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Langmuir 2004, 20, 572-574
Particle Trapping and Undulation of a Liquid Surface Using a Microscopically Modulated Magnetic Field Tsunehisa Kimura,* Masafumi Yamato, and Akihiro Nara Department of Applied Chemistry, Tokyo Metropolitan University, 1-1 Minami-ohsawa, Hachioji, Tokyo 192-0397, Japan Received September 22, 2003. In Final Form: December 18, 2003 An aluminum/iron-layered block (periodicity of 300 µm) was placed in a homogeneous magnetic field (ca. 1 T) to produce a periodic modulation of the magnetic field over the block surface. This modulation caused an undulation of the surface of a thin liquid layer spread over the block. The same modulated field was used to trap polystyrene spheres (20 µm in diameter suspended in a liquid) in a periodic line pattern. The spheres were trapped above the iron layers of the block where the field strength is lower in the present experimental setup. Upon drying, the trapped spheres formed self-organized packing.
Introduction A number of reports have been published recently about the magnetic effects on feeble magnetic materials. This is partially due to the recent advances in superconducting magnet technology, including the generation of high magnetic fields attained at high magnetic field centers around the world and the advent of compact liquid-helium free superconducting magnets that have become available at the level of individual research laboratories. Diamagnetic levitation,1-3 magneto-Archimedes levitation,4 and so forth are good examples. Under a magnetic field gradient, a force acts on a diamagnetic particle, repelling it toward the direction of the decreasing field strength. If this force is large enough to balance with the gravitational force, a particle levitates in the air. Unlike levitation in space and flotation assisted by hydrostatic buoyancy, the diamagnetic levitation can be used to trap particles:2 diamagnetic particles are trapped at a minimum of the magnetic energy. This trapping force can also serve to modulate a free surface of a liquid.5,6 So far, phenomena under macroscopic field gradients (spatial change over centimeter orders) have been focused on in most cases, but it is clear that similar phenomena can take place at a microscopic level. In fact, a high field gradient generated at the edge of a permanent magnet is used for the analyses of particles with microscopic size.7 Also, in the field of magnetic separation strong gradients created in the vicinity of thin steel wires are utilized to trap magnetic materials. A higher field gradient is easily created at the microscopic level. A levitating force is approximately proportional to (∆B)2/L, where ∆B is the difference in magnetic flux density between two sites separated by L. A typical value for a superconducting magnet used for levitation is, for example, (∆B)2/L ) 252/0.5 T2/m, which is about the * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Beaugnon, E.; Tournier, R. Nature 1991, 349, 470. (2) Berry, M. V.; Geim, A. K. Eur. J. Phys. 1997, 18, 307. (3) Kitamura, N.; Makihara, M.; Hamai, M.; Sato, T.; Mogi, I.; Awaji, S.; Watanabe, K.; Motokawa, M. Jpn. J. Appl. Phys. 2000, 39, L324. (4) Ikezoe, Y.; Hirota, N.; Nakagawa, J.; Kitazawa, K. Nature 1998, 393, 749. (5) Ueno, S.; Iwasaka, M. J. Appl. Phys. 1994, 75, 7177. (6) Hirota, N.; Hommma, T.; Sugawara, H.; Kitazawa, K.; Iwasaka, M.; Ueno, S.; Yokoi, H.; Kakudate, Y.; Fujiwara, S.; Kawamura, M. Jpn. J. Appl. Phys. 1995, 34, L991. (7) Watarai, H.; Namba, M. Anal. Sci. 2001, 17, 1233.
