Programmable Assembly of Colloidal Particles Using Magnetic

Mar 2, 2004 - A substrate of thin micromagnets covered by a template of microwells is used to direct the assembly of superparamagnetic colloidal beads...
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Langmuir 2004, 20, 2553-2559

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Programmable Assembly of Colloidal Particles Using Magnetic Microwell Templates Benjamin B. Yellen* and Gary Friedman Electrical and Computer Engineering Department, Drexel University, 3141 Chestnut Street, Commonwealth Hall Room 411, Philadelphia, Pennsylvania 19104 Received July 3, 2003. In Final Form: December 4, 2003 A substrate of thin micromagnets covered by a template of microwells is used to direct the assembly of superparamagnetic colloidal beads into two-dimensional arrays. It is confirmed that the magnetization of the micromagnets can direct beads to programmed locations on the substrate with assistance of externally applied magnetic fields. Empirical investigations on this topic were guided by mathematical models with the intent to elucidate the conditions that promote a single bead to be assembled in the desired microwells. To demonstrate that this technique is programmable, heterogeneous arrays of colored beads are produced.

Introduction Controlled assembly of colloidal building blocks is desired in many devices and materials for photonic,1-3 electronic,4,5 magnetic, and sensor6 applications. In some applications, such as photonic crystals,7-10 the entire device can be built using the same type of building block. Other devices, however, function properly only with builtin heterogeneity. Chemically heterogeneous surfaces, for example, are a requirement for biochemical sensors used in genetic discovery11 and for assembling arrays of living cells.12 Yet most self-assembly techniques are limited to placing only one type of microscopic object in multiple locations on a passive surface. Building heterogeneous structures by self-assembly requires an active surface, which can be programmed to accept or reject building blocks at recorded locations. In this paper, a programmable self-assembly method for the placement of two or more different types of superparamagnetic colloidal beads onto lithographically defined magnetic microwell templates is demonstrated. Magnetostatic assembly enjoys certain advantages over other assembly methods, such as electrostatic, van der Waals, and surface tension interactions.13 For one, magnetic fields act in much longer range than van der Waals, surface tension, and electrostatic fields in polar solvents. * Author to whom correspondence should be addressed. E-mail: [email protected]. (1) van Blaaderen, A. MRS Bull. 1998, 23, 39-43. (2) Lu, Y.; Yin, Y. D.; Xia, Y. Adv. Mater. 2001, 13, 34-37. (3) Maier, S. A.; Brongersma, M. L.; Kik, P. G.; Meltzer, S.; Requicha, A. A. G.; Atwater, H. A. Adv. Mater. 2001, 13, 1501-1505. (4) Hostetler, M. J.; Murray, R. W. Curr. Opin. Colloid Interface Sci. 2000, 2, 42-50. (5) Shipway, A. N.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18-52. (6) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829-832. (7) Yin, Y.; Xia, Y. Adv. Mater. 2002, 14 (8), 605-608. (8) Ozin, G. A.; Yang, S. M. Adv. Funct. Mater. 2001, 11 (2), 95104. (9) Van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321324. (10) Yang, P.; Deng, T.; Zhao, D.; Feng, P.; Pine, D.; Chmelka, B. F.; Whitesides, G. M.; Stucky, G. D. Science 1999, 282, 2244-2246. (11) Fodor, S.; Rava, R. P.; Huang, X. C.; Pease, A. C.; Holmes, C. P.; Adams, C. L. Nature 1993, 364, 555-557. (12) Craighead, H. G.; James, C. D.; Turner, A. M. P. Curr. Opin. Solid State Mater. Sci. 2001, 5, 177-184. (13) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718-8729.

