Langmuir 2006, 22, 3941-3944
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Colloidal Optomagnetic Dimmer L. E. Helseth,*,† H. Z. Wen,‡ and T. M. Fischer§ School of Physical and Mathematical Sciences, DiVision of Physics and Applied Physics, Nanyang Technological UniVersity, Singapore, Nanyang Crescent, Singapore, and Department of Chemistry and Biochemistry, Florida State UniVersity, Tallahassee, Florida ReceiVed NoVember 15, 2005. In Final Form: January 26, 2006 We demonstrate a colloidal optomagnetic dimmer based on the interaction between micrometer-sized paramagnetic colloidal spheres and a magnetic film. The colloidal particles undergo Brownian motion, which when exposed to light results in characteristic intensity fluctuations, and we demonstrate that weak magnetic fields that are typically 200 A/m (2.5 G) can be used to control both the average intensity and the intensity fluctuations. The system can be used as a colloidal optical dimmer in microfluidic systems.
1. Introduction In the last few decades, a significant amount of research focusing on functionalizing colloids in order to design new materials and sensors has been conducted. Optical sensors based on colloids are particularly promising because they allow us to miniaturize systems and to use weak external fields as control parameters.1-5 Such optical sensors may expand the applicability of both optical microscopy and lithography and have therefore attracted considerable attention in recent years. For example, it was found that single microscopic spheres manipulated with optical tweezers can be used as objectives for imaging details that conventional microscopes cannot observe.6 Furthermore, by combining colloids of different sizes using chemical bonds, it is possible to obtain an asymmetric system that is sensitive to alignment with incident light.7 Takei and Shimizu invented an interesting method for monitoring localized chemical bond formation using electric forces.8 First, they evaporated a thin gold film on one side of a fluorescent latex bead and then coated the gold film with a self-assembled monolayer. The microsphere could be aligned in an electric field, which allowed them to probe the specific binding to the underlying substrate by observing the asymmetric fluorescent emission. It should also be pointed out that total internal reflection microscopy (TIRM) has been used as a highly sensitive method for the detection of molecular forces and also provides an opportunity to control the average position of colloids with electrostatic forces.9 Recently, we demonstrated another technique where the lensing action of microspheres undergoing Brownian motion close to an underlying substrate could be studied using polarization microscopy, and we used this to probe the collective motion of colloidal crystals.10,11 Because the spheres have symmetric absorption †
Nanyang Technological University. ‡ Nanyang Crescent. § Florida State University. (1) Osterloh, F. J. Am. Chem. Soc. 2002, 124, 6248. (2) Kim, J. Y.; Osterloh, F. E.; Hiramatsu, H.; Dumas, R. K.; Liu, K. J. Phys. Chem. B 2005, 109, 11151. (3) Abe, M.; Orita, M.; Yamazaki, H.; Tsukamoto, S.; Teshima, Y.; Sakai, T.; Ohkubo, T.; Momozawa, N.; Sakai, H. Langmuir 2004, 20, 5046. (4) Vasquez, Y.; Sra, A. K.; Schaak, R. E. J. Am. Chem. Soc. 2005, 127, 12504. (5) Xu, X.; Majetich, S. A.; Asher, S. A. J. Am. Chem. Soc. 2002, 124, 13864. (6) Sasaki, M.; Kurosawa, T.; Hane, K. Appl. Phys. Lett. 1996, 70, 785. (7) Brody, J. P.; Quake, S. R. Appl. Phys. Lett. 1999, 74, 144. (8) Takei, H.; Shimizu, N. Langmuir 1997, 13, 1865. (9) Fagan, J. A.; Sides, P. J.; Prieve, D. C. Langmuir 2004, 20, 4823. (10) Helseth, L. E.; Wen, H. Z.; Heinig, P.; Fischer, T. M. Langmuir 2004, 20, 6556. (11) Helseth, L. E.; Fischer, T. M. Opt. Express 2004, 12, 3422.
