REVIEW
www.rsc.org/annrepc | Annual Reports C
Particle-localized AC and DC manipulation
and electrokineticsw
Orlin D. Velev,*a Sumit Gangwala and Dimiter N. Petsevb
DOI: 10.1039/b803015b
Colloidal particles suspended in water respond to direct (DC) or alternating
current (AC) fields in a variety of ways, including directional motion along
or across the field direction, field-gradient dependent response and induced
particle–particle interaction. We review here some of these effects and their
applications in new techniques for particle manipulation and assembly,
making of novel biomaterials and designing of new self-propelling microdevices. The coupling of the counterionic layer mobility, fluid flows and the
resulting particle motion are the basis not only of the classic electrophoretic
effects, but also of the recent developments in AC electrohydrodynamics
and induced charge electrophoresis of asymmetric particles. We also discuss
how dielectrophoresis (particle interaction with external AC field gradients),
could be used to manipulate and assemble objects on any size scale. We
discuss the interactions leading to the assembly of such structures, ways to
simulate the dynamics of the process and the effect of particle size and
conductivity on the type of structure obtained. Finally, we demonstrate how
an additional level of complexity can be engineered to turn miniature
semiconductor diodes into prototypes of self-propelling micromachines
and micropumps. The diodes suspended in water propel themselves
electro-osmotically when a uniform alternating electric field is applied
across the container. Semiconductor diodes embedded in channel walls
could serve as distributed microfluidic pumps and mixers powered by a
global external field.
1. Major AC and DC effects in water-based systems
The recent experimental advances in the areas of microfluidics, nanoscience, and
microelectromechanical systems (MEMS) have kindled an intense interest in the
motion and manipulation of particles by electrical fields. Colloidal particles
suspended in water exhibit a wide range of phenomena when subjected to direct
(DC) or alternating current (AC) fields, which arise from particle polarization,
motion of the ions in the electric double layer coupled with fluid flow, and forces
resulting from gradients in the field. The experimental advancements in the last few
years have made possible the fabrication of particles of well-defined shape, anisotropic polarizability or nonlinear conductance. These particles respond to external
a
Department of Chemical & Biomolecular Engineering, North Carolina State University,
Raleigh, USA. E-mail: odvelev@ncsu.edu; Fax: +1-919-515-3465; Tel: +1-919-513-4318
b
Department of Chemical & Nuclear Engineering and Centre for Biomedical Engineering,
University of New Mexico, Albuquerque, USA
{ The HTML version of this article has been enhanced with colour images.
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Fig. 1 Schematics of a few categories of particle-localized DC and AC electrokinetic phenomena. (a) Electrophoresis—upon application of a DC field, particles migrate toward the electrode
of opposite charge. (b) Dielectrophoresis—particles are attracted to or repelled from the highest
electric field intensity region due to interaction of induced dipole with the gradient of a DC or AC
electric field. (c) Induced-charge electrophoresis (ICEP)—unbalanced electroosmotic flows
around the Janus particles surface resulting from different electrical properties of each hemisphere
causes the particles to move normal to applied AC electric field direction. (d) Diode rectification
of an AC field converted to localized DC electrophoresis—diode self-propels in one direction due
to AC field rectification between diodes electrodes.
fields in a variety of ways, which may include directional motion or self-assembly in
new types of lattices. We overview here the different mechanisms by which such
particles respond to the field and provide examples of how they can be used to
assemble new materials and create new self-propelling microdevices.
A summary of the types of systems and effects discussed in this review is presented
in Fig. 1. We first examine the origin of the conventional electrophoretic motion of
particles in DC fields (Fig. 1a). The interaction of particles with non-uniform AC
electric fields leads to dielectrophoretic motion and assembly (Fig. 1b), which will be
discussed in the second section. While regular symmetric particles do not respond to
uniform AC fields, asymmetric particles can move in alternating fields by effects such
as ‘‘induced-charge electrophoresis’’ (ICEP) or AC particle electrophoresis, caused
by electric field gradients leading to unbalanced liquid flows around the particle
surface (Fig. 1c). In the last section we will present a new effect, where semiconductor
diodes acting as particles rectify an external AC field and propel against the liquid by
local electroosmotic flows along the particle surface (Fig. 1d).
2. Electrophoresis
2.1.
DC Particle electrophoresis
Electrophoresis and electrokinetic phenomena were first observed by Reuss in the
early 19th century.1 He found that liquid water in a tube filled with quartz sand starts
moving if an external electric field is applied on both ends. In a second experiment he
found that suspended clay particles will directionally migrate under the action of an
electric field. The first phenomenon is known as electro-osmosis while the second as
electrophoresis. While Ruess was unable to suggest a quantitative explanation of
these phenomena it was clear that the quartz or the clay particles somehow
‘‘electrified’’ the water making it receptive to the externally applied field. The first
attempt for quantifying electro-osmosis was done by Widenmann,2 who
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demonstrated that the electroosmotic bulk flow rate is linearly proportional to the
electric current that passes through the channel. Later, Quincke showed that if fluid
is forced through a microchannel or porous plug by applying a pressure drop a
potential difference arises between the ends.3 This effect is somewhat opposite to
electro-osmosis and the resulting potential is known as streaming potential. A
phenomenon that is in a similar way opposite to electrophoresis was discovered
by Dorn.4 When particles settle due to gravity a potential difference might develop
between the top and bottom of the tube where the settling takes place. This
difference is known as sedimentation potential. All the above observations are part
of the so-called electrokinetic phenomena.
The first extensive attempt to develop a theory of electrokinetic phenomena was
performed by Helmholtz.5 A central concept in his analysis was that of the electric
double layer (EDL). The EDL layer originates at the solid/liquid interface by locally
charging the two phases at the plane of contact. Helmholtz suggested that the
charges form a capacitor where one type of charge is at the solid surface while the
opposite charge is located in the liquid but in the immediate vicinity of the interface.
The solid wall was considered insulating while the liquid phase was a conductor. In
the presence of an external electric field that is directed parallel to the interface, the
charged liquid would slide and move with respect to the solid in a laminar
electroosmotic flow. Helmholtz derived the following expression for the electroosmotic velocity Ueo
Ueo ¼ ee0 C
E
Z
ð1Þ
where C is the potential drop across the capacitor at the interface, e0 =
8.854 1012 F m1 is the dielectric constant of vacuum, e is the dielectric
permittivity of the solvent (equal to 78.3 for water at room temperature
T = 298 K), Z is the solvent viscosity and E is the externally applied electric field
magnitude.
Major progress in developing the theory of electrokinetics has been made by
Smoluchowski6 who realized that the capacitor notion is an idealization and the
electroosmotic fluid flow field in a straight capillary follows the shape of the
potential distribution. Further he showed that for electric double layers that are
much smaller than the channel width the precise shape of the electrostatic potential is
irrelevant. Finally he pointed out that the important electrostatic property at the
interface is not the potential drop C but rather a different quantity historically
known as z (zeta) potential. This is the potential at the plane of shear where the fluid
starts moving relative to the solid surface or vice versa (Fig. 2). Smoluchowski has
accounted for the diffusion distribution of the dissolved ions in the vicinity of the
solid surface by relating the local electrostatic EDL potential C to the local charge
density re via the Poisson-Boltzmann equation
r
e X 0
zi eC
:
ð2Þ
r2 C ¼ e ¼ zi ni exp
ee0 i
kT
ee0
For flat (or thin) EDL the velocity field and the electrostatic potential are similar,
which means that
Zr2v = (ee0r2C)E.