Magnetic fields do not interfere with most biological or biochemical functions. Magnetic fields do not cause movement of ions in liquids, thus avoiding frequently unwanted electrochemical reactions and fluid flows that may occur in electrostatics-assisted assembly methods. In addition, the highly nonlinear behavior of magnetic materials can be exploited to allow nonvolatile operation and switching between attractive and repulsive magnetic interactions, something that has not been widely employed in colloidal assembly techniques. The analogue to magnetostatic assembly, electrostatic assembly of colloidal building blocks has also been investigated by several different authors. Some of this work has been based on the assembly of charged objects onto lithographically patterned surfaces,14-22 while other work has been based on dielectrophoretic assembly of wires, spheres, and other shapes onto patterned contacts.23-29 Programmable assembly is theoretically possible by electrostatic assembly methods; however, it would require the ability to individually control surface elements (14) Tien, J.; Terfort, A.; Whitesides, G. M. Langmuir 1997, 13 (20), 5349-5355. (15) Jacobs, H. O.; Whitesides, G. M. Science 2001, 291, 1763-1766. (16) Fudouzi, H.; Kobayashi, M.; Shinya, N. Langmuir 2002, 18, 7648-7652. (17) Demers, L. M.; Mirkin, C. A. Angew. Chem., Int. Ed. 2001, 40 (16), 3069-3071. (18) Chen, K. M.; Jiang, X.; Kimerling, L. C.; Hammond, P. T. Langmuir 2000, 16 (20), 7825-7834. (19) Grzybowski, B. A.; Winkleman, A.; Wiles, J. A.; Brumer, Y.; Whitesides, G. M. Nat. Mater. 2003, 2, 241-245. (20) Aizenberg, J.; Braun, P. V.; Wiltzius, P. Phys. Rev. Lett. 2000, 84, 2997-3000. (21) Jiang, X. P.; Clark, S. L.; Hammond, P. T. Adv. Mater. 2001, 13, 1669-1673. (22) Fudouzi, H.; Kobayashi, M.; Shinya, N. Adv. Mater. 2002, 14, 1649-1652. (23) Hermanson, K. D.; Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Science 2001, 294, 1082-1086. (24) Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Appl. Phys. Lett. 2003, 82 (6), 949-951. (25) Huang, Y.; Duan, X.; Wei, Q.; Lieber, C. M. Science 2001, 291, 630-633. (26) Cui, Y.; Lieber, C. M. Science 2001, 291, 851-853. (27) Duan, X.; Huang, Y.; Cui, Y.; Wang, J.; Lieber, C. M. Nature 2001, 409, 66-69. (28) Smith, P. A.; Nordquist, C. D.; Jackson, T. N.; Mayer, T. S.; Martin, B. R.; Mbindyo, J.; Mallouk, T. E. Appl. Phys. Lett. 2000, 77 (9), 1399-1401. (29) Walti, C.; Wirtz, R.; Germishuizen, W. A.; Bailey, D. M. D.; Pepper, M.; Middelberg, A. P. J.; Davies, A. G. Langmuir 2003, 19, 981-984.

10.1021/la0352016 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/02/2004

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Figure 1. The illustrations I, II, and III are the cross-sectional sketches of the three general types of magnetic microwell templates used in the experiments. In type I, the poles of the micromagnet are positioned at the bottom edges of the microwell. In type II, one pole of the micromagnet is positioned at the center of the microwells. In type III, both poles of the micromagnets are positioned in the center of the microwells. The optical images in I, II, and III show lithographically patterned substrates used to investigate the three typical template designs. The cobalt micromagnets (white) used to investigate type I templates are 10 µm in length and 3 µm in width; for type II, the micromagnets are 10 µm in length and 5 µm in width; and for type III, the micromagnets are 20 µm in length and 4 µm in width. The microwells in all types are 10-µm square and approximately 8-µm deep.