Figure 1. Schematic drawing of the magnetic film and the colloids immersed in water. The system is observed with a polarization microscope with the polarizer and analyzer in crossed positions. The blue color indicates the height of the liquid, which is much larger (typically 0.1-1 mm in the experiment conducted here) than the colloid size.
properties, only linear Brownian motion perpendicular to the substrate is of importance, and no coating of the spheres is necessary. Here we demonstrate that when paramagnetic colloids are placed on top of a homogeneous magnetic film their lensing action can be controlled effectively with an external magnetic field. This phenomenon can be used to create a novel optomagnetic dimmer where the average brightness and brightness fluctuations of the colloids can be controlled by tuning the magnetic field. 2. Experimental Details Magnetic garnet films of composition Lu2.5Bi0.5Fe5-qGaqO12 (q ) 0-0.1) grown by liquid-phase epitaxy on 0.5-mm-thick gadolinium gallium garnet substrates were used here. The magnetic films had a thickness of about t ) 5 µm and a magnetization of Ms ) 105 A/m and were used as a substrate on which the colloidal solution was deposited. Carboxyl-modified superparamagnetic polystyrene beads of radius a )1.4 µm (M270) and effective susceptibility χ ) 0.17 were purchased from Dynal. The colloids consist of a nanoscale iron oxide grain in a polymer matrix, which gives them paramagnetic behavior. The beads were visualized with a Leica DMPL polarization microscope used in reflection mode, and the images were captured with a CCD camera with a temporal resolution of 1/30 s. The focal depth of the objectives used here was about 5 µm and therefore larger than the diameter of the colloids. A schematic diagram of the system under study is shown in Figure 1. A small volume of
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Figure 2. Typical image taken with a reflection polarization microscope with the polarizer and analyzer in crossed positions. Some colloids appear dark, and others appear bright, thus reflecting their distance to the magnetic film.
Figure 3. Schematic drawing of the focusing mechanism of a single colloid. Light passes through the colloid, which focuses it at a point close to the surface of the magnetic film. The magnetic film reflects a considerable part of the light back through the colloid and toward the CCD camera. paramagnetic beads immersed in water at a density 106 beads/mL of colloidal solution was confined within the boundaries of a glass cell located on top of the garnet film. To obtain a well-defined surface charge, the magnetic film was immersed in 1 g/L poly(sodium-4-styrenesulfonate) (PSS) for 5 min and then washed with excessive amounts of water. This creates a nanometer-thick surface charge, and when the beads eventually approach the solid-water interface because of gravity, they do not stick because of electrostatic double-layer repulsion. The beads are therefore not in close contact with the magnetic film but instead levitate a small distance h above it so that the distance between the center of the colloid and the magnetic film surface is z ) a + h. After the colloidal system has equilibrated, one observes that the beads are located randomly on the magnetic film. A typical image is displayed in Figure 2. As was noted in ref 10, characteristic intensity fluctuations take place because of Brownian motion in the z direction. This can be seen from Figure 2, where some particles are dark and others are bright. For beads of radius smaller than 2 µm, the light absorption is negligible, and they therefore act as nearly transparent microlenses focusing the light onto the reflecting magnetic film. The light reflected by the substrate is reflected back through the bead and finally emerges at the camera. Because the colloids move up and down because of Brownian motion, the reflecting surface of the magnetic film is moving in and out of focus; consequently, the colloids collect more or less light appearing as intensity fluctuations. The focusing process is seen in Figure 3, and the colloid will appear brighter when the surface of the magnetic film coincides with the focal point of the colloid. Upon repeating the experiments with a glass slide instead of a garnet film, we found intensity fluctuations as well but only when using polarized reflection microscopy. In transmission, no intensity fluctuations were observed. The polariza-
Helseth et al.
