Langmuir 1997, 13, 2417-2420
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In Situ Measurement of Dielectrophoretic Mobility of Single Polystyrene Microparticles Hitoshi Watarai,* Takashi Sakamoto, and Satoshi Tsukahara Department of Chemistry, Graduate School of Science, Osaka University, Machikaneyama, Toyonaka, Osaka, 560 Japan Received October 31, 1996. In Final Form: February 11, 1997X
Introduction A number of separation and characterization methods for molecules, including high-performance liquid chromatography, capillary zone electrophoresis, and solvent extraction, have been widely applied in many fields. However, for relatively large particles (0.1-10 µm in diameter), such as colloids, liposomes, and biological cells, there are few methods available for separation and characterization, e.g., ultrafiltration, zonal centrifugation, field-flow fractionation (FFF),1 and electrophoresis. In these techniques, only differences in electric charge, density, or size of particle are measurable. To develop the colloidal characterization or separation, it is required to construct new methods to measure other properties of particles, such as conductivity, permittivity, and refractivity. The motion of particles, with a dielectric permittivity different from that of the surrounding liquid medium, in a nonuniform electric field was termed by Pohl as dielectrophoresis (DEP).2 The strength and direction of the DEP force depend on relationships between dielectric properties (permittivity and conductivity σ) of the particles and those of the medium. “Positive DEP” means that a particle is attracted to a region of stronger electric field, and “negative DEP” is the opposite phenomenon.2 Using DEP, it has been demonstrated that dead and living cells3-5 and ill and healthy cells6 can be distinguished, that protoplasts can be collected to fusion them,7 and that mineral-powder mixtures can be separated into their component parts.8 Recently it was reported that a single cell can be manipulated with a DEP microring-ring electrode9 and that a metal molybdenum tip is coated with diamond powder with DEP force.10 The DEP technique is applicable to all kinds of particles. Furthermore, this technique provides an attractive noninvasive method for investigating the electrical properties of individual particles, colloids, and cells. In analytical chemistry, various kinds of particles or colloids are utilized, e.g., ion-exchange or chelating resin, chemically bonded silica gel, microcapsules, microemulsions, zeolite, and clay, but no DEP study on these particles has been found in this field. X
Abstract published in Advance ACS Abstracts, April 1, 1997.
(1) Giddings, J. C. Unified Separation Science; John Wiley & Sons: New York, 1991. (2) Pohl, H. A. Dielectrophoresis; Combridge University Press: Cambridge, 1978. (3) Ting, I. I.; Jolley, K.; Beasley, C. A.; Pohl, H. A. Biochim. Biophys. Acta 1971, 234, 324. (4) Pohl, H. A.; Crane, J. Se. Biophys. J. 1971, 11, 711. (5) Iglesias, F. J.; Lopez, M. C.; Santamarı´a, C.; Dominguez, A. Biochim. Biophys. Acta 1984, 804, 221. (6) Gascoyne, P. R. C.; Huang, Y.; Pethig, R.; Vykoukal, J.; Becker, F. F. Meas. Sci. Technol. 1992, 3, 439. (7) Zimmermann, U. Biochim. Biophys. Acta 1982, 694, 227. (8) Verschure, R. H.; Ijlst, L. Nature 1966, 211, 619. (9) Matsue, T.; Matsumoto, N.; Koike, S.; Uchida, I. Biochim. Biophys. Acta 1993, 1157, 332. (10) Choi, W. B.; Cuomo, J. J.; Zhirnov, V. V.; Myers, A. F.; Hren, J. J. Appl. Phys. Lett. 1996, 68, 720.
S0743-7463(96)01057-8 CCC: $14.00
Figure 1. DEP cell with a hyperbolic quadrupole microelectrode and an electric field formed in the central area. (a, top) Photograph of the DEP cell with microelectrodes. Black regions are microelectrodes, and the circle (broken line) shows the working area. The electrodes are made of chromium (lower layer, 100 nm thickness) and gold (upper layer, 50 nm), which are evaporated on a glass plate. Radius of the circle is 65 µm. (b, bottom) DEP factor, ∇|Erms|2, in the working area, which was calculated with eq 4 and Urms ) 3.54 V. ∇|Erms|2 is weakest at the cell center (0, 0) and linearly increases with the distance from the center.
