Adhesion-Inhibited Surfaces. Coated and Uncoated Interdigitated

Jan 15, 1996 - Bernd Wagner,‡ and Gu¨nter Fuhr*,†. Institut fu¨r Biologie, Humboldt-Universita¨t zu Berlin, Invalidenstrasse 42, 10115 Berlin,. German...
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Langmuir 1996, 12, 801-809

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Adhesion-Inhibited Surfaces. Coated and Uncoated Interdigitated Electrode Arrays in the Micrometer and Submicrometer Range Thomas Schnelle,† Torsten Mu¨ller,† Andreas Voigt,† Klaus Reimer,‡ Bernd Wagner,‡ and Gu¨nter Fuhr*,† Institut fu¨ r Biologie, Humboldt-Universita¨ t zu Berlin, Invalidenstrasse 42, 10115 Berlin, Germany, and Fraunhofer-Institut fu¨ r Siliziumtechnologie (ISiT), Dillenburger Strasse 53, 14199 Berlin, Germany Received January 30, 1995. In Final Form: October 16, 1995X Individually-addressable, interdigitated electrode arrays energized either by ac or by traveling-waves can create electric field shields. Some arrays were coated with thin dielectric layers to improve stability. In conductive aqueous solutions (up to 7 S/m) and at frequencies between 1 kHz and 200 MHz, microscopic particles and living cells showing negative dielectrophoresis are repelled from the electrode plane. Calculations were carried out to estimate the forces acting on particles and the heat production (losses) for various electrode geometries and properties of the insulating layer. We show, both experimentally and theoretically, that surfaces can be protected from cells adhesion and deposition of most artificial particles with effective diameters above 100 nm for many days. Additionally, the presented structures can be used as efficient microparticle filters.

I. Introduction A major problem affecting sensors in active environments (e.g., living systems or seawater) is adhesion of particles and cells to the sensor surfaces. This reduces working lifetime and accuracy (for an overview about biofouling and biocorrosion processes see, e.g., refs 1-3). Since the early work of Pohl,4 it is known that polarization (ponderomotive) forces are strong enough to move microparticles toward regions of lower or higher electric field strength. These phenomena are now called negative and positive dielectrophoresis (DEP), respectively. Levitation of air bubbles, dielectrics, and cells were investigated in detail by Jones and Kaler,5-8 and the pumping of inhomogeneous liquids was investigated by Melcher.9 Both phenomena were attributed to ponderomotive forces. We propose to use dielectrophoresis to keep particles away from surfaces, thereby preventing adhesion. Effective application of dielectrophoresis requires electric fields which are inhomogeneous on the scale of the particles to be manipulated. Extremely small electrodes are needed to achieve this for cells and microparticles. Such electrodes can only be fabricated to sufficiently high quality by applying semiconductor-manufacturing technologies. Microelectrodes on silicon or glass can generate well-defined, local, field gradients, just beyond the range of surface forces of the substrate.10-14 Recently, it has been shown that living cells suspended in a natural * To whom correspondence may be addressed: Fax, +49/030/ 28972635; e-mail, [email protected]. † Humboldt-Universita ¨ t zu Berlin. ‡ Fraunhofer-Institut fu ¨ r Siliziumtechnologie. X Abstract published in Advance ACS Abstracts, January 15, 1996. (1) Vadgama, P. Sens. Actuators 1990, B1, 1. (2) Flemming, H. C. Bioforum 1994, 3, 61. (3) Sethi, R. S. Biosens. Bioelectron. 1994, 9, 243. (4) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, 1978. (5) Kaler, K. V. I. S.; Pohl, H. A. IEEE Trans. Ind. Appl. 1983, IA 19/6, 1089. (6) Jones, T. B. J. Electrost. 1986, 18, 55. (7) Kaler, K. V. I. S.; Jones, T. B. Biophys. J. 1990, 57, 173, . (8) Jones, T. B.; Bliss G. W. J. Appl. Phys. 1977, 48, 1412, . (9) Melcher, J. R. Phys. Fluids 1966, 9/8, 548. (10) Masuda, S.; Washizu, M.; Kawabata, I. IEEE Trans. Ind. Appl. 1988, 24, 217.