Figure 4. Histogram that shows the intensity distribution in zero magnetic field obtained from about 3600 measurements taken by recording the intensity of 4 colloids over a period of 30 s. tion of the light changes after being reflected by the magnetic film and propagating back through the microlens, thus allowing us to collect this associated fraction of the reflected light by a CCD camera using a pair of crossed polarizers. The intensity fluctuations were most pronounced when using objectives with a small numerical aperture (NA < 0.5) but sufficiently large magnification so that the beads could be clearly resolved. It should be mentioned that heat due to the absorption of light may in principle increase the temperature in the colloids by a very small amount. However, such effects have not been observed here or in previous studies, which indicates that this effect is not important for the current system. Because we use a pair of nearly crossed polarizers, the beads appear as bright spots with a thin dark cross due to geometric depolarization. It should also be mentioned that the intensity fluctuations were most pronounced when using objectives with a sufficiently small numerical aperture (NA ) 0.5 or smaller) because otherwise the focused light may appear inside the colloids instead of on the magnetic film. Previously we showed that magnetic domain walls are able to attract paramagnetic beads and change their brightness.10 The new feature reported here is the ability to actively control the average intensity and intensity fluctuations by applying an external magnetic field to a homogeneous magnetic film in the absence of domain walls. Figure 4 shows the intensity distribution of the colloids in the absence of an external magnetic field. The intensity is measured in gray levels, where one gray level corresponds to an intensity of approximately 1 µW/cm2. The histogram displayed in Figure 3 is obtained from about 3600 measurements taken by recording the intensity of 4 colloids over a period of 30 s. It is seen that the distribution is broad with an intensity (gray level) average of Im ≈ 21. Upon applying an external magnetic field of H ) 960 A/m perpendicular to the garnet surface (z direction), we observed that the average intensity was reduced to Im ≈ 9. At the same time, the variance is considerably smaller, as can be seen from Figure 4. We have therefore “turned off” the colloids by turning on the magnetic field. This phenomenon can be used to create an optomagnetic switch, as demonstrated in Figure 5. Here the intensity of a single colloid was recorded as we switched the magnetic field on and off. As discussed above, the colloid is “blinking” in the absence of a magnetic field. However, once we turn on a strong magnetic field, the colloid turns nearly black, and the blinking disappears. To gain a better understanding of the system, we determined the average intensity Im as a function of the magnetic field obtained from distributions such as the ones seen in Figures 3 and 4. The results are shown as squares in Figure 6. Note that the intensity decreases monotonically with increasing magnetic field. Similarly, the root-mean-square deviation ∆I seen in Figure 7 (squares) was found to decrease with increasing magnetic field strength. It is found that whereas Im decreases by a factor of 2 as the magnetic field
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Figure 5. Histogram that shows the intensity distribution in H ) 960 A/m obtained from about 3600 measurements taken by recording the intensity of 4 colloids over a period of 30 s.
Figure 6. Upon turning the magnetic field on and off, we may control the intensity and intensity fluctuations associated with the colloids. This phenomenon can be used to create an optomagnetic switch, as shown here. The average intensity and intensity fluctuations are large when the magnetic field is turned off. The magnetic field was controlled manually. increases from 0 to 960 A/m, ∆I decreases by a factor of 5. These measurements indeed demonstrate that both the average intensity and fluctuations are controlled by the external magnetic field, with the latter property being more strongly influenced.
3. Discussion The total force on the colloid from the magnetic film can be evaluated asF B ) -∇ E, where the total energy of the colloid is given by E ) Ed + Ee + Eg. Here, Ed is the magnetic interaction energy, Ee is the electrostatic interaction energy, and Eg is the gravitational energy. To understand the force on a single magnetic bead, we note that the external magnetic field induces a magnetic B T where H BT ) H B dipole moment in the colloid, m b ) (4π/3)a3χH +H B mag is the sum of the external magnetic field and that from the magnetic film. We will here assume that the latter field is much weaker than the external magnetic field. However, the colloidal magnetic dipole moment sets up a magnetic field that interacts with the magnetization vector M B of the magnetic film. The magnetic interaction energy between the colloid and the magnetic film is given by
Ed ) -µ
∫∫∫MB ‚HBd dV
(1)
Figure 7. Measured average intensity as a function of the magnetic field (0), where each value is obtained from about 3600 measurements taken by recording the intensity of 4 colloids over a period of 30 s. The solid line corresponds to the theoretical curve found using eq 7 and p ) 108 m-1, κ ) 2 × 107 m-1, and B ) 1000 kBT.
Figure 8. Measured root-mean-square values (0) of the intensity (∆I) as a function of the external magnetic field, where each value is obtained from about 3600 measurements taken by recording the intensity of 4 colloids over a period of 30 s. The solid line corresponds to the theoretical curve found using eq 10, p ) 109 m-1, and κ ) 2 × 107 m-1.
where µ is the permeability of water and the magnetic field from the colloid is given by
H Bd )
(
b ‚b) r b r m 1 3(m b - 3 5 4π r r
)
(2)
We note from ref 10 that the magnetic film has strong in-plane anisotropy, which means that it can reorient easily within its own plane. However, tilting the magnetization vector entirely out of the plane (i.e., along the z axis) requires a field of about 105 A/m, which is much larger than the magnetic fields applied here. Thus, we may assume that the magnetic field from the colloid only reorients the magnetization vector in the plane so that it is pointing radially outward, as seen in Figure 8. We may therefore write the magnetization vector asM B ) Msb eF, where b eF is a radial unit vector in the xy plane, and the magnetic moment m b ) me bz of the colloid is in the z direction. The magnetic interaction
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Figure 9. Magnetic moment of the colloid induces a dipole moment that interacts with the magnetization vector of the magnetic film. The easy axis of the magnetic film is in-plane, which means that it is easy to align the magnetization vector in any direction in the film plane but difficult to create a magnetization component perpendicular to the film plane. Thus, the radial component of the colloidal dipolar field interacts with the magnetization vector whereas the z component does not interact.
