pubs.acs.org/Langmuir © 2010 American Chemical Society
Magnetic Field Induced Assembly of Highly Ordered Two-Dimensional Particle Arrays Alexander Weddemann,* Frank Wittbracht, Bernhard Eickenberg, and Andreas H€utten Department of Physics, Thin Films and Physics of Nanostructures, Bielefeld University, PB 100131, 33501 Bielefeld, Germany Received July 14, 2010. Revised Manuscript Received November 6, 2010 Suspended magnetic beads are exposed to an external homogeneous magnetic field which rotates around the axis perpendicular to the field direction. Because of dipolar interactions, magnetic beads assemble in highly ordered twodimensional hexagonal arrays perpendicular to the rotation axis. By continuous provision of the particle concentration, the growth modes of two-dimensional particle clusters and monolayers are observed. The structure of the resulting assembled objects is analyzed for different field frequencies and particle concentrations. We identify dynamic processes which enhance stability and reduce lattice distortions and, thus, allow for the application of these particle agglomerations as dynamic components in lab-on-a-chip technologies.
Introduction With a wide range of applications in microfluidic lab-on-a-chip technologies, magnetic beads and nanoparticles were thoroughly studied during the past decades.1-4 Their permanent magnetic moment allows for a manipulation by external (inhomogeneous) magnetic fields5,6 and the detection by magnetoresistive sensors via their magnetic dipolar stray field.7,8 In these applications, the individual magnetic object acts as a carrier or marker for various substances or biomolecules to be manipulated or analyzed. Therefore, experiments are executed with very low particle concentrations which allows to neglect the interplay between them. However, at sufficiently high concentrations, particle coupling via magnetic stray fields gains importance.9 The agglomeration in suprastructures similar to the self-assembly processes in nanoparticular systems10,11 is entailed. Recently, programmable and reconfigurable matter attracted a lot of interest in lab-on-a-chip devices.12,13 Individual components assemble under the influence of an external constraint, execute various functional tasks, and, afterward, decay once the perturbation potential is switched off again. The controlled *Corresponding author. E-mail:
[email protected].
(1) Pamme, N. Lab Chip 2006, 6, 24–38. (2) Gijs, M. A. Microfluid. Nanofluid. 2004, 1, 22–40. (3) H€utten., A.; Sudfeld, D.; Ennen, I.; Reiss, G.; Wojczykowski, K.; Jutzi, P. J. Magn. Magn. Mater. 2005, 293, 93–101. (4) Sudfeld, D.; Ennen., I.; H€utten, A.; Gotta-Schindler, U.; Jaksch, H.; Reiss, G.; Meissner, D.; Wojczykowski, K.; Jutzi, P.; Saikaly, W.; Thomas, G. J. Magn. Magn. Mater. 2005, 293, 151–161. (5) Panhorst, M.; Kamp, P. B.; Reiss, G.; Br€uckl, H. Biosens. Bioelectron. 2005, 20(8), 1685–1689. (6) Lehmann, U.; Vandevyver, C.; Patashar, V. K.; Gijs, M. A. M. Angew. Chem. 2006, 118, 3132–3137. (7) Loureiro, J.; Ferreira, R.; Cardoso, S.; Freitas, P. P.; Germano, J.; Fermon, C.; Arrias, G.; Pannetier Lecoeur, M.; Rivadulla, F.; Rivas, J. Appl. Phys. Lett. 2009, 95, 034104. (8) Albon, C.; Weddemann, A.; Auge, A.; Rott, K.; H€utten, A. Appl. Phys. Lett. 2009, 95(2), 023101. (9) Mikkelsen, C.; Hansen, M.; Bruus, H. J. Magn. Magn. Mater. 2005, 293, 578–583. (10) Ghazali, A.; Levy, J. Phys. Rev. B 2003, 67. (11) Levesque, D.; Weis, J. J. Phys. Rev. E 1994, 49, 5131. (12) Kalontarov, M.; Tolley, M.; Lipson, H.; Erickson, D. Microfluid Nanofluid 2009, in press; DOI: 10.1007/s10404-010-0572-9. (13) Tolley, M.; Krishnan, M.; Erickson, D.; Lipson, H. Appl. Phys. Lett. 2008, 93, 254105.