0743-7463/96/2412-0801$12.00/0

environment (e.g., culture media) exhibit negative dielectrophoresis (they are repelled from the electrodes) over a large frequency range (kHz-GHz).15-17 In chemically active media, long term stability can only be achieved if the electrodes are covered with inert layers. Electrolysis is widely suppressed and direct contact of cells or other biomaterials with metallic surfaces is avoided. This is especially important if sensors have to be implanted into living organisms. Semiconductor technologies offer a variety of dielectric coverings, e.g., silicon oxinitride. In this paper, we investigate the influence of insulating layers on the ability of electrodes to repel particles from surfaces, using both high-frequency alternating- and traveling-electric fields. We discuss planar, interdigitated electrode arrays as these can easily be fabricated down to the submicrometer range and analytical estimations for electric fields and dielectrophoretic forces (DEPF) can be made. It is shown that many types of particles (e.g. Sephadex and latex spheres between 0.1 and 100 µm in diameter) and living cells can be repelled by the negative dielectrophoretic forces induced by ac or traveling electric fields, at frequencies up to 200 MHz, in aqueous solutions due the high permittivity of water. II. Material and Methods Microelectrode Fabrication. The microelectrodes were fabricated on glass or oxidized silicon substrates. Using photolithography, patterns with a minimum line width of 3 µm were defined. Chips with two different types of metalization were produced: single layer gold electrodes and a double layer Pt/Au metalization. (11) Pethig, R.; Huang, Y.; Wang, X.-B.; Burt, J. P. H. J. Phys. D: Appl. Phys. 1991, 24, 881. (12) Fuhr, G.; Arnold, W. M.; Hagedorn, R.; Mu¨ller, T.; Benecke, W.; Wagner, B.; Zimmermann, U. Biochim. Biophys. Acta 1992, 1108, 215. (13) Wang, X.-B.; Huang, Y.; Burt, J. P. A.; Markx, G. H.; Pethig, R. J. Phys. D: Appl. Phys. 1993, 26, 1278. (14) Schnelle, Th.; Hagedorn, R.; Fuhr, G.; Fiedler, S.; Mu¨ller, T. Biochim. Biophys. Acta 1993, 1157, 127. (15) Fuhr, G.; Mu¨ller, T.; Schnelle, Th.; Hagedorn, R.; Voigt, A.; Fiedler, S.; Arnold, W. M.; Zimmermann, U.; Wagner, B.; Heuberger, A. Naturwissenschaften 1994, 81/12, 528. (16) Fuhr, G.; Glasser, H.; Mu¨ller, T.; Schnelle, Th. Biochim. Biophys. Acta 1994, 1201, 353. (17) Fuhr, G.; Schnelle, Th.; Mu¨ller, T.; Glasser, H.; Wagner, B. Sens. Mater. 1995, 712, 131.

© 1996 American Chemical Society

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Figure 1. (A) Schematic diagram of the experimental setup and driving conditions to produce traveling and ac electric fields. (B) Wire bonded chip with E-beam processed submicrometers electrodes in a leadless ceramic carrier and fixed with glue (Epo-tek 302-3, Polytek, Waldbronn, Germany). (C) Section of B: bar, 7 µm; electrodes, width ) 380 nm, gap ) 220 nm (central part). (D) Working traveling-wave electrode design with 700 nm high SiOxNy tracks (darker horizontal strips) of different width, filled with suspended latex particles (diameter 14.9 µm, Serva): driving conditions, ac, voltage 2 V, f ) 5 MHz; electrodes, width ) 30 µm, gap ) 30 µm. In the first case a sputtered 40 nm/40 nm thick Cr/Au plating base and a local electroplating process were used to form 0.50.9 µm thick gold electrodes. Subsequently, the plating base was removed by ion milling. In the second case, a 20 nm/180 nm thick Ti/Pt layer was evaporated and structured in a lift-off process. Then a 700 nm thick silicon oxinitride (SiOxNy) dielectric layer was deposited by PECVD (plasma-enhanced chemical vapor deposition). After the contact holes were etched, a second metal layer was added using the gold electroplating process described above. The submicrometer-structures were formed with an electron beam writer (LEICA EBPG 4HR) at 50 kV acceleration voltage. An electrode-size dependent exposure dose was calculated taking into account the effect of backscattered electrons (proximity effect). In some cases the electrodes were embedded in 300 nm thick SiO2 or Si3N4 to build a nearly flat surface and to isolate the electrodes. Electrodes with pitch and height of 200 nm could be made. Typical electrode structures are shown in Figure 1 (for more details see ref 18). Field Generation and Application. Two generators (Hewlett-Packard 8131 A and 8116 A, USA) were used to produce phase-shifted rectangular electric pulses. In the case of traveling waves (HP 8131 A), the field frequency could be varied between 2 kHz and 200 MHz and the amplitude between 0 and 5 V (18) Reimer, K.; Ko¨hler, C.; Lisec, T.; Schnakenberg, U.; Fuhr, G.; Hintsche, R.; Wagner, B. In Proceedings of Eurosensors VIII, Toulouse, 1994; pp 25.

