Download An Equivalent Electrical Model for Numerical Analyses of ODEP

An Equivalent Electrical Model for Numerical Analyses of
ODEP Manipulation
Wenfeng Liang1,2, Shue Wang1,2, Yanli Qu1, Zaili Dong1, Gwo-Bin Lee1,3, Wen J. Li1,4,*
1
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, China
2
Graduate University of the Chinese Academy of Sciences, 100049, China
3
Center for Micro/Nano Technology Research, National Cheng Kung University, Taiwan
4
Centre for Micro and Nano Systems, The Chinese University of Hong Kong，Hong Kong
Abstract-Opticaldielectrophoresis(ODEP)has been explored experimentally with success in manipulating microscale objects in the
last 5 years. However, not much theoretical analyses have been
performed to understand its operating principles in depth and
also determine its limitations as a tool to manipulate micro- and
nano-scale objects. In this paper, we present our work on
establishing an equivalent electrical model to analyze the
important physical interactions when optically induced dielectrophoretic force is used to manipulate micron-sized polystyrene
beads. Simulation results show that the ODEP manipulation of
microbeads is frequency-dependent and that the electrothermal
effect is negligible. Furthermore, the relationship between the
frequency of the applied voltage and the maximum manipulation
velocity of the microbeads obtained from simulation is consistent
with our experimental measurements. In addition, simulation
results also show that the minimum radius of a bead that can be
manipulated exponentially decreases with respect to the size of the
illuminated spot. For instance, when the illuminated spot size is
1μm, ODEP can theoretically manipulate 100nm beads – indicating that ODEP can be extended to manipulate nano-scale
objects if the illuminated spot size can be significantly reduced.
Keywords-ODEP; OET；DEP；simulation; polystyrene beads;
I.
beads. But electrothermal (ET) force affects on the trapped
beads during the manipulation process were not mentioned.
In this paper, we will theoretically analyze and compare the
following forces exerted on suspended particles in liquid
medium: DEP force, ET force, and Brownian motion, and
present a more accurate explanation to the phenomenon of
manipulating micro-particles using ODEP technique.
II.
MODELING AND SIMULATION
2.1 Equivalent electrical model of the OET device
As shown in Fig. 1, the OET device used on our simulation
and experiments is composed of a sandwich structure,
including a top layer of transparent and conductive Indium Tin
Oxide (ITO) glass, a 35um liquid layer containing micro-scale
particles, and a bottom layer with two thin films deposited on
another ITO glass. The two thin films include a 1μm
photoconductive material layer of hydrogenated amorphous
silicon (a:Si-H), and a 20nm insulating film of nitride
silicon(SiN).
INTRODUCTION
Micro/nano-scale manipulators are important tools in many
fields, such as in biological research and in assembling
micro/nano-scale sensors and devices. There are several forces
that can be used to move and trap particles. Although
mechanical structures can be used to grip microparticles[1],
however it is difficult and costly to scale mechanical devices
for the parallel manipulation of single particles. Conversely,
fluid drag can transport many cells[2], but it is extremely
difficult to achieve single-cell manipulation using fluidic
manipulation. Optical tweezers[3] can manipulate a single
particle, but it suffers from a high optical power requirement.
Dielectrophoresis (DEP)[4]can be also used to trap particles,
but it requires a static pattern of metal electrodes, which cannot
be dynamically reconfigurable. A novel manipulation tool
called optoelectronic tweezer (OET) was reported by P. Y.
Chiou et al., in 2005 [5], which enabled massively parallel
manipulation of micrometer-scale objects. This new technique
holds excellent potential in terms of realizing parallel
fabrication of nano-devices, which is our team’s current
research interest.
P. Y. Chiou has theoretically analyzed the order of
magnitude of the DEP force [6], which is based on the
assumption that the OET is modeled as the resistance of the
photosensitive layer in series with the resistance of the liquid
layer. A. T. Ohta et al., have calculated the electrical field
distribution and DEP force [7] using light to trap polystyrene
*Contacting Author: Wen J. Li, is a professor in the Dept. of Mechanical
and Automation Engineering, The Chinese University of Hong Kong,
Hong Kong, and an affiliated professor at the State Key Laboratory of
Robotics, Shenyang Institute of Automation, CAS, China (e-mail:
[email protected]).