in real time. It would require making substantial circuitry and contacts on the surface and simultaneously applying potentials to enormous numbers of electrodes. Magnetic materials, on the other hand, have memory that can be remotely programmed with external recording devices. Previously, we have demonstrated that a template of micromagnets can be used to guide the assembly of colloidal superparamagnetic beads onto a surface with high precision.30-34 It was also proven that externally applied magnetic fields can assist the assembly process by directing where on the micromagnet the colloidal beads will be deposited.30-34 However, while a pattern of micromagnets alone is suitable for capturing magnetic beads, its control over the number of beads that populate the area of interest is relatively poor because magnetic beads interact strongly with each other and do not effectively shunt the micromagnet’s field. Moreover, it was found that beads are easily washed away when the solution is removed. In this work, to improve control over the spatial distribution and number of beads deposited at specific locations, micromagnets are used in conjunction with a set of microwells. The microwells serve two functions. The first function is to restrict the number of beads that may approach the micromagnet. The second function is to protect beads inside the microwells from being washed away when the fluid is removed. Beads deposited outside the microwells, on the other hand, can be washed away with light rinsing and agitation of the fluid. The process of bead assembly onto three different types of magnetic microwell templates is mathematically modeled and experimentally tested to determine the optimum conditions for bead assembly. Mathematical models indicate that an externally applied magnetic field can further assist the assembly process by directing beads (30) Yellen, B. B.; Friedman, G.; Feinerman, A. J. Appl. Phys. 2003, 93 (10), 7331-7333. (31) Yellen, B. B.; Friedman, G.; Feinerman, A. J. Appl. Phys. 2002, 91, 8525-8527. (32) Yellen, B. B.; Friedman, G. J. Appl. Phys. 2003, 93 (10), 84478449. (33) Plaks, A.; Tsukerman, I.; Friedman, G.; Yellen, B. B. IEEE Trans. Magn. 2003, 39 (3), 1436-1439. (34) Hovorka, O.; Yellen, B. B.; Friedman, G. IEEE. Trans. Magn. 2003, 39 (5), 2549-2551.

into or out of specific microwells, thereby providing the first step for a programmable self-assembly technique.30 External magnetic fields will be used in this paper to assist the assembly and arrangement of two different fluorescently labeled beads into controlled patterns on a surface. Experimental Methods Micromagnets were patterned in 100-nm-thick electron-beamevaporated cobalt film using standard photolithographic lift-off methods. In the lift-off process, an image is defined by exposing photoresist to ultraviolet radiation through a patterned mask. The photoresist pattern is developed, and then metal is evaporated onto the patterned wafer. Finally, the remaining photoresist is stripped to produce a pattern of cobalt. While negative or multilayer resists are frequently utilized to obtain an undercut resist profile, positive Shipley 1813 photoresist yielded satisfactory results. Next, a protective layer of SU-8 film was patterned and aligned on top of the micromagnets. The protective layer consists of an array of square microwells patterned at various positions over the poles of the micromagnet and designed to permit one bead only to enter the microwell. A cross section of the resulting structures is sketched in Figure 1 (I-III), and overhead photographs of some templates are shown for each type. The micromagnets were magnetized to saturation with an external permanent magnet. Magnetic force microscopy (MFM) imaging revealed a multidomain structure of the remanent state with one large elongated domain in the center, aligned parallel to the magnetized direction (Figure 2). The contrast between the domain patterns of the magnetized state and that of the demagnetized state supports the assumption in empirical and theoretical investigations that thin cobalt micromagnets with high shape anisotropy behave approximately like single-domain magnets. After magnetization, the substrate was immersed in a bath of deionized waterr, and commercially available superparamagnetic colloidal beads (8.0-µm-diameter beads conjugated with Biotin and purchased from Spherotech) were injected into the bath while the process of bead assembly onto the templates was observed. To track the assembly of the different beads, the 8.0µm beads were labeled with fluorescent streptavidin conjugates [Texas Red, and fluorescein isothiocyanate (FITC) streptavidin conjugates were purchased from Zymed]. The zeta potential of the Biotin beads was also measured at neutral pH in deionized water using a Zeta-meter 3.0+ (purchased from Zeta-meter, Inc.). The Biotin-coated beads had a zeta potential of -45.3 ( 3.6 mV. The zeta potential of colloidal beads is a good indicator of the stability of a colloidal suspension (i.e., whether the beads will

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where χ is the magnetic material susceptibility and V is the volume of the spherical bead. By analogy, the nonlinear constitutive relation is given by the following formula:

m b ) G(H B) )

H B 3χ Vf(|H B |) χ+3 |H B|

(2)

where f is an appropriately normalized scalar nonlinear function. A Langevin-type function is often used to model the nonlinearity. However, for the purposes of the calculations reported below a hard saturation model was assumed (linear region followed by constant magnetization region) to allow comparison with completely linear models. The magnetic field for the nth bead due to external sources and other beads is given by