(typically 5 MHz and 2 V, for more details see refs 16 and 19). The electrodes were in a repeating pattern so that every fourth one was connected to the same terminal. The four terminals were driven with 90° phase shifted signals (see Figure 1A). For ac field generation, the HP 8116 A was also used allowing amplitudes up to 15 V and frequencies between 200 Hz and 50 MHz. The whole system was wire-bonded to a leadless ceramic carrier (LCC-68, Kyocera Corp., Japan) and connected by 50 Ω coaxial wires. Particle behavior was recorded by a microscope-video system (Leitz-Metallux 3, Kappa, type CF 15/2, Germany; see Figure 1A). Microparticles and Media. Artificial Particles. Commercially available, cross-linked dextran spheres (Sephadex G15, Pharmacia-LKB., Sweden), and Standard Dow Latex spheres (0.2-15 µm, Serva, Germany) and FluoSpheres (0.014 µm, 0.1 µm, Molecular Probes Inc., Eugene, OR) were diluted in aqueous solutions (10-4-7 S/m), the conductivity was adjusted by addition of KCl, NaCl, CaCl2, and MgCl2. Living Cells. We used the Swiss mouse embryo fibroblast cell line 3T3 cultured in DMEM medium (Seromed/Biochrom, Germany, F0435) supplemented with 10% fetal calf serum containing penicillin and streptomycin at 100 IU/ml each (Seromed/Biochrom, Germany, L2143) at 37 °C under 5% CO2. (19) Mu¨ller, T.; Arnold, W. M.; Schnelle, Th.; Hagedorn, R.; Fuhr, G.; Zimmermann, U. Electrophoresis 1993 ,14, 764.

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Figure 2. Freshly suspended mouse fibroblasts 3T3 (average diameter 15 µm) incubated for 30 min in DMEM (conductivity 1.3 S/m) above uncovered interdigitated electrodes: (A) without electric field; (B) with ac driving of the electrodes at measurement conditions: cell density, 1.8 × 106 cells/mL; electrodes, width ) 3 µm, gap ) 3 µm (central part) driving conditions, voltage ) 1.5 V, f ) 5 MHz (after washing with DMEM). With ac driving the cells strongly adhere only to electrode-free regions and to the thick glue coating (on the bottom of part B). To maintain log-phase, the cultured cells were detached from the culture flask with 0.05/0.02% trypsin/EDTA (ethylenediaminetetraacetic acid, Seromed/Biochrom, L2143) in phosphate buffered saline solution (PBS) at 37 °C for 3-5 min every 3 days. Cells were subjected to two to three washing cycles with culture medium to remove the enzyme and, if required, brought into the measuring solution (HBSS, HANKS’ balanced salts Seromed/ Biochrom L2045; D-PBS or Dulbecco’s buffered saline Seromed/ Biochrom L1815; DMEM). Measurements were made with cells cultivated for 1 day in the subculture.

III. Results and Discussion Experimental Results. Figures 2 and 3 (and also Figure 1D) show typical experimental findings of the inhibition of particle adhesion by dielectrophoretic shielding. We found, that both ac (Figure 2) and travelingwave (Figure 3) excitation of electrodes (with widths down to 180 nm and gaps down to 80 nm) can protect surfaces from the adhesion of cells and particles at least for the experimental time interval. Figure 2 illustrates the adhesion inhibition effect for mouse fibroblasts. Figure 2A shows the control experiment (without field) with a uniform distribution of anchored cells. The application of an ac electric field to the ultramicroelectrodes keeps them and their interelectrode gaps totally free of cell adhesion (Figure 2B). Since the applied high-frequency field is well tolerated by the cells,16 the adhesion inhibition is not caused by cell destruction but by repulsion. In Figure 3A the application of traveling waves is shown. Although there is an electrohydrodynamically induced

