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Induced dipoles and dielectrophoresis of nanocolloids in electrolytes

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Abstract

Electric induced dipoles of nanocolloids the size of the Debye length are shown to be one order stronger than predicted by the classical Maxwell-Wagner theory and its extensions. The difference is attributed to normal ion migration within the diffuse layer, and adsorption onto the Stern layer at the poles. The characteristic relaxation frequency (the crossover frequency for dielectrophoresis) is shown to be inversely proportional to the RC time of the diffuse layer capacitance and resistance, and has an anomalous -1 scaling with respect to the product of the Debye length and the particle size.
Induced dipoles and dielectrophoresis of nanocolloids in electrolytes
Sagnik Basuray and Hsueh-Chia Chang
*
Center for Microfluidics and Medical Diagnostics, Department of Chemical and Biomolecular Engineering, University of Notre Dame,
Notre Dame, Indiana 46556, USA
Received 15 March 2007; published 25 June 2007
Electric induced dipoles of nanocolloids the size of the Debye length are shown to be one order stronger than
predicted by the classical Maxwell-Wagner theory and its extensions. The difference is attributed to normal ion
migration within the diffuse layer, and adsorption onto the Stern layer at the poles. The characteristic relaxation
frequency the crossover frequency for dielectrophoresis is shown to be inversely proportional to the RC time
of the diffuse layer capacitance and resistance, and has an anomalous −1 scaling with respect to the product of
the Debye length and the particle size.
DOI: 10.1103/PhysRevE.75.060501 PACS numbers: 82.45.h, 47.57.jd, 47.65.d, 66.10.Ed
Dielectrophoresis DEP has become an increasingly
popular means of manipulating and identifying immunocol-
loids, bioparticles, and DNA molecules in microfluidic de-
vices 13. The dielectrophoretic force on the particle re-
sults from induced ac particle dipoles, which can develop by
either conductive or dielectric polarization mechanisms ac-
cording to classical Maxwell-Wagner MW theory 2. For
conducting particles with low permittivity, conductive polar-
ization dominates at low frequency and dielectric polariza-
tion at high frequency, with opposite dipole orientations with
respect to the applied field and opposite positive toward
high field and negative toward low field DEP mobility. As
the length of both the particle capacitor and the resistor is the
particle size a, the dipole orientation and RC relaxation time,
as determined by f
c.m.
=
˜
P
˜
M
/
˜
P
+2
˜
M
, the Clausius-
Mossotti factor, is size independent. The complex permittiv-
ity
˜
is related to the real permittivity and conductivity
via the ac field frequency
for both particle P and medium
M. Hence, there exists a crossover frequency
CO
, defined
by Ref
c.m.
=0, when the induced dipole vanishes, which the
MW theory predicts to be size independent:
MW
=
1
2
P
M
兲共
P
+2
M
M
P
兲共
P
+2
M
. 1
This MW theory was recently found to be inaccurate for
nanocolloids 36. The
CO
data of Green and Morgan 6
in Fig. 1 for nanosized latex particles clearly show a particle
size dependence. In fact, according to the classical MW
theory Eq. 1, latex particles with permittivity and conduc-
tivity both lower than the medium are not expected to exhibit
any crossover phenomenon. Ermolina and Morgan 7 have
suggested that, for latex and other particles with negligible
native conductivity,
p
should be dominated by Stern and
diffuse layer conduction effects, as described by the classical
theories for electrophoresis, see the review in 8兴兲. With
negligible native conductivity, the corrected particle conduc-
tivity becomes
p
=2K
s
/a+ 2K
D
/a, where K
s
is the Stern
layer conductance and K
D
the diffuse layer conductance,
which includes a dependence on the particle
potential due
to osmotic flow effects. However, that the effective conduc-
tance is the sum of the two conductance contributions from
the Stern and diffuse layers reflects the implicit assumption
in the classical theories that the conduction “surface” cur-
rents are tangential. This is true for the Stern layer, which is
always thin compared to the particle, and hence its internal
field is always tangential to the latex insulator particle. It is,
however, inaccurate for diffuse layers with Debye length
=
M
D/
M
1/2
D is the ion diffusivity comparable to a.
