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Anal. Chem. 2001, 73, 5661-5668

Flow Fractionation of Microparticles under a Dielectrophoretic Field in a Quadrupole Electrode Capillary Satoshi Tsukahara, Katsuyuki Yamanaka, and Hitoshi Watarai*

Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

A technique of fractionation for microparticles was proposed that utilized a unique combination of a dielectrophoretic (DEP) field generated by a quadrupole electrode and a laminar flow in a capillary of 82.5 µm in radius. The fabricated capillary possessed four platinum wires in its inside wall as a quadrupole electrode. In a nonuniform electric field generated by the quadrupole electrode, microparticles, such as polystyrene and carbon, in water experienced DEP forces in the radial direction. When a sample solution was pumped in, an ideal laminar flow perpendicular to the DEP force was formed inside the capillary. The microparticles dynamically migrated by the DEP force across the laminar flow while they were carried by the flow. A theoretical model taking the DEP force and the laminar flow pattern into account predicted the elution profiles of the single microparticles quantitatively. The elution times of the microparticles depended on the dielectric properties and the sizes of the microparticles, as well as the voltage and frequency of the applied alternating current. There are a number of separation and characterization methods for molecules and ions, including high-performance liquid chromatography, capillary zone electrophoresis, and solvent extraction. On the other hand, separation and characterization methods of micrometer-sized particles (0.1-10 µm in diameter) in liquids, such as colloids, liposomes or biological cells, are still limited, although new methods are highly required in colloidal chemistry, environmental chemistry, and biological technology. Several techniques reported so far on the separation of microparticles include centrifugation,1 electrophoresis,2 or ultrafiltration. Recently, laser photophoresis3 has been proposed as a new separation technique for microparticles. These techniques can distinguish the differences in electric charge, density, size, or refractivity of particles. As for biological cells, both fluorescence-4 and magneticactivated cell-sorting techniques5 took advantage of the differences in immunological surface markers. * To whom correspondence should be addressed: Phone and fax: +81-66850-5411. E-mail: [email protected]. (1) Bauer, J. J. Chromatogr. B 1999, 722, 55-69. (2) Golovanov, M. V. Cell Electrophoresis; Bauer, J., Ed.; CRC Press: Boca Raton, FL, 1994; pp 181-196. (3) Monjushiro, H.; Hirai, A.; Watarai, H. Langmuir 2000, 16, 8539-8542. (4) Villas, B. H. Cell Vision 1998, 5, 56-61. 10.1021/ac010824e CCC: $20.00 Published on Web 11/06/2001

© 2001 American Chemical Society

The migration of particles in a nonuniform electric field caused by induced dipoles is called as dielectrophoresis (DEP).6 The strength and direction of the DEP force depend on the differences in complex permittivities between the particles and the surrounding liquid medium. “Positive DEP” refers to the behavior that a particle migrates to a region of larger electric field strength and “negative DEP” is the opposite behavior. The DEP technique is applicable to any kind of particles regardless of charges, and this technique provides a noninvasive method for investigating the dielectric properties (permittivity and conductivity) of individual microparticles. DEP was applied for the segregation of dead and living cells,7 or ill and healthy cells.8 Single cells were manipulated with a DEP microelectrode,9 and a metal molybdenum tip was coated with diamond powder by a DEP force.10 Reichle et al. have developed a new microsystem for cell electrorotation measurements combining DEP forces and laser tweezers.11 Since a photolithographic technique allows us to make planar microelectrodes of complicated structure with excellent precision, this type of microelectrode was widely applied for the DEP separation with microscopic observation.7,8,12-17 Recently, we reported a method to observe and analyze DEP migration of single particles quantitatively in a nonuniform electric field formed by a planar quadrupole microelectrode.18-20 (5) Handgretinger, R.; Lang, P.; Schumm, M.; Taylor, G.; Neu, S.; Koscielnak, E.; Niethammer, D.; Klingebiel, T. Bone Marrow Transplant. 1998, 21, 987993. (6) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, 1978. (7) Matsumoto, N.; Matsue, T.; Uchida, I. Bioelectrochem. Bioenerg. 1994, 34, 199-202. (8) Gascoyne, P. R. C.; Huang, Y.; Pethig, R.; Vykoukal, J.; Becker, F. F. Meas. Sci. Technol. 1992, 3, 439-445. (9) Matsue, T.; Matsumoto, N.; Koike, S.; Uchida, I. Biochim. Biophys. Acta 1993, 1157, 332-335. (10) Choi, W. B.; Cuomo, J. J.; Zhirnov, V. V.; Myers, A. F.; Hren, J. J. Appl. Phys. Lett. 1996, 68, 720-722. (11) Reichle, C.; Schnelle, T.; Muller, T.; Leya, T.; Fuhr, G. Biochim. Biophys. Acta 2000, 1459, 218-229. (12) Rousselet, J.; Salome, L.; Ajdari, A.; Prost, J. Nature 1994, 370, 446-448. (13) Fiedler, S.; Shirley, S. G.; Schnelle, T.; Fuhr, G. Anal. Chem. 1998, 70, 1909-1915. (14) Washizu, M.; Suzuki, S.; Kurosawa, O.; Nishizaka, T.; Shinohara, T. IEEE Trans. Ind. Appl. 1994, 30, 835-843. (15) Huang, Y.; Wang, X.-B.; Gascoyne, P. R. C.; Becker, F. F. Biophys. J. 1997, 73, 1118-1129. (16) Velev, O. D.; Kaler, E. W. Langmuir 1999, 15, 3693-3698. (17) Wang, X.-B.; Yang, J.; Huang, Y.; Vykoukal, J.; Becker, F. F.; Gascoyne, P. R. C. Anal. Chem. 2000, 72, 832-839. (18) Watarai, H.; Sakamoto, T.; Tsukahara, S. Chem. Lett. 1998, 279-280. (19) Tsukahara, S.; Sakamoto, T.; Watarai, H. Langmuir 2000, 16, 3866-3872.

