnitude of electric field and µ is the viscosity. In the present study, the ζ-potential
is calculated by equation given by Scales et al. (1992), that is,
ζ = ( −0.058log10 pH + 0.026 ) × ( − log10 c0 )
1.02
( 2.8 ≤ pH ≤ 10, 10
−4
,
)
M ≤ c0 ≤ 10−2 M .
Figure 11 exhibits the two-dimensional distribution of ζ-potential calculated by using calibration curves in figure 7 and
the above equation. One can directly obtain the EOF velocity distribution using the ζ-potential and the distribution of
electric field. From these figures it can be concluded that the spatial and temporal distribution of the EDL thickness
depends on the bulk K+ concentration in EOF.
4. CONCLUSIONS
An experimental study was performed to investigate the spatial and temporal structure of electric double layer at an
interface between an electrolyte and the glass surface of T-shaped microchannel. A fluorescence imaging technique was
developed by using large-area evanescent wave light illumination. The two-dimensional distributions of EDL near the
surface in time series were obtained by detecting the fluorescent intensity that is closely related to the EDL thickness. A
flow comprised of a HEPES buffer was driven by pressure or the electric field. The important conclusions obtained
from this work are summarized below.
9
(1)The spatial distribution of EDL thickness is dependent on the molecular diffusion of K+ in a buffer solution in the
vicinity of the wall surface.
(2)The two-dimensional distribution of ζ-potential, which governs an EOF velocity, was obtained, so that the nanoscale
structure of EOF will be investigated by the present measurement technique.
ACKNOWLEDGEMENTS
The authors would like to thank Professor K. Hishida at Keio University for his technical assistance. This work was
subsidized by the Grant-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science and
Technology (No. 14702030 and 15206024).
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