Dielectrophoretic Handling of Mesoscopic Objects

Diego C. POLITANO, Paolo V. PRATI, Shao-Jü WOO,

Otte J. HOMAN

*)

, Felix M. MOESNER and Andreas STEMMER

Institute of Robotics, Nanotechnology Group

*)

Laboratory of Fieldtheory and Microwave Electronics

Swiss Federal Institute of Technology Zurich (ETHZ)CH - 8092 Zurich, Switzerland

ABSTRACT

Efficient handling of minute objects in individual or col-lective mode is a delicate and most demanding task.Electric fields applied over a micro-patterned electrodearray possess the capability to produce contactless driv-ing forces on small conducting or non-conducting parti-cles as presented in a former paper [1]. The transportand precise positioning of charged micro particles up to400 µm in diameter has been demonstrated on the x-yplane, where an addressable electrode geometry allowsflexible particle actuation trajectories. In this paper, the electrode pattern is further miniatur-ized allowing a gap width in the order of a 1 µm. Theadvantage of this downscaling is a clear reduction ofCoulomb heating when small objects are transported inionic solution. Additionally, high frequency electricfields are necessary to impart actuation forces onto thesuspended objects in liquid environment as described in[2 - 4]. Since the electric field strength is a function ofthe gap between the electrodes and the applied voltage,a miniaturized pattern requires lower voltage amplitudesin order to attain a certain electric field strength. The electrodes are designed as a spiraled meander andfabricated by photolithographic processes within amonolayer. Under the application of six-phase voltages,a traveling electric field wave is created above the elec-trode array, immersed mesoscopic objects becomepolarized and negative dielectrophoretic effects causeobject motion. It is shown that optimal object actuationoccurs in a narrow, material-specific frequency spec-trum. Various simulations and their results are presentedin this paper.

I. I

NTRODUCTION

A particle suspended in a medium becomes electricallypolarized when subjected to an electric field. If the spatialdistribution of phase and field magnitude are inhomoge-

nous, a dielectrophoretic (DEP) force acts on the particle,as a result of the interactions between the induced polar-ization and the field. The DEP-induced particle motion isstrongly dependent on the field frequency, the spatial con-figuration of the field, the dielectric properties of the sus-pending medium and, more importantly, of the particleitself.

II. T

HEORETICAL

B

ACKGROUND

The term dielectrophoresis was coined by Pohl [5] to de-scribe the force exerted by a non-uniform electric field ona small polarized but uncharged particle. Most theoreticaland experimental work in dielectrophoresis used the gen-erally accepted force expression of Pohl [5], namely

(1)

where is the non-uniform electric field and isthe effective dipole moment to be discussed in more de-tail in this paper. The simplest derivation of the dielectro-phoretic force is accomplished by summing the forces ontwo equal but opposite electric charges (+q,-q) placed avector distance apart in a non-uniform electric field(see Fig. 1).

The net force on this small dipole is given as [6]

. (2)

If

and only the lowest-order term of the Taylorseries in

is retained, we get

. (3)

FDEP peff Ñ×è øæ ö Eo×=

E0peff

d

FDEP

FDEP q Eo

r d+( ) q Eo

× r×–× ×=

d 0®d

FDEP q d Ñ×( ) Eo× ×=

The product (

q

) is interpreted as an electric dipole

,

so we have [5, 6]:

(4)

where [7]

(5)

is the value of the induced dipole moment. Here,

a

isthe distance between the two charges and the dielectricconstants of the media and the particle are

e

m

and

e

p

, re-spectively.

We modified this situation considering the generalcase, where the field varies sinusoidally in time andwhere both particle and suspending medium possess afinite conductivity (

s

p

and

s

m

respectively). The abso-lute permittivity is then a complex quantity, having realand imaginary components given by

(6)

where and

w

is the angular frequency. Weshould note that the permittivity factor

e

m

outside thebrackets of Eq. (5) derives from the Gauss law and assuch is not considered to include the effect of conduc-tivity losses. Now, the induced dipole is given by [7, 8]as

. (7)

We can finally go back to Eq. (4) and find that the di-electrophoretic force acting on a particle in anon-uniform traveling field is composed of two compo-nents.