Fig. 1 Schematic illustration of the operating principle of the OET chip.The
particles can be concentrated by the positive DEP force.
As shown in Fig. 2(a), between the interface of the liquid
and solid layer, there is an electric double layer (EDL) which
behaves as a capacitor. When the external AC bias is applied
between the top and bottom electrodes, these multiple layers
can be modeled as serially connected lum circuit elements (Fig.
2(b)). In ideal optically-induced DEP force generation process,
the applied voltage drops across the amorphous silicon layer if
the layer is not illuminated; but, if the layer is under
illumination, all the voltage drops across the liquid layer.
Realistically, however, some of the voltage may drop across
the EDL layer or the insulating layer, which will decrease the
amplitude of the voltage and the DEP force induced in the
liquid layer. Fig. 2(c) shows the impedance as a function of
frequency of the equivalent circuit model of the OET device.
The voltage will drop across the insulating layer when the
applied frequency is below 10kHz and will drop across the
liquid layer when the applied frequency is above 140kHz with
no incident light (for the values of the parameters as indicated
in the caption of Fig. 2). That is, given the set of physical
parameters as shown in Fig. 2, when no light is illuminated on
the photoconductive layer and the applied electric field
frequency across the OET device is lower than 140kHz, the
impedance of the a:Si-H layer is higher than all other layers
(including the liquid layer). So, the voltage will drop across the
a:Si-H layer. However, when the frequency is lower than
10kHz, the voltage will drop across the SiN layer or EDL layer,
regardless if there is an incident light or not, which is not
expected. Therefore, ODEP manipulation of microbeads can be
implemented in the frequency range from 10kHz to 140kHz,
i.e., with an incident light, the impedance of the a:Si-H will be
sharply decreased in this frequency range, and the voltage will
be shifted to the liquid layer.
K (ω ) =
ε *p − ε m*
(2)
ε *p + 2ε m*
Where ε* = ε–jσ/ω, ε and σ are the permittivity and
conductivity, respectively, and ω = 2πf, where f is the applied
voltage frequency across the liquid medium. The subscript, p
and m, denotes the particle and the liquid solution, respectively.
The DEP force acting on a particle can be positive or negative,
depending on the sign of the real part of CM factor. If the
particle is attracted to higher electric field, it is called positive
DEP, while if the particle is pushed towards lower electric field,
it is called negative DEP. For polystyrene beads (with radius R),
the conductivity can be expressed as[8]:
σ p = σ bulk + 2 K s / R
(3)
Where σp is the conductivity for polystyrene beads, σbulk the
bulk conductivity and Ks the surface conductivity (for
polystyrene beads σbulk=1×10-16S/m, Ks =2×10-9S/m).Eq. (3)
shows that the conductivity of the particle is thus dominated by
the surface conductivity and is inversely proportional to the
particle’s size. Combing the Eq. (2) and Eq. (3) and neglecting
the bulk conductivity (i.e., the magnitude of the bulk
conductivity is much lower than the surface conductivity, and
hence can be neglected)of the polystyrene beads, the real part
of the CM factor can be rewritten as:
 2 K s − σ m R  jωτ 0 + 1 


Re[ K (ω)] = Re 
 2 K s + 2σ m R  jωτ ω + 1 
Where τ ω =
ε p + 2ε m
2 K s + 2σ m R
R and τ 0 =
ε p − εm
2K s − σ m R
(4)
R
Then, the high- and low-frequency limits for Re(K(ω)) can
be given
lim Re[ K (ω)] =
2K s − σ m R
2 K s + 2σ m R
lim Re[ K (ω)] =
2ε s − σ m R
2 K s + 2σ m R
ωτ 0 →0
ωτ ω →0
Fig. 2 (a) Schematic and (b)equivalent electrical model for a typical OET.(c)
Impedance of an equivalent circuit model of the OET system (assume
thethickness of the EDL is 25nm, and the area of the OET device is 100cm2).