(3)
Note that this approach assumes that the EDL potential C is independent on the
external field E and vice versa. This is a reasonable approximation for the cases
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Fig. 2 Schematic of the origins of electrophoresis of a negatively charged particle in a DC
electric field. The zoomed in area on the right side of the particle reveals the electric double layer
at the particle surface with the surface charge, the layer of bound counterions, the Stern layer
and the diffuse layer. The variation in electrical potential with distance x away from the surface
is also shown.
where the field in the EDL is much greater than the externally applied one and works
particularly well for straight capillaries where the external field vector is normal to
that in the EDL.7
Smoluchowski solved eqn (3) for the case of electrophoretically moving particles
with very thin EDL in which case the problem is one-dimensional and reads
Z
d2 v
d2 C
¼ ee0 2 E:
2
dx
dx
ð4Þ
where n is the tangential component of the velocity. The boundary conditions are
dv
dC
¼ 0;
¼ 0; v ¼ Uep at x ! 1
dx
dx
v ¼ 0 and C ¼ z at x ¼ 0:
ð5Þ
and the electrophoretic velocity of a particle with radius R becomes
Uep ¼
ee0 zp
E; kR ! 1:
Z
ð6Þ
where zp is the electrokinetic potential (zeta-potential) of the particle and k1 is the
Debye screening length. Another extreme is the situation where the particle radius is
much smaller than the EDL thickness. This case was analyzed by Huckel who
obtained a different relationship for the electrophoretic velocity8
Uep ¼
2ee0 zp
E; kR ! 0:
3Z
ð7Þ
The difference between expressions (6) and (7) is due to the fact that in the thin EDL
case the main resistance to the particle motion is the electrophoretic retardation
while for large EDL the dominant resisting force is viscous friction.7 The
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intermediate case was studied by Henry9 who suggested the following equation for
the electrophoretic mobility
mep ¼
Uep 2 ee0 zp
¼
f1 ðkRÞ where
E
3 Z
ðkRÞ2 5ðkRÞ3 ðkRÞ4 ðkRÞ5
þ
16
48
96
96
"
#
ZkR
4
6
ðkRÞ
ðkRÞ
expðtÞ
dt:
expðkRÞ
t
8
96
f1 ðkaÞ ¼ 1 þ
ð8Þ
1
Ohshima suggested the following much simpler empirical formula10 for the correction function f1(kR) which is accurate within 1% when compared to Henry’s result
3
1
5
1þ
ð1 þ 2 expðkRÞÞ
:
ð9Þ
f1 ðkRÞ ¼ 1 þ
2
2kR
Additional complication in the theoretical analysis of electrokinetic phenomena
follows from the possibility of EDL polarization from the electric and hydrodynamic
velocity fields. In this case the ionic distribution is no longer described by the
equilibrium Poisson–Boltzmann eqn (2). Instead one needs to solve the more general
Poisson equation
r
e X þ þ
r2 C ¼ e ¼ ðzi ni z
ð10Þ
i ni Þ
ee0 i
ee0
where the ionic concentrations n+
i and ni are determined from the respective mass
11
balance
@n
z
i
i e
rc
n
þ r j
¼
0;
j
¼
D
rn
ð11Þ
i
i
i
i
i v:
kT
@t
The velocity field v is obtained from solving the Navier–Stokes equations for the flow
around an electrophoretically moving particle.12,13
The electrophoretic motion of particles in DC fields has been used for many years
for measuring their z-potential. One complication in the experimental implementation
of such measurements is the background electroosmotic mobility of the liquid in the
channels. Avoiding the electroosmotic drift requires that the velocity of particles is
measured in the stagnant layer of fluid situated at a certain distance away from the
walls. The manipulation of particles by DC fields is thus always complicated by the
background electroosmotic flows. The AC dielectrophoresis described in the next
section has proven to be more convenient and straightforward to implement and
control.
2.2 AC Dielectrophoresis
2.2.1 Principles of dielectrophoresis. Almost any type of particle in any type of
media can be manipulated using alternating voltage. AC electric fields, as opposed to
DC fields, have the advantage of permitting high field strengths without water
electrolysis and largely avoiding electro-osmotic currents.14,15 The forces that the
AC electric fields exert on particles can be efficiently controlled by adjusting field
parameters such as magnitude, frequency, wave shape, wave symmetry, and
phase.14,16–18 The origin of the AC effects is the frequency-dependent polarization
of particles in AC fields applied across suspensions. The sign and magnitude of the
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dipoles induced in the particles are given by the real part of the Clausius–Mossotti
function, K
RejKj ¼
e2 e1
3ðe1 s2 e2 s1 Þ
þ
e2 þ 2e1 tMW ðs2 þ 2s1 Þ2 ð1 þ o2 t2MW Þ
ð12Þ
where e1 and s1 are the dielectric permittivity and conductivity of the media, and,
e2 and s2—of the particles.15,19 Metallic and highly conductive particles are always
strongly polarized (with Re(K) 4 0) at most AC field frequencies. The Clausius–
Mossotti factor for metallic particles approaches the limit of its maximum value at K = 1.
The frequency-dependant polarizability response of dielectrics is given in their
complex permittivity (which is a function of AC field frequency, o, ~e ¼ eo er iðsÞ
o ),
where e0 is the dielectric permittivity of vacuum (8.854 1012 C2 N1 m2), er is the
relative permittivity, i is the imaginary unit and s is the electrical conductivity.15 The
electrical double layer around particles dispersed in water is more polarizable than
the media at low field frequencies because of the high conductance of the counterionic atmosphere. Even dielectric particles whose bulk permittivity is lower than the
water media, exhibit higher polarizability at low frequencies (Re(K) 4 0) because of
the strong polarization induced in the double layer with higher conductivity then the
media. For such dielectric particles in water, however, the Clausius–Mossotti
function changes sign (i.e., the dielectrophoretic force discussed below changes from
attractive with Re(K) 4 0 to repulsive with Re(K) o 0) at a crossover frequency of
16,19
oc = t1
where tMW is the Maxwell–Wagner charge relaxation time
MW,
e2 þ2e1
tMW ¼ s2 þ2s1 . Such a frequency-dependent change of the sign of the interactions is
commonly observed with synthetic microspheres and live cells in water14,16,20–28 and
allows a high degree of control of the induced forces. The strength of the electric
field-induced dipole in particles has been calculated numerically using the electrokinetic theory of Mangelsdorf and White29,30 and the values for Re(K) have been
obtained for both static and oscillating fields.31 The impedance of the double layer is
also frequency-dependent and can alter the electric field strength and distribution
shape near the electrodes, shifting the field maxima and minima location as a
function of field frequency.32
The interaction of the dipoles induced in the particles with a non-uniform electric
field leads to the emergence of dielectrophoretic (DEP) force. The time-averaged
force on each homogenous particle, FDEP, is dependent on the gradient of the field
squared, rE2 and the radius cubed (effectively volume) of the particle, r3,15,19–22,33,34
!
FDEP ¼ 2pe1 RejKðoÞjr3 rE2rms
ð13Þ
It is important to note that particles experience DEP force only in a non-uniform
electric field and the DEP force does not depend on the field polarity. If the electric
field is uniform, then the force acting on each of the poles of the induced dipole
within the particles is equal and opposite and there is no net motion of the particle.15
Particle movement in field gradients occurs because the force acting on the two poles
is not the same due to the gradient in the field. Particles that are more polarizable
than the media (Re(K) 4 0) are pulled along the gradient into the areas of highest
field intensities (positive DEP).15,19 Particles that are less polarizable than the media
(Re(K) o 0) are pushed away from these areas (negative DEP). Thus, dielectrophoresis allows for collection of particles or their levitation above the electrodes.
DEP forces can occur in both AC and DC electric fields. In principle, DC
dielectrophoresis results in the largest magnitude of the induced dipoles in the
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particles. However, large DC field strengths cannot be applied to aqueous media in
an experimental cell as water electrolysis and DC electrophoresis can occur.