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Field-flow fractionation (FFF) is a powerful technique for particle separation, because it possesses high separation resolution, and it can use a large number of fields.21 Many kinds of fields, such as sedimentation, thermal, electrical, or magnetic fields, were applied to FFF, and the segregations of particles by the differences in electric charge, density, size, or magnetic susceptibility were attained. Also, FFF using an ultrasonic standing wave has been carried out for the separation of particles according to their size and acoustic properties.22 The nonuniform electric field was combined with the FFF in order to achieve higher resolution in DEP separation.14,15,17,23 In a DEP-FFF channel, a DEP electrode array is placed on the inner lower wall of the channel and a laminar flow pattern of solvent is generated above the electrode. The linear velocity of solvent in the laminar flow is a function of the distance from the electrode array of the channel; it is fastest at the center height of the channel and slowest at the channel wall. A microparticle is levitated at the position where its DEP and gravitational sedimentation forces are balanced, and some microparticles were separated by the laminar flow. This technique has an advantage that a little difference in DEP force results in a relatively larger difference in elution time than the previous DEP multichannel technique. The present study proposes a novel concept and technique for controlling the dynamic migration of microparticles in a capillary having a quadrupole electrode in its inside wall. The established method is considerably different from the conventional FFF methods; particles in the capillary do not show any equilibrated position where two opposite forces are equalized. However, we believe that the present method belongs to the category of FFF. EXPERIMENTAL SECTION Chemicals and Apparatus. Polystyrene carboxylate microparticle (Polybead carboxylate Sampler Kit-I, 3.0 ( 0.1 µm in diameter) and polystyrene microparticle (Polybead polystyrene microspheres, 14.6 ( 1.7 µm in diameter) certified as particle size standards were purchased from Funakoshi Co. (Tokyo), and carbon microparticle (4.4 ( 0.6 µm in diameter) was obtained from Biotech Research Co. (Saitama). Other reagents were of analytical reagent grade. To minimize the effect of the buoyancy during DEP, the density of the aqueous solution was adjusted to that of the microparticles with urea. Urea is highly soluble in water and has no charges, and furthermore, its aqueous solutions have a viscosity as low as water. The increase in the conductivity causes the electrolysis of the electrode and Joule heating, and the increase in the viscosity causes retardation of particle velocity. A urea aqueous solution of 18.8% (by weight) was adopted to adjust the density of the polystyrene microparticles (1.05 g cm-3).24 The urea solution has 1.16 × 103 Pa s in viscosity at 20 °C,24 and the viscosity of the urea solution was estimated as 1.03 × 103 Pa s at 25 °C.25 In the (20) Watarai, H.; Sakamoto, T.; Tsukahara, S.; Langmuir 1997, 13, 2417-2420. (21) Schimpf, M. E.; Caldwell, K.; Giddings, J. C. Field-Flow Fractionation Handbook; John Wiley & Sons: New York, 2000. (22) Johnson, D. A.; Feke, D. L. Sep. Technol. 1995, 5, 251-258. (23) Davis, J. M.; Giddings, J. C. Sep. Sci. Technol. 1986, 21, 969-989. (24) CRC Handbook of Chemistry and Physics, 80th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, 1999; p 8-83, 12-60. (25) By assuming that the ratio of viscosity of pure water to that of the urea solution is maintained at every temperature, the viscosity of the urea solution at 25 °C was estimated.