The first one is the "in-phase" component (convention-al dielectrophoresis):

(8)

whereas the second one is the "out-of-phase" compo-nent (traveling wave dielectrophoresis) [9]:

(9)

where

l

is the wavelength of the traveling field and

(10)

the so-called Clausius-Mossotti factor.

dp

FDEP peff Ñ×è øæ ö Eo×=

peff 4pa3

em

ep em–( )

ep 2em+( )----------------------------Eo=

e* e jsw----è ø

æ ö–=

j 1–=

peff 4pa3

em

ep* em

*–( )

ep* 2em

*+( )----------------------------------Eo=

FDEP

FCDEP 2pa3

emÂeep

* em*–( )

ep* 2em

*+( )----------------------------------

è øç ÷æ ö

E2

Ñ=

F w( )

4p–2

a3

emÁmep

* em*–( )

ep* 2em

*+( )----------------------------------

è øç ÷æ ö

E2

l------------------------------------------------------------------------------------=

f CM

ep* em

*–( )

ep* 2em

*+( )----------------------------------=

FIGURE 1:

Dipole in non-uniform electric field as shown in Cartesian xyz system.

y

z

x

r-

+

-q

+q

d

E(r+d)

E(r)

DIPOLE

FIGURE 3:

Micro channels covering the electrode meander structure. The channels have the function of

guiding the particles and serve as a reference for observation under the microscope.

FIGURE 2:

Magnified design of the electrode pat-tern SNAIL. Six-phase voltages are supplied to the

pads on the left side. The constant electrode gaps dif-fer for each of the four quadrants.

In conclusion, we find the final expression for the di-electrophoretic force referring back to [9] as

(11)

III. E

LECTRODE

P

ATTERN

The electrodes are designed as a spiraled meander andconsequently named as SNAIL. We previously demon-strated that the best translation results have beenachieved with six-phase electrodes [10 - 12]. Now, thenovel miniaturized structure consists of six parallelelectrodes designed as shown in Fig. 2. Every side ofthe structure features a different gap width between theelectrodes resulting in 4 segments with different elec-tric field strength. The electrical contact to the powersupply is provided by large pads which also provide forimpedance transformation from the microelectrodes tothe supply wires.

The structure SNAIL is fabricated by photolithograph-ic processes within a monolayer and is then – as an al-ternative – covered by a thin isolation film. On eachside, only few microchannels (Fig. 3) are designed,where the particle interacts directly with the electrodes.These channels function as a guidance for the particlesand as reference for the observation under the light mi-croscope.

The electrode-free window in the middle of the struc-ture is designed for statistical measurements and forfurther applications such as optical-tweezer (laser-trap-ping) methods.

The microelectrodes are fabricated on glass or Indium-phosphide (InP) substrate. Using optical photolithogra-phy, patterns with a minimum linewidth of 1

m

m are de-fined. Samples are produced as a single layer of goldmetallization using a Galvanic process. Some criticalspots for the fabrication process are shown in Fig. 4.

IV. M

ESOSCOPIC

P

ARTICLES

& S

USPENDING

M

EDIA

The mesoscopic particles used in later experiments areLatex (Polystyrene) spheres with a diameter

d

= 1 µm,mass density

r

= 1,05 g/ml, dielectric constant

e

= 2.5and electrical conductivity

s

p

= 0.009 S/m (Ernest F.Fullam, pdf@fullam.com).

The suspending medium is water with some Ethanolwhich acts as bacteria-killer. The dielectric constant is

e

= 80 and the electrical conductivity

s

m

= 5 10

-6

S/m

F w( ) 2pa3

em Re f CM( ) EÑ2

Im f CM( ) Ex2

jx Ey2

jyÑ Ez2

jzÑ+ +Ñè øæ ö+è ø

æ ö=

FIGURE 4: Magnified view of the critical points of the electrode pattern. a) and b) show central

termination of electrodes; c) is the central window; d) is the pad connection to one phase electrode.

a) b)

c) d)

FIGURE 5: Block diagramm of the six-phase oscillator.

φi=180οout

Inverter

−60ο −120ο

φ1=−60ο φ2=−60ο φ3=−60οin

Allpass Allpass

−180ο

φi=180οInverterφi=180οφi=180ο

60ο 240ο 120ο 300ο 180ο 360ο

Allpass

FIGURE 6: Output frequency vs. controlling dc voltage of the sine quadrature VCO.

0

2 104

4 104

6 104

8 104

1 105

1.2 105

0 5 10 15 20 25

Adjustment of Output-Frequency

Osc

illat

ion

Fre

quen

cy [H

z]

Control Voltage [V]

FIGURE 7: Two-phase field distribution over the SNAIL electrode array.

FIGURE 8: Six-phase field distribution over the SNAIL electrode array.

which can be raised up to 10 S/m by addition of salt re-sulting in an ionic solution.

V. POWER SUPPLY

Quadrature generators producing two signals of identi-cal frequency and amplitude but different phase angleare used in a variety of applications and described in[13].

We have further enhanced this technique in order tobuild a generator that produces 6 signals of identicalfrequency and amplitude. In this case, the frequencyshift is 60o.

