Particle-localized AC and DC manipulation and...

Particle-localized AC and DC manipulation

and electrokineticsw

Orlin D. Velev,*aSumit Gangwal

aand Dimiter N. Petsev

b

DOI: 10.1039/b803015b

Colloidal particles suspended in water respond to direct (DC) or alternatingcurrent (AC) fields in a variety of ways, including directional motion alongor across the field direction, field-gradient dependent response and inducedparticle–particle interaction. We review here some of these effects and theirapplications in new techniques for particle manipulation and assembly,making of novel biomaterials and designing of new self-propelling micro-devices. The coupling of the counterionic layer mobility, fluid flows and theresulting particle motion are the basis not only of the classic electrophoreticeffects, but also of the recent developments in AC electrohydrodynamicsand induced charge electrophoresis of asymmetric particles. We also discusshow dielectrophoresis (particle interaction with external AC field gradients),could be used to manipulate and assemble objects on any size scale. Wediscuss the interactions leading to the assembly of such structures, ways tosimulate the dynamics of the process and the effect of particle size andconductivity on the type of structure obtained. Finally, we demonstrate howan additional level of complexity can be engineered to turn miniaturesemiconductor diodes into prototypes of self-propelling micromachinesand micropumps. The diodes suspended in water propel themselveselectro-osmotically when a uniform alternating electric field is appliedacross the container. Semiconductor diodes embedded in channel wallscould serve as distributed microfluidic pumps and mixers powered by aglobal 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, aniso-

tropic polarizability or nonlinear conductance. These particles respond to external

aDepartment of Chemical & Biomolecular Engineering, North Carolina State University,Raleigh, USA. E-mail: [email protected]; Fax: +1-919-515-3465; Tel: +1-919-513-4318

bDepartment 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.

Annu. Rep. Prog. Chem., Sect. C, 2009, 105, 213–246 | 213

This journal is �c The Royal Society of Chemistry 2009

REVIEW www.rsc.org/annrepc | Annual Reports C

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

Fig. 1 Schematics of a few categories of particle-localized DC and AC electrokinetic pheno-

mena. (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.

214 | Annu. Rep. Prog. Chem., Sect. C, 2009, 105, 213–246


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 electro-

osmotic velocity Ueo

Ueo ¼ �ee0CZ

E ð1Þ

where C is the potential drop across the capacitor at the interface, e0 =

8.854 � 10�12 F m�1 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 fluidstarts 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

r2C ¼ � reee0¼ � e

ee0

Xi

zin0i exp

�zieCkT

� �: ð2Þ

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 theexternal field E and vice versa. This is a reasonable approximation for the cases



where the field in the EDL is much greater than the externally applied one and worksparticularly well for straight capillaries where the external field vector is normal tothat 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

Zd2v

dx2¼ ee0

d2Cdx2

E: ð4Þ

where n is the tangential component of the velocity. The boundary conditions are

dv

dx¼ 0;

dCdx¼ 0; v ¼ Uep at x!1

v ¼ 0 and C ¼ z at x ¼ 0:

ð5Þ

and the electrophoretic velocity of a particle with radius R becomes

Uep ¼ee0zpZ

E; kR!1: ð6Þ

where zp is the electrokinetic potential (zeta-potential) of the particle and k�1 is theDebye 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 ¼2ee0zp3Z

E; kR! 0: 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

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.



intermediate case was studied by Henry9 who suggested the following equation for

the electrophoretic mobility

mep ¼Uep

E¼ 2

3

ee0zpZ

f1ðkRÞ where

f1ðkaÞ ¼ 1þ ðkRÞ2

16� 5ðkRÞ3

48� ðkRÞ

4

96þ ðkRÞ

5

96

� ðkRÞ4

8� ðkRÞ

6

96

" #expðkRÞ

ZkR1

expð�tÞt

dt:

ð8Þ

Ohshima suggested the following much simpler empirical formula10 for the correc-

tion function f1(kR) which is accurate within 1% when compared to Henry’s result

f1ðkRÞ ¼ 1þ 1

21þ 5

2kRð1þ 2 expðkRÞÞ

� �� 3: ð9Þ

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

r2C ¼ � reee0¼ � e

ee0

Xi

ðzþi nþi � z�i n�i Þ ð10Þ

where the ionic concentrations n+i and n�i are determined from the respective mass

balance11

@n�i@tþr � j�i ¼ 0; j�i ¼ �D�i rn�i �

z�i e

kTrc

� �� n�i v: ð11Þ

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



dipoles induced in the particles are given by the real part of the Clausius–Mossotti

function, K

Re Kj j ¼ e2 � e1e2 þ 2e1

þ 3ðe1s2 � e2s1ÞtMWðs2 þ 2s1Þ2ð1þ o2t2MWÞ

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 atK=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 eoer � iðsÞo ),

where e0 is the dielectric permittivity of vacuum (8.854 � 10�12 C2 N�1 m�2), er is therelative 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 counter-

ionic 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

oc = t�1MW,16,19 where tMW is the Maxwell–Wagner charge relaxation time

tMW ¼ e2þ2e1s2þ2s1. 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 electro-

kinetic 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

F!DEP ¼ 2pe1Re KðoÞj jr3rE2

rms 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, dielectro-

phoresis 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



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 seconddenotes the convective transport, the third term is the electromigration [mi being theelectrophoretic 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 particlesobtains the form

n ¼ eme0R2K

12pZð15Þ

The dielectrophoretic effects also lead to structuring when higher concentrations ofparticles are present between the electrodes. The dipoles induced in the particlesinteract with each other if the particles are close enough. The particles align in chainsalong the direction of the field lines. This ‘‘chaining’’ force, Fchain, is dependent onthe field strength squared, E2 and the radius squared of the particle, r2

Fchain = � Cpe1r2K2E2 (16)

where the coefficient C ranges from 3 to4103 depending on the distance between theparticles and the length of the particle chain.14,16,19 The chaining force acting onparticles of similar electrical properties is always positive and attractive. Particles ofthe same type always align along the field lines, regardless of whether theirpolarizability is higher or lower than the media, while mixtures of particles of lowerand higher polarizabilities than the media could form various types of alternatingchains 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 dielectro-

phoretic 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



(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

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.



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 techni-

ques 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.



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 struc-

tures 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 micro-

fluidics.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 hydro-

phobic, 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 dielectro-

phoresis.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,



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

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.



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



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 biocompo-

sites 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,

FParticle ¼R

Particle

f dV. The electrostatic field intensity is obtained from a finite element



calculation of the set of PDEs for the system geometry using the FEMLABmultiphysics

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 sizeE 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

Fig. 5 (a) Chain of live yeast cells and 0.95 mm diameter magnetic particles assembled at

17 V mm�1 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.



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 fibro-

blasts, 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



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 cm�1)

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



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 cm�1 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.



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 cm�1), 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



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 ¼2Ree0E2

ZsgnðzpÞ: 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 ‘‘induced-

charge 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



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 cm�1), 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 beB10, 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

consistent with the bands of characteristic driving frequencies, t�1e r o r t�1p for



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.



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 lLD , 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 lRD . The characteristic frequencies

for our system are t�1e E 20 Hz and t�1p 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

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 cm�1), 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 mMNaCl. The ICEP

velocities were highest between the upper and lower characteristic frequencies for electrode and

particle charging (t�1e E 20 Hz and t�1p E 12 kHz, respectively). (a), (b) Reprinted with

permission from ref. 238. Copyright 2008, American Physical Society.



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 ¼1

2

R2

ðR1 þ R2 þ R3ÞVext 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 electro-

osmotic 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.



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

ld¼ 1

2ðEext � Ed0Þ 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 ¼ee0zp2ZðEext � Ed0Þ: 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 self-

propelling 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 conven-

tional 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 �ee0z2ZðEext � Ed0Þ 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



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 cm�1. 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.



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 electro-

phoretic 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

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.



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).

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.



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