5662 Analytical Chemistry, Vol. 73, No. 23, December 1, 2001

Figure 1. Schematic illustration of the planar DEP cell having hyperbolic quadrupole microelectrode and the wiring system. Black regions are microelectrodes on a glass substratum, which are made of chromium (lower layer, 100 nm in thickness) and gold (upper layer, 50 nm), and the inscribed circle indicates the working area (radius, d ) 65 µm). A gradient of square electric field strength (∇|E|2) of the nonuniform electric field generated by the quadrupole electrode is also schematically displayed as a function of the position of the working area. The DEP force is proportional to ∇|E|2.

case of carbon microparticles, 18.8% urea and 0.001% (by weight) Triton X-100 aqueous solution was employed. The nonionic surfactant was used for the dispersion of the uncharged carbon microparticles. In each case, the solution was filtrated with a membrane filter (pore size, 0.45 µm) before being used for the preparation of the microparticle suspension. The conductivity of the medium was measured as σm ) 5.4 × 10-2 S m-1. The concentration was 1.3 × 10-3% for each polystyrene microparticle and 2.5 × 10-3% for the carbon microparticle. The pH of the aqueous solution was 7.7. Conductivity was measured with a conductometer (CM-40V, TOA Electronics, Tokyo). A planar DEP cell with a hyperbolic quadrupole microelectrode, shown in Figure 1, was the same as the cell reported previously.20 One electrode and its opposite electrode were wired to be the same polarity of alternating current (ac). Ac was applied with a function generator (FG-273, Kenwood). An ideal nonuniform electric field was generated by the quadrupole electrode. The gradient of square electric field strength (∇|E|2) is also shown schematically in Figure 1 as a function of the position of the working area.26 ∇|E|2 increases proportionally with the radial distance, and DEP force is also proportional to the ∇|E|2 value. Thus, the DEP force linearly increases with an increase in the radial distance. The DEP behavior of the microparticles in the planar quadrupole microelectrode was observed using a microscope (BX60, Olympus) equipped with a cooled CCD camera (ImagePoint, Photometrix). DEP Behavior of Single Microparticles in Planar Quadrupole Microelectrode.20 An aliquot (3 µL) of the sample solution was dropped into the working area of the planar DEP cell, and a small glass cover plate (3 × 3 × 0.14 mm thick) was placed on it. An applied voltage (Urms, root-mean-square) was fixed to 3.5 V, and the frequency (f) of ac was changed in the range of 1.0 kHz1.0 MHz by the function generator. Experiments were performed in a thermostated room at 25 ( 1 °C. The distance (R) from the DEP cell center to a microparticle was obtained as a function of time. The working area (65 µm in radius) of the DEP cell was observed under the microscope with the CCD camera, and the image was recorded using a video cassette recorder. The recorded image was then transferred as a digital picture to a personal computer at certain time intervals. (26) Huang, Y.; Pethig, R. Meas. Sci. Technol. 1991, 2, 1142-1146.

quadrupole was shown in the previous reports.19,20 Briefly, when an ac voltage, Up cos(ωt), is applied to the quadrupole microelectrode, the time-averaged motive force 〈FDEP〉 of the particle caused by DEP is expressed as18-20,27

〈FDEP〉 ) 2πβrDEP3m∇|Erms|2Re[Ke] ) β

4πrDEP3mRUrms2Re[Ke] d4

(1)

where ω is the angular frequency () 2πf) of ac; β, the efficiency of DEP force; rDEP, an effective DEP radius of the microparticle; m, the permittivity of the medium; Re[Ke], the real part of the Clausius-Mossotti factor Ke; R, the radial distance of the particle from the quadrupole center; and d, the radius of the inscribed circle in the working area of the microelectrode (65 µm for the planar DEP cell; see Figure 1). Urms2 is equal to Up2/2. The frictional force that a migrating spherical particle undergoes from a medium is given by the Stokes equation Figure 2. Schematic illustration of the fabrication procedure for the DEP capillary with a quadrupole electrode: (a) put two fluorocarbon lines (49 µm in radius) and a platinum wire on a glass plate; (b) cover them with a sheet of glassine paper; (c) put two platinum wires and a fluorocarbon line (82.5 µm in radius) on the paper; (d) cover them with another paper; (e) put two fluorocarbon lines and a platinum wire on the second paper; (f) tie the whole with fine threads; (g) remove the papers; (h) fix the whole by epoxy adhesive; (i) remove the center fluorocarbon line; and (j) photograph of the cross section of the fabricated DEP capillary, where the black and white regions are platinum wires and fluorocarbon lines, respectively.