With the normal length scale comparable to the tangential
one in such thick layers, the normal field and current become
important in the diffuse layer, and this effect is not captured
by the classical theories. Moreover, modeling just conduction
electromigration in the diffuse layer is inadequate, as the
neglected diffusive flux can counter electromigration to pro-
duce tangential equilibrium or Poisson-Boltzmann distribu-
*
Author to whom correspondence should be addressed.
hchang@nd.edu
FIG. 1. Green and Morgan’s 6 crossover frequency data for
557 black triangles and 93 nm unfilled triangles latex particles.
The classical MW theory with a conducting Stern layer is shown as
a dotted line. The Stern layer conductance is 1.46 nS for 93 nm
particles and 1.92 nS for 557 nm particles, calculated from the data
asymptote at low medium conductivity. The dashed line is from an
extended theory of 7 that includes tangential conduction in the
diffuse layer with the same surface conductance as ours and
potential of 67 mV for 93 nm and 45 mV for 557 nm particles from
Fig. 5 of 7兴兲. The solid line corresponds to the scaling theory of Eq.
2 with a scaling constant of 2.5 and D=510
−9
m
2
/s.
PHYSICAL REVIEW E 75, 060501R兲共2007
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1539-3755/2007/756/0605014 ©2007 The American Physical Society060501-1
tions. We hence expect the improved MW theories to be
valid only at lower conductivity when ␭Ⰷa, or for large
particles, aⰇ␭.
At the limit of infinitely low medium conductivity, the
Stern layer conduction contribution dominates that from the
diffuse layer even in these theories, and the crossover fre-
quency with negligible native permittivity approaches
=1/2
K
s
/
2a
M
. Using this limiting value for the particle
data of Green and Morgan 6 to estimate K
s
for different
particle sizes see inset of Fig. 2, the MW theory with Stern
layer conduction dotted curve is shown in Figs. 1 and 2 for
various particle sizes. It is shown to accurately capture the
measured crossover frequencies of large particles, but still
fails to describe the data for nanocolloids with smaller di-
mensions, at medium conductivities corresponding to a ,
as shown in Fig. 1. Although this new crossover frequency is
size dependent, it falls monotonically with respect to the me-
dium conductivity, instead of exhibiting the order-of-
magnitude rise for the smaller particle 93 nm. The dashed
curve in Fig. 1 corresponds to the extended theory, which
includes diffuse layer conduction and electro-osmotic flow
convection. Using
potential estimates from Fig. 5 of 7 for
all latex particles, and our Stern layer conductance values as
shown in the inset in Fig. 2, the crossover now exhibits a
shallow maximum, but is still lower than the actual data by a
factor of 4. Allowing for a conductivity-dependent
poten-
tial produces similar results.
Considerable empirical evidence 912, particularly for
ion-selective conducting particles, suggests that a normal ca-
pacitive current, missing in the classical theories, is respon-
sible for the discrepancy seen in Figs. 1 and 2 at the critical
region of a. If the migrating ions are allowed to accumu-
late at the opposite poles, an induced dipole that favors posi-
tive dielectrophoresis increases
CO
. If we assume that the
diffuse layer permittivity and conductivity are similar to
those of the bulk medium, the diffuse layer capacitance
would be
M
/ and its resistance along the particle a/
M
.
Consequently, we expect
CO
of this theory to scale as the
inverse RC time of the diffuse layer,
DL
M
a
M
=
D
a
. 2
This simple expression quantitatively captures
CO
for
smaller particles, as seen in Figs. 1 and 2. Its ratio to
, the
low-conductivity limiting frequency from the MW theory, is
1/2
兲共
2
M
/
p
兲共/a, and this ratio increases monotoni-
cally with medium conductivity
M
. As is evident from the
93 nm data in Fig. 1, this scaling can be almost a factor of 10
larger than
MW
.
Our theory, which quantitatively confirms the above scal-
ing, uses Stern layer conduction to describe
p
, but describes
both tangential and normal conducting and diffusive fluxes
in the diffuse layer explicitly. It follows that of Gonzalez et
al. for electrode double-layer polarization 12 with a Debye-
Hückel linearization for a symmetric monovalent electrolyte,
whose dynamic space charge fluctuation and charge density
are small compared to the dc ion concentrations. However,
Gonzalez et al. consider the thin double-layer limit of
a / 1, while we include the full Laplacian for the Pois-
son equation and for the charge transport equation for a.
