J. Phys. Chem. B 2008, 112, 16525–16528
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Magnetically Actuated Colloidal Microswimmers Pietro Tierno,*,†,‡ Ramin Golestanian,§ Ignacio Pagonabarraga,‡,| and Francesc Sague´s†,‡ Departament de Quı´mica Fı´sica, UniVersitat de Barcelona, Martı´ i Franque`s 1, 08028 Barcelona, Spain, Department of Physics and Astronomy, UniVersity of Sheffield, Sheffield S3 7RH, United Kingdom, Departament de Fı´sica Fonamental, UniVersitat de Barcelona, Martı´ i Franque`s 1, 08028 Barcelona, Spain, and Institut de Nanocie`ncia i Nanotecnologia IN2UB, UniVersitat de Barcelona, Barcelona, Spain ReceiVed: September 19, 2008; ReVised Manuscript ReceiVed: October 14, 2008
To achieve permanent propulsion of micro-objects in confined fluids is an elusive but challenging goal that will foster future development of microfluidics and biotechnology. Recent attempts based on a wide variety of strategies are still far from being able to design simple, versatile, and fully controllable swimming engines on the microscale. Here we show that DNA-linked anisotropic colloidal rotors, composed of paramagnetic colloidal particles with different or similar size, achieve controlled propulsion when subjected to a magnetic field precessing around an axis parallel to the plane of motion. During cycling motion, stronger viscous friction at the bounding plate, as compared to fluid resistance in the bulk, creates an asymmetry in dissipation that rectifies rotation into a net translation of the suspended objects. The potentiality of the method, applicable to any externally rotated micro/nano-object, is finally demonstrated in a microfluidic platform by guiding the colloidal rotors through microscopic-size channels connected in a simple geometry. Introduction Realization of microscale devices capable of propelling themselves in a controlled way through narrow channels represents a necessary step toward further miniaturization of chemical and biochemical liquid carriers to be integrated into microfluidics chips. If such devices could be chemically functionalized, as it is the case of colloidal particles, they would bind and deliver chemical cargos1 on a much smaller scale than in actual microfluidic devices.2 Potential applications of dirigible microdevices immersed in confined fluids are various and refer, among others, to microtechnological3 and biomedical fields.4 When the device size is very small, fluid viscosity dominates over inertia (low Reynolds number conditions) and the time reversible nature of fluid flow5 impedes swimming by simple reciprocal motion,6 i.e. a periodic back and forward displacement. Thus one is forced to adopt subtle and ingenious designs to allow directed motion of micro/nano-objects. Recent examples comprise catalyzing a chemical reaction at one end of elongated Au-Pt nanorods,7 half-coating Pt particles,8 using actuated magnetic filaments,9 paramagnetic particles above a magnetic substrate,10 or applying an electric field to semiconductor millimeter-scale diodes.11 Despite such attempts, the design of versatile swimming engines which could be easily controlled and directed in restricted microfluidic geometries is still a major challenge which continues to stimulate analytical and biomedical research. We here realize a simple externally actuated colloidal microswimmer by imposing a modulated magnetic field to water dispersed paramagnetic colloidal doublets. This realization supposes an inert, perdurable, and economic way of transport on a micron scale, while allowing control over speed, direction, * Correspondingauthor.E-mail:
[email protected]:+34934020138. † Departament de Quı´mica Fı´sica, Universitat de Barcelona. ‡ Institut de Nanocie`ncia i Nanotecnologia IN2UB, Universitat de Barcelona. § University of Sheffield. | Departament de Fı´sica Fonamental, Universitat de Barcelona.