Fabrication of DEP Microcapillary. Four platinum wires (50 µm in radius), two kinds of fluorocarbon lines (49 and 82.5 µm in radius), thin glassine paper, and epoxy adhesive were used to fabricate a DEP microcapillary. Figure 2a-i shows the outline of the fabrication procedure. All procedures were carried out under a microscope. Figure 2j shows a photographic image of a cross section of the fabricated capillary before removing the center fluorocarbon line. The center line was positioned just at the center, and the other lines and wires were located symmetrically. The fabricated DEP capillary was 2.35 cm in length. Elution Time of Single Microparticles from the DEP Capillary. After the center fluorocarbon line (82.5 µm in radius) was removed, a silica capillary (75 µm, outer radius; 37.5 µm, inner radius) and a glass tube (330 µm, outer radius; 95 µm, inner radius) were connected just at the entrance and exit of the DEP capillary, respectively. Sample solutions were introduced to the DEP capillary using a microsyringe through the silica capillary. The microsyringe was set to a syringe pump (model 11, Harvard) to supply the sample solutions at a constant flow rate (Q ) 5.0 µL h-1 or 15.0 µL h-1). Urms and f of ac were changed in the range of 0.071-7.1 V and 1.0 kHz-1.0 MHz, respectively. Single microparticles at the inlet and outlet of the DEP capillary were detected using a microscope, and the elution time of the microparticles was measured. THEORETICAL DEP in Quadrupole Microelectrode. The detailed method of analysis for DEP in a nonuniform electric field formed by the

FSt ) 6πηre

dR dt

(2)

where η is the viscosity of the medium and re, the intrinsic particle radius. From eqs 1 and 2, the radial distance, R(t), of the particle is expressed as a function of time, t, as

ln R(t) ) Rt + ln R0

(3)

where R0 is the R value at t ) 0, and R is a DEP mobility coefficient defined as

R)β

2rDEP3mUrms2Re[Ke] 3reηd4

(4)

Re[Ke] is expressed in the frequency range used in the present study (1.0 kHz - 1.0 MHz) as

Re[Ke] ≈

σ p - σm σp + 2σm

(5)

where σp and σm are conductivities of the particle and the medium, respectively. Dynamic Traveling of Microparticles in the DEP Capillary. Figure 3 displays the schematic illustration of the movement of microparticles in the DEP capillary having a quadrupole electrode in its inside wall. We define the Cartesian axes (x, y, and z) and the radial distance, R () xx2+y2), as shown in this figure. When the solvent is supplied to the DEP capillary by a pump from the right-hand side in Figure 3a, a laminar flow is generated in the capillary. The linear velocity, v(R), (in µm s-1) of the laminar flow is a function of R at a flow rate of Q as28

v(R) )

2Q 2 (d - R2) πd4

Analytical Chemistry, Vol. 73, No. 23, December 1, 2001

(6) 5663

Figure 3. The principle of the flow fractionation under a dielectrophoretic field in a quadrupole electrode capillary and the definition of the x, y, and z axes. (a) Combination of a laminar flow and the negative or positive DEPs, (b) cross-sectional view of the capillary showing the negative or positive DEPs.

where d is the inner radius of the capillary. This equation means that the linear velocity is fastest at the capillary center (R ) 0) and lowest at the capillary wall (R ) d). In a nonuniform electric field formed by the quadrupole electrode, the microparticle undergoes a positive or negative DEP force (eq 1), depending on its dielectric properties. As a result, the microparticle migrates in the radial (x or y) direction, and its R value is expressed by eq 3. At the same time, it is carried to the z direction by the laminar flow at the linear velocity, depending on the R value as eq 6. When a microparticle shows negative DEP under a certain condition, the microparticle is carried faster by the laminar flow, and vice versa, as shown in Figure 3a. A combination of DEP force and the laminar flow pattern can control the elution time of microparticles. RESULTS AND DISCUSSION DEP in a Planar Quadrupole Microelectrode. There are sulfonate groups as well as carboxylate groups on the surface of the polystyrene carboxylate microparticle,29 whereas on the surface of the polystyrene microparticle, sulfonate groups exist that come from polymerization initiators.29 It was reported that the surface conductivity, as well as the intrinsic (or inner) conductivity, of particles affected their DEP migrations14,19 and electrorotations.30,31 The contribution of the surface conductivity was larger in a lower frequency range, and this effect was partially attributable to the movement of ions (or dynamic ion cloud) around the particle. Therefore, positive DEPs were observed in a lower frequency range as a result of the higher surface conductivity than media σm, and negative DEPs were detectd in a higher frequency range as a result of the lower intrinsic conductivity of particles. We quantitatively analyzed the influence of the surface conductivity and dynamic ion cloud on the DEP migration by the following equations,19

rDEP )

rDEP,l - re 2 2

1+ωτ

+ re σp )

2λ0 rDEP(1 + ω2τ2)

+ σp,h (7)

where rDEP,l was the DEP radius at the limiting low frequency (27) Benguigui, L.; Lin, I. J. J. Appl. Phys. 1982, 53, 1141-1143. (28) Miyake, S. Butsurigaku Tsuron I (General Physics I); Saiensu-sha Co., Ltd.: Tokyo, 1976. (29) Zhao, J.; Brown W. J. Colloid Interface Sci. 1996, 179, 255-260.