B extn + H Bn ) H Figure 2. MFM images of ellipsoidal magnetic islands with dimensions from 5 to 20 µm. The domain structure image in part a is consistent with that of the demagnetized ferromagnetic film, while the image in part b containing an elongated domain in the center is consistent with that of the magnetized ferromagnetic film. agglomerate together). A large zeta potential (typically larger than 25 mV in magnitude) is helpful in reducing the bead-tobead and bead-to-surface interactions. The assembly process of beads onto the templates was observed with a Leica DM LFS microscope through a fluid-immersion lens. During these experiments, the bath was agitated to increase the probability that each bead finds its nearest potential well. The experiments usually lasted a few minutes. External magnetic fields were applied perpendicular or parallel to the substrate using a solenoid coil with iron core. The apparatus for creating magnetic fields was designed to provide substantially uniform magnetic fields across the extent of the substrate. To create fields perpendicular to the substrate, a solenoid with a 2.5-cm-diameter iron core was positioned a few millimeters beneath the substrate. Applied magnetic fields in the range of 10-200 G were sufficient to bias the magnetic moments of the beads in the direction of the field. However, when applied perpendicularly to the substrate the same field had practically no effect on the micromagnet because of its shape anisotropy (the micromagnet is very thin compared with its in-plane dimensions). To create fields parallel to the substrate, two solenoids with 10-cm-diameter iron cores were positioned a few centimeters away from each other on either side of the substrate. In this case, applied magnetic fields in the range of 10-20 G were used to bias the beads. These fields were below the micromagnet coercivity measured to be around 30 G.

Computational Methods The experimental investigations were guided by mathematical models, which attempted to analyze the force on individual beads in various conditions. Several assumptions were made to reduce computation complexity; however, these assumptions still allow orders of magnitude estimates of the forces on magnetic particles to be obtained. One assumption is that each superparamagnetic bead behaves like a point dipole. This assumption is realistic because the magnetic material inside each bead is encapsulated in glass or polymer and cannot come into direct contact with magnetic material inside other beads. In the case of a linear relationship between magnetization and the magnetic field, the bead’s magnetic moment is given by eq 1:

m b )

3χ VH B χ+3

(1)

1

N

∑ 4πk)1

[

3(m b k‚r bkn)r bkn rkn5

-

m bk

]

rkn3

(3)

where H B extn is the field created by the magnetized substrate and uniform external field at the location of the nth particle, b rkn is the vector from particle k to n, and rkn is the magnitude of this position vector. The magnetic moments of the beads are found through a relaxation-based iterative method obtained by using eq 3 in conjunction with the following equation:

b n-1 - λ[m b n-1 - G(H B n-1)] m bn ) m

(4)

where the relaxation constant λ (in our case λ ≈ 1) was selected for the fastest convergence. Having found the dipole moments of all magnetic particles, the force on the nth particle can be determined accordingly:

b n‚∇)H Bn F Bn ) µ0(m

(5)

Results The process of bead assembly onto type I, II, and III templates was investigated, and each type of template design was found to have certain advantages and disadvantages. One of the main concerns in magnetostatic assembly is whether beads that are in the microwells will still attract other beads on top. The ability of populated microwells to shunt the magnetic field is desirable, because then populated microwells would not be competing with unpopulated microwells for new beads. The key advantage to using type I templates is that beads inside the microwells are in close proximity to two micromagnet poles, as shown in Figure 3a. In this configuration, the bead shunts the magnetic field in the microwell very effectively, and subsequent beads that approach the microwell are either weakly attracted to or even repelled by the populated microwell. Therefore, type I templates were found to be very effective in assembling large closely packed arrays of beads, as shown in Figure 3b. In addition, type I templates are easier to fabricate because the microwell itself can be used as a mask for etching the cobalt film. Therefore, manual alignment of the two patterns is unnecessary because these are “selfaligned” templates. Type I templates do have a disadvantage, however, in that the magnetic fields must be applied parallel or antiparallel to the micromagnet’s magnetization to bias the beads to be attracted to or repelled from the microwells, as shown in Figure 3a. When a repulsive bias is desired, for example, the magnetic field bias must be applied