The circuit utilizes 3 allpass filters with a 60o shift and4 inverters as shown in Fig. 5. As long as the inverterstage does not add any additional phase error (fi =180o) the sum of the allpass stages must amount tof1+f2+f3+f4+f5 = 180o for oscillation.

The frequency can be tuned with a VCO working be-tween 0 and 25V DC. A frequency range from 20 MHzup to 119 MHz can be covered as shown in Fig. 6.

VI. SIMULATIONS

vi.i. Electric Field Distribution on the SNAIL

In order to reach the maximal traveling effect on theparticle, we tried to optimize it through the electrodestimulation. The electric field distribution on theSNAIL was investigated by various simulations withthe program tool MMP (Multiple Multipole) developedat ETH-Zurich by Dr. Pascal Leuchtmann [14]. The re-sults of our simulations are summarized in the two fig-ures Fig. 7 and Fig. 8.

In Fig. 7, a two-phase distribution was simulated. Thissolution was adopted in a previous research [7]. Thefield distribution shows the abrupt transition betweendifferent phases; so that we can postulate that this solu-tion can’t assure a perfect control on the moving parti-cles.

We have further simulated the six-phase setup. Fig. 8shows its field distribution on the SNAIL. The transi-tions are much smoother. Therefore, this solution waschosen as it assures good particle moving control.

Further, the influence of the particle on the local fielddistribution was also investigated. As shown in the the-ory, the local non-uniformity of the field is a decisiveparameter in the dielectric force calculation (see Eq.(8)). Fig. 9 shows a representation of the distribution ofE2 near the electrode in presence of a particle.

Fig. 10 shows the potential distribution on the elec-trodes. The graph clearly indicates the reduction of themagnitude for greater height above the electrodes.

FIGURE 10: The picture shows the potential distri-bution on the electrodes. The magnitude becomes reduced for greater height above the electrodes.

00.5l

l1.5l

2l2.5l

3l

0

0.1l

0.2l

0.3l

0.4l

0.5l

0.6l

0.7l

0

Electrodes [l]

Height [l]

+Vpeak

-Vpeak

45

67

89

10

-5

-4

-3

-2

-1

0

1

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Frequency [Log(Hz)]

Conductivity [Log(S/m)]

pDEP

nDEP

FIGURE 12: Imaginary part of fCM in function of frequency and medium conductivity sm.

-5

-4

-3

-2

-1

0

1

4

5

6

7

8

9

10

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

Frequency [Log(Hz)]

Conductivity [Log(S/m)]

E-FieldDirection

FIGURE 9: The representation of the E2 distribution showing the particle influence within the local field.

FIGURE 11: Real part of fCM in function of fre-quency and medium conductivity sm.

vi.ii. The Influence of the Clausius-Mossotti Factor

In this paper, the influence of the Clausius-Mossottifactor is investigated with respect to some critical par-ticle handling consequences. Starting from the repre-sentation of the real part (Fig. 11) and the imaginarypart (Fig. 12) of the Clausius-Mossotti factor fCM, wefound the interesting result shown in Fig. 13. The con-ventional dielectrophoresis (cDEP) causes trapping orrepulsion from the electrode, while only the imaginarycomponent (traveling wave dielectrophoresis, twDEP)is responsible for particle translational motion. Fig. 13states that the best frequency spectrum is between 10MHz and 100 MHz, where cDEP is negative and causesrepulsion from the electrodes, and where the magnitudeof twDEP is big enough to induce a motion on the par-ticle.From the results shown in Fig. 13, we can postulate thefeasibility of sorting particles with different dielectricproperties or dimensions (e.g. separating living fromnot living cells) [15].It is now possible to calculate the speed of a particle onthe fabricated electrode pattern. If the Stokes frictionforce is

(12)

with h as the viscosity and as the motion velocity.Together with the twDEP force

(13)

we assume that

(14)

so we find

(15)

(16)

and finally, the particle velocity in translational x-direc-tion as

(17)

VII. CONCLUSION

From a theoretical point of view, the traveling electric

field induces a complex dipole moment on a suspendedparticle. As a result, a complex dielectrophoretic forceis exerted on it. The real component of this force causestrapping while the imaginary component is responsiblefor translational particle actuation. The overall electro-kinetic behavior of a particle is determined by com-bined effects of these two forces, and is a function of itsdielectric properties and the frequency of the appliedtraveling field. It is shown that optimal actuation occursin a narrow, material-specific frequency spectrum. Fur-ther, the interesting possibility of particle sorting ispostulated. The field-induced forces increase as fieldgradients become stronger. An increase of field gradi-ents can be obtained by a further miniaturization of theelectrodes. From a technical point of view, electrodeswith typical dimensions in the submicron range can befabricated with existing photolithographic technolo-gies.

