Anal. Chem. 2001, 73, 5214-5219
Magnetophoretic Velocimetry of Manganese(II) in a Single Emulsion Droplet at the Femtomole Level Masayori Suwa and Hitoshi Watarai*
Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
We developed a new experimental technique named magnetophoretic velocimetry to determine a small amount of paramagnetic species in a single microdroplet. The magnetophoretic velocity of an aqueous droplet containing paramagnetic metal ion dispersed in an organic medium could response to a very small amount of the metal ion under an inhomogeneous magnetic field. The paramagnetic droplet (2∼8 µm diam) used as a test sample in this study was the aqueous droplet of manganese(II) chloride dispersed in ethylbenzoate whose density was nearly equal to water. A pair of small Nd-Fe-B magnets placed with a gap of 400 µm generated an inhomogeneous magnetic field between the edges, at which the product of the magnetic flux density and the gradient, B(DB/Dx), was as high as 410 T2 m-1. When a silica capillary containing the emulsion was inserted into the gap between the magnets, the magnetophoretic migration of the droplets was observed with a video microscope. The magnetophoretic velocity divided by the squared radius of the droplet was proportional to the MnCl2 concentration in the droplet, as predicted by a theoretical calculation. The estimated detection limit in this simple method was lower than 10-16 mol for manganese(II). The development of analytical techniques for micrometer-sized particles in liquid samples has been extensively required, not only in colloidal chemistry but also in environmental chemistry and biological technology.1-2 Electrophoresis and sedimentation are currently the most popular migration analyses for biomolecules and cell composites,3-4 utilizing an electric field and a gravitational field, respectively, to generate migration forces. Although there are several other external fields that might be utilized for migration analyses of microparticles, they have rarely been investigated. Recently, some external fields were investigated in our laboratory for the development of new migration analyses. A nonuniform electric field was utilized in the dielectrophoresis,5 a homogeneous magnetic field applied perpendicularly to an electric current was * Corresponding author. Fax: +81-6-6850-5411. E-mail:
[email protected]. (1) Springston, S. R.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1987, 59, 3441-3449. (2) Mesaros, M.; Gavin, P. F.; Ewing, A. G. Anal. Chem. 1996, 68, 3441-3449. (3) Giddings, J. C. Unified Separation Science; John Wiley and Sons: New York, 1991. (4) Li, S. F. Y. Capillary Electrophoresis; Elsevier: Amsterdam, 1992. (5) Tsukahara, S.; Sakamoto, T.; Watarai, H. Langmuir 2000, 16, 3866-3872.
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employed in the electromagnetophoresis,6 and a scattering force of laser radiation pressure was used in laser photophoresis.7 The separation method using an inhomogeneous magnetic field, called high gradient magnetic separation (HGMS), has been practically used for the separation of magnetically susceptible particles since the 1970s,8-10 but the migration velocities of individual particles have not been studied for the purpose of analysis. The motion of particles with a magnetic susceptibility different from that of the surrounding liquid in a nonuniform magnetic field is called magnetophoresis.11-13 The strength of the force that works on particles under the nonuniform magnetic field depends on the magnetic properties of the particle and medium as well as on the magnetic gradient. When the magnetic susceptibility of a particle is higher than that of the medium, the particle moves in the direction of the stronger magnetic field. In the reverse situation, the particle migrates in the opposite direction. The magnetic force strength depends on the volume of particles as well as the drag force expressed by Stokes’ law. Hence, magnetophoresis could be employed for the size separation of polystyrene latexes in a microcapillary.14 In addition, magnetophoresis is expected to afford information about the number of magnetic compounds included in a microparticle that