and sense of motion. The potentiality of the method, applicable to any externally rotated micro/nano-object close to a bounding plate, is finally demonstrated in a microfluidic platform by guiding the colloidal rotors through microscopic-size channels connected in a simple geometry. Experimental Section We prepared anisotropic colloidal doublets by mixing polystyrene paramagnetic colloids coated with streptavidin and having different diameters, d1 ) 2.8 µm, d2 ) 1.0 µm (Dynabeads). The doublets were linked by means of biotinterminated cDNA strands with 25 bp and 8 nm long. By using our experimental protocols, we could obtain either doublets, triplets, or particles with higher order multiplets. Moreover more complicated architectures like chains or larger clusters are also possible to build up. The doublets were dispersed in Millipore water at a concentration of ∼106 particles/mL and were deposited above a glass plate. Due to the competition between gravity and electrostatic repulsion between the ionic double layers of the doublet and substrate, after few minutes the doublets reach an equilibrium distance above the plate of the order of ∼200 nm.14 The particles are paramagnetic due to the doping of the polystyrene matrix with small iron oxide grains (5-20 Å in diameter). Under an external magnetic field H, the doublet acquires an induced moment m ) Vdχ|H|n which tries to align it with the field. Here Vd is the doublet volume (12 µm3), and n is the director along the doublet axis. The effective magnetic susceptibility χ was estimated to be χ ) 0.44 using the values provided in refs 12 and 13. Setup. The external magnetic field was provided by using three custom-made coils oriented along three perpendicular directions. Each coil was made by ∼1100 turns with 4 mm diameter wire and had 5 (2) cm of outer (inner) diameter. A rotating magnetic field in a plane was achieved by connecting two coils to a waveform generator (TTi TGA1244) fed by a current amplifier (IMG STA-800). A constant magnetic field along one direction was obtained by connecting the third coil
10.1021/jp808354n CCC: $40.75 2008 American Chemical Society Published on Web 11/24/2008
16526 J. Phys. Chem. B, Vol. 112, No. 51, 2008
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Figure 1. (a) Schematic of a doublet subjected to an external magnetic field H precessing around the y-axis. Ω and ϑ denote frequency and precession angle of the field while θ is the precession angle of the director n. (b) Microscope image of a particle and a doublet under a magnetic field with Ω ) 62.8 s-1, ϑ ) 75°, and H ) 4695 A/m. Superimposed are the trajectories after time t for the particle (blue line) and the doublet (red line). (c) Doublet velocity versus frequency at three precession angles. The dashed line shows the initial linear behavior of V with Ω.
to a DC power supply. The particles were imaged with a 100X oil immersion objective mounted in a light microscope (Nikon). Videos for image analysis were taken at 30 fps by using a charge-coupled device (CCD) color camera (Basler A311F). Particle positions are analyzed with a custom-made tracking routine written in MATLAB. DNA Linkage Procedure. The two single complementary strain sequences are the following: 5′-/5Bio/AAA AAA AAA AAA AAA AAA AAA AAA A-3′ and 5′-/5Bio/TTT TTT TTT TTT TTT TTT TTT TTT T-3′ (IDT Technologies, Inc.). The particles are washed and redispersed in two separate individual batches of 20 mM NaCl buffer solution (pH 8.0) at a concentration of ∼107 particles/mL. A 6 µL portion of a ssDNA solution containing one of the two sequences is then added to the corresponding batch. Prior to mixing, the particles are allowed to equilibrate for approximately 30 min. Later the batches are mixed and placed in a spatially homogeneous magnetic field (∼0.5 T) for 15 min. The field align the particles into chains and thus promotes the linkage between the DNA strands. Results and Discussion To move the doublet, we applied an external magnetic field which precesses with a frequency Ω around one direction (y-axis), parallel to the glass plate H(t) ) H(sin ϑ sin Ωt, cos ϑ, sin ϑ cos Ωt); see Figure 1a. The external rotation induces a gyroscope-like precession of the doublet around the y-axis, with the big particle pratically at rest and the small one rotating around the doublet center of mass in the (x,z) plane, with z being perpendicular to the solid substrate. The result of such precession is a net translational motion along the x direction, as illustrated by the red trajectory of the doublet in Figure 1b. Together with the doublet, we capture in the same image the motion of an