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Figure 4. Plot of the DEP mobility coefficient, R, against the frequency, log f, for the polystyrene microparticles of different diameters, (O) 3.0 and (b) 14.6 µm. Urms ) 3.5 V. The detailed experimental conditions are shown in Table 1. The solid lines are the fitting curves by eqs 4, 5, and 7. The parameters for 3.0 µm polystyrene were obtained from ref 19. Table 1. Intrinsic Radius (re), the DEP Radius (rDEP,l) at the Limiting Low Frequency, the σp at the Limiting Low Frequency, the Conductivity (σp,h) at the Limiting High Frequency, the DEP Relaxation Time (τ), and the Efficiency (β) of the Polystyrene Carboxylate Microparticle in the KCl Systema and Those of the Polystyrene Microparticle in the Urea System medium

re/µm rDEP,l/µm σm/S m-1 σp(ω f 0)b/S m-1 σp,h/S m-1 τ/µs β corr coef

KCl, 2.9 × 10-3 M

urea, 18.8 wt %

1.5 2.06 ( 0.06 4.17 × 10-2 (1.10 ( 0.05) × 10-1 0.022 ( 0.004 8(1 0.39 0.998

7.3 7.8 ( 0.1 5.44 × 10-2 (2.32 ( 0.04) × 10-2 0c 0.55 ( 0.35 0.14 0.99

a Ref 19. b Calculated using eq 7. c The σ p,h value was fixed as 0 in this fitting.

(ω f 0); τ, the DEP relaxation time; λ0, the surface conductivity of the particle at the limiting low frequency (ω f 0); σp,h, the conductivity of the particle at the limiting high frequency (ω f ∞). Figure 4 shows the plot of R against log f for polystyrene microparticles of different sizes (3.0 and 14.6 µm in diameter). The larger particles did not show anomalous positive DEP in the whole frequency range observed (1.0 kHz - 1.0 MHz), implying a larger contribution of the intrinsic conductivity and a smaller contribution of the surface conductivity. The DEP parameters were obtained by fitting the observed points in the figure to eqs 4, 5, and 7, as listed in Table 1, where a typical value for microparticles, 9.1 × 10-8 S, was used as the value of λ0.32 The solid lines in the figure show the regression curves calculated using the obtained parameters, which are in good agreement with the observed points. In the previous report, we already showed that the values of R and the dependence of R on f for the polystyrene and polystyrene carboxylate microparticles were close to each other.19 (30) Arnold, W. M.; Schwan, H. P.; Zimmermann, U J. Phys. Chem. 1987, 91, 5093-5098. (31) Gorre-Talini, L.; Jeanjean, S.; Silberzan, P. Phys. Rev. E 1997, 56, 20252034. (32) Paul, R.; Kaler, K. V. I. S.; Jones, T. B. J. Phys. Chem. 1993, 97, 47454755.

Figure 5. A laminar flow pattern measured from the linear velocity, v, of microparticles (14.6 µm in diameter) against the radial distance, R, at the outlet of the capillary without a DEP field in 18.8% aqueous urea solution at a flow rate of Q ) 15.0 µL h-1. The solid line represents the fitting curve by eq 6.