migrates under a magnetic field gradient. In the present study, we investigated the magnetophoretic velocities of paramagnetic droplets of manganese(II) chloride aqueous solution in a diamagnetic organic medium under a high gradient magnetic field. In this situation and depending on the amount of manganese(II) chloride in the droplet, the paramagnetic droplet migrated in the direction of the stronger magnetic field. From these phenomena, we developed a new experimental technique of video velocimetry that enabled us to determine a trace amount of the paramagnetic element from the magnetophoretic velocity of the droplet. In this report, we describe the (6) Namba, M.; Watarai, H.; Takeuchi, T. Anal. Sci. 2000, 16, 5-9. (7) Monjushiro, H.; Hirai, A.; Watarai, H. Langmuir 2000, 16, 8539-8542. (8) Oberteuffer, J. A. IEEE, Trans. Magn. 1973, 9 (3), 302-306. (9) Melville, D.; Paul, F.; Roath, S. IEEE, Trans. Magn. 1975, 11 (6), 17011704. (10) Coe, B. T.; Gerber, R.; Witts, D. IEEE, Trans. Magn. 1998, 34 (4), 21262128. (11) Fuh, C. B.; Chen, S. Y. J. Chromatogr. A 1998, 313-324. (12) Chalmers, J. J.; Zborowski, M.; Sun, L.; Moore, L. Biotechnol. Prog. 1998, 14, 141-148. (13) Zborowski, M.; Fuh, C. B.; Green, R.; Sun, L.; Chalmers, J. J. Anal. Chem. 1995, 67, 3702-3712. (14) Namba, M.; Watarai, H. International Symposium on New MAGNETOSCIENCE, Proceedings of the 3rd meeting 1999, 494-502. 10.1021/ac010418v CCC: $20.00
© 2001 American Chemical Society Published on Web 09/28/2001
Figure 1. Experimental setup for the measurement of magnetophoretic velocity: (a) xy stage, (b) optical microscope, (c) CCD camera, (d) video recorder, (e) monitor, (f) capillary, (g) rare earth magnet, and (h) aluminum spacer.
experimental observation of the magnetophoretic migration of emulsion droplets of aqueous manganese(II) in ethylbenzoate medium and discuss principal factors that govern the magnetophoretic velocity and the sensitivity of the magnetophoretic velocimetry. EXPRIMENTAL SECTION Chemicals. Manganese(II) chloride (GR) and ethylbenzoate (GR) were purchased from Kishida Chemicals (Osaka, Japan) and Katayama Kagaku (Osaka, Japan), respectively. Ethylbenzoate was chosen as the organic solvent, because the density is nearly equal to that of water. A 10- to 50-µL portion of manganese(II) chloride aqueous solution was added to 5 mL of ethylbenzoate that had been saturated with water. Then the mixture was sonicated for 1 min to disperse the aqueous solution into ethylbenzoate as micrometer-sized emulsion droplets. The concentration of Mn(II) in the aqueous solution was changed in the range of 0.01 to ∼1.0 M. The water was purified by a Milli-Q system (Millipore, Bedford, U.K.). Magnetophoresis. Figure 1 shows the apparatus used in this experiment. Using aluminum spacers, two plates of square-shaped Nd-Fe-B magnets (NEOMAX, Sumitomo Special Metals, Osaka, Japan) were faced so as to have a gap of 400 µm between them. The size of the square-shaped permanent magnets was 17 ×19 × 3 mm. To adjust the observed region by a microscope, the pair of magnets was held on an xy stage (LD-647-S2, Chuo Precision Industrial, Tokyo, Japan). A square, flexible, fused-silica capillary (Polymicro Technologies, Phoenix, AZ), which had a 100- × 100µm inner section and was 20 cm long, was used for the migration cell. The capillary cell containing the sample solution was inserted into the gap between the two magnets. Soon after the insertion, the behavior of the droplets was observed by an optical microscope equipped with a CCD camera (CN42H, ELMO, Nagoya, Japan). The CCD image was displayed on a monitor and also recorded on a videocassette. The migration velocity was measured from the images captured in a computer. The magnetic volume susceptibilities of manganese(II) chloride solutions and ethylbenzoate were determined uisng a
Figure 2. Typical magnetophoretic behavior of paramagnetic droplets in the region of 200 µm inside the edge of the magnets: (a) glass wall, (b) manganese(II) chloride droplet, and (c) ethylbenzoate as the organic medium. This picture was reconstructed from the images captured at a rate of 1 frame/second. Manganese(II) chloride concentration in these droplets was 0.8 M.