The DEP technique is especially useful when only a few particles or even one is available. However, the global DEP migration of particles in a system was commonly observed so far.2,6,11 Nowadays, there is an effective method of investigating the DEP behavior of a single particle, i.e., a static levitation method, where particles are held by DEP force against gravity.12,13 Some experiments have been done with this technique, and theoretical discussions were carried out.13,14 On the other hand, the theoretical treatment of DEP migration for a single particle has been scarcely reported, although control of the DEP migration of a single particle would lead to more effective separation. In this report, we present an apparatus to observe and a method to analyze the DEP migration of a single particle in a nonuniform electric field. Experimental Section Chemicals and Apparatus. Polystyrene carboxylate latex particles (3.00 µm in diameter) used as certified particle size standards were purchased from Funakoshi Co. (Tokyo). A sample containing 2.1 × 106 particles was suspended in 20 mL of an aqueous solution containing (0-5.0) × 10-3 M KCl and 2.6 × 10-7 M Rhodamine B (Wako, Kyoto). Solution pH ranged from 6.08 to 6.80. To change the conductivity of the aqueous solution, KCl was added. The particles were aged with fluorescent Rhodamine B to aid in observing the behavior of the particles (11) Santamarı´a, C.; Iglesias, F. J.; Domı´nguez, A J. Colloid Interface Sci. 1985, 103, 508. (12) Kaler, K. V. I. S.; Jones, T. B. Biophys. J. 1990, 57, 173. (13) Jones, T. B.; Kraybill, J. P. J. Appl. Phys. 1986, 60, 1247. (14) Paul, R.; Kaler, K. V. I. S.; Jones, T. B. J. Phys. Chem. 1993, 97, 4745.
© 1997 American Chemical Society
2418 Langmuir, Vol. 13, No. 8, 1997
Notes
Figure 2. Successive pictures demonstrating DEP migration of the particles. σm ) 7.01 × 10-2 S/m; Urms ) 3.54 V. (a) Positive DEP. The particle in the circle migrates to the edge of an electrode. f ) 1 kHz. Contrast is reversed for clearness. (b) Negative DEP. The particles migrate to the cell center. f ) 1 MHz. clearly. Conductivity was measured with a conductometer (CM40V, TOA Electronics, Tokyo). A DEP cell with a hyperbolic quadrupole microelectrode, shown in Figure 1a, was made by an ordinary photolithographic technique on a glass plate at Shimadzu Corp. (Kyoto). An electrode and its opposite were wired to be the same polarity of alternating current (ac), and a condenser was inserted to eliminate any direct current. The nonuniform electric field of conical shape shown in Figure 1b was calculated for the DEP cell.15 Excitation and emission wavelengths of a fluorescence microscope BX60 (OLYMPUS) were set to 520-550 and 580800 nm, respectively, for the measurement of Rhodamine B fluorescence. Measurement of Migration of Single Particles. An aliquot (3 µL) of the sample solution was dropped in the working area of the DEP cell, and a small glass cover plate (3 mm × 3 mm × 0.15 mm) was placed on it. An applied voltage (Urms, root mean square) and frequency (f) of ac were changed in the range 2.55.0 V and 1 kHz to 1 MHz, respectively, by a function generator (FG-273, KENWOOD). Experiments were performed in a thermostated room at 25 ( 1 °C. The distance (R) from the DEP cell center to a particle was obtained as a function of time. The working area of the DEP cell with a radius of 65 µm was observed under the fluorescence microscope with a CCD camera (ImagePoint, Photometrix), and the image was recorded with a video cassette recorder (HOR-30, Victor). The image was then transferred as a digital picture to a computer (Power Macintosh 8100/100AV, Apple) at certain time intervals. The distance of a particle from the center of the picture was obtained from the pixel number and then converted to real distance.
Results and Discussion The conductivity of the sample solution was in the range 3.11 × 10-4 to 7.01 × 10-2 S/m. Successive pictures of DEP behavior are shown in Figure 2. Figure 2a shows positive DEP of the particles; all particles migrated to the electrode edge, where the electric field was the strongest. Illustrated in Figure 2b is negative DEP; all particles migrated to the center of the cell, where the electric field was weakest. For both positive and negative DEP migrations, the trajectory was radial; that is, the motion was linear. The R values are plotted against the DEP time (t) in Figure 3. The measurement of R was made in (15) Huang, Y.; Pethig, R. Meas. Sci. Technol. 1991, 2, 1142.
