Download Theory - Northwestern University

Manipulation of Microbeads
and Nanoparticles by
Dielectrophoresis
ME 395
March 16, 2004
Ned Cameron, Christine Darve,
Christina Freyman, and Li Sun
1
Theory
Dielectrophoresis is the term used to describe the polarization and associated motion induced in abiotic
and biotic particles/microbeans (e.g. mammalian cells, bacterial, fungi, protozoa, subcellular organelles,
viruses and other non-cellular biological agents) by a non-uniform electric field. The phenomenon
arises from the difference in the magnitude of the force experienced by the electrical charges within an
unbalanced dipole, induced when a non-uniform electric field is applied. In a non-uniform field, the
convergence of the field lines encourages uneven charge alignment and formation of an induced dipole
moment (see Figure 1).
Figure 1. Effects of Uniform & Non-uniform Electric Fields on Charged and Neutral Particles
The result is an imbalance in force upon the particle, enabling it to migrate toward the region of greatest
field intensity, such as an electrode, determined by dielectric properties of the particles and suspending
medium. The dielectrophoretic force, F, is given by the following general expression:
where is the effective polarizability of the particle, E is the electric field, is the del vector operator
and v is the particle volume. This equation shows that the force is zero except in areas where the field is
non-uniform.
For a homogeneous sphere (having no net charge) of radius r, the dielectrophoretic force is given by the
following equation:
where
is the medium permittivity, and
and
are the complex permittivities of the medium and
particle. The complex permittivity is defined by:
2
where
and
are the permittivity and conductivity, and
 is the angular frequency of the electric field
The term Re[ ] denotes the real component of Clausius-Massotti factor. This term may vary between
-0.5 and +1, determined by the properties of the medium and particle. If this is positive, the force exerted
upon the particle will be positive and the particle will move towards areas of high electric field gradient
- positive dielectrophoresis, as shown in Figure 2(a). If this is negative, the force exerted upon the
particle will also be negative, and the particle will move towards areas of lowest electric field gradient negative dielectrophoresis, as shown in Figure 2(b).
E
FDEP

m1

E
FDEP

m2

Figure 2. (a) positive dielectrophoresis (b) negative dielectrophoresis
Figure 3 shows the plot of the real and imaginary parts of the Clausius-Mossotti factor. It should be
emphasized that positive dielectrophoresis leads to an attractive force, actively holding the particles in
the areas where field gradient is at a maximum. Negative dielectrophoresis, however, is a repulsive
force, and once the particles have been repelled to areas of zero or lowest field gradient, there will no
longer be any dielectrophoretic force exerted upon them.
Figure 3 shows the plot of the real (solid) and
imaginary parts of the Clausius-Mossotti factor
3
For practical application, there is a scaling law of DEP force relating to the applied voltage and the
characteristics of electrodes, which is expressed as
FDEP 
V2
Le3
where V is the applied voltage and Le is the characteristic length of the electrodes. The magnitude of
DEP is inverse proportional to the cubic of the dimension of electric field. So we can get enough DEP at
small voltage with small electrodes. And the small electrodes can be made with fabrication technique.
Figure. 4 shows four kinds of electrodes that are commonly used in research, the analysis of the electric
field of these electrodes are also shown.
Figure 4 (a) Polynomial Electrode array and its electric field analysis [2]
3
Figure 4 (b) Castellated Electrode array and its electric field analysis [2]
4
Figure 4(c) Parallel / Tip-Tip Electrode array and the electric field analysis between two tips
[4]
For small particles (<1  m diameter) it can be seen from the expression of DEP force that large
electrical field gradients are required to produce the forces required to induce motion. The use of
micro-fabricated electrodes to generate high fields has meant that the dielectrophoretic movement of
submicrometre particles has been established beyond doubt. However, observations of the movement of
sub-micrometer particles in planar micro-electrode arrays as a function of the frequency and applied
voltage have not been undertaken in any detail. On this scale the dielectrophoretic force can be of the
same order as other forces acting on the particle and it is important to be able to distinguish each force.
These forces can be generally classed into those which act indirectly on the particle through viscous
drag due to fluid movement, namely electrohydrodynamic (EHD) forces, and those acting directly on
the particle, such as sedimentation and Brownian motion.