energy is now given by
Ed ≈ -µMs
∫∫∫HFd dV ) -µχa3HMs ∫∫∫rz4 dV
(3)
Figure 6 shows Im as a function of the magnetic field when p ) 108 m-1, κ ) 2 × 107 m-1, and B ) 10 000 kBT. These parameters were selected to obtain the best possible fit and are reasonable given the fact that the magnetic film is covered with PSS (which is expected to give high B and κ values because of its charged nature). It is seen that the theory agrees well with the experimental data as long as the magnetic field is nonzero. However, when H ) 0 the theory predicts a considerable increase in intensity not seen in our measurements. It is clear that the linear relationship between intensity and height h is only a rough approximation. An understanding of this relationship awaits precise measurements of the height h and accurate modeling based on wave optics and is therefore outside the scope of the current study. To understand the intensity fluctuations using this model, we expand the energy to second order at about the equilibrium height hm:
E(h) ≈ E(hm) +
z+t z
(4)
In addition to magnetic interactions, there are electrostatic interactions between the colloid and the magnetic film, with the interaction energy given by
Ee ) Be-κz
(5)
where B is a constant that depends on the surface charges (of the film and colloid) and lD ) 1/κ is the Debye length. Finally, there are also gravitational forces acting on the colloid given by
Eg )
4π (F - Fw)a3gz 3 c
(6)
where Fc ) 1600 kg/m3 is the density of the colloids, Fw ) 1000 kg/m3 is the density of water, and g ) 10 N/kg. We now assume that h , a and take advantage of the fact that a , t. Then it is easy to minimize the energy to find the average height hm,
(
1 hm ≈ ln κ
κB 4π πµχa HMs + a3(Fc - Fw)g 3 2
)
(7)
It is important to note that the average height can be tuned by altering the Debye length (e.g., by altering the salt concentration) or the surface charge. In the current study, we have coated the magnetic film with PSS so that the spherical colloid focuses the light inside the magnetic film. The exact relationship between intensity and distance h above the magnetic film surface is not yet precisely known, but we will here assume that this relationship is nearly linear. In this approximation, the average intensity is directly proportional to hm such that Im ) phm, where p is a constant. The solid line in
(h - hm) +
hm
( )
1 d 2E 2 dh2
(h - hm)2 (8)
hm
We note that the first term of eq 9 is a constant and the second term is zero when ∆h ) h - hm ) 0. However, the mean-square deviation of the height is not zero, and upon taking the proper average, we get
where H Fd is the radial component of the magnetic field from the colloid at the position of the magnetic film. Upon evaluating this integral over the volume of the magnetic film, we find that
Ed ≈ -πµχa3HMs ln
() dE dh
〈(∆h)2〉 ≈
2kBT
( ) d2E dh2
(9)
hm
where 〈 〉 denotes the average, kB is the Boltzmann constant, T ) 300 K, and we have used 〈E(h) - E(hm)〉 ≈ kBT. Evaluating eq 9 and using I ) ph gives the following expression for the mean-square deviation of the intensity:
〈(∆Ith)2〉 ≈
2p2kBT 4π πµχaHMs(κa - 1) + κa3(Fc - Fw)g 3
(10)
The solid line in Figure 7 shows ∆Ith ) 〈(∆Ith)2〉 as a function of H using the parameters above but with p ) 109 m-1. The reason for the selected value of p is that it gives the best fit to the curve, and p ) 108 m-1 gives values of ∆Ith that are too small. Both experiment and theory predict a significant decrease in the intensity fluctuations with increasing magnetic field. However, the difficulty in obtaining a reliable constant p suggests that a thorough theoretical study is necessary to understand how the colloids act as lenses (i.e., how they scatter and focus light near interfaces in polarized microscopy setups). For example, it is clear that the linear approximation I ) ph used here may not be valid for all of the intensities sampled by the CCD. Such a study is outside the scope of this article.
4. Conclusions We have introduced a novel optomagnetic switch where the brightness and fluctuations of colloids can be controlled by an external magnetic field. It was shown that phenomena can be explained by an interplay of gravitational, electrostatic, and magnetic forces, where the latter ones can be tuned precisely in real time. The optomagnetic switch may have applications in microfluidic systems or for probing small distances. LA0530900