After a Fourier transform in time, the dimensionless ac com-
ponents of the charge density
scaled by 2n
0
e, the medium
and particle potential scaled by k
B
T/e, the spatial coordi-
nates scaled by a, and the time scaled by
M
/
M
, the two
potentials and charge density satisfy
2
M
=−
a
2
,
2
P
=0,
2
=
ia
2
D
冊冉
␻␴
M
M
+
a
2
= s
2
a
2
, 3
where
, the dimensionless frequency, has been scaled by
M
/
M
, and the complex number s is defined by s
2
=1
+i
. The Laplacian on the left of the charge density repre-
sents diffusion, while the two terms on the right represent
accumulation and electromigration, respectively.
With a uniform unit dimensionless far field in e
ˆ
Z
, the rel-
evant axisymmetric charge density solution to the Bessel
equation 3 can be expressed as a Bessel function of frac-
tional order, and the particle and medium potentials contain
the related spherical harmonics,
=
BK
3/2
a
sr
r
1/2
cos
,
P
= Dr cos
,
M
=
BK
3/2
a
sr
s
2
r
1/2
+
A
r
2
r
cos
, 4
where the first term in the medium potential represents the
polarized space charge distribution in the diffuse layer and
the second term represents the field due to the induced par-
ticle dipole. As the space charge contribution to the potential
decays exponentially as expasr/, it is clear from Eq. 4
that the potential seen by any second-order applied field with
a finite gradient is predominantly due to the dipole and not
FIG. 2. Scaled data of Green and Morgan for four different latex
particle dimensions in different KCl and NaCl electrolytes with D
=510
−9
m
2
/s to resolve the data points across a wide range of
/a. The Stern layer conductance using the data asymptote at low
conductivity for different particle sizes is shown as the inset. The
scaling theory of Eq. 2 captures the anomalous rise of the 93 nm
data when a.
SAGNIK BASURAY AND HSUEH-CHIA CHANG PHYSICAL REVIEW E 75, 060501R兲共2007
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the space charge. We hence do not need to be concerned with
the Maxwell force on the space charge, nor the resulting
electro-osmotic convection. The space charge is nevertheless
important, as it screens the external field such that the par-
ticle dipole is different from the unscreened one as for
/ a 1. With negligible space charge contribution to the
electric force on the particle, the coefficient A for the com-
plex charge of the induced dipole can be used directly
in the classical expression for the dipole force,
4
M
ReAa
3
E
ˆ
·
ˆ
E
ˆ
, to obtain the DEP velocity u
DEP
=
M
a
2
/6
ReA
ˆ
E
ˆ
2
, where E
ˆ
is the dimensional elec-
tric field.
The specific values of A , however, require determination
of the coefficients in Eq. 4. The MW theory uses as surface
boundary conditions the potential continuity
=0 and the
complex displacement continuity in dimensional form,
˜
n
=0 5
where · denotes a jump across the particle surface, and the
Stern layer effect is included in the particle conductivity.
Equation 5 is derived by eliminating the surface charge q
s
from the surface charge accumulation due to the conductive
flux imbalance, i
q
s
=
/
n, and the displacement jump
due to the surface charge, q
s
=
/
n, where the ac sur-
face charge resides at the diffuse/Stern layer interface. How-
ever, an additional boundary condition on this interface is
needed for the space charge density
. For the normal diffuse
layer current to be a charging current, the space charge must
adsorb onto the surface.