For EHD forces, there are two main kinds, the first one is called Electro-osmotic force, which
would lead to a fluid pumping action. This is in fact the interaction of the tangential electric field with
the diffuse double layer above the electrode surfaces. As we know, when the high electrical fields used
to manipulate small particles imply that there is a large power density generated in the fluid surrounding
the electrodes. Therefore, there is an additional “shell” having its own distinct dielectric properties
constructed outside of the particles as well as the electrodes, as shown in Figure 5. It includes the
surface-charge layer, the bound ions (Stern layer) and diffuse double layer. For a small surface charge
density on the particle, the concentration of ions within a diffuse layer falls exponentially with
increasing distance from the surface with a characteristic Debye-Hückel screening length, d, given by:
The Electro-osmotic force can be several orders of magnitude larger than the dielectrophoretic force,
which would construct fluids to move beads out across the electrode from the edge to the center [5], as
shown in Figure 6. Thus to avoid the negative effect of Electro-osmotic force, coating electrodes with
an insulating layer with the thickness equaling Debye-Hückel screening length is often employed.
5
Figure 5. Stern Layer/Double layer
Figure 6. An outline of the electrostatic situation
on a parallel plate electrode array showing how the
radial field can be resolved into normal and
tangential components. The tangential component
of the field gives rise to a Coulomb force on the
fluid, namely electro-osmosis.
The other EHD force is Electro-thermal force, which would lead to a fluid convection. It is due to
localized heating of the medium causing discontinuities of medium conductivity and permittivity. While
in most cases it is insignificant due to the small volumes these discontinuities occupy (as the electrodes
are so small).
Since a temperature gradient gives rise to a change in fluid density and thus natural convection is to
be expected. The magnitude of this effect can be estimated by comparing the electrothermal force and
the buoyancy force. The buoyancy force is given by
where g is the acceleration due to gravity. Even for a characteristic length of 100  m the
electrothermal force is in the range 0.1–0.7 N m, which is still much bigger than the buoyancy force, and
thus, for all situations involving micro-electrode structures, the effects of natural convection are
negligible compared with those of the electrical forces.
Forces other than electrical and gravitational also act to move particles. The principal
non-deterministic force acting on an ensemble of sub-micrometer particles is that due to diffusion.
Diffusion driven by Brownian motion was generally regarded as a ‘disrupting’ force in that it was
considered that the dielectrophoretic movement of sub-micrometer particles could not be achieved at
realizable field strengths. However, recent experimental work has shown that the DEP force required to
induce movement of sub-micrometer scale particles is in the sub-pico Newton range. Brownian motion
is a stochastic process, so the time averaged movement of a particle undergoing Brownian motion is
zero. Irregular motion of the molecules in the liquid imparts random forces on a particle in suspension.
The collisions are irregular and over time the distribution of the random displacement of the particles
6
follows a Gaussian profile with a mean squared displacement (in one dimension) given by
where D is the diffusion coefficient. For a spherical particle of radius a, this is given by
where kB is the Boltzmann constant. It has been studied that the randomizing effect of Brownian motion is
not significant enough to hinder DEP collection.
In a word, although the DEP-induced deterministic movement of sub-micrometre particles can be
complicated by hydrodynamic effects, it has been shown that the forces on particles can be predicted
and therefore controlled. Consequently it can be foreseen that recent technological advances in
dielectrophoresis could be applied, together with electrohydrodynamic fluid movement, to develop new
methods for the characterization, manipulation and separation of sub-micrometre and nano-scale
particles.
Reference:
[1] Pohl H A 1978 Dielectrophoresis (Cambridge: Cambridge University Press)
[2] Michael Pycraft Hughes, AC Electrokinetics: Applications for Nanotechnology
http://www.foresight.org/Conferences/MNT7/Papers/Hughes/
[3] N G Green and H Morgan, Dielectrophoretic separation of nano-particles,J. Phys. D: Appl. Phys. 30
(1997)
[4] N G Green and H Morgan, Dielectrophoretic investigations of sub-micrometre latex spheres, J. Phys.
D: Appl. Phys. 30 (1997) 2626–2633.
A Ramosy, H Morganz, N G Greenz and A Castellanosy. Ac electrokinetics: a review of forces in
microelectrode structures J. Phys. D: Appl. Phys. 31 (1998) 2338–2353.
7
Applications
Dielectrophoretic (DEP) methods have a growing impact on state-of-the-art research, in particular
in medical and pharmacological fields. DEP applications permit to manipulate and characterize cells
(bacteria, DNA, lymphocyte, plant cells, etc) and microparticles by application of an electric field on
microelectrodes arrays [Fuhr-1994]. New hybrids can be formed and cultivated using tools with size of
the order of 10 microns. For instance, single and multiple cells can be trapped and manipulated by using
negative DEP. Figure 1 summarizes biological applications in the context of handling single cells.