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employment of such on-demand assemblies requires a strong understanding not only of the properties of resulting agglomerations but also of their formation dynamics. Riley and Lidell14 proposed a method for manufacturing of highly ordered assemblies on the basis of particles with a mushroom cap-shaped morphology. The process is based on particle sedimentation within a 2D confining wedge, and therefore, long time scales are entailed. In contrast, high formation and decay rates are preferred for the application in lab-on-a-chip devices.15 Consequently, a stronger driving force than gravitational effects is necessary. The magnetic interactions between superparamagnetic beads and particles form a promising candidate for such an approach. A particular advantage of these systems is that after formation the stability of the magnetic equilibrium state can be overcome by thermal excitation which accelerates the decay of suprastructures upon removal of the external constraint. The agglomeration process of magnetic particles may be initiated by an external magnetic field. If a homogeneous field is applied, there is no force acting on individual particles, but their magnetic moment vectors feel a torque which aligns moments parallel to the field orientation. Such increase of the effective magnetization of superparamagnetic objects entails an increase of the generated stray fields. Since the dipolar particle field is inhomogeneous, magnetic objects nearby are strongly attracted and particles start to assemble in one-dimensional suprastructure.16 As shown by Climent et al.,17 the governing driving forces for the formation dynamics are not restricted to magnetic coupling, but also Brownian motion and multibody hydrodynamic interactions play an important role. Such one-dimensional assemblies have already found various applications: Lacharme et al.18 demonstrated the static employment of spontaneously arranged particle chains for the initialization of a sandwich immunoassay in an on-chip structure. Derks et al.19 succeeded in the realization of a micropump by the (14) Riley, E. K.; Liddell, C. M. Langmuir 2010, 26(14), 11648–11656. (15) Whitesides, G. M. Nature 2006, 442, 368–373. (16) Promislow, J. H. E.; Gast, A. P.; Fermigier, M. J. Chem. Phys. 1995, 102 (13), 5492–5498. (17) Climent, E.; Maxey, M. R.; Karniadakis, G. E. Langmuir 2004, 20, 507–513. (18) Lacharme, F.; Vandevyver, C.; Gijs, M. A. Anal. Chem. 2008, 80(8), 2905– 2910.
Published on Web 11/23/2010
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employment of magnetic beads as dynamic components: particles assembled and were dragged through the carrier liquid by an inhomogeneous field contribution. The resulting momentum transfer from the confined objects to the solvent induced a flow profile within the microchannel. Though also assemblies of higher dimension were studied,20 the complex interplay of the dipolar particle coupling21,22 makes the
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employment of higher dimensional suprastructures a challenging task. Grzybowski et al.23 employed 2.08 mm particles as seeds for assemblies of 1.27 mm objects which assemble along a liquid air interface. However, such a highly localized initialization process will be difficult to implement in a wide range of already existing applications. Therefore, this work tries to bridge the gap between the complex self-organization processes of two-dimensional particle structures and easy to handle applications. We provide an easy method for the creation of highly ordered on-demand twodimensional particle assemblies and monolayers by the employment of time-dependent, rotating magnetic fields which can be easily integrated into existing lab-on-a-chip devices.
Experimental Section Magnetic Microbeads. Superparamagnetic microbeads Dyna-
Figure 1. Resulting monolayer of magnetic beads. (a) Particles assemble in highly ordered hexagonal structures. The intensity plot shows the Fourier transform of the particle positions within a grain. (b) Zero- and one-dimensional lattice distortions are present. (c) Dark spots are particles in a higher layer.
beads M-270 SA24 were purchased from Invitrogen Corp. (batch H78300). These microbeads have a radius of 1.4 μm and an iron content of 14%, are coated with streptavidin, and stabilized in PBS buffer solution (pH=7.4). The stock solution has a microbead concentration of 10 mg/mL. In order to avoid salt crystallization after spotting and liquid evaporation, the buffer was exchanged with deionized water (18 MΩ 3 cm, Millipore). From a volume of 100 μL of the stock solution, microbeads were collected by centrifugation and resuspension in 100 μL of DI water. The process was repeated three times. Afterward, three solutions at concentrations of 0.2, 1.0, and 5.0 mg/mL were prepared by diluting the particle suspension with DI water. Rotating Magnetic Field and Microbead Spotting. The magnetic field used for the microbead assembly is created by a magnetic stirrer RCT classic (IKA) at a field strength of 330 Oe. Assemblies were performed on a silicon wafer. Prior to spotting, the wafer was sonicated for 15 min in acetone (VWR) and afterward rinsed in ethanol (VWR). The wafer was positioned in the
Figure 2. Dynamic ordering processes. (a) A magnetic cluster absorbs a one-dimensional particle chain. During the absorption, the perfect symmetry of the cluster remains. (b) Merging of multiple clusters; the insets show several fragments before agglomeration. Along the marked junction areas, the symmetry is broken. (c) Under the time-dependent field influence, one-dimensional defects (indicated by black markers) may reorder which entails the creation of vacancies (highlighted by white markers) during the process. 19226 DOI: 10.1021/la102813w
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center of the hot plate of the magnetic stirrer. Spotting of 1 μL bead suspension was achieved with a pipet. The magnetic stirrer was started with a delay of 5 s to enable the formation of bead chains before the magnetic field is set into rotation. Data Evaluation. After evaporation of the liquid, the spotting was either repeated or microscopy data were collected by employment of a digital optical microscope VHX-600 (Keyence Inc.) depending on the experimental parameters. The microscopy images were analyzed in regards to different properties of the assemblies: (a) number of magnetic beads per cluster, (b) number of vacancies, (c) length (measured in particles) of one-dimensional defects, (d) number of particles in secondary layers, and (e) number of particles within a grain, i.e., an area of unbroken hexagonal symmetry. The respective values are obtained by evaluation of the number of pixels in a specified area with a defined color value. In comparison to the manually counted, exact numbers, this method entails an error of 2.43% of the actual value due to contrast fluctuations.