magnetic balance (MSB-AUTO, Sherwood Scientific, LTD, Cambridge, U.K.). The densities of the sample solutions were measured using a specific gravity bottle. All measurements were carried out in a thermostatic room at 25 °C. Computer Simulation. The shape of the magnetic field generated between the magnets was calculated using the magnetostatic field simulation software SUPER MOMENT.15 In the present experiment, the midpoint in the gap at the edge of the magnets was defined as x ) 0 and y ) 0 (see Figure 1). The x direction was set parallel to the capillary, and the direction from the edge to the inside of the gap was defined as positive. The y direction was set perpendicular to the face of the magnet plate. RESULTS AND DISCUSSION Magnetophoresis of Manganese(II) Droplet. Figure 2 shows a typical magnetophoretic behavior of an aqueous droplet soon after the insertion of the capillary cell. The picture shown in Figure 2 was made by superimposing images captured in the computer with at 1-s intervals. The left-hand side in this picture is the positive direction for x. In the region of x ) 0 to 300 µm, the paramagnetic droplets of larger radii migrated faster to the inside of the gap. However, around the point of x ) -100 µm, the droplets moved slowly toward the direction apart from the magnets. The x component of the magnetophoretic velocities of the droplets was measured from the superimposed images, such as Figure 2. Figure 3 shows the plots of the x component of the velocities against x for various droplets. The larger the droplet was and the more increased the manganese(II) concentration was, the faster the droplet migrated. The magnetophoretic velocity showed a maximum value in the region between x ) 200 and 300 µm, irrespective of the size and the concentration of manganese(II). The velocities of the droplets must be affected by the gradient of the magnetic field along the x axis. The magnetic field gradient (15) Sekiya, H. “SUPER MOMENT”, http://www.vector.co.jp/soft/win95/edu/ se078148.html.
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Figure 3. Dependence of the migration velocities of the aqueous manganese(II) droplets with various diameters, vx, on the location of the diameter, x. The manganese(II) concentrations of the droplets were (a) [MnCl2] ) 0.15 M and (b) [MnCl2] ) 0.3 M.
in this system was calculated using the computer software SUPER MOMENT. The y component of the magnetic flux density, By, in the x,y plane is shown in Figure 4a. There appeared a maximum gradient of By near the edge of magnet. In the region of x < -100 µm, By < 0, therefore, the direction of the magnetic flux was reversed. By comparison of Figures 3 and 4a, it was found that the magnetophoretic velocity depended on the magnetic flux density and its gradient. Analysis of Magnetophoretic Velocity. When a droplet that has a magnetic volume susceptibility, χp, and a volume, V, is in a magnetic field with the flux density B, the magnetic potential energy of the droplet, U, is represented by
χp U)VB2 2µ0
defined as (Bx, By, Bz). The magnetic force working on the droplet, Fp, is equal to -grad U. Therefore, the x component of the force, Fpx is written as
Fpx )
χp ∂B VB µ0 ∂x
(1)
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(2)
The magnetic force also works on the medium, so the droplet experiences the magnetic buoyancy, Fmx, expressed by the following equation
Fmx ) -
where µ0 is the vacuum magnetic permeability and B is a vector 5216
Figure 4. (a) The y component of the magnetic flux density, By, in the xy plane simulated by SUPER MOMENT. There was a maximum gradient in the region near the edge, and By had a negative value outside of the magnets. (b) The simulated value of By(∂By/∂x) as a function of x. By(∂By/∂x) had a large positive value at 0 < x < 200 µm and was negative when x < -100 µm.
χm ∂B VB µ0 ∂x
(3)
where χm is the magnetic volume susceptibility of the medium. When the droplet migrates, the viscous drag force, FDx, acts on
the droplet. FDx is represented by Stokes’ law
FDx ) -6πηrvx
(4)
where η, r, and vx, are the viscosity of the medium, the radius of the droplet, and the magnetophoretic velocity of the droplet in the x direction, respectively. Eqs 2, 3, and 4 can be combined for Newton’s equation of motion
Fpx + Fmx + FDx ) max
(5)
where ax and m are the acceleration and the mass of the droplet. Since max is negligibly small, vx is represented by
vx )
2 ∆χ 2 ∂B rB 9 µ0η ∂x
(6)
where ∆χ ) χp - χm. B(∂B/∂x) is a vector product expressed as the following.16
∂Bx ∂By ∂Bz ∂B ) Bx + By + Bz ∂x ∂x ∂x ∂x
B
Figure 5. Magnetophoretic velocity vs the square of radius of the droplet. [MnCl2] was (a) 0.3 M, (b) 0.5 M, (c) 0.8 M, and (d) 1.0 M. The dashed line was obtained by the least-squares method. The migration velocity was proportional to the square of the radius, as predicted.