Figure 1: Single cell technology
Selected parameters and principles
In the described applications, an alternating current, AC, is preferred to a DC current. Indeed,
the electric field acts through the Coulomb’s force on the charge of the particles to produce
electrophoresis at low-frequencies. An AC field also induces a frequency-dependent dipole on the
polarized particle. The interaction of the dipole and the non-uniform field gives rise to dielectrophoresis,
electrorotation and traveling-wave dielectrophoresis. The dipole strength and hence the force exerted on
the particle depsnds on frequency, which is one of the main parameters to control the DEP process.
Fluid flow and heating of particles is produced by the use of high electric field strengths. The interaction
of the electric field with the fluid produces frequencies dependent forces, like electro-osmosis and
8
electrothermal forces, which exert a drag force on the particle and therefore produces an observed
motion. Manipulation of cell or microparticles by the application of high-frequency electric field
requires field strengths of between 2 and several hundred kV m-1.
The polarized cell or particle motion depends on the conductivity of the medium and the frequency of
the AC electric field. Figure 2 shows the influence of the polarization forces acting on cells in low
conductivity and highly conductive fluids, as a function of the frequency of the electric field. For a given
electrical field, E, the dielectric body can polarize in two different ways. The particles can be either
attracted (positive DEP) or repelled from the electrodes (negative DEP). Highly conductive solution
displays negative dielectrophoresis, i.e. particles are repelled from the electrodes and can be trapped in
potential wells, as discussed later
According to Ohm’s law the current through the fluid is directly proportional to the field strength and
the electrodes area. In addition an increase of the conductivity of a solution increases the current flow
between the electrodes. Therefore raising the conductivity limit requires miniaturization of the
electrodes. If we wish to maintain the field strength and to increase the conductivity of the solution,
without changing the total net current, it is hence necessary to reduce the electrodes area. A reduction of
the area of the electrodes by a factor of 100 to 10,000 is possible with lithographic techniques, leading to
electrodes and spaces of several hundred microns upwards, and making an increase of the fluid solution
conductivity by the same orders of magnitude.
Long-term application of static electric fields on the electrodes can lead to uncontrolled cell loading and
damage. This is an additional advantage of the use of AC electric field, which avoids electrolysis and
electro-osmosis.
9
Figure 2: Polarization forces
Particle dynamics
Polarized cells and particles evolving in a conductive solution react to an electrical field applied
at microelectrodes suitably placed to form a field gradient pattern that is used to manipulate the position
or orientation of the cells and particles. In addition, the gravity (by mean of the buoyancy force) is the
main external influence inducing forces to the cell or particle. In addition, for sub-micrometer particle,
Brownian motion stemming from thermal effect forces the cell to move. Although Brownian motion
has zero average, it is important to consider this thermal effect, since the amplitude of its fluctuations,
x, needs to be overcome in order for a polarized particle to be trapped during negative DEP [Hughes –
1998]. Finally, cells and particles moving in a solution experience a drag force due to the viscous shear.
In summary, cells and particles motion in DEP conditions is governed by the equilibrium balance of the
DEP force, FDEP, the buoyancy force, FBUOYANCY, the Brownian force, FBROWNIAN inducing a
random-walk motion and the drag force, FDRAG.
FTOTAL  FDEP  FBUOYANCY  FBROWNIAN  FDRAG

(1)
The dielectrophoretic force, FDEP, acting on a homogeneous dielectric sphere, is given by:

FDEP  2m R 3 Re f CM  E rms
2
(2)
where m is the permittivity of the particle,  , is the del vector operator, Erms is the local rms electric
field and Re{fCM} is the real part of the Clausius-Mossotti factor fCM, which can be written:
f CM
 *p   m*
 *
 p  2 m*
(3)

   j

*
where  is the angular frequency, p and m are the complex permittivities of the medium and
particles, respectively.

The Buoyancy force, FBUOYANCY, can be expressed by:
FBUOYANCY 
4
gR 3 (  f   p )
3
(4)
where g is the acceleration due to the gravity, f and p are the densities of the fluid and the particle,
respectively.

The drag force, FDRAG, resulting in the cell motion in a fluid, can be characterized as follows in
the approximation of small Reynolds numbers:
10
FDRAG  6R(v f  v p )
(5)
where R is the particle radius,  is the fluid viscosity, vf and vp are the velocities of the fluid and the
particle, respectively.