2.2 Clausius-Mossotti (CM) factor for polystyrene beads
The time averaged DEP force on a spherical object is given
in [8]:
FDEP = πR 3ε m Re[ K (ω )]∇E 2
(1)
Where R is the particle radius, εm the permittivity of the liquid
medium, E the electric field, and 𝐾(𝜔)the Clausius-Mossotti
(CM) factor, expressed as:
(5)
As shown in Eq. 5, the value of the Re(K(ω)) for the
polystyrene bead is dominated by the magnitude of the εpand
εm when the applied frequency is very high and is dominated
by the Ks, σm, and R when the applied frequency is extremely
low.
Fig. 3(a) shows the crossover frequency (DEP force equal
to zero) for different sizes of the polystyrene beads vs. the
liquid conductivity. The left bottom of each curve indicates the
positive DEP force zone, and the right top of that indicates the
negative DEP force. For example, a bead with diameter of
10µm will experience a negative DEP force when the liquid
conductivity is 1×10-3S/m. Fig. 3(b)shows the real component
of the CM factor as a function of frequency for different
microbead radii. At the same applied frequency, the bigger the
bead, the smaller the real part of CM factor. As shown, the
10μm beads will always only experience negative DEP,
regardless of applied voltage frequency. On the other hand, the
1μmbeads will experience negative DEP force in the frequency
range of higher than 1.1MHz, and will experience positive
DEP force when the frequency is lower than 1.1MHz. This
suggests that using the different directions of DEP force to
separate different diameters of the beads is possible.
Fig. 3(a) The crossover frequency for different sizes of polystyrene beadsvs.
the liquid conductivity. (b) Re[K] at different applied frequencies fordifferent
sizes of polystyrene beads.
2.3 Simplified electro-hydrodynamics of polystyrene beads
2.3.1 DEP force
In order to theoretically analyze the principle of
manipulation of a 10um polystyrene bead，we assume a light
ring as the incident light pattern with the inner radius equal to
20μm and with ring with of 25μm (the three dimensional
geometry model is shown in Fig. 4(a)). Because this model is
axially symmetric, we can use the two dimension model (Fig.
4(b)) to calculate the distribution of the electric field, based on
the parameters that the conductivity of the deionized water is
8×10-3S/m, the light conductivity of the amorphous silicon is
10-5S/m, and the dark conductivity is 10-11S/m (these data were
measured using the Keithley 2410 Source Meter).The
simulation boundaries conditions are also presented in Fig. 4(b).
The condition at the interface between the deionized water and
photoconductor layers is that both the potential and the normal
component of the current are continuous. The numerical results
can then be obtained by finite element method if the electric
field E can be obtained by E = −∇∅ in the subdomain of the
liquid chamber. Fig. 4(c) shows the simulation results for the
right-half of Fig. 4(b)’s geometric model because the
two-dimension model is axis-symmetric. The simulation result
is for the application of 20Vp-p (peak to peak value) at 100kHz
across the liquid layer. We have neglected the electric field in
the amorphous silicon layer because this layer’s electric field
cannot influence the particles suspended in the liquid. We have
also neglected the SiN insulation layer in the simulation
because in the actual OET device it is only ~20nm thick, and
hence can not significant affect the E-field distribution.
Fig. 4(a) The simplified three dimension geometry for a ring pattern used for
ODEP manipulation. (b)The two dimensional geometry model for the
calculation with theboundary conditions for the electrical field and the
parameters of each layer.The ‘Center’ indicates the center of the light ring, the
‘R1’ indicates the positon of the inner radius and the ‘R2’ the position of the
externalradius.(c) Distribution of the magnitude and direction of the electric
field. The arrow represents the direction of the negative DEP force and
thesurface plot indicates distribution of the electric field.
The simulation result shows that the electric field is
nonuniform in the liquid chamber, and the magnitude of the
electric field is higher in the areas where there is an incident
light compared to the areas where there is no incident light.