Adsorption of counterions at the Stern layer has been well
documented 1315, and a reversible adsorption isotherm is
usually assumed, as the adsorption and desorption kinetic
times across the Stern layer are expected to be on the order
of nanoseconds or shorter. This corresponds to an ion asso-
ciation reaction, as the counterion is condensing onto a sur-
face charge of opposite sign, and available quasielastic neu-
tron scattering QENS and NMR studies of association time
scales 10
−9
s are indeed much shorter than the inverse
crossover frequencies of nanocolloids, except for very large
hydrated ions 16. We model this Stern layer of thickness
s
to have the same conductivity and permittivity as the me-
dium. The adsorbed Stern layer charge
s
is distinct from the
surface charge q
s
responsible for the complex MW condition
Eq. 5, where q
s
is due to smaller charge carriers than the
adsorbed ions and exists at the inside solid boundary of the
Stern layer. We hence exchange the potential continuity
equation at the particle surface with the Stern layer condition
of a potential jump across the Stern layer, with adsorbed
Stern layer charge related to the space charge
by an equi-
librium isotherm
s
=K
eq
,
P
M
= K
eq
S
, 6
where K
eq
=K
eq
/. Accumulation of
s
in the Stern layer due
to imbalance in particle and medium fluxes yields, using the
same isotherm, the dimensionless condition
a
冊冉
S
i
M
P
=
r
+
M
r
P
M
P
r
. 7
As the field is the same in the Stern layer and on the
medium side, we use the dimensionless version of Eq. 5
with Eqs. 6 and 7 on the particle surface to solve for the
three complex coefficients in Eq. 4. We use a reasonable
value for the equilibrium constant K
eq
=K
eq
/=1 and the lit-
erature value 17 for the Stern layer capacitance
m
/
S
=80
Fcm
−2
. The Stern layer RC time is simply the capaci-
tance term in Eq. 7 and yields a characteristic frequency
Stern
=D / a兲共
S
/
DL
. With Stern layer adsorption, the
diffuse layer also becomes a capacitor. However, since both
Stern and diffuse layer capacitors are in series relative to the
normal charging current, it is the diffuse layer with lower
FIG. 3. Color online Real part of the dipole strength A for 93
and 557 nm particles for
M
=1 mS m
−1
, =37 nm, K
s
=1.46 nS for
93 nm particles and K
s
=1.92 nS for 557 nm particles, relative per-
mitivities of
M
=78.5 and
P
=2.25, and D =10
−9
m
2
/s. The Stern
layer parameters are K
eq
=1.0,
m
/
S
=80
Fcm
−2
. Charge density
contours for representative conditions are shown in the insets.
FIG. 4. Comparison of our present theory to Green and Mor-
gan’s data using the parameters in Fig. 3. The Stern layer conduc-
tance for each particle is given in the inset in Fig. 2. The symbols
are the same as in Fig. 2. Dotted curve, MW theory with conducting
Stern layer; solid curve, current theory.
INDUCED DIPOLES AND DIELECTROPHORESIS OF PHYSICAL REVIEW E 75, 060501R兲共2007
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060501-3
capacitance and higher inverse RC time that dominates, such
that
DL
of 2 captures the data in Figs. 1 and 2.
The coefficients are determined from a series expansion
of the complex functions. The real part of the charge density
distribution within the diffuse layer is plotted in Fig. 3 for the
two particles of Fig. 1 with roughly the size of the smaller
one. There is negligible space charge in the diffuse layer of
the larger particle for all frequencies, as in the MW theory.
For the smaller particle, the Stern layer capacitor is saturated
at frequencies much lower than
Stern
, and the tangential
conduction in the diffuse layer drains the space charge away.
At higher frequencies, the ac period is too small for charging
current to penetrate the diffuse layer to reach the Stern layer.
These limits, hence, correspond to the conductive and dielec-
tric polarization mechanisms of the MW theory, and there is
again no space charge. At about
Stern
10
5
Hz, however,
the charge density of the smaller particle becomes dramati-
cally higher due to Stern layer charging. ReA is also shown
in Fig. 3 for both nanocolloids. While the larger colloid
shows a small correction to classical MW dipole intensity
that decreases with increasing frequency, a sharp maximum
is observed for the smaller particle at a frequency near
Stern
.
As shown in Fig. 4, all the crossover frequency data for
various particle sizes by Green and Morgan can be captured
with this model by using the proper a / for each experiment
and using the Stern layer conductance obtained from the
asymptotic crossover of the latex particles at low medium
conductivity. Adjusting the equilibrium constant K
eq
and the
Stern layer capacitance, the only unknown parameters, over
one order of magnitude does not change the curves signifi-
cantly, provided
Stern
DL
.
We thank Z. Gagnon, F. Plouraboue, and H. H. Wei for
valuable discussions on this subject and acknowledge finan-
cial support from the Center of Applied Math and NSF.