The Brownian motion is a thermally induced random motion that can be described by a
diffusion equation characterized by a diffusion constant, D:
D
kB T
6R
(6)
where kB is the Boltzmann constant, and T is the temperature of the solution. The r.m.s. amplitude of the
motion can be obtained from the following expression

2
x  2Dt
(7)
which should be compared to the extension of the electric cage to insure that particles and cells can be
trapped in the potential minimum
of the DEP force.
Particles
In several experiments, latex spheres of different diameters are used for DEP
experiments. Typical particles such as those used in the examples that are presented in
figures 14-18, have size in the range of few hundreds of nm. As an example Figure 3 shows
the scanning electron microscope images of latex spheres with two different sizes, 282 nm
and 557 nm.. The spheres need a careful preparation for a successful experiment. For the
example reported below, the spheres are carboxylate-modified with a net negative surface
charge and have pre-loaded with a yellow-green fluorescent dye, which allows single
particle observation by fluorescence microscopy. The latex spheres are then centrifuged
and washed three times in either 1 or 10 mM potassium phosphate buffer at pH 7.2. They
are suspended to a final concentration of 0.02% by volume for the experiments.
11
Figure 3: Scanning electron microscope images of two sizes of latex spheres (282 nm and 557 nm) as
typically used for DEP experiments.
Negative DEP
Electric cages
The occurrence of negative DEP permits scientists to trap single/multiple cells/particles. In the
case of a low conductivity solution (which decreases net current flow at the electrodes), negative DEP
occurs for high frequency as shows in figure 2. An electric cage or potential well is created by using a
suitable arrangement of the electrodes configuration. Cells can be levitated in fluid solution and held in
stable position or rotated by applying traveling electric fields. Figure 4 shows examples of electric cages.
The field cage can be opened or closed by changing the amplitude, frequency or phase of the electrode
signals. The modification of the potential barrier permits to release or trap cells in the electric cage.
12
Figure 4: Example of electrode configurations creating electric cages.
Applications of DEP technology
DEP is used more and more frequently for the manipulation of single particles, cells, viruses and similar.
Examples of these applications are becoming abundant in the literature. Cells and viruses can be
collected in the electric trap to study their properties, single particles can be manipulated and directed in
specific direction on a one-by-one basis, or particles of different dimensions can be filtered from a
solution. Another very promising example of negative DEP is to concentrate colloids from solution, so
that single parts for nano-machines can be collected on the “assembly site” using negative DEP. Such
parts can be
• Two or more interlocking molecules, normally in a highly dilute solution can be concentrated by DEP
13
into a confined space where they are assembled.
• "Fuel" for a nano-machine from solution can be collected in the electrical cage. Self-assembly reaction
takes place at the collection point.
The section below gives specific examples.
Example 1: HSV-1 [Hughes – 1998]
In this example human Herpes simplex virus (HSV-1) is used. The 250 nm diameter enveloped
human virus and viral capsid of Herpes simplex (HSV-1) are shown in figure 5.
Figure 5: Herpes Simplex Virion (HSV-1), virus and its envelope.
Microelectrodes used to trap the HSV-1 virus were fabricated using photolithography with masks
written by electron beam lithography. They were based on the polynomial design with dimensions of 6
m between opposing electrodes and with 2m gaps along the arms between adjacent electrodes, as
shown in figure 6 (a).
The electric field was applied using a generator that sweeps a range of frequency from 1 Hz to 20 MHz.
This field was applied to an EDTA solution, with conductivity of 5 mSm-1.
Stable levitation of a single viral capsid in the potential well was observed. Numerical simulation
permitted to validate experimental results. Figure 6 (b) and figure 7 show the simulation of variation of
Erms . Particles will be trapped in the potential well if the DEP forces overcome the Brownian motion.
2
Scientists observed the influence of Brownian motion on a single particle within the confines of the
electrical field cage. Single virions were observed to levitate in a stable position at the height of
approximately 7 m above the electrodes.
14
(a)
(b)
Figure 6: (a) Photograph of polynomial electrode array with selected lines a-a and b-b. (b) Variation of
Erms along a-a and b-b lines.
2
Figure 7: 3-D plot of the variation Erms in a plane 7 m above the electrode.
2
Example 2: microscopic biosensors [Velev- 1999]
A second example show 14 nm diameter fluorescently labeled latex spheres precipitated from
an aqueous solution by positive (Figure 8 - a) and negative (Figure 8 - b) DEP.