The extensive studies of dielectrophoresis originated with the work of Pohl.33
Wang et al. derived a general expression for the DEP force using the Maxwell stress
tensor method and theoretical relationships to link the dielectric properties of a
suspension of colloidal particles to dielectrophoretic behaviour exhibited by a single
suspended particle.35–37 Washizu et al. provided multipolar DEP theory to express
the net DEP force as the gradient of a series of scalar electromechanical potential
functions.38 Clague et al. recently used the method of Green’s functions39,40 to
develop an analytical solution calculating the gradient in the electric field strength
produced by a two-dimensional array of parallel electrodes.41 Single phase fluids do
not experience DEP force. For multiphase systems however (e.g., particle
suspensions) the total flux ji for component i with concentration ci is given by42
ji = Dirci + civ cimiE + civir(E E)
(14)
The first term on the right hand side of eqn (14) corresponds to diffusion, the second
denotes the convective transport, the third term is the electromigration [mi being the
electrophoretic mobility, see eqn (8)] and the last term is due to the DEP transport.
The quantity ni has the equivalency of DEP mobility and for spherical particles
obtains the form
n¼
em e0 R 2 K
12pZ
ð15Þ
The dielectrophoretic effects also lead to structuring when higher concentrations of
particles are present between the electrodes. The dipoles induced in the particles
interact with each other if the particles are close enough. The particles align in chains
along the direction of the field lines. This ‘‘chaining’’ force, Fchain, is dependent on
the field strength squared, E2 and the radius squared of the particle, r2
Fchain = Cpe1r2K2E2
(16)
3
where the coefficient C ranges from 3 to 410 depending on the distance between the
particles and the length of the particle chain.14,16,19 The chaining force acting on
particles of similar electrical properties is always positive and attractive. Particles of
the same type always align along the field lines, regardless of whether their
polarizability is higher or lower than the media, while mixtures of particles of lower
and higher polarizabilities than the media could form various types of alternating
chains in the perpendicular direction.15,43
The change in sign of polarizability due the AC frequency and its effect on the
interactions of a pair of dielectric polystyrene microspheres of 5 mm diameter is
illustrated in the electrostatic simulations of the electric energy density in Fig. 3. The
simulation takes into account the bulk dielectric properties and the polarizability of
the counterionic atmosphere with its higher conductivity. The electric energy of a
system is dependent on the electric field intensity, which is related to the dielectrophoretic force.44 For particles that experience positive DEP the minimum potential
energy is reached when the particles are closest to the point of highest electric field
strength.45,46 At low AC field frequencies, the counterions in the double layer have
enough time to follow each change in sign of the field direction and migrate in and
out of the double layer to the bulk solution. The particles are attracted to each other
(indicated by the high energy density red color) due to positive DEP (Fig. 3a). At
high frequency the ions in the counterionic atmosphere do not have enough time to
follow the change in sign of the field and the lower core latex permittivity value
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Fig. 3 Simulations illustrating the electric energy density for a pair of polystyrene particles
with 100 nm thick counterionic atmosphere in (a) low frequency (1 kHz) AC field and (b) a high
frequency (100 MHz) AC field. The bars to the right indicate the intensity of the electric energy
density. The direction of the AC electric field is shown with the double-headed red arrows. The
simulation demonstrates how latex particles subject to low frequency applied AC fields
experience positive DEP due to the conductive nature of the induced electrical double layer.
However, at high frequency AC fields the induced double layer does not have time to form and
thus the low particles are less polarizable than the media and experience negative DEP.
(as compared to the water media) determines the particles electrical properties. The
particles experience negative DEP and the high field intensity is not at the poles of
the particles in the direction of the electric field but rather at the particle equators
(Fig. 3b).
2.2.2 Applications of DEP in particle manipulation. Dielectrophoresis has become
a major tool for microscale control, manipulation and assembly of particles. Dipolar
chaining and 3D structuring due to dielectrophoresis have been initially observed in
electrorheological fluids.19,47–50 AC fields are presently used in the assembly of
organized particle materials and various structures and devices discussed in the next
section.14–16,42 The research topic of DEP manipulation, separation and assembly of
nonconductive particles is extensively developed. Much of the pioneering work and
recent research in DEP are focused on the sorting, trapping and manipulation of live
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cells51–68 and DNA.69–80 Similar techniques also encompass the concentration of
cells81,82 and molecules like DNA that otherwise would be difficult to detect.74 In one
of the few applications of DC field dielectrophoresis, Lapizco–Encinas et al. have
selectively concentrated and released live and dead Escherichia coli bacterium using
insulator-based
(electrodeless) dielectrophoresis (iDEP).83
DEP has served as basis of multiple separation techniques. It has been used to sort
particle suspensions84 and to separate live cells and polymer spheres.20,51,55,57,63,85
The frequency-dependent cell membrane polarizability can be used to separate an
incoming cell suspension into streams of live and dead cells and cells of different
genotype in flow-through devices.24,26,52,55,86–91 Kim et al. used a deflection method
to separate protein-bound particles.92 Li et al. have found close agreement between
experimental and modeling results for a dielectrophoretic filter for bacteria, spores,
yeast cells, and polystyrene beads.93 Krupke et al. have used AC dielectrophoresis to
develop a method to separate metallic and semiconducting single-walled carbon
nanotubes (CNTs) from suspension where the metallic CNTs experience positive
DEP and the semiconducting CNTs experience negative DEP.94 Lee et al. have
generated a three-dimensional electric field gradient to filter out and deposit metallic
CNTS from a mixture of semiconducting CNTs.95
More recently, researchers have synergistically combined DEP with other techniques within lab-on-a-chip and microfluidic devices. Chiou et al.96 have deployed
optoelectronic tweezers that utilize direct optical imaging to create high-resolution
DEP electrodes for the parallel manipulation of single particles. This device can
concentrate live human B cells from a mixture of live and dead cells. DEP has been
used as one of the forces to concentrate and separate polystyrene microparticles in
an optoelectrofluidic platform.97 DEP has also been incorporated in an optically
induced cell lysis device that can target a single specific cell and individually and
sequentially rupture it or only lyse the cell membrane without disrupting the
nucleus.98
Besides the collection and sorting of particles/molecules, the dielectrophoretic
force has been used to manipulate and move larger objects such as droplets on high
density liquid surfaces and semiconductor diodes (which will be discussed in section 5).
Earlier electrowetting devices move droplets by combining electrocapillarity with
dielectrophoresis and effectively changing the contact angle of the droplet.99–111 This
technique might have problems with surface fouling as the droplets are in direct
contact with solid walls. To avoid that problem, we developed a new microfluidic
chip based on dielectrophoretic manipulation of freely-suspended microdroplets
floating on a denser, immiscible liquid. Each of the microdroplets suspended on the
surface of high density fluorinated liquid and manipulated by the field can serve as a
microscopic container and reactor.112 Controlled on-chip assembly, drying,
encapsulation and polymerization were used to make anisotropic ‘‘eyeball’’ and
striped supraparticles, polymer capsules and semiconducting microbeads.14,113 We
completed a detailed study on the liquid flow and particle distribution inside single
floating microdroplets, combined with simulation of the heat and mass transfer
inside the droplets.114 Finally, we showed how the results of such ‘‘droplet
engineering’’ could be used in new types of microbioassays.115
AC dielectrophoresis can also be an efficient tool for the organization and
assembly of conductive and dielectric particles into functional structures. The
assembly of isotropic particles (both conductive and insulating), Janus particles
and live cells is discussed in the next section.
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3. AC Particle assembly
3.1 Field-driven assembly of regular particles
The dielectrophoretic assembly of colloidal particles into microscopic functional
structures holds promise for the fabrication of a wide variety of new materials and
devices. Promising nano- and microstructures have been developed by assembling
particles and large molecules via capillary forces, polyelectrolytes, DNA, biospecific
protein recognition, lipid bilayers, liquid crystals and electric fields.116–133 New
materials and devices may be developed by directed assembly of particle structures
with electrical functionality.16,129–136 Biosensors and bioassays where particle structures directly interface electronic chips have a number of potential advantages
compared to the present assays with optical detection.137–141 Unique opportunities
emerge by combining these structures with the rapidly growing field of microfluidics.142–144 One of the major challenges in the particle assembly area is the
development of techniques that are rapid and controllable. Many of the forces
involved in spontaneous assembly, such as van der Waals, electrostatic and hydrophobic, are difficult to control and modify.145 One of the most effective solutions to
this problem is the use of AC electric fields as a means of effecting and guiding the
assembly.