The arrow in Fig. 4(c) represents the direction of the negative
DEP force. As shown, the negative DEP force will repel the
trapped particles from the light-patterned area of the ring to the
center of the ring. Hence, the DEP force generated in the OET
device with a photoconducting layer is called optically-induced
DEP force because the nonuniform field is induced by the
light-dark optical patterns on the photoconductor layer. The
selectively illuminated photoconductor layer can thus be
described as a dynamic “virtual electrode”.
2.3.2 Stokes drag force
Because the electric field is nonuniform in the liquid
chamber of the OET, so the spherical bead will be influenced a
DEP force expressed by Eq. (1). Under the action of the DEP
force, the particle will be accelerated and moved. Once it
moves, the opposing Stokes’ drag force will be produced, as
discussed in[9]:
Fd
(6)
fr
where υ is the particle velocity, u the liquid velocity, Fd the
drag force and fr the friction factor of the particle in the fluid.
For a spherical particle fr = 6πηR, where η is the dynamic
viscosity of the medium. Assuming that the liquid velocity can
be neglected because the initial condition of the liquid solution
is nearly static, so the drag force, expressed as: Fd = 6πηR𝜈.
We note here that, in this kind of ODEP-based device,
electro-osmosis should be taken into account only when a
low-bias frequency (<1kHz) is applied to the OET as discussed
in [10]. Then, at equilibrium, in the direction of the particle
linear motion (assumed as x-direction), the forces acting on the
bead should satisfy the following equation: FDEPx = Fd, i.e., the
particle will reach a stable horizontal maximum velocity.
Moreover, when the negative DEP force (Re[𝐾(𝜔)]<0) is
exerted on the bead, the bead will be repelled away from the
light-illuminated area of the ring. That is, if a single bead is
surrounded by a light ring pattern projected on the a-Si layer
though a projector, the negative DEP force will always push
horizontally the bead to the center of the light ring. So when
we move the light ring by an animation software at a certain
velocity, the trapped bead will follow the motion of the
projected optical pattern. In this way, the bead can be moved to
any a desired location in the fluidic medium close to the a-Si
substrate.
υ=u+
To estimate the magnitude of the horizontal DEP force in
the liquid vs. the radial distance from the center of the light
ring, the vector 𝛻𝐸 2 in the Eq. (1) should be calculated. As
shown in the Fig. 5(a), the cross-sectional distribution of the
x-component of the vector ∇𝐸 2 (denoted as ∇𝐸𝑥2 ) can be
simulated based on the boundaries settings in the Fig. 4(b). We
also know that the DEP force sharply decreases along the
vertical direction and is of axial symmetry with regard to the
center of the light ring, which has the largest value around the
inner edge of the light ring for bead trapped in a ring. The
trapped particle will be left behind the light ring when the
moving velocity of the light ring exceeds a certain velocity
because a trapped particle experiences a maximum DEP force
according to the formula:
FDEPx = πε m R 3 Re[K (ω )]∇ E x
2
max
(7)
Hence, when the velocity of the light ring is increased, the
equilibrium position of the trapped particle will change from
the light ring center to the inner edge of the light ring within
the ring trapping. So the horizontal DEP force would increase.
When the particle moves to the inner edge of the light ring, the
magnitude of the horizontal DEP force will reach the
maximum value because the ∇𝐸𝑥2 has the maximum at this
position. We know that the Stokes’ drag resistance force is
proportional to the particle velocity through the Eq. 6. So when
the moving velocity reaches a threshold value, i.e., the
maximum horizontal DEP force will not overcome the Stokes’
drag resistance force, and the trapped particle will be left
behind the moving optical ring and becomes lose trapped. This
threshold velocity value can then be estimated by the following
formula (i.e., by equating Fd in Eq. 6 to FDEPx in Eq. 7 and
solve for v):
υ max =
R 2ε m Re[ K (ω )]∇ E x2
6η
max
(8)
Fig. 5(a) The magnitude distribution of the cross-sectional of the x-component
of the vector ∇E 2.(b) The absolute value of the horizontal component of the
velocity induced by the DEP force, which results in a maximum velocity of
about 35μm/s.