Using this technique microspheres and colloidal gold particles bound to antibodies were used to
construct microscopic biosensors [Velev-1999]. The particles with an active antibody were attracted to
the center of the cage, where Velev and Kaler managed to bind them on contact, and stack particles of
different types. This is a typical example of a microscopic biosensor factory.
15
Figure 8: 14 nm diameter, fluorescently labeled latex spheres precipitated from an aqueous solution
(conductivity adjusted to 2.5 mSm-1 by addition of KCl) by dielectrophoresis. The electrodes have 500
nm between adjacent electrodes and 2 µm across the inter-electrode gap. In photograph (a), the spheres
collect in the high-field regions between the electrode edges when a 8Vpp, 2MHz signal is applied. In
photograph (b) the spheres collect in a ball at the centre of the trap, which is levitated a few µm above
the electrode plane when the applied signal is changed to 10Vpp, 10MHz.
Example 3: Dielectrophoretic separation and transportation of cells on
microfabricated chips [Xu]
Microchip with a suitable array of electrodes can produce controlled transport and
switching electric fields. In the current example the electric field pattern is switched so that
human blood cells are transported from the top of the chip to the left side. Figure 9 shows
the transport of blood cell along channels, using 3-way switches.
Diluted blood samples were introduced in a fluidic chamber containing a sinusoidal
electrode array. Electrical fields from 1 to 5 MHz were applied to generate DEP forces.
Microelectrodes were able to capture and retain white blood cells on the electrode edges
while red blood cells did not experience large attractive forces and were carried away from
the chamber by the fluid flow forces. The two difference forces generated by DEP for the
white and red blood cells resulted from their different dielectric properties. The chip was
able to collect several thousand white blood cells as the fluid flow rate was 5 µl/min.
Then the diluted blood cells can be transported and switched along the three branches. Electrical signals
of ~ 100 kHz were applied to the guide electrodes and the resulting negative DEP forces from the guide
electrodes. Repulsion forces direct cells towards the central regions between the guide-electrode pairs.
Simultaneously, traveling-wave DEP forces were generated and cells transported as phase-quadrature
signals with frequencies between 50 and 300 kHz were applied to traveling-wave electrodes. Various
16
phase-sequences were applied so that cells were transported and switched in and between the three
branches. Cell velocity was between 5 and 30 µm/sec was achieved with an applied voltage < 1 V RMS.
Figure 9: Three-way switch for the manipulation of blood cells. The lower pictures show details of the
chip and a blood cell that enters the chip from the top, comes in the three-way central switch and is
deflected on the left.
Example 4: Dielectrophoretic size-sensitive particle filter for micro-fluidics
applications [Auerswald]
From equation (2), we note that the dielectrophoretic force, FDEP, and the cross-over frequency
from positive to negative DEP, depend on the particle radius, R. Indeed, at given frequency, particles
with smaller radius tend to experience positive DEP whereas particle with larger radius experience
negative DEP.
Hence, by proper geometry arrangement of electrodes and operating frequency selection it is possible to
trap particles selectively based on their size. Figure 10 shows the relation between the frequency and the
particle size that results in positive DEP force (below the curve) and negative DEP (above the curve).
17
Figure 10: relation between particle size and frequency resulting in positive or negative DEP
This frequency dependence can be used as illustrated in Figure 11 that represents a solution containing
particles of different radii. Passing close to the electrodes powered at an appropriate frequency, particles
with different size are either attracted or repelled by the electrodes. The particles attracted are hence
filtered from the flowing solution, and only the repelled particles exit the filter. Figure 11 shows a
schematic of the separation of 6 m and 2 m polystyrene beads. The small beads are retained at the
electrodes by positive DEP when the frequency is 100 kHz. Simultaneously, the larger beads are
repelled by negative DEP and a carried away.
Figure 11: Example of a filter based on DEP.
18
Example 5: Separation of metallic and semi-conducting nano-tubes [Krupke-2003]
Separation of metallic and semi-conducting single-walled carbon nano-tubes (SWNTs) for
nano-scale electronics research and applications was developed. Metallic and semiconducting carbon
nano-tubes subjected to an inhomogeneous AC field were suspended in a solution of D2O containing 1
weight % of the surfactant sodium dodecyl sulfate (SDS) under sonication.
The difference between the relative dielectric constants was used to ensure this separation. The metallic
nanotubes (and bundles containing at least one metallic nano-tube dominating the dielectric properties)
are attracted at the electrodes, whereas the nano-tubes remaining in the suspension are semiconducting.