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The rapid, sensitive, and selective detection of target analytes using electrochemical sensors is challenging. ESSENCE, a new Electrochemical Sensor that uses a Shear-Enhanced, flow-through Nanoporous Capacitive Electrode, overcomes current electrochemical sensors' response limitations, selectivity, and sensitivity limitations. ESSENCE is a microfluidic channel packed with transducer material sandwiched by a top and bottom microelectrode. The room-temperature instrument less integration process allows the switch of the transducer materials to make up the porous electrode without modifying the electrode architecture or device protocol. ESSENCE can be used to detect both biomolecules and small molecules by simply changing the packed transducer material. Electron microscopy results confirm the high porosity. In conjunction with the non-planar interdigitated electrode, the packed transducer material results in a flow-through porous electrode. Electron microscopy results confirm the high porosity. The enhanced shear forces and increased convective fluxes disrupt the electric double layer's (EDL) diffusive process in ESSENCE. This disruption migrates the EDL to high MHz frequency allowing the capture signal to be measured at around 100 kHz, significantly improving device timing (rapid detection) with a low signal-to-noise ratio. The device’s unique architecture allows us multiple configuration modes for measuring the impedance signal. This allows us to use highly conductive materials like carbon nanotubes. We show that by combining single-walled carbon nanotubes as transducer material with appropriate capture probes, NP-μIDE has high selectivity and sensitivity for DNA (fM sensitivity, selective against non-target DNA), breast cancer biomarker proteins (p53, pg/L sensitivity, selective against non-target HER2).
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Globular proteins exhibit dielectrophoresis (DEP) responses in experiments where the applied field gradient factor ∇E² appears far too small, according to standard DEP theory, to overcome dispersive forces associated with the thermal energy kT of disorder. To address this dilemma a DEP force equation is proposed that replaces a previous empirical relationship between the macroscopic and microscopic forms of the Clausius‐Mossotti factor. This equation relates the DEP response of a protein directly to the dielectric increment δε⁺ and decrement δε⁻ that characterize its β‐dispersion at radio frequencies, and also indirectly to its intrinsic dipole moment by way of providing a measure of the protein's effective volume. A parameter Γpw, taken as a measure of cross‐correlated dipole interactions between the protein and its water molecules of hydration, is included in this equation. For 9 of the 12 proteins, for which an evaluation can presently be made, Γpw has a value of ∼4,600 ± 120. If, as a result of denaturation or aggregation, the protein specimen does not exhibit a sizeable dipole moment or β‐dispersion its DEP response should be interpreted in terms of either an induced moment or polarization of its electrical double layer. These conclusions follow an analysis of the failure of macroscopic dielectric mixture (effective medium) theories to predict the dielectric properties of solvated proteins. The implication of a polarizability greatly exceeding the intrinsic value for a protein might reflect the formation of relaxor ferroelectric nanodomains in its hydration shell. This article is protected by copyright. All rights reserved
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Dielectrophoresis can move small particles using the force resulting from their polarization in a divergent electric field. In liquids, it has most often been applied to micrometric objects such as biological cells or latex microspheres. For smaller particles, the dielectrophoretic force becomes very small and the phenomenon is furthermore perturbed by Brownian motion. Whereas dielectrophoresis has been used for assembly of superstructures of nanoparticles and for the detection of proteins and nucleic acids, the mechanisms underlying DEP of such small objects require further study. This work presents measurements of the alternating‐current (AC) dielectrophoretic response of gold nanoparticles of less than 200 nm diameter in water. An original dark‐field digital video‐microscopic method was developed and used in combination with a microfluidic device containing transparent thin‐film electrodes. It was found that the dielectrophoretic force is only effective in a small zone very close to the tip of the electrodes, and that Brownian motion actually facilitates transport of particles towards this zone. Moreover, the fact that particles as small as 80 nm are still efficiently captured in our device is not only due to Brownian transport but also to an effective polarizability that is larger than what would be expected on basis of current theory for a sphere in a dielectric medium. The high‐frequency dielectrophoretic response of gold nanoparticles with a diameter of less than 200 nm in water is studied using dark‐field digital video‐microscopy in combination with a custom‐made microfluidic device containing transparent thin‐film electrodes.