Because of the diameter of the polystyrene bead being
10μm, so the maximum DEP force exerted on the bead can be
reckoned at the position of a height of 6µm above the bottom
of the a-Si layer, then the trapped particle will be right on the
interface between the insulating layer and the liquid layer, and
the abs of the maximum value of the horizontal velocity is
~35μm/s.
2.3.3Electrothermal flow
The phenomena that the energy of the incident photos
absorbed in a:Si-H film is dissipated through either
electron-hole pairs or photo generation has been analyzed by
[11], which concluded that the temperature of the liquid
solution increased by the incident light is so low that it can be
neglected. However, joule heating in the liquid cause by an
external electric field applied across the liquid may be
significant. Here we analyze this ‘electrothermal’ effect.
Joule heating in a liquid caused by an applied electric field is
given as [9]:
W = σ mE2
(9)
Where W is the power generated per-unit volume and 𝜎𝑚 is
the conductivity of the liquid solution. Localized joule heating
gives rise to gradients in the solution’s permittivity and
conductivity, which interact with the surrounding electric field
to cause the fluid motion. This phenomenon is generally
known as the electrothermal (ET) effect. So particles in the
fluid may also be influenced by the motion of the fluid caused
by this phenomenon. The ET effects on moving and trapping a
particle can be analyzed by coupling the electrical, temperature
and flow fields in the fluid medium. As shown in Fig. 6(a).the
temperature increase due to ET effect is ~3K, which is
insignificant. Also as shown in Fig. 6(a), ET induced flow can
recirculate in the internal and external edge right above the
light ring. So, the suspended particles will be pushed away
from the location where there is an incident light. However,
compared with the particle maximum velocity (Fig. 5(b)) under
the influence of the DEP force and Stokes’ drag force, the
particle’s velocity induced by the ET flow (Fig. 6(b)) is so
small that the ET effect can be neglected.
In addition, we theoretically analyzed and calculated the
minimum radius of beads that can be manipulated by ODEP
force. Theoretically, suspended particles can be trapped or
focused by DEP force when the maximum DEP force
generated by an incident light pattern overcomes the thermal
perturbation force caused by Brownian motion. Because DEP
force scales with R3, it sharply decreases as the diameter of the
manipulated object is scaled down, especially in the nanoscale
domain. On the other hand, the thermal perturbation force
scales with R-1,so it is critical to analyze the magnitude of these
two competing forces as objects scale down in size. Assuming
that an incident light pattern is a light spot with its diameter
being 1μm, 5μm, 10μm, 15μm, 20μm, 30μm and 40μm,
respectively, we can calculate the maximum DEP force
generated by this light spot respective to its diameter size in the
light chamber. By balancing the maximum DEP force and the
thermal perturbation force, the minimum radius value of the
beads can be obtained. The results for the minimum radius of a
bead manipulable by ODEP force vs. light spot size is plotted
in Fig. 7. Simulation results show that the minimum radius of a
bead that can be manipulated exponentially decreases with
respect to the size of the light spot. The curve-fit equation that
relates the minimum radius (r) and light spot size (x)can be
expressed as:
r=101exp(0.04x)
(10)
As shown, when the light spot radius is 1μm, ODEP force can
theoretically manipulate 100nm radius beads. This means the
ODEP force can be used to manipulate nanometer-scale
particles using smaller projected light image. Note that the
simulated results shown in Fig. 7 is obtained by balancing the
maximum DEP force with the force caused by Brownian
motion, which is give by [12] as:
FBrownian = K BT /(1.39 R)
the ring (velocity of ~10µm/s),as shown in Fig. 8(b).As long as
the ring velocity is below the velocity at which Stokes’ drag
force is equal to the induced DEP force, the bead remains
trapped in the ring (i.e., as shown in Fig. 8(c), where the ring
velocity is ~20µm/s). For the experimental configuration
shown in Fig. 8, when the velocity of the light ring exceeds
25μm/s, the bead will be left behind the light ring, i.e., it
becomes “untrapped” (Fig. 8(d); repeated experiments indicate
the ~25μm/s is the ring velocity at which the bead becomes
“untrapped”). Note that the maximum velocity of manipulation
of a single 10µm polystyrene bead is 25μm/s in DI water as
stated above, which is in the same order of magnitude of our
simulation result of 35μm/s (Fig. 5(b)).