Figure 12 shows the experimental set-up, with the microelectrodes wired to a chip carrier. Metallic
nanotubes (black) are deposited from a drop of nanotube suspension onto the electrodes by AC DEP.
This process permits to leave the semiconducting tubes (white) in suspension. The electrodes used in
this set-up are gold material, 30 nm thick and 50 m wide. A 50 m pitch on a p-type silicon substrate is
shown with 600 nm of thermally oxidized SiO2 and a thin titanium adhesion layer was used.
Suspension drop
electrodes
Figure 12: SWNT experimental set-up
Positive DEP was obtained by operating a generator at a frequency of 10 MHz and 10 Volts
peak-to-peak. The resulting sample were characterized by a confocal Raman microscope (CRM) exited
with an Ar+ ion laser. The Raman spectra of SWNTs deposited via AC DEP clearly show the separation
of radial breathing mode (RBMs) associated with metallic from those associated with semiconducting
SWNTs.
19
Example 6: Positive and negative DEP [Green – 2000]
Figure 13 shows the photograph of polynomial electrode array using a light microscope with
amplitude (x40). The polynomial electrode array was used for DEP manipulation of latex spheres shown
in figure 3. The polynomial electrode array is designed with dimensions of 6 m between opposing
electrodes and with 2m gaps along the arms between adjacent electrodes.
Figure 13: Photograph of polynomial electrode array used for DEP manipulation of latex
spheres shown in figure 3.
Figure 14 shows digitized video images of fluorescently loaded latex sphere observed with a
fluorescence microscope. The latex spheres diameters are 282 nm. They are trapped by positive DEP at
100 kHz and with an applied voltage of 4 V peak-to-peak. The suspended buffer for this example was 10
mM potassium phosphate of conductivity 0.17 Sm-1.
20
Figure 14: Digitized video images of fluorescently loaded latex sphere during positive
DEP.
Figure 15 shows the negative and positive DEP of 557 nm diameter latex spheres shown in figure 3 with
polynomial and castellated electrode arrays. The applied signal for figure 15 (a) is 5 Volts peak-to-peak
at 5 MHz. The applied signal for figure 15 (b) is 8 Volts peak-to-peak at 8 MHz. For both negative DEP
cases, the spheres can be clearly observed collecting in the low field regions.
The applied signal for figure 15 (c) is 5 Volts peak-to-peak at 500 kHz. The applied signal for figure 15
(d) is 8 Volts peak-to-peak at 700 kHz. For both positive DEP cases, the spheres can be clearly observed
collecting in the high field regions. For figure 15 (d), the spheres collect at the high field regions marked
by point B and C (at the back of the bays).
21
Figure 15: DEP of 557 nm diameter latex spheres shown in figure 3 (a) Negative DEP with
polynomial electrode array. (b) Negative DEP with castellated electrode array. (c) Positive
DEP with polynomial electrode array. (d) Positive DEP with castellated electrode array.
Additional collecting sphere configuration can be observed. Figure 16 (a) shows the schematic of fluid
flow observed in polynomial arrays at high frequencies. The flow moves into the electrodes array into
the gaps between adjacent electrodes and then up and out in the center. The particles are typically
pushed along with the fluid flow and settle in a levitation position above the center of the array. If thus
fluid flow intensity was stronger than the dielectrophoretic force, then this collection in the center would
be observed if the particles were experiencing either positive or negative DEP.
Figure 16 (b) shows the schematic diagram of the fluid of pattern of fluid behavior at lower frequencies
(~3-4 MHz) and low potentials (5 Volts peak-to-peak). The flow is directed towards the center of the
array from the bulk but also down into the center of the electrode array and outwards. This results in four
regions where particles collect over the gap between the electrodes. When the potential or the frequency
(or both) was increased, the flow velocity into the electrode array increased and the four collections of
particles moved into the center of the electrode array, as in figure 16 (a).
Figure 16 (c) shows the experimental image of the flow described in figure 16 (b) using 282 nm
22
diameter latex spheres at a potential of 12 Volts peak-to-peak and 6 MHz. The particles at the four
collection points whirl in circular patterns in a plane perpendicular to the electrode surface and the gap.
Figure 16 (d) shows the experimental image of the flow using 557 nm diameter latex spheres at a
potential of 5 Volts peak-to-peak and 3 MHz. Some particles are trapped in the center of the electrodes,
by negative DEP (point A) and some are pushed to the four fluid collection points by fluid flow (point
B). Outside the electrodes, the negative DEP force pushing the particles away from the electrodes
balances the drag force due to the fluid flowing into the electrode arrays (point C).