Results and Discussion A typical example of a monolayer is shown in Figure 1. The insets present several details about the particle assemblies: (a) Assemblies are highly ordered; a manifestation of the degree of ordering can be seen in the corresponding Fourier transform of the particle grid positions. Only a very small number of lattice distortions can be found that are either zero-dimensional vacancies or onedimensional dislocations (b). Via one-dimensional defects, a grain structure is introduced within the monolayers. (c) The degree of particles on top of the first layer (dark spots) is very low (approximately below 5%), and therefore, this method allows for the accurate patterning of two-dimensional particle layers. In principle, this method can be extended to the creation of closed monolayers. However, in the setup employed, closed particle layers cannot withstand the surface energy during the evaporation and break under induced shear stresses. Thus, different liquids will need to be tested in the future in order to employ this method for the manufacturing of highly ordered mono- or multilayers on a substrate. In liquid phase, no breaking of clusters after a prior agglomeration can be observed. Therefore, such assemblies are promising candidates for programmable dynamic components in lab-on-a-chip devices which are generated once the rotating magnetic field is switched on. Independent of the dimension of the defects, lattice impurities originate from the same mechanism: Figure 2a shows the absorption of an one-dimensional particle chain by a larger cluster due to the dipolar particle coupling.25 During this process, the chain breaks into several fragments that are distributed around the cluster surface. The previously perfectly ordered cluster remains without defects. Therefore, we may already conclude that a slow cluster growth due to a low particle configuration will generate enlarged areas of high symmetry. Instead, defects result from the agglomeration of several clusters. Figure 2b shows a larger object which is formed of several fragments; three of them are displayed in the insets. Along the marked junction areas, the symmetry is broken and the behavior resembles the situation of grain boundaries (19) Derks, R. J. S.; Frijns, A. J. H.; Prins, M. W. J.; Dietzel, A. Microfluid. Nanofluid. 2010, 9, 357–364. (20) Golosovsky, M.; Saado, Y.; Davidov, D. Appl. Phys. Lett. 1999, 75(26), 4168–4170. (21) Schaller, V.; Wahnstr€om, G.; Sanz-Velasco, A.; Enoksson, P.; Johansson, C. J. Magn. Magn. Mater. 2009, 321(10), 1400–1403. (22) Weddemann, A.; Auge, A.; Kappe, D.; Wittbracht, F.; H€utten, A. J. Magn. Magn. Mater. 2010, 322(6), 643–646. (23) Gyzybowski, B. A.; Jiang, X.; Stone, H. A.; Whitesides, G. M. Phys. Rev. E 2001, 64, 011603. (24) M-270 streptavidin datasheet: www.invitrogen.com. (25) Hayes, M. A.; Polson, N. A.; Garcia, A. A. Langmuir 2001, 17, 2866–2871.