(7)
The simulation using SUPER MOMENT showed that Bx(∂Bx/ ∂x) and Bz(∂Bz/∂x) were negligibly smaller than By(∂By/∂x) in this system. Hence, the velocity is rewritten as
vx )
2 ∆χ 2 ∂By rB 9 µ0η y ∂x
(8)
Thus, it can be expected that the magnetophoretic velocity is directly proportional to ∆χ, r2, and By(∂By/∂x). The calculated value of By(∂By/∂x) from the computer simulation is shown in Figure 4b as a function of x. From the value of By(∂By/∂x), vx was predicted to have a maximum value in the region of 0 < x < 200 µm and to be negative in the region of x < -100 µm. This theoretical prediction generally coincided with the feature of the experimental results, but it was difficult to calculate precisely the magnetic field strength in a micrometer region by this method. Because By(∂By/∂x) is solely the function of the position, it has a constant value at the fixed position of x. Therefore, the magnetophoretic velocity was measured at fixed position of x ) 200 µm where By(∂By/∂x) was experimentally determined as 410 T2 m-1 in the previous study.14 Figure 5 shows the dependence of the velocity at x ) 200 µm on the squared radius of the droplet. The migration velocity was linearly proportional to the square of the radius, and the slope of the fitted straight line, which represented vx/r2, was dependent on the Mn2+ concentration, [Mn2+], in the droplet, as shown in Figure 7. Magnetic volume susceptibilities of aqueous MnCl2 solutions and ethylbenzoate were measured using a magnetic balance. The (16) The x component of B‚∇B is expressed by the following equation, (B‚∇B)x ) Bx(∂Bx/∂x) + By(∂Bx/∂y) + Bz(∂Bx/∂z) ) Bx(∂Bx/∂x) + By(∂By/∂x) + Bz(∂Bz/∂x), because in our experimental system, Maxwell’s equation is given as rotB ) (∂Bz/∂y - ∂By/∂z, ∂Bx/∂z - ∂Bz/∂x, ∂By/∂x - ∂Bx/∂y) ) 0.
Figure 6. Difference between the magnetic volume susceptibilities of MnCl2 aqueous solution and ethylbenzoate, ∆χ, measured at various MnCl2 concentrations. The straight line is the fitted one as ∆χ/10-6 ) 181.5 [MnCl2] + 0.46.
plot of ∆χ vs [Mn2+], which indicates that ∆χ varies in proportional to [Mn2+] with the following relation, is shown in Figure 6.
∆χ/10-6 ) 181.5 [Mn2 +] + 0.46
(9)
Theoretically, ∆χ can be represented by M M ∆χ ) χMnCl [Mn2 +] + χH [H2O] - χVEB 2 2O
(10)
M M where χMnCl and χH are the molar susceptibilities (M-1) of 2 2O MnCl2 and water, respectively, and χVEB is the volume susceptibility of ethylbenzoate. The concentration of water, [H2O], was little varied when [Mn2+] increased from 0.01 to 1.0 M, so eq 10
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Figure 7. Magnetophoretic velocity divided by the square of the radius of the droplet versus [MnCl2]. The solid line was a fitted straight line. The filled circles were the results obtained by using the watersaturated ethylbenzoate as the medium, and the open circles were the results obtained when dry ethylbenzoate was used.