Figure 16: (a) Schematic of fluid flow observed in polynomial arrays at high frequencies. (b) Schematic
of fluid flow observed at low frequencies and low potentials. (c) Experimental image (12 Volts
peak-to-peak, 6 MHz). (d) Experimental image (5 Volts peak-to-peak, 3 MHz).
Figure 17 shows diagrams and experimental images of AC electro-osmosis for two designs of electrodes
(polynomial and castellated). For the polynomial electrode array the particles are pushed away from the
edges, collecting on the top of the electrodes. For the castellated electrode array, the fluid pushes the
particles into diamond shaped collections along the symmetry line of the electrodes.
23
Figure 17: Diagrams and experimental images of AC electro-osmosis for two designs of
electrodes. (a) Schematic diagrams for polynomial electrode arrays. (b) Schematic
diagrams for castellated electrode arrays. (c) Experimental image for polynomial electrode
arrays. (d) Experimental image for castellated electrode arrays.
Figure 18 shows experimental images of 557 nm diameter latex spheres over three decades of frequency
on castellated electrode arrays at an applied potential of 8 Volts peak-to-peak and a solution
conductivity of 2 mSm-1. At 8 MHz, the particles experience negative DEP and collect in triangular
shapes in every bay. At 0.7 MHz the particles collect at high field points on the electrode edges under
conditions of positive DEP. The diamonds and wavy stripes in figure 18 (c) at 70 kHz are caused by the
combination of positive DEP and AC electro-osmotic flow. Where the DEP force is strongest particles
remain trapped but at the high field points at the back of the bays, there is sufficient flow to push the
particles away from the edges. This produces diamond shapes on the symmetrical electrodes where the
electrodes are narrow and wavy stripes on the asymmetrical electrodes. At 7 kHz, the velocity is the
dominant effect and the particles are pushed onto the electrodes to form diamond shapes at the widest
part of the symmetrical electrodes and wavy lines where the electrodes are asymmetrical.
24
Figure 18: Experimental images of 557 nm diameter latex spheres over three decades of frequency on
castellated electrode arrays at an applied potential of 8 Volts peak-to-peak and a solution conductivity of
2 mSm-1.
From this last example we conclude that the electrokinetic forces due to AC non-uniform electric fields
and applied to microelectrodes is a very useful technology to measure and to separate particles. Short
movies related to electro-rotation
25
Polynomial electrodes set-up at Northwestern University
An interesting experiment to set-up in laboratory is the use of polynomial electrode array to
observe negative DEP. Due to lack of instrumentation and time, we did not set-up this very experiment,
and therefore we use above examples from literature to describe the results of this measurements and to
propose a new experiment for next quarter.
The aim of this test is to better visualize trapping conditions and to look for frequency dependence to
verify positive and negative DEP.
We propose a set-up composed of four polynomial electrodes arrays as shown in figure 6. The four
electrodes are excited by Y1, Y2, Y3 and Y4. AC electrical field would have the following
characteristics:
Y1 = A · sin(t)
Y2 = A · sin(t +п/2)
Y3 = A · sin(t +п)
Y4 = A · sin(t +3п/2)
Two opposite electrodes would be out of phase of .
“A traveling wave is made when different electrodes are lined up, and have phase-shifted AC signals
going through them. The actual traveling wave describes the way in which the electric field moves over
the electrodes, and is the inspiration behind the device described in this paper. If four electrodes are
lined up so that each is 90° phase-shifted from the last, then each electrode will hit its peak voltage at a
different time, and non-uniform electric fields will be created. The principles behind this are very
similar to those that move a 3-phase AC motor, in that a dipole moves with the changing electric field.
The difference is that the electrodes are arranged in a plane instead of a circle. Figure 20 shows a basic
diagram of the device that will be used to create traveling wave dielectrophoresis” [John Zelena-2004].
Figures 19 and 20 show the distribution of the phase and the potential solution and particle that we could
use [John Zelena-2004].
Particles to analyze could be SWNT, bacteria or Latex spheres as introduced in figure 3.
The size of particles, conductivity and medium used could be of identical to example 5 or example 6.
26
Figure 19: Side view of traveling wave device described for the proposed NU laboratory. (above)
Figure 20: Top view of device design (below)
Y1 = A . sin(t)
Y2 = A .sin(t +/2)
Y3 = A . sin(t + )
Y4 = A . sin(t +3  /2)
References
[Auerswald] J. Auerswald, H.F. Knapp, Micro Center Central Switzerland.
