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Linking synchronization to self-assembly using magnetic Janus colloids

Abstract

Synchronization occurs widely in the natural and technological worlds, from the rhythm of applause and neuron firing1 to the quantum mechanics of coupled Josephson junctions2, but has not been used to produce new spatial structures. Our understanding of self-assembly has evolved independently in the fields of chemistry and materials, and with a few notable exceptions3,4 has focused on equilibrium rather than dynamical systems. Here we combine these two phenomena to create synchronization-selected microtubes of Janus colloids, micron-sized spherical particles with different surface chemistry on their opposing hemispheres, which we study using imaging and computer simulation. A thin nickel film coats one hemisphere of each silica particle to generate a discoid magnetic symmetry, such that in a precessing magnetic field its dynamics retain crucial phase freedom. Synchronizing their motion, these Janus spheres self-organize into micrometre-scale tubes in which the constituent particles rotate and oscillate continuously. In addition, the microtube must be tidally locked to the particles, that is, the particles must maintain their orientation within the rotating microtube. This requirement leads to a synchronization-induced structural transition that offers various applications based on the potential to form, disintegrate and fine-tune self-assembled in-motion structures in situ. Furthermore, it offers a generalizable method of controlling structure using dynamic synchronization criteria rather than static energy minimization, and of designing new field-driven microscale devices in which components do not slavishly follow the external field.

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Figure 1: Single- and two-particle dynamics in precessing fields.
Figure 2: Synchronized self-assembly.
Figure 3: Synchronization-induced structural transitions.

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Acknowledgements

This work was supported by the US Army Research Office, grant award number W911NF-10-1-0518 (Y.J., S.C.B. and S.G.) and by the National Science Foundation under award number DMR-1006430 (M.B. and E.L.). The methods of Janus particle fabrication were supported by the US Department of Energy, Division of Materials Science, under award number DE-FG02-07ER46471 through the Frederick Seitz Materials Research Laboratory at the University of Illinois at Urbana-Champaign. We acknowledge support from the National Science Foundation, CBET-0853737 for equipment and from the Quest high-performance computing facility at Northwestern University. We thank J. Whitmer for writing the original version of the simulation code.

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Authors and Affiliations

Authors

Contributions

J.Y. and S.G. initiated this work. J.Y. and S.C.B. built the set-up; J.Y. performed the experiments; M.B. and E.L. performed the modelling and simulations. J.Y., M.B., E.L. and S.G. wrote the paper.

Corresponding authors

Correspondence to Erik Luijten or Steve Granick.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-7, Supplementary Figures 1-13 and additional references. (PDF 912 kb)

Single particle motion in a precessing magnetic field

This video shows a single particle in a magnetic field of 5 mT, precessing at 20 Hz and θ = 50°. Each frame of the video compares experiment to different cross sections of the trajectory predicted from the equations of motion, demonstrating excellent agreement. The precession axis is perpendicular to the image in the first part, and horizontal in the image in the second part of this video, respectively. The video is slowed down 30 times. (MOV 3478 kb)

Single particle motion in a precessing magnetic field with lower θ

This video shows a single particle in a magnetic field of 5 mT, precessing at 20 Hz and θ = 30°. Each frame of the video compares experiment to different cross sections of the trajectory predicted from the equations of motion, demonstrating excellent agreement. The precession axis is perpendicular to the image in the first part, and horizontal in the image in the second part of this video, respectively. The video is slowed down 20 times. (MOV 5854 kb)

Multiple particles in a precessing magnetic field

This video shows multiple particles in a magnetic field of 5 mT, precessing at 20 Hz and θ = 50° such that they maintain large separations with minimal dynamic coupling. Precession axis is perpendicular to the imaging plane. The video is slowed down 10 times. The view size is 57.4 × 55.1 μm2. (MOV 3535 kb)

Synchronization of two particles

This video shows two particles approaching synchronization in the laboratory (part 1) and in simulation (part 2). The particles finish synchronized with a phase difference of π in both oscillation and rotation. In the simulation, the particles are initially separated by 3.5 particle diameters and the initial phase difference of 30° is close to experiment. Parameters for the external magnetic field are 20 Hz, 5 mT, θ = 25°, with precession axis lying vertical in the imaging plane. Both videos are slowed down 5 times. For experiment, the view size is 16.0 × 9.3 μm2. (MOV 10870 kb)

Spontaneous formation of tubular structure

This video shows the spontaneous formation of (kk0) microtubes in the laboratory. The video is sped up 2 times and starts 10 s after the magnetic field is turned on. Particles evolve from disordered chains into regular (330) or (440) structures by a nucleation-and-growth mechanism. Parameters for the external magnetic field are 20 Hz, 5 mT, θ = 20°, with precession axis lying horizontal in the imaging plane. The final structure is slightly tilted because other parts along the chain, not visible in the video, translate at a different speed. The view size is 93.1 × 53.2 μm2. (MOV 10839 kb)

Coordinated swaying of particles insides a (330) microtube

This video shows the coordinated, internal swaying of particles that comprise a rotating microtube. Parameters for the external magnetic field are 20 Hz, 5 mT, θ = 25°, with precession axis lying horizontal in the imaging plane. The video is slowed down 20 times. The view size is 117.0 × 24.7 μm2. (MOV 1431 kb)

Top view of stable and unstable (330) microtube in simulation

This video shows the simulated dynamics of particles within a (330) microtube and compares stable with unstable conditions. The magnetic field is 5 mT at 20 Hz. Shown in the videos is the top view of the middle 4 layers of particles. Part 1: zoomed-in particles at θ = 18° (slowed down 50 times), showing phase lock of particles in the same layer. Part 2: tidal locking at long times (played in real time). Part 3: loss of tidal locking and disassembly at θ = 30°, which is above θc (slowed down 5 times). Note that a first phase slip leads to a higher-energy structure; a second phase slip leads to disassembly. (MOV 6566 kb)

Unbraiding of (330) microtube above θc

This video of experiment shows how a (330) structure falls apart above θc (stable structure formed at θ = 25°, increase to θ = 30°). The magnetic field is 5 mT at 20 Hz, with the precession axis lying horizontal in the imaging plane. Note unbraiding from the ends. The reason is that particles at the ends have fewer neighbors and hence weaker attraction and smaller ε. The video is played in real time. The view size is 103.2 × 49.1 μm2. (MOV 6638 kb)

Chiral (123) helices

This video shows chiral (123) structures (Boerdijk–Coxeter helices) with apparent waves. The particles, different from those used in most of the experiments, are synthesized using 2.8 μm paramagnetic polystyrene particles (Dynabeads, Invitrogen) with 18 nm nickel coating. Part 1: An apparent wave travels from the right to the left of a right-handed helix. As a guide to the eye, the small red dot follows one phase as it migrates to the left. Part 2: An apparent wave travels from the left to the right of a left-handed helix. The magnetic field is 3 mT at 20 Hz, with θ = 20° and the precession axis lying horizontal in the imaging plane. Videos are played in real time. For Parts 1 and 2, the view size is 106.4 × 26.6 μm2 and 53.2 × 21.3 μm2, respectively. (MOV 4881 kb)

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Yan, J., Bloom, M., Bae, S. et al. Linking synchronization to self-assembly using magnetic Janus colloids. Nature 491, 578–581 (2012). https://doi.org/10.1038/nature11619

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