The AC field-directed assembly of particles typically combines DEP with dipolar
chaining force resulting in particle chains, crystals, and micro- or nanowires. Richetti
et al.146 have used alternating electric fields to assemble ordered 2D aggregates of
polyvinyl-toluene latex spheres by confining the particles in thin cells. Since this early
work, AC fields have been used to organize 2D crystals by induced dipolar repulsion
when polystyrene particles are confined into a thin gap of the order of
their diameter.146–155 The research groups of Saville151,152 and Marr153–155 have
performed similar AC field induced particle assembly studies. Our research group
has been among the first to explore the potential and demonstrate the formation of
electrically functional microdevices by interfacing colloidal assemblies with on-chip
electronic circuits.137 Microscopic electronically readable biosensors were assembled
in situ from latex particles by combining dielectrophoresis with tuning of the
colloidal forces. We have also used DEP to assemble switchable two-dimensional
photonic crystals of silica and polystyrene particles.14,16,134,135,156
The assembly of conductive particles by DEP can be used to make electrical
microcircuits, biosensors, chemical sensors, DNA detecting probes and others. Gold
nanoparticles,157,158 carbon nanotubes,159–171 and gold nanoparticles conjugated to
DNA133,138 have been assembled by DEP and studied.14 Other conducting particles
that have been assembled by DEP include quantum dots (CdSe semiconductor
nanoparticles), DNA and protein molecules, gold nanoparticles functionalized with
oligonucleotides, and metal nanowires and nanorods.14 Recently, CNTs have been
arranged into highly aligned micro-probes for single-cell experimentation and
delivery172 and into nanosensors for thermal sensing applications.173
Our research group has shown that 12–15 nm gold nanoparticles can be rapidly
assembled from suspension into electrically conductive microwires using AC dielectrophoresis.174 A suspension of nanoparticles is placed in a thin experimental chamber
(similar to the one depicted in Fig. 4a, but with a height of 0.1 mm) and AC electric
fields are applied resulting in microwire growth from one electrode to the other, until
the microwire bridges the inter-electrode gap and short circuits the electrodes. The
DEP-driven particle aggregation into microwires is irreversible. The key parameters
controlling the speed of the microwire assembly are AC field frequency,
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Fig. 4 Assembly process of polystyrene microspheres in a thin experimental cell under an AC
electric field. (a) Schematic of a co-planar electrode experimental cell. The spacer can be created
using Teflon tape or hydrophobic PAP pen yielding a cell height of 60–100 mm or 10–20 mm,
respectively. (b, c) Optical micrographs illustrating the two-stage mechanism of crystallization
for latex particles. (b) Shortly after the field is applied, the particles align in chains due to
dipolar attraction. Simultaneously, the DEP force due to the field gradient attracts the particles
to the high field intensity region. (c) The particle chains confined on the surface form
2D-hexagonal crystals aligned with one axis in the direction of the field.135 (b), (c) Reprinted
with permission from ref. 14. Copyright 2006, RSC.
concentration of electrolyte and of nanoparticles in the suspension, and viscosity and
dielectric constant of the media.17 We have identified diffusion as the rate-limiting
step, and performed electrostatic simulations of the process kinetics.17 Two modes of
assembly are identified: (1) bulk microwire assembly where wires grow through the
bulk of the suspension as porous cylindrical structures; and (2) surface microwire
assembly where wires grow directly on the glass surface of the experimental cell as
half cylindrical structures.14,17 The microwires possess ohmic conductance for both
AC and DC currents and can be used to form self-repairing circuits in liquids.174
These electrically functional structures could have applications as chemical sensors
or wet electronic and bioelectronic circuits. Using similar experimental setups, other
researchers have studied the formation of microwires of conductive materials
including colloidal gold, carbon black, and carbon nanotubes.175–177 Xiong
et al.178 have used micro and nanoscale templates with AC electric fields to assemble
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polystyrene nanoparticles and gold nanoparticles into nanowires. La Ferrara et al.
have assembled palladium nanowires using DEP to investigate as hydrogen
sensors.179
The AC dielectrophoretic assembly of dielectric particles can lead to colloidal
crystal formations by the combined action of the dipole-field DEP and dipole–dipole
chaining interactions. We have found that AC electric fields applied to latex or silica
particle suspensions in a gap between planar electrodes lead to the rapid and
reversible assembly of colloidal crystals.14,16,134,135,156 The experimental cell and
the crystallization process are illustrated in Fig. 4. The hexagonal crystals that form
are up to 25 mm2 in area and always have one axis aligned with the direction of the
electric field.135 Diffraction patterns of a laser beam transmitted through the particle
suspension and direct microscopic observations allows us to follow the crystal
formation process and identify two stages.134,135 In the first rapid (o5 s) stage
(Fig. 4b), the particles form particle chains along the field direction due to induced
dipole–dipole interactions by the chaining force.135 The particle chains are then
attracted to the high field intensity area on the bottom glass surface between the
electrodes by the DEP force (and facilitated by sedimentational force) acting on the
particles and particle chains. In the second, slower stage (Fig. 4c) once the field has
been on for B15 s, the particle chains attract laterally to assemble and crystallize
into hexagonal particle crystal arrays.135 The process is switchable and the particles
can be assembled or disassembled on demand simply by turning the voltage on or
off.135 The sharp and reproducible diffraction patterns prove that much of the crystal
is defect-free. The disassembly of the particles is driven by their thermal energy
leading to random displacement of the particles once the particles are released from
the electric field.135
The assembly process is studied by varying particle type (silica and latex
microspheres), particle size, electrolyte concentration, electric field strength and
frequency, and media viscosity and dielectric permittivity. Adding electrolyte (up to
0.001 M NaCl) decreases the spacing between the particle surfaces.134,135 The field
strength required to crystallize the particles increases monotonically with the
frequency for a given particle size. At a fixed particle type and field frequency, weak
dependence of particle size on the electric field intensity crystallization threshold of
the particles is found by plotting riEi (from the chaining force, eqn (16)) versus
frequency. It is hypothesized that smaller particles (o0.7 mm diameter) could be
made to crystallize at higher electric field intensities.135 Mittal et al.180 have recently
reinterpreted the order-disorder transition which we reported for micrometer-sized
polystyrene particles. They have measured forces on the order of piconewtons
between micrometer-sized polystyrene latex particles in AC electric fields and
have found that the field strength required to assemble latex particles into a
crystal increases with increasing field frequency and is dependent on the particle
size, decreasing with particle diameter.180 Lele et al.181 have investigated the
transition of ordered structures to disordered bands and vortices formed in colloidal
suspension systems under AC electric fields. Hoffman et al. have found experimental
evidence of distinct Stern-layer and diffuse-layer (which comprise the electrical
double layer) conductance contributions to the DEP-induced particle polarization
of polystyrene particles and have characterized the resulting DEP effects on colloidal
assembly.182
Recently, Xie et al.183 have applied alternating electric fields using lithographically
templated electrodes to 3 mm diameter polystyrene particles to reversibly and rapidly
assemble the colloidal particles into grid patterns. Herlihy et al. have used DEP to
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assemble micrometer-sized monodisperse anisotropic polymer particles with disk,
rod, fenestrated hexagon (hexnut), and boomerang shapes and found that these new
shapes can result in interesting packing and crystallization behavior.184 Winkleman
et al. have assembled 100 mm glass microspheres in AC electric field in a dry system
that does not require suspending liquid.185 Zhang et al. investigated the pre- and
post-nucleation processes of AC electric field driven assembly on electrode surfaces
for colloidal latex microspheres186 and characterized the formation of crystals of
different size as a function of frequency.187
3.2 DEP assembly of biocomposite materials from live cells and particles
The co-assembly of live cells and particles into on-chip biodevices and larger scale
biomaterials is an important and largely unexplored field where directed assembly
can produce devices and materials with a high level of functionality, which cannot be
produced by conventional dry microfabrication techniques. The fabrication of
patterns and biomaterials from cells is of significant interest.188,189 Traditionally,
similar biomaterials are fabricated by adsorbing proteins and live cells onto
patterned surfaces.190,191 More recently, cell arrays have been formed on
scaffolds made by microcontact printing with oligopeptides,192–195 laminar flow
patterning196,197 and dielectrophoresis.198 DEP has also been used for on-chip cell
patterning.199 This area has attracted significant interest for tissue engineering200–206
and development of biosensor technologies.207–209 This field is still in its infancy and
a large science and technology benefit can be derived from introducing new
techniques for assembly of cell-based composite biomaterials.