liquid streaming19 with a velocity of about 30 µm/s from left to right, the electrode array and the right-hand side of the channel remain free of 100 nm latex spheres. These accumulate on the left-hand side of the interdigitated electrode array. This phenomenon leads to an efficient microparticle filtering procedure. For the sake of clarity, a sketch of the experimental situation is given in Figure 3B. Similar results for adhesion inhibition were obtained with red blood cells, pollen grains, plant protoplasts, yeast, cell organelles (e.g., chloroplasts) and a variety of artificial colloidal particles, e.g., glass and Sephadex spheres. Instead of water, other dielectric liquids, e.g., alcohol can be used. Theoretical Explanation. A (uncharged) particle suspended in a liquid of different dielectric properties becomes polarized in an electric field. The interaction of a spatially inhomogeneous, electric field with the induced multipoles can result in particle motion (dielectrophoresis). In dipole approximation, the dielectrophoretic force F BDEP (corresponding to DEPF) acting on a dielectric particle of radius R in a time periodic (sinusoidal) electric field E B can be expressed as

F BDEP(t) ) (m b (t)‚∇ B )E B (t)

(1)

B (t) (see with the induced dipole moment m b (t) ) 4πR3lfCME

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Figure 3. Traveling wave driven electrodes in a 100 µm high channel through which is flowing a suspension of 100 nm diameter latex particles: (A) Microscopic view (inner frame of B) by laser-scanning (Leica, Wetzlar, Germany): electrodes, width ) 1 µm, gap ) 2 µm (central part) driving conditions, voltage ) 2.5 V, f ) 16 MHz liquid, water, conductivity 3 mS/m. (B) Scheme of the experimental situation. The interdigitated electrodes were processed on the bottom of a several hundred µm wide channel. The electrohydrodynamically induced liquid streaming occurs in the direction opposite to the propagation of the traveling-electric field.

e.g., 4, 20). Additionally, in rotating fields the particle experiences a torque N B (t) ) m b (t) × E B (t). fCM represents the Clausius-Mosotti factor for the particle (which has been calculated for multishelled particles21,22 ). For a homogeneous particle it has been found to be

fCM )

σp - σl + iω(p - l) σp + 2σl + iω(p + 2l)

(2)

with ω ) 2π/T (T, period of the electric field),  the absolute permittivity (relative permittivity multiplied by 8.86*10-12 As/Vm) and σ the specific conductivity of liquid (index l) or particle (index p). In fields with spatially nonuniform amplitude, the condition for negative dielectrophoresis Re[fCM] < 0 is

ω2(p - 1)(p + 21) + (σp - σl)(σp + 2σ1) < 0 (3) Therefore, if the permittivity or the conductivity of the particle is smaller than that of the liquid, there is a frequency above or below which negative dielectrophoresis occurs. Due to the high permittivity of water, many particles are repelled from electrodes at high frequencies. In the case of living cells suspended in culture media (natural environment) both the effective permittivity and conductivity are smaller than that of the liquid16 (for cells, at least one shell of low permittivity and conductivity representing the membrane has to be introduced). Consequently, negative DEP is found in the whole frequency range (Hz to GHz) under these conditions (Figures 2 and 4). In the experiments presented here, rectangular pulses were used instead of sinusoidal ones. However, in highly (20) Huang, Y.; Wang, X.-B.; Tame, J. A.; Pethig, R. J. Phys. D: Appl. Phys. 1993, 26, 1528. (21) Fuhr, G.; Gimsa, J.; Glaser, R. Stud. biophys. 1985, 108, 149. (22) Huang, Y.; Ho¨lzel, R.; Pethig, R.; Wang, X.-B. Phys. Med. Biol. 1992 , 37/7, 1499.

Figure 4. Normalized dielectrophoretic force Re(fCM) as function of the radian frequency ω of the electric field: (a) liquid, water, r ) 80 (relative permittivity), σ ) 0.25 S/m; particle, erythrocyte modeled as oblate ellipsoid of rotational symmetry (axes ratio 1:2, see ref 23), rinterior ) 50, σ interior ) 0.5 S/m, membrane capacity 0.0082 F/m2, membrane conductivity 0.001 S/m2; (b) liquid (high conductive cell culture medium), r ) 80, σ ) 1.3 S/m; particle, erythrocyte, same parameters as in part a); (c) liquid, r ) 80, σ ) 1.3 S/m homogeneous particle (Sephadex), r ) 40, σ ) 0.001 S/m. Full lines correspond to sinusoidal electric fields, the dashed ones give half the value of Re(fCM) for rectangular driving of the electrodes.

conductive media, the dielectrophoretic force acting on a particle is only slightly dependent on the actual signal form if compared at the same mean square value of the applied electric field (see Figure 4). We prefer rectangular pulses because the voltage can be reduced by a factor of 21/2 compared with sinusoidal signals. The fundamental frequency should be at least some MHz to ensure negative dielectrophoresis (especially in low conductive media, e.g., distilled water or alcohol), to avoid electrolysis and to (23) Gimsa, J.; Schnelle, Th.; Zechel, G.; Glaser, R. Biophys. J. 1994, 66, 1244.