Figure 3. Plots of R against DEP time (t). Conditions are the same as those in Figure 2. (a) Positive DEP and (b) negative DEP.
the range 0.1d e R e 0.9d, where d is the radius of the inscribed circle (see Figure 1a). The lower limit was chosen to minimize the error that might be caused by very slow migration around the center. The higher limit was to eliminate the effect of the electrode edge. As a particle approached the electrode edge, its velocity increased for positive DEP. On the other hand, for negative DEP a particle that migrated to the center slowed down. Parts a and b of Figure 4 show plots of ln R versus t for positive and negative DEPs, respectively. They show linear relationships in both cases with good correlations (correlation coefficient > 0.99). The slope of the linear relationship is defined as the DEP mobility coefficient, R. The sign of R corresponds to the sign of DEP. We worried about joule heating. When σm and Urms
Notes
Langmuir, Vol. 13, No. 8, 1997 2419
Figure 5. Linear dependence of the DEP mobility coefficient (R) on squared ac voltage (Urms2). σm ) 3.11 × 10-4 S/m, (a) positive DEP, f ) 10 kHz, and (b) negative DEP, f ) 1 MHz.
1b from ref 15. It is 2
∇|Erms| ) Figure 4. Linear relationship between ln R and t. Conditions are the same as those in Figure 2.
were 7.01 × S/m and 3.54 V, respectively, the rms alternating current was measured as about 500 nA. This corresponded to 1.8 × 10-6 J/s, and thus 1.4 × 10-4 K/s for 3 µL of aqueous solution. Since the DEP measurement time was within 10 min, the joule heating was negligibly small. The time-averaged motive force 〈FDEP〉 of a particle caused by DEP in an ac electric field, Ep cos(ωt), is expressed as16 10-2
〈FDEP〉 ) 2πre mRe[Ke]∇|Erms| 3
2
(1)
where ω is the angular frequency ()2πf), re is the radius of the spherical particle, m is the permittivity of the medium, Re[Ke] is real part of the Clausius-Mossotti factor Ke, ∇ is the del vector, and |Erms|2 is the squared electric field intensity (root mean square), which is equal to Ep2/2. The underline indicates a complex property. The Re[Ke] is expressed as16
Re[Ke] )
p - m 3(mσp - pσm) + p + 2m τ(σ + 2σ )2(1 + ω2τ2) p m
(2)
where p, σp, and σm are the permittivity of the particle, the conductivity of the particle, and the conductivity of the medium, respectively, and τ denotes (p + 2m)/(σp + 2σm). Equation 2 is rearranged as
Re[Ke] )
(p - m)ω2τ2
(σp - σm) 2 2
(p + 2m)(1 + ω τ )
+
(σp + 2σm)(1 + ω2τ2) (3)
Re[Ke] is mainly controlled by σp and σm when ω < 1/τ and approaches the limiting value of (σp - σm)/(σp + 2σm) as ω f 0. For ω > 1/τ, Re[Ke] is mainly governed by p and m, and the limiting value is (p - m)/(p + 2m) as ω f ∞. The point of inflection for the plots of Re[Ke] versus log f is located at f ) 1/(2πτ). The hyperbolic quadrupole microelectrode generates the DEP factor shown in Figure (16) Benguigui, L.; Lin, I. J. J. Appl. Phys. 1982, 53, 1141.
2RUrms2 d4
(4)
The frictional force which a migrating particle will undergo is given by the Stokes equation:
dR FSt ) 6πηre dt
(5)
where η is the viscosity of the medium. From Newton’s equation of motion, the following equation is obtained after integration (see the Appendix).
ln R )
2re2mUrms2 Re[Ke]t + ln R0 3ηd4
(6)
where R0 is the initial R value. According to eq 6, ln R is expected to be a linear function of t. As shown in Figure 4a,b, ln R is linearly correlated with t in both cases of positive and negative DEPs. Furthermore, the values of R obtained from the slopes were linear in the squared ac voltage for both positive and negative DEPs, as shown in Figure 5, which is consistent with eq 6. These results strongly supported the foregoing assumptions and equations. The mobility coefficient, R, is, then, equated to the proportionality constant in eq 6,
2re2mUrms2Re[Ke] R)
3ηd4
(7)
All properties on the right-hand side of eq 7 are positive, except for Re[Ke]. Therefore, the sign of R is the same as that of Re[Ke]. By changing f and σm, various values of R were obtained. Figure 6 shows the dependence of R upon both f and σm. When σm was 3.11 × 10-4 S/m, the point of inflection was estimated as about 70 kHz, by substituting m for 78.30 (0, permittivity of vacuum) and assuming p < m, σp ≈ σm. The result is consist with the estimation. The positive Re[Ke] in the lower f range indicates σp < σm. The high conductivity value for the particle is not to be understood as a value for the real polystyrene particle, but may be explained by postulating a surface conductivity.14,17 Carboxylate at the surface of polystyrene carboxylate latex (17) Shang, J. Q.; Inculet, I. I.; Lo, K. Y. J. Electrostat. 1994, 33, 229.