We demonstrated how AC dielectrophoresis can be used to assemble biocomposites from live cells and functionalized particles.210 Baker’s active yeast cells
(Saccharomyces cerevisiae) in suspension can be readily organized in chains by the
use of DEP in the two-electrode cell (similar to the setup in Fig. 4a), however, cells
collected by the field come apart when the voltage is turned off. We bound these cells
into permanent structures by using functionalized nano- and microparticles as
biocolloidal ‘‘glue’’ (Fig. 5a). These particles have on their surfaces chemically
attached lectins (Concanavalin A), which bind selectively to specific polysaccharides
on the outer cell membrane.211 The application of the AC fields in the low-frequency
domain leads to incorporation of the particles into the cell chains and arrays, where
they are trapped in the junctions between the cells and bind to their surfaces.
Consecutive application of the field in a second direction perpendicular to the first
one in a chip with four point electrodes allows assembling closely packed single-layer
cell membranes. Thus, chains and membranes of cells permanently attached by
particles can be assembled on the chips.210
Simulations were performed to model the particle-cell chain formation process by
calculating the electric field distribution and electrostatic force vectors acting on an
ensemble of two cells and two particles placed randomly in an AC field (Fig. 5b).210
The distribution of the electrostatic field in the system is very complex (being locally
modified by the particles) and can not be described adequately by simple pair
interactions. While the thermal (Brownian) motion of the large cells is small, the
hydrodynamic interactions are important. The simulation that allowed for better
understanding and reconstructing of the dynamics of cell-particle assembly is based
on computing the force on each particle by integration over its volume of the
electrostatic force density, f, originating in each element of the simulation space,
R
FParticle ¼
f dV. The electrostatic field intensity is obtained from a finite element
Particle
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Fig. 5 (a) Chain of live yeast cells and 0.95 mm diameter magnetic particles assembled at
17 V mm1 and 100 Hz, which can readily be rotated by an externally applied magnet. The scale
bar size is 20 mm. (b) Simulation of the electric field distribution around assembled particle and
cell chain at an AC field frequency of 100 Hz. The red color indicates higher field intensity
whereas the blue color indicates lower field intensity. (c) Low microscope magnification optical
micrograph of manipulation (folding) of a large magnetic yeast cell membrane by externally
applied magnetic fields. The membrane is only one cell layer thick. (d) SEM of a closely-packed
fixed yeast cell membrane bound together by Concanavalin-A functionalized microparticles.
Reprinted (a–d) with permission from ref. 210. Copyright 2008, RSC.
calculation of the set of PDEs for the system geometry using the FEMLAB multiphysics
modeling package (Fig. 5b), where we also incorporate the complex permittivity (which
is a function of the field frequency) of the cells. This force is used to calculate at the next
stage the displacement of each particle by calculating the hydrodynamic resistance and
the distance traveled per unit time. After the new particle configuration is established,
the electrostatic field distribution is calculated again and the new set of forces is
established; the loop is repeated iteratively until an equilibrium particle structure is
reached. This procedure is broadly similar to a molecular dynamics simulation of the
cell/particle motility under complex electrostatic interactions. The simulation was in
good agreement with the experimentally observed dynamics of formation of alternating
cell-particle structures at a frequency of 100 Hz.210
The particles in these assemblies can not only be used as a ‘‘gluing’’ element in the
biocomposite arrays, but could impart additional functionality on their own. By
using lectin-coated magnetic microparticles as binding units, we were able to
manipulate the chains and membranes by external magnets. Examples of magnetic
cell chains and membranes of size E cm2 are shown in Fig. 5c with an SEM image in
Fig. 5d.210 One important question that arises with regards to the potential
application of these materials is whether the cells in the assemblies are alive and
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viable to the same extent as the freely suspended ones before the DEP treatment.
Theoretically, there are no reasons to expect that fields used of a magnitude
50–100 V/cm could damage the cells. These fields induce a potential difference
of o100 mV across a typical 10 mm cell. This field is not lethal to live cells212,213 and
is on the order of the ones routinely used in cell levitation experiments and in
DEP-based separations of cells of various genotypes in continuous flow devices.22–26
In order to prove that the yeast cells retain their metabolic activity after treatment on
the DEP chips, we performed fluorescence tests of cell viability by the FUN-1 dye
method. The proportion of metabolically active cells in the biomagnetic arrays was
approximately the same as the one in the original suspension (E90%).210
This DEP on-chip co-assembly technique could also be used for manipulation and
assembly of mammalian cells, which are considerably more delicate and have more
specialized functions than yeast or microbial cells. We demonstrated the assembly of
permanently bound 1D and 2D composites of trypsinized NIH/3T3 mouse fibroblasts, which could also be bound by lectin-functionalized microparticles.210 These
results open a wide range of research possibilities in field-driven biocomposite
fabrication. Cell-particle assemblies formed on a chip could potentially be used as
biosensors to electrically detect changes in cell impedance caused by toxins or
changes in environment, artificial tissues for microsurgery, advanced vaccines and
drugs, smart biomaterials or chemical sensors.210
3.3 Field-driven assembly of Janus particles
The assembly of anisotropic particles and colloidal building blocks is a new research
area with the goal to form novel materials. There is growing recognition that
anisotropic shape and interactions through ‘‘patchiness’’ could be used in the
programmed assembly of engineered nanostructures.214 ‘‘Janus’’ particles (whose
halves are physically or chemically different) are a class of anisotropic colloids whose
name was originally proposed by Casagrande and de Gennes.214–216 Various
methods for the synthesis of such particles have been developed.217–224 Thermal
evaporation225 and gold sputtering226,227 have been used to produce anisotropic
Janus particles with two hemispheres of different polarizability or conductance.
Hong et al. have assembled spherical particles having opposite electric charge on
each hemisphere.228 The assembly of such dipolar Janus particles has been simulated
theoretically by using molecular simulations.229–233
The response of Janus particles to AC fields reveals a rich variety of electrostatic and
electrokinetic effects. The area was sparsely investigated until recently. Behrend et al.
have tracked orientation and rotation of Janus particles in applied magnetic fields to
infer the torques acting on the particles.234 Takei et al. have applied low frequency
(0.1–1 Hz) electric fields to anisotropic particles after chemically modifying the gold
hemisphere of the particles with charged thiols. The orientation of these dipolar particles
in an electric field is controlled by the charge of the functionalized hemispheres and is
dependent on the pH.225 Crowley et al. found that 100 mm diameter ‘‘gyricon’’ balls
(having hemispheres of different polarizabilities and colors) suspended in a liquid can be
rotated when a uniform electric field is applied to them.235 Kim et al. used a similar
technique to rotate and flip Janus balls (of B300 mm) with optical and electrical
anisotropy (prepared using a high-throughput optofluidic device) confined in oil-filled
cavities with an AC electric field.236
We synthesized micron-sized Janus particles with one dielectric hemisphere and
one conductive hemisphere (Fig. 6) and applied AC electric fields to these particles
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after suspending them in water.44 The metallodielectric microspheres are prepared
by depositing particle submonolayers on microscope glass slides using a convective
assembly method we have previous engineered237 and subsequently coating the
exposed hemispherical surface of the particles with 20 nm of gold in a metal
evaporator. We characterized the phase space for electric field intensity and field
frequency for particle concentrations large enough to form a monolayer on a glass
surface between two gold electrodes in an experimental cell similar to the one
depicted in Fig. 4a.