value necessary for the levitation of a water droplet (ca. 1400 T2/m). A similar value is attained even with a much more moderate value of ∆B, for example, 1 T, if this ∆B is realized at a separation of ca. L ) 1 mm. In this paper, we demonstrate microundulation of a liquid surface using a periodic layer of iron and aluminum that creates a modulated field profile at a microscopic level. This modulated profile is also used for micropatterning of polystyrene spheres. The polystyrene spheres are self-assembled in patterned lines. Experimental Section An iron sheet of 300 µm thickness and three sheets of an aluminum foil of 100 µm thickness were alternately piled up and pressed with a vise to form a block (ca. 1 cm × 1 cm × 3 cm) of an iron/aluminum periodic structure with 300 µm periodicity. A surface of the block normal to the periodic structure was mechanically polished to make it flat. This block was placed between two pole pieces of a Tamagawa TM-WTF6215C electromagnet generating a horizontal field of ca. 1 T. The direction normal to the layers coincided with the field direction (Figure 1). A piece of Kapton film (25 µm thick) was put on the top surface of the block onto which a droplet of a liquid or a suspension containing polystyrene spheres was dropped. Observation was carried out from above the block using a CCD camera (magnification of 5-40 and 150-800), and images were recorded on a computer. A suspension of polystyrene spheres (20 ( 0.1 µm in diameter, 0.3%) purchased from Duke Scientific Corp. was used as received as well as with addition of manganese chloride (MnCl2). The suspension is described by the manufacturer as containing a small amount of dispersant and surfactant. For the surface modulation study, mixtures of water, ethanol, and manganese chloride were prepared.
Results and Discussion Microscopic Modulation of the Liquid Surface. Figure 2 shows a simulation result of the field profile of Bx at each height z from the block surface as a function of the horizontal direction x. The field being applied in the horizontal direction, the magnetic flux density is higher above the aluminum layers than the iron layers. The modulation of the magnetic flux density might persist above the block surface over a distance of about the same order as the pitch of the substrate periodic layer. The shorter the pitch, the thinner the available persistence. In the present case, the pitch is 300 µm, and hence the field modulation could persist as high as this distance above the block surface. Because the thickness of the
10.1021/la035768m CCC: $27.50 © 2004 American Chemical Society Published on Web 01/10/2004
Letters
Figure 1. Experimental setup. A block, composed of alternate aluminum (300 µm) and iron (300 µm) layers, was put between two pole pieces (P) of an electromagnet (EM), and the sample on the block was monitored by a CCD camera.
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Figure 4. Polystyrene latex sample used as received. (a) Polystyrene spheres are dispersed uniformly in the absence of the magnetic field. Pairs of three lines are due to aluminum layers each composed of three 100 µm foils. (b) Upon application of the field (1 T), spheres accumulate to form broad lines on the iron layer parts. It took about 15 min.
of a chemical potential gradient ∇G and an applied field gradient ∇B2, a flux J is induced:
J ) c (-NA-1∇G + (2µ0)-1∆χV ∇B2)
Figure 2. Profile of magnetic flux density Bx at various heights z from the block surface. Minima correspond to iron layers.
(1)
where c [mol m-3] is the concentration of the particle, [m2 s-1 J-1] is the mobility of the particle that is related to the diffusion constant through the Einstein relation (D ) kBT, with kB being the Boltzmann constant), NA is Avogadro’s constant, µ0 is the magnetic permeability of a vacuum, B [T] is the magnetic flux density, and ∆χ ) χ1 - χ2. If zero flux condition is imposed, that is, J ) 0, we obtain
∇G ) (2µ0)-1NA∆χV ∇B2
(2)
This equation describes the spatial profile of the chemical potential under the applied field profile. The chemical potential is related to the concentration as
G ) G0 + RT ln c Figure 3. (a) CCD observation of the liquid (2:6:1) surface in the absence of the field. The large white broad area is due to the reflection of illuminating light on the liquid surface. The surface is flat. (b) Appearance of the surface when a magnetic field (1 T) is applied. Undulation of the surface is observed. The pitch is ca. 300 µm.