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Figure 3. Cluster properties and growth for the particle concentrations c=0.2 and 1.0 mg/mL for 1, 3, and 5 iterative concentration replenishments (a); the inset shows the behavior without an external magnetic field. Defect concentrations for (b) iterative concentration replenishments and (c) different field frequencies. Since the zero field reference sample does not entail ordered structures, the defect concentration cannot be discussed for this case. Because of the evaluation method, an relative error of 2.43% of the respective value is entailed for all given data.
within nanostructured materials.26 In this regard, the external magnetic field acts as an external stress which induces a complex magnetic and geometric ordering. Therefore, if there is a sufficient amount of space, reordering processes can be found (Figure 2c) which may leave isolated vacancies. For a quantitative analysis of cluster and monolayer growth and properties, the particle solution was iteratively replenished after all isolated components had aggregated and the solvent had been evaporated. Subsequently, droplets of defined particle concentrations were added under the influence of the rotating homogeneous magnetic field with frequencies f=400, 800, and 1200 rpm. Depending on the specific concentration, each droplet contains 10 000-100 000 magnetic beads. The resulting assemblies were evaluated after placing 1, 3, and 5 droplets onto the substrate. Cluster Growth. For the analysis of particle clusters, concentrations of 0.2 and 1.0 mg/mL were employed. The results are summarized in Figure 3. Without a magnetic field applied (inset, upper right), particles are randomly dispersed within the plane; no self-assembled structures are present. Since the zero field reference sample does not entail ordered structures, the defect concentration cannot be discussed for this case. Under the influence of an external rotating magnetic field, the assembly of highly ordered two-dimensional particle clusters is induced. The size of such obtained objects may be shifted to higher particle numbers via the provision of high particle concentration. In this regard, the growth mechanism resembles the behavior of Ostwald ripening dynamics27 in nanoparticle fabrication: the (26) Ovid’ko, I. A. Encycl. Nanosci. Nanotechnol. 2004, 4, 249–265. (27) Ostwald, W. Lehrbuch der allgemeinen Chemie; Leipzig: Germany, 1896; Vol. 2, Part 1.
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generation of few large clusters is favored over formation of many small assemblies. According to our data, the frequency of the applied field does not seem to influence the cluster size. Additionally, the defect concentrations show several tendencies: for low particle concentrations the number of defects decreases with a higher number of particles within the sample (Figure 3b,
Figure 4. Layer properties for a particle concentration c = 5.0 mg/ mL for 1 and 3 iterative concentration replenishments (a). The microscopy image shows the reference behavior of a sample prepared without the influence of an external magnetic field. The Fourier analysis reveals that there is no ordering. (b) Defect concentrations for iterative concentration replenishments. Since the zero field reference sample does not entail ordered structures, the defect concentration cannot be discussed for this case. Because of the evaluation method, an relative error of 2.43% of the respective value is entailed for all given data.
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red lines). Such a trend can no longer be found if highly concentrated particle suspensions are employed (Figure 3b, blue lines). This observation is in accordance with the mechanism proposed for the defect generation: Because of the lack of accessible free volume, reorganization processes as shown in Figure 2c are strongly inhibited which results in an increase of the defect concentration. Further, we find an influence of the frequency of the applied magnetic field. A higher field frequency entails a higher defect concentration. This is due to the different time scales of geometric and magnetic reordering processes within the clusters. While remagnetization dynamics in magnetic beads can usually be found on a nanosecond time scale,22 the geometrical reordering process can no longer follow the transient magnetodynamics and reordering processes are impeded. Layer Growth. In order to analyze layers of magnetic particles, a solution with the concentration c=5.0 mg/mL was employed. As shown in Figure 1, one-dimensional defects lead to a grain structure within the monolayer; the size distribution of such grains is shown in Figure 4a. As the Fourier transform of the particle positions within the zero field reference sample reveals (Figure 4, inset), no ordering can be found without a magnetic field applied. A shift to smaller grains for a higher number of particles can be reported. This observation is in accordance with the results of the analysis of particle clusters. Again, the lack of room prohibits the perfect ordering. Additionally, the grain structure entails a larger amount of grain boundaries/one-dimensional defects. Similar to the low-concentration systems, the amount of defects can be controlled by the magnetic field frequency: lower frequencies lead to lower defect concentrations as shown in Figure 4b. According to the experimental data, the resulting assemblies after the deposition of three droplets consist of grains with an average grain size of 463 particles which corresponds to an area of ∼2850 μm2. This value is similar to other methods: Riley and Lidell14 estimated the existence of grain boundaries and defects in a roughly 2900 μm2 region. An even higher degree of ordering was obtained by Masuda et al.,28 who employed surface tension effects of the evaporating solvent and realized an almost perfect ordering. However, in contrast to these approaches, our method can be