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Figure 5. Isopotential curves and field lines above an ac-driven interdigitated electrode array (section, electrodes are symbolized by black bars).

reduce the induced transmembrane voltage to physiologically tolerable values of a few millivolts. If higher multipoles are neglected, the calculation of forces reduces to the determination of the electric field in the absence of particles. The evaluation of higher moments requires, in general, a self-consistent recalculation of the external field taking into account the changes due to the particle (see below). For the sake of simplicity we will concentrate on fields produced by planar interdigitated electrode arrays. Cartesian coordinates (x,y,z) are defined with y ) 0 in the plane of the electrodes. The electrodes are assumed to be elongated along parallels to the z-axes from z ) -∞ to z ) ∞. Then, only a two-dimensional model has to be investigated. For ac drive of an infinite planar array of electrodes, the potential Φ can be found using the following approach:

Φ(x,y,t) ) Re[2A(x,y) - 1] cos(ωt)

(4)

where the conform mapping24

A(x,y) )

Vp+p K(p)

with

[{

[

F g -cos 2π

]}| ]

x + iy p λ

[x

(z2 + 1)(z - z1)

g(z) ) arcsin

]

(z2 - z1)(z + 1)

is determined by the amplitude Vptp and the geometric parameters

[ ]

z1 ) -cos

[

z2 ) -cos p)

πwel λ

]

π(wel + 2wg) λ

4 sin[πwg/λ]

Figure 6. Contour-plot of time averaged heat production q above an ac-driven interdigitated electrode array: (A) electrode width/interelectrode gap ) 1 spatial average/((Vptp/gap)2 σliq), 0.24 J/(V2 S); (B) electrode width/interelectrode gap ) 1/2 spatial average/((Vptp/gap)2 σliq), 0.33 J/(V2 S); (C) electrode width/ interelectrode gap ) 2 spatial average/((Vptp/gap)2 σliq), 0.14 J/(V2 S). In all three pictures the abscissa ranges from 0 to λ/2 and the ordinate from 0 to λ/4, only half of the two electrodes are shown (black bars).

Averaging over times much larger than 1/ω, the heat production can easily be calculated from Ohm’s law. As can be seen from Figure 6 the heat production mainly occurs within a height of λ/4 (the heating of solution has a period λ/2 in the x-direction, see eq 4) and can be reduced at fixed field strength by reducing the interelectrode gaps (increasing the area of the electrodes). Evaluating eq 1, the y-component of the DEPF can be calculated using the analytic property

∂ ∂ A(x,y) ) -i A(x,y) ∂x ∂y

(1 + sin[πwg/λ])2

λ ) 2(wel + wg) wel denotes the widths of the electrodes and wg that of the gap. F and K represent the incomplete and complete elliptic integral, respectively. λ is the smallest length in which the potential is periodic (see Figure 5). In analogy to the traveling-wave regime discussed below, it is referred to as wavelength. (24) Aoki, K.; Morita, M.; Niwa, O.; Tabei, H. J. Electroanal. Chem. 1988, 256, 269.

to be:

〈Fy(x, y)〉t 2πlR3 Re[fCM]

[ [

) Re Im

] [ ] [

] ]

∂ ∂2 A(x, y) Re 2 A(x, y) + ∂y ∂y

∂ ∂ A(x, y) Im 2 A(x, y) e 0 (5) ∂y ∂y

(in addition there is a component of the DEPF in the x-direction which can be calculated from eq 5 after

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and that of an image dipole (with the same orientation pointing to or away from the electrode surface). Since the equations for the coefficients are rather complicated, they are not given here. Therefore, λ should be chosen as small as possible to allow the DEPF to keep very small particles away and to minimize losses (heating). This makes the investigation of submicrometer electrodes very interesting. For the currently available microstructures, dielectric manipulation is, however, limited to particles with effective diameters (i.e., that of the particle and solvent surface layers) not much smaller than 100 nm (e.g., viruses, ribosomes, macromolecules). Furthermore, adhesion forces become very large in the vicinity of surfaces.25 Scaling laws like R/d2 are typical for the force acting on a spherical particle at a distance d from an infinite plane,26 whereas the DEPF do not diverge in the vicinity of the electrodes (if not near to an edge) and between the electrodes (see Figure 6). If the particle is much larger than λ or if many particles are suspended, the simple dipole approximation will not yield reliable results. However, it can theoretically and experimentally be shown that a sufficiently high negative DEPF will also occur in these cases. We neglect the curvature of a large particle or consider a dense particle suspension as a “carpet” (as is actually observed in our experiments) and assume that the field in the electrode plane can be represented by periodic functions (sin, cos) and consider the force exerted by that field on an infinite plane (“carpet”-liquid interface) at a distance d from the electrode plane. The electric field can now easily be determined using the approach:

{

[

φ(x,y,t) ) Re [bneky + cne-ky]eiωt Figure 7. Contour plot of the dielectrophoretic force acting in the normal direction (y) of the plane above of an ac-driven interdigitated electrode array: (A) electrode width/interelectrode gap ) 1; (B) electrode width/interelectrode gap ) 1/2; (C) electrode width/interelectrode gap ) 2. In all three pictures the abscissa ranges from 0 to λ/2 and the ordinate from 0 to λ/4, only half of the two electrodes are shown (black bars).

replacing on the right hand side the derivatives with respect to y by those of x). According to the contour plots in Figure 7 the repelling DEPF (y-component) becomes widely independent on the location above the electrodes for y > λ/4. For smaller values of the DEPF, the particles are likely to form lines parallel to the electrode strips above the middle of and between the electrodes. This can also be seen by evaluating the x-component of the DEPF. Interestingly, particles which are both much smaller than the width of the electrodes and close to the electrode surface are likely to be attracted to the electrodess independent of their dielectric properties. This can be seen from the following argument. If such a small particle is situated near the electrode surface but not near an edge, then the external field can be assumed to be homogeneous. The interaction between a spherical particle and an infinite metal surface can be calculated up to arbitrary multipole order by introducing image multipoles (placed at the same distance from the metal surface on the vertical but on the other face and with a sign of -1m, where m stands for the multipole order). To see that the particle is likely to be attracted to the electrode, we consider only the dipole momentum (m ) 2). The induced dipole experiences an attraction near the electrode because it is placed in an electric field composed of the applied homogeneous one

eikx cos(kx)

}]

(6)

with the wavenumber k ) 2π/λ satisfying the Laplace equation in each layer (the upper case in braces in eq 6 corresponds to the traveling wave and the lower one to ac driving of electrodes). The coefficients have to be determined from the boundary conditions at the interfaces

B p) × b ey ) B 0 and ((σl + iωl)E Bl y ) d, (E Bl - E B p)‚e by ) 0 (7) (σp + iωp)E y ) 0, φ(x,0,t) )

{

Vptp cos(ωt - kx) 2 cos(ωt) cos(kx)

}

and φ f 0 for y f ∞. This results in a simple linear system of equations. The resulting force can be determined by integration of Maxwell’s stress tensor

F B)

∫

[

 E B En A

E B2 2

]

b e n dA

(8)

where A is the surface of integration and n denotes the “normal direction” and the integration has to be performed on both sides of the liquid-“particle-carpet” interface.27 (25) Kendall, K. Adhesion: Science 1994, 263, 1720. (26) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Nauka: Moscow, 1985; p 322 (in Russian). (27) Landau, L. D.; Lifschitz, E. M. Elektrodynamik der Kontinua, In Lehrbuch der theoretischenPhysik; Akademie-Verlag: Berlin, 1991; Vol. 8, Chapter 16 (in German).

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Figure 8. Dielectrophoretic pressure on an planar interface depending on the distance d between the electrode plane and the interface: ac driving at 3Vptp , 1 MHz; dielectric properties, rl ) 80, σl ) 1 S/m, rp ) 50, σp ) 0.5 S/m (typical value for culture media (l) and cells (p)). Distance units are wavelengths λ ) 2 µm. The absolute value of the adhesion pressure corresponds to a line with slope -3.