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Dielectrophoresis (DEP), the migration of particles due to polarization effects under the influence of a nonuniform electric field, was employed for characterizing the behavior and achieving the separation of larger (diameter >5 μm) microparticles by exploiting differences in electrical charge. Usually, electrophoresis (EP) is the method of choice for separating particles based on differences in electrical charge; however, larger particles, which have low electrophoretic mobilities, cannot be easily separated with EP-based techniques. This study presents an alternative for the characterization, assessment, and separation of larger microparticles, where charge differences are exploited with DEP instead of EP. Polystyrene microparticles with sizes varying from 5 to 10 μm were characterized employing microdevices for insulator-based dielectrophoresis (iDEP). Particles within an iDEP microchannel were exposed simultaneously to DEP, EP, and electroosmotic (EO) forces. The electrokinetic behavior of four distinct types of microparticles was carefully characterized by means of velocimetry and dielectrophoretic capture assessments. As a final step, a dielectropherogram separation of two distinct types of 10 μm particles was devised by first characterizing the particles and then performing the separation. The two types of 10 μm particles were eluted from the iDEP device as two separate peaks of enriched particles in less than 80 s. It was demonstrated that particles with the same size, shape, surface functionalization, and made from the same bulk material can be separated with iDEP by exploiting slight differences in the magnitude of particle charge. The results from this study open the possibility for iDEP to be used as a technique for the assessment and separation of biological cells that have very similar characteristics (shape, size, similar make-up), but slight variance in surface electrical charge.
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Frequency-resolved electric birefringence experiments are carried out on dilute colloidal suspensions of charged, rodlike particles over a wide frequency range. The Kerr constant displays new relaxation features impossible to identify with dielectric spectroscopy. Our data provide the first explicit evidence of Maxwell-Wagner relaxation of the electric polarizability of charged colloids. We successfully explain the observed behavior with a model combining electrokinetic and Maxwell-Wagner approaches. Our particles behave as constant charge entities.
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Displacement of air bubbles in a circular capillary by electrokinetic flow is shown to be possible when the film flow around the bubble is less than the bulk flow behind it. In our experiments, film flow reduction is achieved by a surfactant-endowed interfacial double layer with an opposite charge from the wall double layer. Increase in the film conductivity relative to the bulk due to expansion of the double layers at low electrolyte concentrations decreases the field strength in the film and further reduces film flow. Within a large window in the total ionic concentration Ct, these mechanisms conspire to induce fast bubble motion. The speed of short bubbles (about the same length as the capillary diameter) can exceed the electro-osmotic velocity of liquid without bubble and can be achieved with a low voltage drop. Both mechanisms disappear at high Ct with thin double layers and very low values of zeta potentials. Since the capillary and interfacial zeta potentials at low concentrations scale as log Ct-1 and log Ct-1/3, respectively, film flow resumes and bubble velocity vanishes in that limit despite a higher relative film conductivity. The bubble velocity within the above concentration window is captured with a matched asymptotic Bretherton analysis which yields the proper scaling with respect to a large number of experimental parameters.
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Electrified interfaces span from metaVsemiconductor and metaVelectrolyte interfaces to disperse systems and biological membranes, and are notably important in so many physical, chemical and biological systems that their study has been tackled by researchers with different scientific backgrounds using different methodological approaches. The various electrified interfaces have several common features. The equilibrium distribution of positive and negative ions in an electrolytic solution is governed by the same Poisson-Boltzmann equation independent of whether the solution comes into contact with a metal, a colloidal particle or a biomembrane, and the same is true for the equilibrium distribution of free electrons and holes of a semiconductor in contact with a different conducting phase. Evaluation of electric potential differences across biomembranes is based on the same identity of electrochemical potentials which holds for a glass electrode and which yields the Nernst equation when applied to a metal/solution interface. The theory of thermally activated electron tunneling, which was developed by Marcus, Levich, Dogonadze and others to account for electron transfer across metaVelectrolyte interfaces, is also applied to light induced charge separation and proton translocation reactions across intercellular membranes. From an experimental viewpoint, the same electrochemical and in situ spectroscopic techniques can equally well be employed for the study of apparently quite different electrified interfaces.
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The model developed in Part 1 is used to investigate the effects of Stern-layer transport on the high-frequency electrokinetic transport properties of spherical colloidal particles throughout the range of the zeta potential. The equations are solved numerically for Stern model (i) (adsorption of ions onto available free surface area). The effects of varying individual Stern-layer parameters on the magnitude and phase of the electrophoretic mobility and the real and imaginary parts of the dipole coefficient, are discussed and compared to the case where Stern-layer conduction is absent. Regardless of the Stern-layer adsorption isotherm used, it is found that the presence of mobile Stern-layer ions causes the mobility magnitude to decrease and the magnitude of the conductivity to increase, compared with the case when Stern-layer conduction is absent. The effects of allowing the particle surface charge density and Stern-layer charge density to vary with time are found to be small in comparison with the overall effect of surface conduction.