Figure 5. Magnetic properties of two-dimensional particle assemblies. (a) Particles in the second layer only have a single direct neighbor in the lower plane (examples are highlighted in the lower subplot). (b) The breaking of particle films during the evaporation of the solvent occurs along straight lines (examples are highlighted in the lower subplot). These breaking dynamics can be related to the magnetic equilibrium state of such assemblies. (c) Magnetic moments form domains of antiparallel orientation. Because of stray field minimization, the coupling energy between adjacent particle stripes of antiparallel magnetization direction is significantly lower than elsewhere within the sample. Therefore, breaking events along these lines are strongly enhanced which entails a breaking pattern as experimentally observed and highlighted in the lower plot of (b). 19228 DOI: 10.1021/la102813w
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directly applied to liquid samples and, therefore, also be employed for the on-demand assembly of particle superstructures in continuous flow lab-on-a-chip structures. Magnetic Substructure. Each two-dimensional layer is assembled according to the closed packed structure. Because of geometric expectations, this result might not seem very surprising. However, an analysis of particle positions in the second layer shows clear indications that there is no continuation of this geometrical order in the out-of-plane direction (stacking ABAB... or ABCABC...), but as shown in Figure 5a, multilayers follow the sequence AAA... (the resolution of the employed digital optical microscope allows for a position estimation exactness of up to 0.375 μm). This observation cannot be attributed to geometric/ steric effects and is, therefore, an indication for the predominant magnetic coupling along the particle assemblies which has already been reported in the works of Albon et al.29 By evaluation of the evaporated samples as shown in Figure 5b, further information on the inner magnetic structure of the clusters can be obtained. The solvent slowly evaporates during the exposure time of the magnetic particles to the rotating magnetic field. The induced fluid flows cannot overcome the magnetic coupling along the assemblies as long as the particle clusters are completely dissolved. However, during evaporation, capillary-induced stresses become the dominating force on the particles under the influence of the moving liquid-air interface. The situation here is slightly different from the corresponding additional ordering processes which may be observed in the dropping procedure of nanoparticles (smaller capillary forces, higher magnetic attraction due to smaller distances and higher magnetization, MS ∼ 1000 kA/m). In particular, in the size range of microparticles, this method is more suitable for applications in a solvent than for particle patterning of substrates. The surface tension during the evaporation process causes the particle films to break along straight lines as indicated. In order to understand this behavior, we apply a simple model describing every particle via a homogeneously magnetized volume of magnetization MS = 300 kA/m. This saturation value is about 3-4 higher than the actual magnetic value of the Dynabeads M-270 SA employed in the experiments; we investigate the case of
Highly ordered clusters and monolayers consisting of magnetic beads have been prepared by the employment of a rotating magnetic field. The properties of such objects can be controlled by the field frequency and the particle concentration in the solution. Further, we have shown first indications of the importance of the inner magnetic structure of such assemblies. In particular, the formation of multilayers and breaking of particle films under high stress are strongly governed by the magnetic interactions and also resemble the inner magnetic configuration. Since these objects may be assembled on-demand by switching on the magnetic field, they may form vital components in the future development of novel programmable microfluidic devices. In particular, the proposed approach can easily be integrated in already existing lab-on-a-chip applications since only a macroscopic external magnetic field is necessary, and no further electromagnetic structures on the microscale are employed. Therefore, we provide a strategy of low complexity to directly exploit magnetic interparticular coupling as an additional degree of freedom for the design of reconfigurable dynamic components. Also, the extension of this method to nanoparticles for the fabrication of highly ordered nanoparticle sheets will be of major interest in future works.
(28) Masuda, Y.; Itoh, T.; Koumoto, K. Langmuir 2005, 21, 4478–4481. (29) Albon, C.; Weddemann, A.; Auge, A.; Meissner, D.; Jutzi, P.; Rott, K.; H€utten, A. Appl. Phys. Lett. 2009, 95(2), 023101.
Acknowledgment. The authors thank the FOR 945 for financial support in the framework of the project 3.
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samples that are dominated by magnetic interactions. The results allow for a qualitative understanding of the breaking mechanism; details on modeling and solving procedure can be found in ref 22. A typical solution for a 13 13 hexagonal particle grid is shown in Figure 5c: The color code indicates the direction of each magnetic moment in the plane of the particle assembly; out-of-plane contributions are small enough to be omitted. In the equilibrium state, magnetic moments form domains of antiparallel orientation. This behavior entails a minimized stray field energy, and therefore, the coupling between adjacent particle stripes of antiparallel magnetization direction is significantly lower than elsewhere within the sample. Consequently, breaking events will occur parallel to these straight lines, which is in good agreement with the experimental findings.
Conclusion and Outlook
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