If the field is known, the time averaged force per unit area is found to be

Fx 1 ) 〈( - a1)Ex*Ey + (p - a*1)Ey*Ex〉x A 4 p Fy 1 ) 〈( - p)Ex*Ex + (p - aa*1)Ey*Ey〉x A 4 1

(9)

where * denotes the complex conjugate, 〈〉 denotes the average over x, and a reflects the dielectric properties of liquid and particle

a)

σp + iωp σl + iωl

The electric field components in eq 9 have to be evaluated just above the interface (in the particle carpet). To obtain eq 9 the boundary condition between the interfaces at y ) d (eq 7) is used again. As can be seen from eqs 6 and 9, no force component in the x direction exists in the case of ac fields. But in the traveling-wave regime, there is an additional “brushing” over the array (see also refs 9 and 19). The y-component is very similar in both cases. Under the same conditions it is reduced to half in the case of ac. But, with ac, only half of the number of electrodes is needed to obtain the same wavelength λ. Furthermore the “brushing effect” is weaker for smaller particles whereas the repulsion is widely size independent. This is due to the fact that both the DEPF and the buoyancy force scale as R3 with the particle radius; but the friction force scales with R only. The DEPF does not diverge if the distance d between the electrode plane and the “particle carpet” becomes small (see Figure 8 for a typical curve). In contrast, the adhesion force per unit area for two infinite planes scales as 1/d3.26 From the analytic property of the potential (in the case of traveling waves) from eq 9, it follows that repulsion occurs if |a| < 1. This yields only a slightly different condition for the occurrence of negative DEP than eq 2. If both effective permittivity and conductivity of the “particle carpet” are smaller than those of the medium, negative DEP is found over the whole frequency range. The experimental verification of the repelling properties of interdigitated electrodes is shown in Figures 1D, 2, and 3. It is to be expected that very small particles ( λ/4). Then, the electric field can be determined using the eq 6 by solving the linear system of equations for the coefficients resulting from the boundary conditions (eq 7, with the only modification that the index l has to be replaced by that of the layer and p by that of the liquid (l)). The DEPF in the liquid (y g d) is found to be

〈FxDEP〉t ) -πl(kR)3Vptp2 Im[fCM]Abs(c)2e-2k(y-d) 〈FyDEP〉t ) -πl(kR)3Vptp2 Re[fCM]Abs(c)2e-2k(y-d) (10) with

c)

2˜ layerekd ˜ layer(1 + e2kd) + ˜ l(e2kd - 1)

and the complex conductivity ˜ ) σ + iω. Consequently, (28) Mu¨ller, T.; Gerardino, A. M.; Schnelle, Th.; Shirley, S. G.; Fuhr, G.; De Gasperis, G.; Leoni, R.; Bordoni, F. Nuovo Cimento Soc. Ital. Fis., D 1995, 17, 425.

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Figure 10. Particle velocity of a Sephadex G15 sphere above interdigitated electrodes (see Figure 1D) as a function of the square of the applied voltage: 9, with dielectric layer (SiOxNy, 700 nm thick); 4, without dielectric layer; driving conditions, traveling wave, 400 kHz in water (conductivity 1.3 mS/m).

the particle will move at same velocity and height if the voltage is scaled with 1/|c|. But even at the same voltage the particle should move with the same velocity, but at a different height (y - d) determined by the equilibrium of sedimenational force and the repelling force 〈FyDEP〉t. Interestingly, Figure 9 shows different velocity spectra for coated and uncoated electrodessespecially in the lower frequency range. This can be explained as follows. In this experiment the conductivity of the liquid was chosen so that only weak DEPF occurred. This means, the particle (diameter ≈ λ) moves near the electrode plane (at about λ/16 in height for f > 106 Hz) and, as Figure 9 shows, at lower height above the interface for coated electrodes. Near a plane, a sphere of radius R experiences a frictional force that rises with decreasing distance h. Goldmann et al.29 found the asymptotic expression

Fxfriction )

16 h h +O πηR log 5 R R

0

() ()

(11)

The differences in velocity become smaller for higher frequencies (for vanishingly small conductivity of the layer, the value of |c| in eq 10 rises with the field frequency) and vanishes for high voltages (Figure 10)ssince the particles are lifted higher above the surface where friction is simply of the Stokes type. Depending upon the type of particle and the strength of the applied field, speeds from 1 µm/s up to several hundred µm/s can be attained. However, in conductive solutions (>1 S/m) the maximum speed is about 10 times less than at 1 mS/m. Finally, the temperature rise due to Ohmic heating and possible nonthermal effects on cells should be discussed. It is a major problem for application of high field strength to conductive liquids, especially if damage of living cells has to be avoided. For traveling-wave excitation, the time averaged heat production, q, in the liquid is found to be