VIII. ACKNOWLEDGMENTS

We thank Mr. S. Müller (Institute of Robotics, ETH Zu-rich) for his excellent work on the six-phase voltage os-cillator. His great engagement in this project allows usto conduct many important experiments in the near fu-ture.

IX. REFERENCES

1. Moesner, F.M., Higuchi, T., "Devices for ParticleHandling by an AC Electric Field," Proceedings IEEEMicro Electro Mechanical Systems, Amsterdam, TheNetherlands, January 1995, pp. 66-71.

2. Muller, T., Gerardino, A., Schnelle, T., Shirley, S.G.,Bordoni, F., De-Gasperis, G., Leoni, R., Fuhr, G.,"Trapping of Micrometer and Sub-Micrometer Parti-cles by High-Frequency Electric Fields and Hydrody-namic Forces," Journal of Physics D (Applied Physics),vol. 29, no. 2; February 1996, pp. 340-349.

3. Jones, T.B., Washizu, M. "Multipolar Dielectro-phoretic and Electrorotation Theory," Journal of Elec-trostatics, vol. 37, no.1-2, May 1996, pp. 121-134.

WR 6pha v×–=

v

FtwDEP 2pa3

Ám f CM( ) E2

xo fx E2

yo fy E2

zo fzÑ+Ñ+Ñè øæ ö=

E2

xo fx E2

yo fy E2

zo fzÑ+Ñ+Ñ E2 2p

l------×=

FtwDEP W– R=

4p–2

a3

emÁm f CM( )w 9MHz=

E2

l-------------------------------------------------------------------------------------------- 6phavtwDEP=

vcDEPx

r2

em3h

-------------Âe f CM( )w 80MHz=

ÑEx2

=

FIGURE 13: Optimal actuation occurs in a narrow, material-specific frequency spectrum.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

4 5 6 7 8 9 10

Frequency [Log(Hz)]

Im(fCM),Re(fCM)

Conductivity of Media sm

10E-2 S/m

10E-5 S/m

10E-3 S/m

10E-1 S/m

4. Fuhr G., Hagedorn R., Müller T., “Linear Motion ofDielectric Particles and Living Cells in Microfabri-cated Structures induced by Traveling Electric Fields”,IEEE MEMS, 1991, pp. 259-264.

5. Pohl H.A., ” Dielectrophoresis”, Cambridge Univer-sity Press, Cambridge, 1978.

6. Jones T.B., Kallio G.A., “Dielectrophoretic ForceCalculation”, Journal of Electrostatics 6, 1979, pp.207-224.

7. Pethig R., “Application of AC electrical fields to themanipulation and characterisation of cells”, Proc. ofthe 4th Toyota Conf., 1990, pp. 159-185.

8. Washizu M., “Manipulation of Biological Objects inMicromachined Structures”, IEEE MEMS, 1992, pp.196-201.

9. Huang Y., Wang X.B., Tame J.A., Pethig R., J Phys.D: Appl Phys. 26, 1993, pp.1528-1535.

10. Moesner F.M, Higuchi T., “Devices for Particle Han-dling by an AC Electric Field”, Proceedings IEEEMicro Electro Mechanical Systems, Amsterdam, TheNetherlands, January 1995, pp.66-71.

11. Moesner F.M., Buehler Ph.S., Politano D.C., PratiP.V., “Electrostatic Propulsion Motor for Tiny Vessels”,IEEE Industry Applications Society ConferenceRecord, 32nd Annual Meeting, New Orleans, October1997, vol.3, pp1874-1878.

12. Moesner F.M, Higuchi T., “Contactless Manipulationof Microparts by Electric Field Traps”, SPIE’s Interna-tional Symposium on Microrobotic and MicrosystemFabrication, Pittsburg, October 1997, vol.3202, pp.168-175.

13. Hölzel R., “A Simple Wide-Band Sine Wave Quadra-ture Oscillator”, IEEE Transactions on Instrumentationand Measurement, Amsterdam, February 1993, Volume42, pp.758-760.

14. Leuchtmann P., Bomholt F., “Field modeling with theMMP-code”, IEEE Transactions on ElectromagneticCompatibility, 1993. Special issue on EMC applica-tions of numerical techniques.

15. Talary M.S., Burt J.P.H., Tame J.A., Pethig R., “Elec-tromanipulation and separation of cells using travelingelectric fields”, J Phys. D: Appl Phys. 29, 1996,pp.2198-2203.