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Figure 3. The cross-sectional sketch in part a shows how type I templates can attract magnetic beads into the microwells with the assistance of uniform magnetic fields applied parallel to the substrate. The optical image in part b provides empirical proof that the type I design with the appropriate bias field can direct 7-µm beads into 10-µm wells with great reliability. The scale bar is 20 µm.

antiparallel to the magnetization of the micromagnets. A large antiparallel magnetic field bias can potentially reverse the micromagnet’s magnetization and cause microwells to be populated that were not intended to be populated. Nonetheless, type I templates can still be used in programmable assembly if the micromagnets have sufficiently high coercivity such that the applied magnetic field bias does not reverse its magnetization. In type II templates, on the other hand, the micromagnet is positioned at the center of the microwell, and magnetic fields must be applied perpendicularly to the substrate to attract or repel beads from the microwell. Type II templates can demonstrate very effectively both the attraction and the repulsion of beads from microwells, as shown in Figure 4b,d. The images shown in Figure 4a,b depict the process and experimental results of how beads can be attracted into the microwells under the assistance of a favorable magnetic field bias applied perpendicularly to the substrate. Alternately, the repulsive bias shown in Figure 4c,d demonstrates that a magnetic field bias applied in the opposite direction causes the beads to aggregate on top of the protective layer but not in the microwells. Because these beads are not protected by the microwells, light rinsing can remove them, resulting in a bare template as shown in Figure 1. The results shown in Figure 4 prove that it is not the microwell template but rather the magnetic pattern underneath that drives the assembly process. One key advantage to using type II templates is that the magnetic field bias is applied perpendicularly to the

Yellen and Friedman

substrate, so there is little concern about reversing the magnetization of the micromagnets (it takes enormous energy to turn the magnetization of the thin magnetic films out of the plane). However, the disadvantage to using type II templates is that the beads populating the microwells do not effectively shunt the magnetic field (because the beads have a free pole exposed). As a result, populated microwells compete with unpopulated wells for new beads, making it more difficult to assemble large closely packed arrays of solitary beads confined inside microwells. Type II templates have another disadvantage in that manual alignment of two different patterns is required. Because of limitations in alignment accuracy and photolithographic resolution, it will be more difficult to reduce these templates into the submicrometer range. Type II templates in conjunction with magnetic recording techniques can be used to assemble many different types of beads one after another at programmed locations on the surface. Accomplishing this task, however, requires the ability to control the magnetization of individual micromagnets. While this can be done theoretically, a much simpler method using type III templates can at least demonstrate the ability to assemble two different types of beads into an array. A two-step assembly process is employed to create a pattern of two differently colored beads. This process is schematically illustrated in Figure 5. The first step shown in Figure 5a depicts beads labeled with green fluorescence preferentially directed toward one pole of the micromagnet by a magnetic field bias that is uniformly applied perpendicularly to the entire substrate. Preferential deposition occurs because the magnetic field bias aligns the magnetic moments of all the beads, causing them to be attracted to one pole of the micromagnet and repelled from the other pole. Once the beads have been deposited at the desired locations, the excess solution of beads is rinsed away. Then in the second step, beads labeled with red fluorescence are introduced into the bath and directed to assemble on the opposite pole by reversing the magnetic field bias. In this way, two different fluorescently labeled beads are deposited at nearby positions on the surface. Beads that were previously deposited at one end are not ejected out of the wells when the magnetic field bias is reversed because the field near the pole of the micromagnet is stronger than the bias field. However, if the applied magnetic field bias is sufficiently strong, then in some cases the previously deposited beads are ejected out of the wells. Although not employed here, this phenomenon may find some interesting future applications. The first step in the template-directed assembly method was checked using unmodified Biotin beads, and the result is demonstrated in Figure 6a. It is clear from the image that beads preferentially deposit in the bottom rows and avoid the top rows of the array. The bead pattern shown in Figure 6a was fluorescently labeled by immersing the wafer in a solution of Texas Red streptavidin conjugate, and the result is shown in Figure 6b. Next, the magnetic field bias was reversed, and the Biotin-labeled beads introduced to the bath were directed to assemble in the top rows of the array. Those Biotin-labeled beads were fluorescently modified by immersing the wafer in a solution of FITC streptavidin conjugate. Figure 6c shows the array obtained after both assembly steps and rinsing of the wafer. Computational Results The computational method just described for determining the force on any number of 8.0-µm superparamagnetic