The smaller σp(ω f 0) value for the larger particles clearly means the smaller contribution of the surface conductivity. The efficiency, β, depends on the geometric relationship between the electrode and particle sizes, because the electrode thickness (0.15 µm) is smaller than the microparticle size,18 and thus, the smaller value of β obtained for the larger particle is qualitatively reasonable. Laminar Flow in the DEP Capillary. At first, the generation of a laminar flow in the capillary was assured by transport of microparticles without DEP field. It was postulated that the laminar flow had only the component of the z-direction, and thus, the x and y positions of a microparticle at the inlet should be kept through the capillary. Hence, microparticles were considered to be carried through the DEP capillary by the laminar flow at a fixed linear velocity depending on the initial x and y positions. By using two microscopes, x and y positions of microparticles at the outlet of the DEP capillary were measured and their R values were calculated. Figure 5 shows the plot of linear velocity, v, against R values of single microparticles at the outlet, where the v values were calculated from the length of the DEP capillary, l, and the elution time, te, as v ) l/te. As was expected, the linear velocity depended on the R value, although the observed points were somewhat scattered. The solid line in the figure shows a regression curve of eq 6, which reproduces the observed points. As a fitting parameter, the Q value was obtained as 15.5 ( 1.2 µL h-1 by fixing d ) 82.5 µm, which was in good agreement with the set value, 15.0 µL h-1. These facts confirmed the generation of the laminar flow in the capillary; however, the v values around 80 µm were relatively larger than the line, suggesting that the microparticles did not approach the capillary wall closely. The particles that were used had a diameter of 14.6 µm, and thus, the maximum R value was expected to be 75.2 µm () 82.5 - 7.3 µm). In comparison with the theoretical line in Figure 5, the maximum R value was estimated to be about 70 µm on average, that is, about 5 µm smaller than the expected value. This disagreement may be caused by an inhomogeneity of the capillary cross section or a roughness of the wall. The dimensionless Reynolds number, NRe, can be used for the criterion of a flow pattern; a laminar flow for NRe < the critical NRe, and a turbulent flow for NRe > the critical NRe. The critical NRe depends on the roughness of the inner wall, but its common value is 2 100-4 000. For the present capillary, the NRe values were

Figure 6. Effect of the ac voltage on the elution profile of polystyrene microparticles (14.6 µm in diameter) at f ) 1.0 MHz (negative DEP regime) in 18.8% aqueous urea solution at a flow rate of Q ) 15.0 µL h-1. (a) No ac voltage; Urms ) (b) 0.071, (c) 0.21, (d) 0.35, (e) 1.2, (f) 2.1, and (g) 3.5 V. Arrows indicate the elution time ranges calculated with eq 8 by setting the initial region of R0 from 0 to 70 µm.

calculated as 1.7 and 5.1 at Q ) 5.0 and 15.0 µL h-1, respectively, which were much less than the critical NRe, predicting a laminar flow in the capillary. Independence of DEP Migration from Laminar Flow. As shown in Figure 4, the microparticles behaved in the negative DEP at f ) 1.0 MHz. Figure 6 shows the effect of Urms on the elution profile of polystyrene microparticles (14.6 µm in diameter) at this frequency. With an increase in the ac voltage, the elution time was shortened, and its deviation became smaller. This fact meant that the increase in the ac voltage raised the negative DEP force that moved the particles to the capillary center, and the particles tended to be carried faster in the z direction. The relatively larger deviation may be caused by the deviation of the microparticle size as well as randomized positioning at the entrance. A model calculation was carried out for prediction of the elution time. The z position, z(t), of a microparticle at time, t, is expressed by integrating the linear velocity by t as

z(t) )

∫ v(R(t)) dt t

0

(8)

where the radial distance at time t, R(t), is given by eq 3. We set z(0) ) 0, meaning that the microparticle is located at the entrance (z ) 0) at t ) 0. z(t) is calculated with only R0 and R values, and this calculation predicts the elution time of the microparticle, because the length of the DEP capillary is known. To estimate R values in the DEP capillary, the following assumptions were made for the efficiency, β. In the case of the planar DEP cell, the β value was found to be 0.3918 and 0.14, depending on the particle size (see Table 1), because the thickness of the electrode (0.15 Analytical Chemistry, Vol. 73, No. 23, December 1, 2001

5665

Figure 8. Fractionation of polystyrene (3.0 µm in diameter, black bars) and carbon microparticles (4.4 µm in diameter, white bars) in the DEP capillary with a quadrupole electrode at Q ) 5.0 µL h-1: (a) without DEP field; (b) elution profiles at f ) 1.0 MHz, Urms ) 7.1 V. The elution time of the polystyrene microparticle was shortened by the negative DEP, whereas that of carbon microparticle was delayed to >700 s. Figure 7. Effect of switching of the condition from a negative DEP regime (f, 1.0 MHz; Urms, 7.1 V; 60 s) to a positive DEP regime (f ) 1.0 kHz; Urms, 3.5 V) on the elution profile of polystyrene microparticles (3.0 µm in diameter) in 18.8% aqueous urea solution at Q ) 5.0 µL h-1. (a) Illustration of the procedure. After applying the ac at the high frequency, the ac at the low frequency (f, 1.0 kHz) was applied for (b) 0, (c) 30, (d) 60, and (e) 90 s.