The particles form a rich variety of structures and perform dynamic particle
motion depending on the applied field strength and field frequency.44 The unique
particle induced-charge electrophoretic (ICEP) motion that occurs at lower
frequency (o10 kHz) and medium to high AC electric field strengths will be
discussed in more detail in the next section of this review.44,238 At high AC
frequencies (410 kHz), the metallodielectric microspheres form novel structures
such as staggered chains, 2D crystals, and 3D bundles.44 These Janus particle
structures are very different from the structures that form in the directed assembly
of plain dielectric or plain conductive particles when fields of similar frequency and
intensity are applied.134,135,174,210 At low electric field intensities (o25 V cm1)
across the field frequencies studied (1–200 kHz), the particles remain disordered and
distributed randomly on the bottom surface of the experimental cell. At higher
electric field intensities various particle chains form across the range of field
frequencies. Regular chains form at lower frequencies (o10 kHz) whereas new
types of staggered chain structures form at frequencies above 10 kHz. The particles
within the regular chains are oriented such that their gold hemispheres face up and
the uncoated halves face the bottom slide. The particles within the staggered chains
are oriented such that the gold-coated halves of neighboring particles align into
metallic lanes throughout the staggered chain and the polystyrene hemispheres face
in alternating directions without contacting another particle (Fig. 7a). The gold
hemispheres of adjacent particles align as a result of the larger dipole induced in gold
portion of particle.44
At the next higher range of field intensities investigated, the regular and staggered
chains are confined together to form two-dimensional (2D) metallodielectric
Fig. 6 SEM image of 4.0 mm Janus particles having one dielectric hemisphere and one
conductive hemisphere. Janus particles are obtained by partially coating polystyrene particles
with 20 nm gold. The gold-coated hemispheres of the particle appear brighter than the uncoated
halves due to their higher conductance. Reprinted with permission from ref. 238. Copyright
2008, American Physical Society
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crystals.44 Again below 10 kHz, the particles form regular 2D crystals, whereas
above 10 kHz the staggered chains come into contact laterally to form 2D lattices of
a couple of different symmetries (one of which is shown Fig. 7b). We characterized
Fig. 7 (a) Optical micrograph of staggered chains of 5.7 mm diameter Janus particles formed at
56 V cm1 at 40 kHz AC field frequency. (b) Optical micrograph of a metallodielectric 2D
lattice of confined staggered chains formed at 125 kHz AC field frequency. (c) Simulation image
of the electrical energy density contour around a staggered metallodielectric chain. The yellow
arc represents the gold shell and the bar to the right indicates the intensity of the electric energy
density in (b). The scale bars in (a) and (b) are 70 and 50 mm, respectively. (a–c) Reprinted with
permission from ref. 44. Copyright 2008, American Chemical Society.
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these 2D crystals using the orientational order and polarization parameter, which
have been used to characterize dipolar liquid crystals. The metallodielectric 2D
lattice structures formed were found to be in a well-aligned antiferroelectric lattice.
At the highest range of electric field intensities (475 V cm1), the metallodielectric
particles form 3D bundles where the particles stack on top of each other, increasing
the particle bundles’ width and height due to the higher DEP and particle chaining
force.44 All of these assembled structures came apart once the electric field was
removed due to Brownian motion similarly to the disassembly process of plain
polystyrene particles assembled in AC electric fields.135 The metal-coated hemisphere
of the particles plays a leading role in the formation of all these structures and the
dynamic particle motion that we observed.44
The experimental results of the orientation of Janus particles in the electric
field and the formation of staggered chains were interpreted by means of
numerical simulations of the electric energy of the system for different particle
orientations and particle configurations. The effect of the polarizable counterionic
atmosphere around the polystyrene portion of the metal-coated particles
was accounted for in the model in order to simulate the higher surface conductivity
of this layer using the complex permittivity.15 The simulations of the energy of
particle orientation and particle configuration agree with the experimentally
observed results and help explain the structures formed during the experiments.
When the field is turned on the particles align such that the plane between their
gold-coated and uncoated halves is aligned in the direction of the electric field. This
allows to induce the largest magnitude dipole within the gold-coated portion of
the particle and this alignment is similar to the alignment of rodlike particles
along the electric field direction.19 The electrical energy density simulation of a
staggered chain (Fig. 7c) was found to be the most favorable configuration amongst
a set of different chain configurations. The results show that the counterionic
atmosphere on the latex half of the particle modulated the interactions in the
system and that the high polarizability of the metal layer coating dominated
the assembly process. The electric field-assisted self-assembly of the Janus
metallodielectric particles at high frequency could be used in the fabrication of
materials with directional electrical and heat transfer and massively parallel
waveguides.44
4. AC Particle electrohydrodynamics (ICEP)
4.1 Principles of ICEP
Nearly all types of colloid particles respond and move in AC fields. The case of motion
in inhomogeneous or non-uniform AC fields is the widely used dielectrophoresis, which
was discussed in the previous section. Interestingly, some, but not all, types of particles
can also move directionally in homogeneous or uniform AC fields. The direction of
motion is not always collinear with the field lines and the reasons for this AC
electrokinetic effect are not as intuitively clear as in DC electrophoresis. Similarly to
DEP, most of the AC electrokinetic phenomena exhibit a nonlinear quadratic
dependence on the applied electric field. An example is the electro-osmosis of the
second kind or electroosmotic whirlwind discovered by Dukhin and co-workers.239–243
It occurs in the vicinity of conducting particles and at high electric fields. As a result
the electric double layer becomes strongly polarized. The polarization enhances the
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relative fluid-to-solid flow rate leading to electrophoresis of the second kind. The
electrophoretic velocity of the second kind of such particle is given by
Uep2 ¼
2Ree0 E2
sgnðzp Þ:
Z
ð17Þ
where R is again the particle radius. The directions of electrokinetic flows of the first
and second kind are the same. The electrophoretic and electroosmotic velocities of
second kind however are BE2 while those of first kind are BE.
The quadratic dependence on the applied electric field implies that directional
translation of fluids and particles can be achieved using AC fields if the particles are
conductive and strongly polarizable as shown by Squires and Bazant244,245 and by
Green et al.15,246–249 These authors presented detailed analyses of the flow patterns
around conductive polarizable cylinders including the transient effects associated
with ionic redistributions. In AC electro-osmotic flow, the tangential component of
the electric field acts on the diffuse counterions outside the outer Helmholtz plane
(OHP) causing them to move transverse to the surface, pulling the fluid along and
generating a flow.15,250,251 A net flow only occurs if the field has a tangential
component to a surface and the flow points in the same direction for each half of
the AC cycle. The flow velocity is strongly dependant on the field frequency and
electrolyte concentration. The velocity is zero at the surface and rises to a maximum
(and constant thereafter) at the slip plane (OHP). The AC electro-osmotic flow
velocity when the radius of the particles is much larger than the Debye length of the
suspension follows Smoluchowski’s DC-field formula250 (eqn (1)). Murtsovkin et al.
first described nonlinear electo-osmotic flows at low frequency AC electric fields
(BkHz) due to polarization of the ionic double layers of particles. Ramos et al.249
and Ajdari252 were the first to describe electro-osmosis at electrodes. Bazant and
Squires244,245 suggested the term ‘‘induced-charge electro-osmosis’’ (ICEO) to
describe all such flows, near a polarizable surface, resulting from the action of an
applied electric field on its own induced diffuse charge. ICEO flows have been
utilized and observed in diverse environments.246,249,253–256 Such induced charge
electrokinetic phenomena lead to very high electrophoretic velocities,242,243 and can
be used for high throughput electro-osmotic fluid pumping,257,258 or to improve
mixing of components in packed beds of ion-permselective particles.259 Rose et al.260
have recently demonstrated ICEO contributions to the rotation of metallic
nano-barcode rods.