Fig. 6(a) The simulation results of the ET effect. The isolines indicate the
logarithmic distribution of the temperature gradient; difference in log10(∇T)
between the any adjacent isolines is 0.15, the surface color indicates the
temperature distribution in the liquid layer, and the arrow represents the
direction of the ET flow.(b) The absolute value of the maximum velocity of a
particle induced by ET effect.
(11)
Where KB is the Boltzmann constant and T is the temperature.
III.
EXPERIMENTAL RESULTS
We have performed several experiments using the ring-shape
light as the virtual electrode，and successfully generated ODEP
force to manipulate10μm beads as shown in Fig. 8(a)-(d). At
first, the light ring pattern is projected onto the
photoconductive layer through a objective lens attached to a
projector, and no voltage potential is applied across the liquid
medium (Fig. 8(a)). When an external AC voltage potential
with peak-to-peak value of 20V is switched on and the light
ring is moved, the bead can be trapped and move along with
Fig. 7 Minimum radius of beads vs. light spot size.
force acting on the particle by the ‘line’ electrode. In Fig. 9 (b),
1µm polystyrene beads were mixed in DI water and were
observed to undergo Brownian motion initially. When the
optical circular spot was illuminated onto the ODEP chip and
the external AC bias was applied across the chip, the
polystyrene beads were shown to be attracted towards the
center of the optical spot (as shown in the right-hand-side
Fig.)due to the induced positive DEP force.
IV.
Fig. 8 Example of DEP manipulation of a single bead(diameter of 10µm) using
optically projected pattern on an ODEP chip.(a) No bias voltage is applied
across the liquid medium.(b) Bias voltage applied and the light ring is moved,
keeping the bead trapped as it moves.(c) The velocity of the moving light ring
is increased. (d) The bead will be left behind when the velocity of the light ring
exceeds 25μm/s.
CONCLUSION
In this paper, we present our work on analyzing the
characteristics of ODEP manipulation of micron-sized
polystyrene beads by establishing an equivalent electrical
model. Simulation results show that the ODEP manipulation of
microbeads is frequency-dependent and that the electrothermal
effect is negligible. Furthermore, the relationship between the
frequency of the applied voltage and the velocity of the
microbeads is consistent with our experimental measurements.
In addition, simulation results show the minimum radius of a
bead that can be manipulated exponentially decreases with
respect to the size of the light spot. For instance, when the
projected light spot size is 1μm, ODEP can theoretically
manipulate 100nm beads--indicating that ODEP can be
extended to manipulate nano-scale objects if projected spot
size can be significantly reduced.
V.
ACKNOWLEDGEMENTS
The present work is supported by a self-sponsored project
of the State Key Laboratory of Robotics(No. 2009Z02). The
authors would like to thank all the members in the Micro/Nano
Automation Group of the State Key Laboratory of Robotics,
SIA, CAS, for their valuable discussions and support.
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[1]
Fig. 9(a) Experimental results of a 10μm polystyrene bead under a negative
DEP force. (b) Experimental results of 1μm polystyrene beads focused into a
circular zone under a positive DEP force.
In addition, we have done experiments on manipulating
10μm beads using a “line” and 1μm beads using a ”circle” as
the light pattern (with AC bias of 20Vp-p at 100kHz) as shown
in Fig. 9(a) and Fig. 9(b), respectively. The results validate the
calculated results in Fig. 3, and also show that the direction of
the DEP force for the polystyrene beads is dependent on the
radius of the beads. In Fig. 9 (a), the particle was stabilized in
the liquid medium initially, and the optical line was then
illuminated onto the ODEP chip. When the external AC bias is
applied across the chip, the particle is repelled away (as shown
in the right-hand-side of the Fig.) from the optical line (which
remains stationary at all times), indicating a negative DEP