[Fuhr-1994] G. Fuhr and S.G. Shirley, Institute fur Biologie, Humboldt Universitat, Berlin, D, IOP,
pp.77-85 (1994).
[Green – 2000] N.G. Green, A. Ramos, H. Morgan, J. Phys. D: Appl. Phys., 33, pp 632-641 (2000)
[Hughes – 1998] M. Hughes and H. Morgan, University of Glasgow, UK, J. of D: appl. Phys. , 31, pp
2205-2210 (1998).
[Krupke-2003] R. Krupke, F. Hennrich, H. Lohneysen, M. Kappes, Universitat Karlsruhe, D, Science,
301, pp 344-347 (2003).
[Velev- 1999] Velev OD, Kaler EW, In situ assembly of colloidal particles into
miniaturised biosensors, Langmuir Vol. 15 pages 3693-2698, (1999)
[Xu] J. Xu, L. Wu, M. Huang, W. Yang, J. Cheng, X-B Wang, AVIVA Bioscences
Corp, CA & Dept. of Biological Sciences and Biotechnolog, Tsinghua
University, Beijing, China.
27
[Zelena-2004] John Zelena (Mechanical Engineering) – Wilkes University, NSF Summer
Undergraduate Fellowship in Sensor Technologies, technical report (2004).
Activity 1: Clausius-Mossotti factor
Plot the real part of the A plot of the Clausius-Mossotti factor versus frequency for 216-nm-and
557-nm-diameter latex particles with a particle permittivity εp = 2.55 and a medium conductivity σm = 1
mSm1. Set the surface conductance at 2.32 nS for both particles. σp ≈ surface conductance/radius of
particle.
Activity 2: Positive Dielectrophoresis
In this activity, you will visual positive dielectrophoresis using fluorescent latex microbeads and an
electric field. Major steps include attaching probes to the electrodes, positioning coverslip, preparing
micropipet, applying electric field, and applying microbeads to electrodes. One important thing to
remember is that the microbead colloid should never touch the probes; the probes should stay dry the
whole time.
Objective: To visualize positive dielectrophoresis using fluorescent latex microbeads.
Procedure:
Set up
1.
2.
3.
4.
5.
6.
Turn on both lamps on microscope
Make sure camera is on and set up properly
Place wafer on x-y platform, and find electrode array under lowest magnification
Attach alligator clips to probes
Using the camera display, position probes on electrode pads
Place cover slip over on electrodes and make sure it doesn’t touch the probes and that the
probes are still properly positioned
Applying Microbeads
1. Fill micropipet with approximately 0.30 l of fluorescent microbead colloid
2. Increase magnification in microscope and position above the electrodes
3. Open all filters on green laser WARNING: Do not look directly at laser light. Always look
through orange UV shield.
4. Careful not to hit the x-y platform, or the cover slip, drop the microbead colloid at the edge
of the cover slip (capillary forces will draw it over the electrodes.
28
Applying Electric Field
1.
2.
3.
4.
Function Generator should be attached to probes via appropriate alligator clips
Begin capturing movie
Apply 5 Vpp and 1 kHz frequency.
Adjust frequency until positive dielectrophoresis is observed
Describe your results.
Activity 3: Negative Dielectrophoresis
Objective: To visualize negative dielectrophoresis using fluorescent latex microbeads.
Procedure:
1.
2.
3.
4.
5.
Use the same set up as with positive dielectrophoresis
Apply microbeads in the same fashion
Begin capturing movie
Apply 5 Vpp and a frequency that gave positive dielectrophoresis
Increase frequency until positive DEP turns to negative DEP
Describe your results.
Activity 4: Carbon Nanotubes
In this activity, you will visualize and observe the change in resistance when carbon nanotubes are
arranged by an electric field to span a gap between electrodes.
Objective: To visualize and observe the change in resistance when carbon nanotubes are arranged by an
electric field to span a gap between electrodes.
Procedure:
1. Be sure wafer is clean before set up
2. Set up is similar to that used with microbeads. Use array with the smallest gap between
electrodes.
3. Apply ohm meter to probes
4. Observe reading
5. Apply carbon nanotubes in a similar fashion to the way the microbeads were applied.
6. Begin movie capture
29
7.
8.
9.
10.
Apply 10 Vpp at 5 MHz
Observe visually and ohm meter reading
Increase and decrease frequency and observe results
At what frequency was positive dielectrophoresis observed? Negative?
Describe your results.
30