The investigations of AC particle electrophoretic motion have been very limited.
AC particle electrophoresis can be created by unbalanced liquid flows around a
particle having anisotropic surfaces. Bazant and Squires have predicted theoretically
how broken symmetries on surfaces could cause polarizable particles that are
conductive and coated on one side with a dielectric layer to move by ‘‘inducedcharge electrophoresis’’ (ICEP) or AC particle electrophoresis, in uniform AC
fields.244,261 Murtsovkin and Mantrov262 experimentally observed the motion of
quartz particles of irregular shapes in different directions. They found this motion to
be dependent on the applied electric field strength squared, but they did not provide
a theoretical reason why. Yariv et al. have derived general mobility relations for
homogenous non-spherical conducting particles.263 These mobility relations have
also been derived for ICEP motion for arbitrary shape perturbations,261 as well as
rod-like spheroidal shapes.264
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4.2 Example of ICEP-self-propelling Janus particles
The asymmetric Janus particles present an excellent system for the study of ICEP
effects. We measured experimentally the AC electrophoretic motion of Janus
metallodielectric particles (having one gold-coated, conductive hemisphere and
one polystyrene, dielectric hemisphere) suspended in water upon the application
of low frequency electrical fields.238 At both low and high frequencies of the applied
fields, the Janus particles orient such that the plane between their gold-coated and
uncoated hemispheres align in the direction of the electric field as soon as the field is
turned on. When fields of low frequencies (o10 kHz) are applied, the aligned
particles begin moving in a direction normal to the applied electric field (Fig. 8a and c)
with their polystyrene hemisphere forward by induced-charge electrophoresis
(ICEP) or AC particle electrophoresis. This unusual phenomenon cannot be
attributed to dielectrophoresis (DEP), and is the first experimental observation of
the effect predicted theoretically by Squires and Bazant.245
The metal-coated hemispheres of the Janus particles are much more strongly
polarized than the uncoated latex halves in an AC electric field. At low field
frequencies, the counterions in the media have enough time to fully form the induced
double layer around the polarized particles and suppress the induced charge. Once
the induced double layer is fully formed, the electric field lines no longer penetrate
the particle surface. The tangential component of the electric field acts on the diffuse
counterions within the induced double layer causing the ions to move tangentially to
the surface of the particles from the poles of the particle (on both sides) toward the
equator while dragging the liquid and generating a flow. Since the metal side is more
strongly polarized, the flow around this half of the particle is stronger than the flow
around the bare polystyrene half resulting in unbalanced flows. These unbalanced
ICEO flows around the two sides of the particles force them to move by ICEP
normal to the applied electric field direction with their dielectric hemispheres facing
forward (Fig. 8c). Thus, the particles begin to propel in defined direction, moving
across uniform electric field lines with velocities up to tens of mm/s while interacting
with other particles along their paths. These particles were also found to be
dynamically attracted to the top and bottom glass walls of the experimental cell.
The simulation of electric field intensity around the Janus particle reveals the
tangential component of the electric field near the top and bottom of the particle
(Fig. 8b).
We characterized the particle velocity as a function AC field strength, frequency,
electrolyte concentration and particle size. The theoretical predictions of Squires and
Bazant were fitted to the experimental results. The particle velocity as a function of
field strength (Fig. 9a) and AC frequency (Fig. 9b) are consistent with ICEP theory
in dilute solutions (r100 mM) for lower field strengths (E o 280 V cm1), but we
observe anomalous behavior at higher electrolyte concentrations, including no
motion above 10 mM, at higher field strengths or large particle sizes.238 In water
(with no salt added) and a dilute solution of 0.1 mM NaCl, the particle velocities
scale as UICEP E E20, which is observed in the good linear fit in Fig. 9a. The ratio of
the differential capacitances of the compact and diffuse layers was calculated based
on the plot in Fig. 9a to be B10, which is somewhat larger than prior work on ICEO
flow in KCl solutions.256
The dependence of ICEP velocity on the AC field frequency was found to be
1
consistent with the bands of characteristic driving frequencies, t1
e r o r tp for
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Fig. 8 (a) Schematic of a Janus particle in one-half cycle of AC electric field in the stable
configuration. The streamlines indicate the ICEO flow around the particle surface. Since the
gold side is more strongly polarized, the flow is greater on this half from the poles to the equator
of the particle causing the particle to move normal to the field with its dielectric face forward.
(b) FEMLAB simulation image of a 2-D Janus particle (of one dielectric half and one
conductive half). The bar on the right side shows the electric field intensity and the arrows
represent the electric field lines. The simulation illustrates a tangential component of the electric
field near the gold/polystyrene surface. (c) Optical micrograph corresponding to the position
and orientation of anisotropic particles of three different diameters (4.0, 5.7 and 8.7 mm) in an
applied AC field of 140 V/cm and frequency 1 kHz. The two particles present on the right side
in the top image have moved out of the plane of view and another particle has moved into the
plane in the bottom image approximately 5 s later. (a), (c) Reprinted with permission from
ref. 238. Copyright 2008, American Physical Society.
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Fig. 9 (a) Effect of electric field E2 and electrolyte concentration on the ICEP velocity of
5.7 mm Janus particles at 1 kHz AC. At lower electric field intensities (EO o 280 V cm1), the
linear fits agree with the experimental ICEP particle velocity values. (b) Effect of field frequency
on ICEP particle velocity for 5.7 mm diameter particles at 200 V/cm in 0.1 mM NaCl. The ICEP
velocities were highest between the upper and lower characteristic frequencies for electrode and
particle charging (t1
E 20 Hz and t1
E 12 kHz, respectively). (a), (b) Reprinted with
e
p
permission from ref. 238. Copyright 2008, American Physical Society.
which ICEO flows have been observed.245 The lower frequency range is determined
by the time it takes for the formation of the induced screening cloud (electrical
double layer) to form around the electrodes, te ¼ lL
D , where 2L is the electrode
separation, l is the Debye length and D is the ion diffusion coefficient. The upper
frequency range is set by the induced double layer formation time (also known as the
characteristic ‘‘RC time’’) around the particle, tp ¼ lR
D . The characteristic frequencies
1
for our system are t1
e E 20 Hz and tp E 12 kHz. Our experimental results are
consistent with these characteristic frequencies and the particle velocities decreased
as each of the frequencies was approached (Fig. 9b). The ICEP velocity increases
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almost linearly with particle size for smaller particle diameters, but the ICEP velocity
reaches a maximum value for 8 mm diameter particles. Such ICEP-propelling
metallodielectric particles could be used for separations or as microscopic mixers,
‘‘shuttles’’ and self-propelling on-chip sensors in MEMS, optoelectronic or
microfluidic devices.