individual isotropic paramagnetic particle which shows Brownian fluctuations (blue trajectory) and is unaffected by the external modulation. This demonstrates the absence of heterogeneities in the magnetic field since otherwise similar uncontrolled drift motion for both micro-objects would have been registered. We characterize the doublet motion in terms of its velocity as a function of the frequency and precession angle of the applied magnetic field, Figure 1c. The velocity of the doublet increases linearly up to a maximum value of 3.2 µm/s for Ω ) 70 s-1 and further decreases down to a value of 0.8 µm/s for Ω ) 120 s-1 with ϑ ) 72°. Thus we can completely control the speed of the doublet by varying the frequency of the applied field. Moreover such trend in terms of the field frequency was confirmed at various precessing angles and field strengths. A theoretical model which accounts for such dependencies will be presented elsewhere.14 To understand the principle behind the doublet motion one has to consider the effect of the bounding glass plate during one rotation. Let us consider one rotation cycle of the doublet, with both particles describing circles with the same sense of motion. Consequently, the center of mass of the doublet is displaced backward and then forward along the x direction, i.e. opposite to its horizontal direction of motion. If the doublet were in a bulk fluid, such displacements would exactly compensate each other and no net motion would follow. However, the presence of the plate breaks the symmetry of the motion. Viscous friction close to the plate is higher in the phase of rotation when the smaller particle in the doublet is closer to the plate than when it is farther away from it. Due to such asymmetry in dissipation, the rotation of the assembly can be rectified into directed motion by periodically repeating the cycle. In fact, the doublet motion could be compared to a microscopic
Magnetically Actuated Colloidal Microswimmers
J. Phys. Chem. B, Vol. 112, No. 51, 2008 16527
Figure 2. Microscope images showing some examples of the various colloidal assemblies achievable with our paramagnetic colloids. Assemblies with similar particles are represented by small (a) and large doublets (c). Assemblies with dissimilar particles are represented by a triplet with elliptical shape (d), chain (e), and chain with head (f). The doublet analyzed in the text corresponds to panel b. On the right-hand side, the respective velocity vs frequency plots are displayed. The videos corresponding to images a-f are deposited as Supporting Information (videos 1-6).
unicycle, which translates by rolling close to a surface but without a mechanical contact. The velocities vs frequencies plotted in Figure 1c can be explained by considering the fact that the precession angle of the doublet director, θ, decreases with increasing the external field frequency.14 At small frequencies, θ is large and increasing Ω the rectification of the doublet rotation into translation increases linearly. When θ becomes too small, at high frequencies, the efficiency in rectification per cycle slows down since the smaller particles is rotating farther away from the plane and, consequently the speed of the doublet decreases. A peak in the speed bridges both regimes. Among the different DNA based colloidal linking procedures in the literature,15,16 the one we use here could be easily implemented to give different assemblies, as mentioned above. Figure 2 depicts some observed assemblies of similar (a and c) and dissimilar (b and d-f) individual particles, together with the corresponding velocity/frequency plots. Higher speeds (up to 10 µm/s) are achieved with larger particles or longer chains. This increment can be attributed to the tendency of heavier assemblies to float closer to the glass plate. Figure 2 shows in particular that the smaller assemblies made by two linked colloids of 1 µm size (video 1 in the Supporting Information) barely move due to their small weight. The velocity/frequency dependences show the same trends for the arrangements based on doublets (a-c), as for triplets (d and e) and higher multiplets (f). However the frequency at which the maximum speed appears depends on the aggregate structures. This shows the potentiality of our method to build colloidal clusters with larger and tunable speeds. The ability to control and transport elongated elementary colloidal assemblies close to a confining surface creates many opportunities to integrate them into microfluidic platforms in a non invasive way. As an illustrative example, we realized a 3.5 µm depth channel network with 40 and 20 µm channel width above a glass plate by using wet etching (HF) technique and dispersed above it a diluted suspension (∼3 × 105 particles/ mL) containing the colloidal assemblies. Microscope image of one doublet traveling along a square channel structure is shown in Figure 3. The external precessing magnetic field (H ) 4695 A/m, ϑ ) 75°, and Ω ) 75.4 s-1) drives the actuated swimmer along the entire path (∼800 µm) in 4.4 min with an average speed of ∼3 µm/s. To guide the microswimmers, we change the sign and configuration of the current through the coils each time the doublet reaches one vertex of the square channel configuration. Besides the basic geometry employed here, more complex patterns like circular trenches, T-junctions, or triangular
Figure 3. Water dispersed doublets traveling along glass etched microchannels (three with 40 µm diameters and one with 20 µm, 3.5 µm depth) in a square geometry. Superimposed in green is the trajectory of one individual doublet driven toward north, west, south, and east directions. The inset shows an enlargement of the colloidal doublet.