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The theory developed (C. S. Mangelsdorf and L. R. White, J. Chem. Soc., FaradayTrans., 1992, 88, 3567) to calculate the electrophoretic mobility of a solid, spherical colloidal particle subjected to an oscillating electric field is reviewed and extended. The equations governing the ion distribution, electrostatic potential and hydrodynamic flow field around the particle are modified to allow for the lateral movement of ions within the Stern layer and a time-dependent particle surface charge density. Two classes of Stern-layer adsorption isotherms are considered: (1) Adsorption of ions onto available surface area and (2) Adsorption of ions onto underlying surface charge. An equilibrium model is used for the changes in particle surface charge density arising from the flux of ions into and out of the particle surface.
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We submit a suspension of Brownian latex spheres in water to a spatially periodic and asymmetric potential successively switched on and off. Such a potential is created by dielectrophoretically induced forces resulting from the application of a high-frequency electric field between a plane electrode and a blazed optical grating. As expected, we observe a net macroscopic drift of the particles. Their average velocities have been measured as a function of the time during which the field is switched off. We observe a quantitative agreement with the theoretical predictions. In particular, the velocities strongly differ according to the size of the latex spheres, which should open the way to devices aimed at the separation of micrometer and submicrometer particles. The geometry of the gratings as well as the concentration and the surface functions of the particles has also been investigated.
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When an electric field is applied across a conducting and ion-selective porous granule in an electrolyte solution, a polarized surface layer with excess counter-ions is created. The depth of this layer and the overpotential V across this layer are functions of the normal electric field j on the granule surface. By transforming the ionic flux equations and the Poisson equation into the Painlevé equation of the second type and by analysing the latter's asymptotic solutions, we derive a linear universal j–V correlation at large flux with an electrokinetic slip length β. The flux-induced surface polarization produces a nonlinear Smoluchowski slip velocity that can couple with the granule curvature to produce micro-vortices in micro-devices. Such vortices are impossible in irrotational electrokinetic flow with a constant zeta-potential and a linear slip velocity.
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Dielectrophoretic behavior of single polystyrene-carboxylate microparticles and polystyrene microparticles was studied with a quadrupole microelectrode. For positive dielectrophoresis (DEP) of polystyrene-carboxylate particle observed in the lower frequency region (≤10 kHz), a DEP mobility coefficient (α) was almost proportional to the square of ac voltage (Urms, root mean square), as was expected from standard theories of DEP. The α values did not depend on the particle radius (re), but depended on the kind of electrolyte in the order HCl KCl ≈ KOH ≥ tetrabutylammonium chloride, showing a specific enhancement by H+. Since this observation was against the standard theories, we introduced a DEP radius (rDEP) of a Debye-type function instead of the particle radius to fit the observed α values in the lower frequency region. The positive DEP behaviors were reproduced by a function of rDEP and the surface conductivity of the negatively charged particles. As for negative DEP observed in the higher frequency region (≥56 kHz), proportional relationships between α and Urms2 and ones between α and re2 were obtained as predicted by the standard theories. The obtained rDEP values increased with a decrease in the ac frequency, and the rDEP value in the HCl system was larger than those for the other systems. These suggested that the rDEP was controlled by the moving distance of cations swung by the applied ac electric field in the dynamic diffusion cloud around the particles.
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A nonuniform electric field exerts a force on a polarizable particle through the Coulomb interaction with the electric dipole induced in the particle, resulting in a motion termed dielectrophoresis. The magnitude of the force depends on the dielectric properties of both the particle and the medium it is suspended in. As a result, measurement of the dielectrophoretic force provides information about the internal and surface dielectric properties of the particle. This paper presents the first detailed measurements of the dielectrophoretic response of submicrometer particles as a function of electrolyte composition and conductivity, applied field frequency, and particle size. Comparisons are made between the experimental results and the classical theory of the dielectrophoretic force derived from Maxwell−Wagner interfacial polarization. For particles of 557 nm diameter, good agreement is obtained between the experimental results and theory of interfacial polarization taking into account the effects of surface conductance. However, the results for smaller sizes of particle (93, 216, and 282 nm diameter) demonstrate that the theory does not adequately explain the dielectric or dielectrophoretic behavior of colloidal particles. The existence of a second low-frequency dispersion is also apparent in the data, attributable to the polarization of the double layer. The data were compared with a theoretical plot generated by modeling the dispersion in terms of a single Debye relaxation.