Kapton film put on the block surface is 25 µm, we obtain a sufficient modulation of the field above the film surface. Figure 3a,b shows a microscopic modulation of a liquid surface. The liquid used is a mixture of water, ethanol, and MnCl2‚4H2O with a composition of 2:6:1 by weight. In the absence of the field, the surface of the liquid is flat as seen in Figure 3a. Upon application of the field of 1 T, the surface is undulated (Figure 3b) in accordance with the field modulation. The modulation proceeds without delay, following the change in field strength. A similar experiment was carried out for a liquid with 6:2:1 composition. This liquid just splits macroscopically upon application of the field. The reason could be that the thickness is large so that the field modulation cannot reach the surface of the liquid. The thickness of a liquid layer is governed by the surface tension of the liquid and the affinity of the liquid to the substrate. In the latter mixture (6:2:1), the surface tension might be higher and/or the affinity to the substrate might be weak, preventing the liquid from spreading to a thin layer. Microscopic Trapping of Particles. The underlying mechanism of the trapping is described first. Let us consider particles each having a volume V [m3] and a diamagnetic susceptibility χ1, suspended or dissolved in a solvent with a magnetic susceptibility χ2. In the presence
(3)
where G0 is a reference chemical potential. Using this relation, we rewrite eq 2 as follows in the one-dimensional case: -1 ∂ ln c µ0 ∆χV ∂B ) B ∂x kBT ∂x
( )
(4)
The integration of the above equation leads to the concentration profile:
(
c(x) ) c(x0) exp
)
(2µ0)-1∆χV(B2(x) - B2(x0)) kBT
(5)
where x0 is a reference position. This gives an equilibrium distribution, that is, Boltzmann distribution. If B(x) has a minimum and ∆χ < 0, the concentration becomes high at the minimum. If the solution is not ideal, eq 3 is replaced with G ) G0 + RT ln γc, where γ is the activity coefficient. The transient behavior from the initial distribution to the equilibrium state is described by the diffusion equation, ∂c/∂t ) -∇‚J. Because the viscosity of the solvent affects the diffusion behavior through the mobility , the pattern formation in a viscous solvent will take a long time. Using the same block as used for surface undulation, we carried out trapping of polystyrene spheres suspended in a liquid. The experiment was carried out in a condition in which no microscopic surface undulation occurs. Figure 4a shows polystyrene spheres suspended in a liquid. The spheres were dispersed uniformly. Upon application of the field, the spheres started to accumulate onto the iron
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Figure 5. (a) Polystyrene spheres in a suspension containing 0.19 M manganese chloride form sharp lines almost immediately after the application of the field. (b) Magnification of patterned lines obtained after drying the suspension in the presence of the magnetic field.
layers to form broad lines (Figure 4b). It took about 15 min for the spheres to complete accumulation as shown in the figure. In contrast, if we add manganese chloride to the suspension (concentration of 0.19 M), the accumulation process is accelerated and the obtained line pattern becomes sharper (Figure 5a). This is mainly attributed to the increase in the absolute value of ∆χ ) χ1 - χ2 < 0, where χ1 and χ2 are magnetic susceptibilities of the polystyrene sphere and the suspending liquid, respectively. The increase in |∆χ| enhances the particle flux through the field gradient term described in eq 1, accelerating the transportation of particles to potential minima located above the iron layers. In the equilibrium state, the width of the particle distribution around the
Letters
minimum is proportional to the ratio kBT/|∆χ|V as seen in eq 5. Therefore, the distribution width becomes narrower with an increase in |∆χ|. The line pattern is maintained even after the evaporation of the solvent of the suspension in the presence of the magnetic field. Magnification of the lines is shown in Figure 5b. Within the line, polystyrene spheres are selfassembled to form a regular arrangement. Conclusions Microscopic modulation of a uniform magnetic field was realized by inserting a block with alternating layers of iron and aluminum of 300 µm periodicity. Using this modulated field, a microscopic undulation of a liquid surface and a microscopic trapping of polymer spheres were carried out. In the present study, only a line pattern was shown as an example, but the technique presented here can be applied to obtain arbitrarily designed microscopic patterns. In addition, narrower patternings, for example, those of nanometer order, could be possible if nanopatterned substrates are used. Acknowledgment. This work was partially supported by the Japan Society for the Promotion of Science through the Research for the Future Program. LA035768M