sections could be easily traveled by our swimmers adjusting the orientation and direction of the imposed field. Conclusions We have demonstrated a simple and general technique to externally control and displace elementary colloidal assemblies immersed in viscous fluids and confined near solid boundaries. As opposed to existing engines, this swimmer propels without modifying its shape and free of thermal fluctuations. We finally show the potentiality of the method by guiding the colloidal rotors through microscopic-size connected channels in a microfluidic platform. Acknowledgment. P.T. was supported by the program “Beatriu de Pinos” BP-B100167. F.S. and P.T. acknowledge financial support by MEC (Project FIS2006-03525) and DURSI (2005SGR00653).R.G.acknowledgessupportfromtheEPSRC.I.P. acknowledges financial support from MEC (Project FIS200501299). Supporting Information Available: Six videos of the motion of the composite particles in Figure 2. This material is available free of charge via the Internet at http://pubs.acs.org.
16528 J. Phys. Chem. B, Vol. 112, No. 51, 2008 References and Notes (1) Tierno, P.; Reddy, S. V.; Yuan, J.; Johansen, T. H.; Fischer, T. M. J. Phys. Chem. B 2007, 111, 13479. (2) Garstecki, P.; Fischbach, M. A.; Whitesides, G. M. Appl. Phys. Lett. 2005, 86, 244108. (3) Terray, A.; Oakey, J.; Marr, D. W. M. Science 2002, 296, 1841. (4) (a) Guo S.; Jun, S.; Qinxue, P. Proceedings of the IEEE/ RSJ International Conference on Intelligent Robots and Systems, 2005; p 2265. (b) Pan, Q.; Guo, S. Proceedings of the IEEE International Conference on Robotics and Biomimetics, 2007; p 256. (5) Happel, J.; Brenner, H. Low Reynolds Number Hydrodynamics; Noordhoff: Leiden, 1973. (6) Purcell, E. M. Am. J. Phys. 1977, 45, 3. (7) Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; Angelo, S. K. St.; Cao, Y.; Mallouk, T. E.; Lammert, P. E.; Crespi, V. H. J. Am. Chem. Soc. 2004, 13, 424. (8) Howse, J. R.; Jones, R. A. L.; Ryan, A. J.; Gough, T.; Vafabakhsh, R.; Golestanian, R. Phys. ReV. Lett. 2007, 99, 048102.
Tierno et al. (9) Dreyfus, R.; Baudry, J.; Roper, M. L.; Fermigier, M.; Stone, H. A.; Bibette, J. Nature 2005, 437, 862. (10) Morimoto, H.; Ukai, T.; Nagaoka, Y.; Grobert, N.; Maekawa, T. Phys. ReV. E 2008, 78, 021403. (11) Chang, S. T.; Paunov, V. N.; Petsev, D. N.; Velev, O. D. Nat. Mater. 2007, 6, 235. (12) Helseth, L. E. J. Phys. D: Appl. Phys. 2007, 40, 3030. (13) Fonnuma, G.; Johanssonb, C.; Molteberga, A.; Mørupc, S.; Aksnesa, E. J. Magn. Mag. Mat. 2005, 293, 41. (14) Tierno, P.; Golestanian, R.; Pagonabarraga, I.; Sague´s, F. in preparation. (15) Valignat, M. P.; Theodoly, O.; Crocker, J. C.; Russel, W. B.; Chaikin, P. M. Proc. Nat. Acd. Sci. U.S.A. 2005, 102, 4225. (16) Milam, V. T.; Hiddessen, A. L.; Crocker, J. C.; Graves, D. J.; Hammer, D. A. Langmuir 2000, 19, 10317.
JP808354N