µm) was less than the microparticle size. The β value for the capillary was assumed to be unity, since the particles were completely inside the nonuniform electric field generated by the quadrupole electrode. The inner radius, d, of the DEP capillary was set to the intrinsic value of 82.5 µm. The ranges of calculated elution time were superimposed with arrows in Figure 6, which agreed well with the observed elution times. In other words, it was confirmed that the DEP migration of the microparticles and the laminar flow independently and collaboratively affected the elution of the microparticles. We investigated joule heating in the planar DEP cell with the quadrupole electrode in detail. When σm and Urms were 7.01 × 10-2 S m-1 and 3.54 V, respectively, the joule heating results in 1.8 × 10-6 J s-1. This corresponded to only 1.4 × 10-4 K s-1 for 3 µL aqueous solution, even if the heating was insulated.20 A detailed examination of joule heating for this DEP capillary was not carried out, but the geometry of the electrode in it is similar to that of the DEP cell, and a similar order of magnitude of heating should be estimated, that is, negligibly small. It was also confirmed by the fact that the theoretical calculations agreed well with the experimental results. As shown in Figure 4, the polystyrene microparticle that was 3.0 µm in diameter showed positive and negative DEPs at 1.0 kHz and 1.0 MHz, respectively. Figure 7a displays the schematic drawing of a switching operation. A model calculation showed that the particle migrated to the capillary center within 60 s under the conditions of f ) 1.0 MHz, Urms ) 7.1 V, and Q ) 5.0 µL h-1. Just after one single microparticle entered, the ac (f ) 1.0 MHz, Urms ) 7.1 V) was applied for 60 s to produce the negative DEP, and 5666 Analytical Chemistry, Vol. 73, No. 23, December 1, 2001

then the conditions were switched to the positive DEP regime. Figure 7b shows the elution profile without positive DEP after applying the negative DEP force, confirming that the microparticles migrated to the capillary center (R ) 0) by the negative DEP force and that their radial positions were maintained through the following transport. Figure 7c-e displays the elution profiles as a function of the applied period of the ac of low frequency (f ) 1.0 kHz, Urms ) 3.5 V), that is, the positive DEP. With the increase in the period of the positive DEP, the elution time tended to be dragged. These results imply that the microparticles migrated to the capillary wall across the laminar flow at the positive DEP regime. This shows that one can control the elution behavior by switching the DEP conditions. Separation by the Difference in Intrinsic Conductivity of Microparticles. As given in the previous report,18 the carbon microparticle showed only positive DEP independent of ac frequency (1.0 kHz - 1.0 MHz). This fact was explained by eq 5, because the carbon microparticle was a conductor, and thus, it possessed much higher conductivity (σp ) 2 × 104 S m-1) than the aqueous solutions. Figure 8a displays the elution profiles of the polystyrene (3.0 µm in diameter) and carbon microparticles. Without the DEP field, the elution profile of the carbon microparticle was close to that of the polystyrene microparticle, that is, no separation between these microparticles. The similarity indicated no serious interaction between the carbon microparticle and the capillary wall. Figure 8b displays the elution profiles at the ac of high frequency (f ) 1.0 MHz, Urms ) 7.1 V). The polystyrene microparticles gave shorter elution time than Figure 8a because of their negative DEP, whereas the carbon microparticles were not eluted from the DEP capillary within 700 s because of their positive DEP. Figure 8b demonstrates an instance of absolute separation by the difference in intrinsic conductivity of microparticles with a DEP field of high frequency. Separation by the Difference in Surface Conductivity of Microparticles. The intrinsic conductivity of polystyrene, σp, was much smaller than the conductivity of aqueous media, σm, and

Figure 9. Fractionation of polystyrene microparticles of 3.0 in diameter (black bars) and 14.6 µm in diameter (white bars) in the DEP capillary with a quadrupole electrode at Q ) 5.0 µL h-1: (a) without DEP field; (b) applying a DEP field at f ) 1.0 kHz, Urms ) 1.8 V.

therefore, the Re[Ke] was simply calculated as -0.5 from eq 5. This seems to predict that the magnitude of the DEP force, FDEP, on the polystyrene microparticles depends on their sizes, rDEP, but that the direction of FDEP is always negative independent of their sizes, as shown in eq 1. However, the observed behavior was more complicated. The ion cloud, as well as the surface conductivity, had significant effects on the magnitude and the direction of the DEP force on the microparticles.19 As shown in Figure 4, the two kinds of polystyrene microparticles of different diameters showed opposite DEP behaviors at lower frequency. The larger microparticle (14.6 µm in diameter) showed a negative DEP at f ) 1.0 kHz, as expected simply from eq 5, but the smaller microparticles (3.0 µm in diameter) gave a positive DEP at this frequency by the significant contribution of the surface conductivity. This result suggests that the DEP technique is promising for the characterization of the surface conductivity of microparticles with high sensitivity. Figure 9 demonstrates the separation of the microparticles by the difference in surface conductivity. Without the DEP field, the elution profiles of both polystyrene microparticles (3.0 and 14.6 µm in diameter) were indistinguishable (Figure 9a). Figure 9b displays one result with a DEP field of low frequency (1.0 kHz). The larger microparticles were eluted at the fastest velocity owing to the negative DEP, whereas the smaller ones were eluted slower, and the two kinds of polystyrene microparticles were separated. Comparison with the Previous DEP-FFF. The first report on the DEP-FFF technique employed a ribbonlike channel possessing a planar electrode on the inner lower wall, where a particle underwent a pair of forces of opposite direction, that is, DEP and gravitational (or buoyancy) forces, perpendicular to the laminar flow.14,15 The strength of the DEP force on the particle increased as it approached the wall, whereas the gravitational force was independent of the horizontal position. This system has a large benefit that when some kinds of particles of the same density undergo DEP forces of the same direction but of different strengths, they show different horizontal positions and are segregated by the laminar flow. In the case of a uniform DEP