2420 Langmuir, Vol. 13, No. 8, 1997
Notes
the DEP cell by photolithography. They also thank Dr. M. Yamaguchi of the Faculty of Engineering Science, Osaka University, for useful suggestions for DEP measurements. Appendix For positive DEP of a particle (mass m), Newton’s equation of motion is
d2R ) 〈FDEP〉 - FSt dt2
m
Figure 6. Dependence of the DEP mobility coefficient (R) on frequency (f) of an ac electric field and conductivity of aqueous solution: (b) σm, 3.11 × 10-4 S/m; (O) σm, 7.01 × 10-2 S/m.
must dissociate in this pH range (6.1-6.8), so the particle has negative charges at the surface. This acid dissociation was supported by the results of electrophoretic mobility for the particle. The negative DEP observed for f g 32 kHz can be understood from p < m. The p value for the polystyrene carboxylate latex in an aqueous solution is estimated as (59 ( 2)0 from the observed R value and eq 2 at f ) 1 MHz. This value is larger than common organic polymers, e.g., 2.550 for polystyrene, 2.10 for PTFE, but these values are obtained in a vacuum. In an aqueous solution, a large influence of the medium may take place. When σm was 7.01 × 10-2 S/m, the point of inflection was estimated as about 16 MHz. Therefore, Re[Ke] is mainly controlled by the conductivities, σm and σp, in the range 1 kHz < f < 1 MHz. Since the σm does not depend on f in this range, the observed change of Re[Ke] would be due to the variation of σp. Experiments and discussion about the dependence of σp on f are now in progress.
(A1)
〈FDEP〉 and FSt are proportional to R and dR/dt, respectively. Therefore, eq A1 is conveniently expressed as
dR d2R ) aR - b dt dt2
m
(A2)
where a and b are positive constants. A general solution for R that satisfies eq A2 is expressed as
R ) R0eβt + R1eγt
(A3)
where β ) (1/2m){-b + xb2 + 4am} and γ ) (1/2m) {-b -
xb2 + 4am}, and R0 and R1 are constants.
If 〈FDEP〉 is 0, i.e. a ) 0, the particle cannot migrate; that is, R is not a function of t. By substituting 0 for a in the equations of β and γ, β ) 0 and γ ) -b/m are obtained. Therefore, R1 must be equal to 0. As a result,
R ) R0eβt
(A4)
For negative DEP,
dR d2R ) -aR + b dt dt2
(A5)
-m Conclusions (1) The DEP behavior of a single polystyrene particle (3.0 µm in diameter) was measured and analyzed in a DEP cell with a hyperbolic quadrupole microelectrode using a fluorescence microscope. (2) A linear relationship between ln R and t was found for both positive and negative DEP of the particle. A DEP mobility coefficient was defined as the slope of ln R versus t plots. The linear relationship between ln R and t was explained by the solution of Newton’s equation of motion. (3) The dependence of R on the frequency f of the applied ac potential and the conductivity of the medium was examined. A positive DEP, which was observed for f e 10 kHz, could not be explained by using the expected values for σp and σm, but could be explained qualitatively by assuming a higher surface conductivity of the particle than σp. A negative DEP migration observed for f g 32 kHz was evaluated by the theoretical DEP equation. Acknowledgment. The authors are grateful to Mr. S. Ishida and Mr. K. Ohkubo of Shimadzu Co. for making
This equation is identical to eq A2 when multiplied by -1. If 〈FDEP〉 is very weak, i.e., b2 . 4am,
β) ≈
1 {-b + b x1 + 4am/b2} 2m
{
(
)}
4am 1 -b + b 1 + 2m 2b2
)
a b
(A6)
In fact, we can calculate the order of a, b, and m values as 2 × 10-7 N/m, 2 × 10-8 N s/m, and 1 × 10-14 kg, respectively. Clearly, b2 . 4am. Finally, ln R can be written as
a ln R ) t + ln R0 b
(A7)
This relation can also be obtained when the acceleration term in eq A1 is neglected. Therefore, 〈FDEP〉 is substantially equal to FSt for these experimental conditions. LA961057V