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Figure 4. The sketch in part a depicts an array of type II templates that are in attractive bias, and the optical image in part b shows 7.1-µm beads attracted into the wells. The sketch in part c depicts the template in repulsive bias, and the optical image in part d shows beads avoiding the wells. The black areas between the microwells are beads resting on top of the thick protective layer near the opposite pole of the island. The black areas are blurred because they are not in the same focal plane as the micromagnets.

Figure 5. The illustration on the left demonstrates the use of a magnetic field bias in the upward direction to direct green fluorescent beads to assemble preferentially in the right-hand wells. Once the green beads are assembled, the magnetic field bias is reversed to the downward direction and the template is exposed to a solution of red fluorescent beads, which are directed to assemble in the left-hand wells, as shown in the illustration on the right.

beads in arbitrary external magnetic fields was implemented using MATHCAD software. Superparamagnetic particles with s typical susceptibility of χ ) 2-3 were assumed to behave linearly with external magnetic fields up to 600 G, above which the particles are saturated. Magnetization of the islands was chosen to be consistent with the remnant magnetization of the cobalt film (around 1000 emu/cm3)35 of 50-nm thickness. The micromagnets were chosen to have a rectangular shape with a 20-µm length and 4-µm width. And the cobalt film is assumed to be uniformly magnetized to justify the approximation of this rectangular configuration as two magnetic line charges with uniform charge density at the poles. The forces on several particles interacting with magnetic microwell templates are computed with statistical variations for 100 trials using randomly generated values for the magnetic susceptibility and radius of each bead. The variation in the beads’ radii was taken to be consistent with commercially available materials and was treated as a random variable with uniform distribution (beads are often sorted with size cutoff filters) between 90 and 110% of a mean value. Because no data on the distribution of the bead susceptibility was known, it was taken to have a log-normal distribution with 90% of its probability density occurring between 0.85 and 1.15 times the mean value. Using statistical trials, the expected force and standard deviation are computed for all the particles in the system. First, the interaction of beads with type I templates was analyzed to determine to what degree the assembly (35) Parker, G. J.; Cerjan, C. J. Appl. Phys. 2000, 87, 5514-5516.

process is self-limiting. Specifically, we would like to know what conditions can cause a second bead approaching the template to be repelled from a microwell that already contains a first bead, as shown in Figure 3a. In this simulation, the only magnetic field sources considered are two opposing line charges located at the wall edges of 10-µm square microwells, as shown in Figure 1 (I). It is assumed that the well is sufficiently deep such that the second particle can only approach the first particle from a vertical descent. The force on the second bead is then computed as a function of both the separation distance between the two beads and an increasing magnetic field bias applied parallel to the micromagnet magnetization. The results from the analysis shown in Figure 7 indicate that populated microwells can actually attract a second particle in low magnetic field bias. The result at first seems nonphysical, but upon more careful consideration it is clear why this should happen. The force on the second bead is due to its interaction with both the first bead and the micromagnet. When the applied external field is weak, both beads are weakly magnetized and, thus, the beadbead repulsion is low. Superimposed on the bead-bead interaction is the attractive interaction between the second bead and micromagnet. The attractive interaction dominates below certain critical applied field strengths, as shown in Figure 7. When the external field is sufficiently large and the beads are close together, the bead-bead repulsive interaction dominates, causing the second bead to be repelled at all practical distances. For the analysis shown in Figure 7, this critical field strength is around 200 G. This analysis indicates that saturating magnetic

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Figure 6. The optical image in part a depicts an array of 8-µm beads that have assembled only in the bottom rows of the array. The fluorescent image in part b depicts the same array in part a that was subsequently exposed to the Texas Red streptavidin conjugate. The fluorescent image in part c shows the arrays in parts a and b after the green beads are directed to assemble in the top rows of the array. One error was observed in part c, which is a missing green bead from the array location in the upper right-hand corner.