field (∇|E|2 is a nonzero constant), only when a DEP force and a gravitational force on a particle are equalized by chance, it is located at the middle position between the upper and lower walls; in other cases, particles are elevated to the upper wall or sedimented to the lower wall. The DEP-FFF method using the ribbonlike channel has various advantages, but there are some difficulties. The bottom electrode was a metal plate array of small bits of 20-50 µm in width. Maximum peaks of ∇|E|2 exist on and above the edges of the metal bits,11,15,16 resulting in a modulated electric field along the laminar flow. Therefore, the quantitative evaluation of ∇|E|2 and, thus, that of DEP forces, were hard to be done. Furthermore, a complicated relation among dielectric properties (ClausiusMossotti factor; eq 5), particle size, and density influenced the elution. In the system proposed in the present paper, the movement of particles is dynamic and somewhat complicated, but ∇|E|2, DEP forces, and trajectories of particles are easily calculated quantitatively. Furthermore, DEP forces are also experimentally measured by the planar DEP cell. The quadrupole electrode of the capillary can generate a larger ∇|E|2 in a limited space than the ribbonlike channel, and it generates a continuous electric field along the laminar flow. The efficiency of the continuous electric field per unit length along the laminar flow is higher than that of an undulated electric field. CONCLUSIONS The present study proposed a new concept and technique of fractionation of single microparticles under a DEP field in the capillary for the first time, where microparticles dynamically migrated across the laminar flow by DEP force. We established the fabrication method of the micrometer-sized DEP capillary of 82.5 µm inner radius, and we confirmed a uniform laminar flow in it. Next, we demonstrated that the DEP capillary could separate various kinds of microparticles of different inner conductivity, surface conductivity, geometric radius, or ion cloud radius, which were difficult to separate by the common method, such as electrophoresis or convenient FFFs. The theoretical model predicted the elution times of the microparticles by DEP parameters, which were determined by the experiments with the planar DEP cell and the laminar flow pattern in the capillary. In the present method, since the differences in DEP behavior are enhanced by the laminar flow in the capillary, even microparticles showing small differences in DEP mobility would also be separable. This DEP capillary cannot treat a large number of particles at the same time because of the small cross-sectional area. However, it is more suitable to analysis and characterization of single microparticles, because the performance per unit length is higher. The present method has no relaxation time at the sample introduction, in contrast to the conventional FFF. Instead of relaxation time, the injection position of sample at the entrance of the DEP capillary should be controlled to reduce the deviation of the elution time, for example, use of a thin needle or precapillary for negative DEP. The DEP capillary does not distinguish particles showing only negative DEP at any frequency, but this can be overcome by a revision of the sample injection. We are now applying the DEP capillary to the separation of single DNA molecules (about 40 kbp). The DEP force is, in Analytical Chemistry, Vol. 73, No. 23, December 1, 2001

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general, proportional to the particle volume and d-4, as shown in eq 1 (d is the inner radius of quadrupole), and thus, thinner DEP capillaries are better for the characterization and separation of smaller (submicrometer) particles and macromolecules, such as proteins and DNA. Furthermore, biological cells, such as leukocytes, possessing their functional structures on their surface, should be well-characterized and separated by DEP-FFF, because DEP is sensitive to the surface properties of particles. DEP-FFF is also promising for the separation of microparticles because of the differences in permittivity under a higher fre-

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quency, such as 10 MHz-1 GHz. Because some industrial materials have relatively larger permittivities, for example, SrTiO3 (332), WO3 (300), rutile TiO2 (86 ⊥, 170 //),24 they will be effectively separated by the DEP-FFF technique from the other materials at the higher frequency.

Received for review July 23, 2001. Accepted September 10, 2001. AC010824E