Therefore, heating cannot be reduced by dielectric layers if the dielectrophoretic force is fixed (see eq 10). The analytic expression for the temperature related to a heating according to eq 12 and a fixed temperature at the bottom (y ) d ) 0, uncoated electrodes) yield a maximum temperature rise (for y f ∞) that is independent of the wavelength λ and proportional to liquid conductivity and square of applied voltage. Nevertheless, the use of ultramicroelectrodes is advantageous for limiting temperature rise. The minimum voltage is determined by the equilibrium of the adhesion force (assumed to be proportional to y-2, see ref 26) and the dielectrophoretic force (eq 10). It can be shown that repulsion of the same particles can be ensured by scaling down the (minimum) voltage with the electrode size as λ1/2. Hence, the maximum temperature rise can be reduced as λ. The assumption of an infinite heating plane does, however, not fully reflect the experimental conditions. The calculation of the actual temperature rise requires a threedimensional approach (for numerics see, e.g., ref 19) which is beyond the scope of this paper. Experimentally, the temperature increase in our structures has been found to be in the range of 1 K (liquid conductivity of 1.3 S/m, at an applied field strength of 1 MV/m between the electrodes of Figure 2), which is not harmful for biological objects. The question arises as to whether cells are damaged by nonthermal effects during repulsion in the strong electric field. Fortunately, cells are typically repelled from the electrodes to a distance of at least an electrode pitch (see Figure 2). There, the field strength is approximately 20 times lower than that between the electrodes (see, e.g., eq 6). Field strength up to 100 kV/m in high-frequency electric fields have been found to be well tolerated by mammalian cells even under prolonged application (In ref 16 it was shown that the characteristic parameters of the growth behavior as anchorage time, lag phase, mobility, and average time of cell cycle remain unchanged.) Under the conditions of Figure 2 (field frequency 5 MHz and this distance) the induced membrane potential is reduced to values below 0.1 V. Preferably, even higher frequencies should be used since the induced membrane potential decreases rapidly with the field frequency in the MHz range. At high frequencies, the interaction of the electric field with membrane enzymes (electroconformational coupling) is unlikely to change the ion transport through the membrane.30 It is possible that, due to differences of dielectric properties, the distribution of proteins in the membrane (e.g., ion channels) is changed in a manner similar to that recently proposed for time independent currents.31 Experimental evidence for this, however, is still missing. The cells shown in Figure 2 were vital during the repulsion and after a few hours of field application they began to build an adherently growing cell carpet on the chip except on the central part. No changes in the cytoskeleton were found between repelled and nonrepelled cells (immunofluorescence staining details will be given in a forthcoming paper). IV. Conclusions

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Force-field structures are particularly interesting for medical technical problems, protection of chemical sensor surfaces, and the development of biocompatible surfaces. It is advantageous to use very small (submicrometer) and flat electrodes because the size of particles that can be repelled is decreased and because the total heating is

(29) Goldman, A. J.; Cox, R. G.; Brenner, H. Chem. Eng. Sci. 1967, 2, 637.

(30) Markin, V. S.; Liu, D.; Gimsa, J.; Strobel, R.; Rosenberg, M. D., Tsong, T. Y. J. Membr. Biol. 1992, 126, 137, . (31) Fromherz, P. Phys. Rev. B: Condens. Mattter 1995, 52/2, 52.

q ) σlk2Vptp2Abs(c)2 e-2k(y-d)

Adhesion-Inhibited Surfaces

reduced. Preferably, the frequency range above 5 MHz should be used as it has the following advantages: (i) The conductivity of the external solution becomes less important and the dielectric properties of the fluidparticle system are dominated by the permittivities. As a result highly conductive fluids like physiological solutions can be used and most particles can be repelled. (ii) The voltage loading of the cell membrane decreases to values of a few millivolts, which is physiologically tolarable.16 (iii) The penetration of the electric field through a thin dielectric layer can be ensured at lower voltages. To gain long term stability, the electrodes have to be covered with thin inert layers (from several nm up to µm). Using structured (inhomogeneous) dielectric layers, it is

Langmuir, Vol. 12, No. 3, 1996 809

additionally possible to create regions of preferential particle adhesion (see also Figure 1D). The further degree of miniaturization that is possible using existing semiconductor techniques can be expected to permit the repulsion of even smaller particles than those studied here, e.g., viruses, ribosomes, and macromolecules. Acknowledgment. We are grateful to Dr. S. G. Shirley for critical reading of the manuscript and to Mr. S. Schmidt for delicate technical manipulations to obtain the microstructures. This work was supported by the BMFT (Grant No. 03120260 A) and the BMFT/VDI (Grant No. 13MV03032). LA950065T