can be rewritten as V M ∆χ ) χMnCl [Mn2+] + χH - χVEB 2 2O
(11)
V where χH is the volume susceptibility of water. Eq 11 corre2O sponds well to eq 9. The proportional constant of 181.5 × 10-6 M-1 in eq 9 is in good agreement with the calculated value of M χMnCl ) 180.4 × 10 - 6 M-1.17 2 Substitution of eq 11 into eq 8 yields
V V M 2+ 2 χMnCl2[Mn ] + χH2O - χEB ∂By By ) µ0η ∂x r2 9
vx
(12)
The observed magnetophoretic velocities normalized by the squared radius of the droplet, vx/r2, were proportional to [Mn2+] (Figure 7), as expected form eq 12. The dashed line in Figure 7 is the theoretical one predicted by eq 12. The observed values are well-represented by the predicted ones. Magnetophoretic Velocimetry. The solid line in Figure 7 can be used as a calibration curve for the determination of manganese(II). From the measurements of vx and r, we can determine the concentration of Mn(II) in the droplet. This method can be named magnetophoretic velocimetry. We have demonstrated the sensitivity and applicability of the magnetophoretic velocimetry for the emulsion prepared by dispersing aqueous manganese(II) chloride into dry ethylbenzoate. In Figure 7, the migration velocities of thus prepared aqueous droplets were plotted against the initial manganese(II) concentrations, [Mn2+]init. As shown in Figure 7, when ethylbenzoate was not saturated with water prior to use, the migration velocities of the aqueous droplets became faster than those in water-saturated system. This means that the magnetophoretic velocimetry could detect the change in Mn2+ concentration in the droplet that was caused by the dissolution of water in the aqueous solution into the organic solvent. From (17) Lide, D. R. Handbook of Chemistry and Physics, 80th ed.; CRC Press: Boca Raton; 1999-2000.
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Figure 8. Solubility of water into ethylbenzoate calculated from the magnetophoretic velocity of the droplets using the calibration line in Figure 7. The solid curve is the calculated one at 25 °C from the MnCl2 activity in water.17-18
the observed values of the velocities, the equilibrium concentrations, [Mn2+]eq, in the droplets were determined using the straight calibration line shown in Figure 7. Furthermore, the concentration of water in ethylbenzoate was determined from the initial and equilibrium concentrations of manganese(II) chloride. Figure 8 shows the solubility of water in ethylbenzoate determined by the velocimetry, when the ethylbenzoate phase was equilibrated with MnCl2 aqueous solution. The solubility is decreased with the increase in the Mn2+ concentration. The solid line is the solubility of water calculated from the available data for the activity of MnCl2 in water.17-18 The water solubility determined in the present study is in good agreement with the calculated one. This means that the decrease in [H2O]0 with the increase in [Mn2+] is ascribable to the decrease of water activity by the hydration to MnCl2. Thus, the magnetophoretic velocimetry could be used for the determination of manganese(II) in a single aqueous droplet in the emulsion, and furthermore, for the determination of water in the organic phase in which the aqueous phase was dispersed. The method of magnetophoretic velocimetry can be applied to any kind of paramagnetic droplet and particles in a liquid, provided that the ∆χ is detectable. CONCLUSION We developed a new method named “Magnetophoretic Velocimetry” which enabled us to determine a trace amount of a paramagnetic species in a droplet or spherical microparticle in a liquid only by the measurements of the magnetophoretic velocity and the size of the droplet. Assuming that the measurable lowest limits of velocity and radius were 1 µm s-1 and 1 µm, respectively, the detection limit of manganese(II) in the present system was calculated as 10-16 mol in a droplet. The detection limit will be greatly improved when the magnetic field is designed to make B(∂B/∂x) larger by using a superconducting magnet. The magnetophoretic velocimetry developed in the present study will be used as a simple magnetophoretic detector in FIA or HPLC, providing that an aqueous eluate is dispersed into an organic solvent as microdroplets. For the samples including mixed species, (18) Riddick, J. A.; Bunger, W. A.; Sakano, T. K. Organic Solvents, 4th ed.; WileyInterscience: New York, 1986.
a combination with HPLC might be recommended. Magnetophoresis is also a promising technique as a new method to be utilized for the analysis of biological or environmental microparticles that have specific magnetic susceptibilities. ACKNOWLEDGMENT The authors thank Dr. Tsunehisa Kimura of Tokyo Metropolitan University for valuable discussions and Sumitomo Special Metals Co. for the donation of NEOMAX magnets. This work was financially supported in part by Research for the Future (RFTF) of Japan Society for the Promotion of Science.
SUPPORTING INFORMATION AVAILABLE Another mathematical process for performing the calculations and a comparison of By(∂By/∂x) and Bz(∂Bz/∂x) around the edges of the pair of magnets. This material is available free of charge via the Internet at http://pubs.acs.org.
Received for review April 11, 2001. Accepted August 8, 2001. AC010418V
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