5. AC Field in combination with semiconductor diodes
5.1 Principle of field generation along diode and self-propellency
Recently we suggested a new method for propelling of microparticles or driving fluid
in microfluidic channels.266 The method is based on using semiconductor diodes in a
fluidic network with globally applied AC field. The diodes can be either suspended in
the fluid or immobilized at specific locations in the network. The overall AC field will
be locally converted into DC voltage by the diodes, which will consequently result in
electroosmotic or electrophoretic motion (Fig. 10). For immobile diodes embedded
in the channel wall this will lead to local electroosmotic pumping while a free diode
particle will move by particle-localized electrophoretic effects. The electric voltage
induced in the diodes by the external fields can be estimated from an equivalent
circuit model including resistors describing the ionic conductance through the bulk
liquid and capacitors for the ionic layers. At low frequencies the resistance is likely to
be the leading contribution. The diode short-circuits the negative half-periods of the
AC current. The resulting DC voltage of magnitude Vd induced in the diode can be
approximated as
Vd ¼
1
R2
Vext
2 ðR1 þ R2 þ R3 Þ
ð18Þ
where R2 is the resistance of the liquid alongside and between the two ends of the
diode and Vext is the AC peak-to-peak voltage applied to the electrodes. The
resistances R1 and R3 are that of the fluid before and after the diode. The 1/2 factor
accounts for the fact that only half of the external AC step field is harvested for
Fig. 10 Schematics of propelling diodes suspended in water showing the localized electroosmotic flow generated from a DC field rectified from an external AC electric field. The
electros-osmotic ionic flux leads to diode motion, which can be in the direction of either the
diode’s cathode or the anode, depending on its surface charge.
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propelling relative diode fluid motion. The other half-periods are shortened by the
diode and lost as heat. Then the electric field over the diode is
Vd 1
¼ ðEext Ed0 Þ
ld
2
ð19Þ
where ld is the diode length and Ed0 is the offset field that characterizes the particular
pn-junction.265 Hence, a diode particle will experience a pulsating driving force that
directly depends on the frequency of the applied field. For observation times much
larger than the inverse field frequency this effect can be ignored and the particle
motion can be considered as uniform with velocity
Uep ¼
ee0 zp
ðEext Ed0 Þ:
2Z
ð20Þ
The diode motility thus should be affected by the usual factors controlling the
electrophoretic or electroosmotic motion. We characterized the diode-fluid relative
velocity as function of the external field strength; field frequency and solution pH
(Fig. 11). The velocity linearly depends on the field strength as expected for
electroosmotic motion (Fig. 11a). This experiment confirms the validity of eqn (20)
above. At the same time there is no noticeable dependence on the field frequency (see
Fig. 11b). This observation is very important for potential applications of selfpropelling diodes and more complex microcircuits in motile devices and prototypes
of ‘‘microbots’’. If the diodes and microcircuits can be supplied by AC fields in the
microwave and/or radio frequency range one might be able to power up and actuate
the microdevices without the use of electrodes in direct contact with the fluid. The
high frequency fields can penetrate through the materials surrounding the fluidic
device and will be locally harvested for performing the desired function by the
diodes. The DC voltage rectified by the diodes can be used to power up additional
electronic or potentially logic functions within the microcircuits.266 Finally the pH of
the solution can be independently used to modify the motion of fluids or diode
particles by recharging the surface (Fig. 11c). This effect is analogous to conventional DC electro-osmosis and electrophoresis where the velocity magnitude and
direction is also pH-dependent. The reason for such behavior is in the dependence of
the surface charge and potential on the pH of the solution.
5.2 AC Diode mixer: hydrodynamic analysis and examples
Diodes can also be fixed alongside the channel wall in a microfluidic device where
they can serve as micropumps or mixers.18,266 Then the external electric field will lead
to electroosmotic fluid velocity at the diode-solution interface that will be given by
Ueo ¼ ee0 z
ðEext Ed0 Þ
2Z
ð21Þ
where the electrokinetic z-potential is the one on the microchannel wall (part of
which may be the casing of the diode). An AC powered diode pump can easily be
fabricated by placing two diodes in parallel orientation alongside the channel walls.
If the diodes are oriented in opposite directions the fluid will form a local vortex
which acts as a mixer (see Fig. 12). The diode mixers have large potential for
applications in microfluidics. At micro-scales the flows occur at low Reynolds
numbers and are viscosity-dominated. Similarly, the diffusion of components occurs
at low Peclet number and forced mixing becomes problematic. Diode mixers present
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Fig. 11 Diode velocity dependence on AC electric field and media parameters. (a) Diode
velocity as a function of the external AC electric field. The velocities of the two different size
diodes are similar even though one is almost four times bigger than the other. (b) Diode velocity
as a function of the external AC field frequency. (c) Diode velocity as a function of pH. At the
isoelectric point of pH = 6.4, the surface charge of the resin body changes sign and results in a
change in the direction of motion. Experiments in (a), (c) were performed at 1 kHz.
Experiments in (b), (c) were performed at Eext = 93 V cm1. The error bars reflect the scatter
in the data of the experimental measurements. (a–c) Reprinted with permission from ref. 266.
Copyright 2007, Nature Publishing Group.
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Fig. 12 Simulation and flow visualization of a diode micromixer. (a) Computational fluid
dynamics simulation of the flow field that develops in the vicinity of two AC powered diodes
oriented in opposite directions and attached to the outside walls of a microfluidic channel.
(b) Micrograph visualizing the circular flow between two diodes (situated on the top and
bottom but not visible in this micrograph, see ref. 266) that are oriented in opposite direction.
The liquid near the top and bottom walls move in opposite directions, which could be used for
microfluidic mixing. The scale bar in (b) is 200 mm. (a) Reprinted with permission from ref. 18.
Copyright 2008, RSC. (b) Reprinted with permission from ref. 266. Copyright 2007, Nature
Publishing Group.
a simple and very convenient solution to this problem. They are easy to fabricate and
are active since they can be turned on and off. This might be a better approach when
compared to alternatives like patterning or designing complex microchannels
structures to mix the solution. Such structures are often difficult to fabricate and
are passive (cannot be turned on and off). A detailed analysis of the mixing
performance has been published in ref. 18.
5.3 AC Diode pump: hydrodynamic analysis and applications
Diode pumps allow decoupling of the electroosmotic fluid flow from the electrophoretic solute motion. This can be accomplished in a loop-shaped channel (see
Fig. 13) and a combination of AC and DC fields. If the loop channel has diodes
placed on one side then the AC field will be rectified to drive the fluid in circular
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Fig. 13 Schematic of the concept for efficient separations during the electrophoretic transport of
fluid and analytes in a loop-shaped channel under the simultaneous action of AC and DC fields.
motion in the channel. Note that the AC field will not lead to a translational motion of
analytes in the system (they may only oscillate). On the other hand the DC field will not
lead to any type of fluid motion due to the loop shape of the channel. It will however
induce electrophoretic motion of the dissolved analytes or suspended particles. Hence, in
part of the loop (the upper half in Fig. 13) the solutes will be moving left to right driven
by both the convective electroosmotic flow and the electrophoretic migration. In the
lower half of the loop however these two fluxes will be opposing each other. Hence,
species with greater electrophoretic mobility will be able to overcome the electroosmotic
flow and move upstream from left to right. The species with lower electrophoretic
mobility will be swept by the electroosmotic fluid flow to the left. Therefore certain
species will accumulate in the vicinity of the electrode on the right while others will
continue circulating in the loop. This concept was experimentally proven and used to
separate two types of colloidal particles (see ref. 266)
6. Concluding remarks
The interest in the effects driven by external and particle-localized electric fields has
surged in the last few years, as demonstrated by a large number of studies, some of
which have been reviewed and categorized here. Much of this interest is a result of
the new applications that such effects can find in microfluidics, lab-on-a-chip devices,
microelectromechanical systems, biosensors, biomedical microdevices and other
high-technology products. Exciting new developments in these areas could be
anticipated as new types of particles interfacing microchips are fabricated and
developed. This research, however, is likely to result in numerous fundamental
investigations as well. The effects described in this review are diverse and numerous;
not all of them have been understood in complete theoretical detail. This is
particularly true for strongly nonlinear processes such as the polarization of
counterionic layers at high electrolyte concentrations and high field intensities, the
electrophoretic behavior of particles of complex shape and anisotropic conductivity,
and response to AC fields of high frequency and asymmetric signal shapes. We
believe that this Review covers only a small fraction of an emerging large and
stimulating research area that is likely to develop rapidly in the near future.
Acknowledgements
This work was supported by grants from the National Science Foundation, USA
(CBET/CHE 0609087 and 0828900).
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