Figure 8. Illustration of type II templates immediately after the uniform magnetic field bias was switched from attractive to repulsive bias. Adjacent beads in the chain now have opposing magnetization, which induces repulsive interactions that break the chain.

Figure 7. Graphical representation of the force on a second bead as a function of increasing magnetic field bias when the two beads are separated by distances of 25, 50, 75, 100, 125, and 150% of a bead diameter along the z axis. The inlay demonstrates that attraction occurs for low magnetic field bias.

fields should be applied to type I templates if the goal is to create uniform particle coverage that is “self-limiting”, meaning that all beads that approach populated microwells are repelled from far away. Models also indicate that this assembly method should work equally well if the system is reduced into the submicrometer range. Next, the interaction of beads with type II templates was analyzed to determine the conditions that promote

only a single bead to be retained in the microwells. These systems are not self-limiting, however, because microwells that are populated with a single bead as shown in Figure 4a still exhibit attraction for additional beads. It is true that the additional beads sitting on top of the first bead are not protected by the microwells and may be rinsed away with light agitation of the fluid; however, there are more elegant methods for reducing the contamination down to a single bead by a magnetic cleaning technique that will be discussed next. Figure 8 is a diagram of the magnetic cleaning technique employed for type II templates. The field produced by the exposed pole is highly inhomogeneous and falls off quickly over dimensions commensurate with that of a typical bead. It is assumed that a chain has been originally formed by application of uniform magnetic fields parallel to the field produced by the exposed micromagnet pole. When the uniform field is reversed to antiparallel orientation, the competition between the fields due to the micromagnet and the uniformly applied bias causes some beads in the

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Conclusions

Figure 9. Graphical relationship of the number of beads remaining in a chain of three beads with a mean diameter of 8.0 µm. The solid line represents the expected breaking link, and the dashed and dotted lines provide the breaking range.

chain to have opposing magnetization and to experience repulsive interactions. The model will investigate the possibility of tuning these repulsive interactions between the beads to control the number of beads remaining in the microwells. In this analysis, a chain of three beads is studied under increasing antiparallel magnetic field bias with statistical trials. The relationship between the breaking link in the chain and the antiparallel magnetic field bias is graphically shown in Figure 9. It is clear from the figure that fields above a certain threshold can eject all particles out of the microwells, while a relatively large range of fields can be applied to leave only one particle in the microwells. This conclusion is of practical importance because it gives the range of conditions that must be followed to not only selectively assemble 8.0-µm beads into designated wells but also to prevent the ejection of previously deposited beads out of both type II and type III templates. Models also indicate that tuning the number of beads left in the chain can be controlled more reliably if the system is reduced into the submicrometer range.

Self-assembly (or bottom-up assembly) is an attractive technique for fabricating ordered structures because it provides a method for simultaneously placing enormous numbers of microscopic objects in many different locations on a surface. Typical self-assembly methods are excellent for creating homogeneous surfaces composed of the same type of object but have difficulty in creating ordered heterogeneous surfaces composed of two or more different types of objects. To create heterogeneous patterns, the surface must be actively programmed to accept or reject colloidal components at specified locations. To our knowledge, the programmable self-assembly method demonstrated in this paper is the first selfassembly demonstrated to place multiple different types of colloidal objects in close proximity on the same surface. This programmable self-assembly technique is accomplished using magnetic fields and ferromagnetic memory elements that can be recorded to promote or prevent colloidal particle deposition at precise surface locations. To prove this technique, heterogeneous superparamagnetic colloidal particle arrays were assembled onto magnetic microwell template patterns under the assistance of externally applied magnetic fields. Magnetically driven assembly has several advantages over other techniques. In particular, the ability to generate both repulsive and attractive forces results in fewer errors and a greater contrast between printed regions. In addition, patterning based on magnetically driven assembly does not employ high-temperature processing or harmful chemical solvents and, therefore, may be suitable for deposition of delicate biological materials such as oligonucleotides, proteins, and cells. LA0352016