Research ArticleAPPLIED PHYSICS

Emergent collective colloidal currents generated via exchange dynamics in a broken dimer state

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Science Advances  06 Mar 2020:
Vol. 6, no. 10, eaaz2257
DOI: 10.1126/sciadv.aaz2257
  • Fig. 1 Assembly procedure of colloidal dimers and binary lattices.

    (A to C) Microscope snapshots showing N = 288 particles in the absence of an external field (A) and driven by a precessing field with B0 = 7.3 mT, θ = 26. 9°, and frequency f = 1 Hz (B) and f = 20 Hz (C). The dispersed particles (A) are first assembled to rotating dimers (B) and later broken into a binary arrangement of up and down particles (C) by raising f. For clarity, particles located close to the upper (lower) plate are shaded in blue (orange); the cell thickness is h = 3.9 μm. Scale bars, 10 μm for all images (movie S1). (D) Schematic showing the particle location inside a thin cell (d < h < 2d) when forming the dimers (top) and the up-down state (bottom). (E and F) Dynamics of single dimer: (E) cyclotron frequency ν of a dimer versus driving frequency f showing the transition from synchronous to asynchronous regime at fc = 9.8 Hz from experiments (scattered data) and simulation (continuous line). In the synchronous phase, ν = f, while above fc the cyclotron rotation decreases following the equation ν=ff2fc2 (24). (F) Driving frequency versus confinement showing the transition of the dimers from synchronous to asynchronous (red, threshold at fc) or from synchronous to rupture (green, threshold at frp). Experimental points are scattered data; theoretical model and simulations are represented by continuous and dashed lines, respectively.

  • Fig. 2 Dynamic colloidal states from experiments and numerical simulations.

    (A) Images illustrating different transition paths observed for B0 = 7.28 mT, θ = 26.9°; all starting from a synchronous orbit at f = 1 Hz. SA: Synchronous Asynchronous rotations (f = 20 Hz), h= 5.1 μm; SEA: Synchronous Exchange of neighbors (f = 8 Hz) Asynchronous (f = 25 Hz), h = 4.4 μm; SER: Synchronous Exchange of neighbors (f = 3 Hz) Rupture (f = 14 Hz), h = 4.4 μm; SR: Synchronous Rupture (f = 9 Hz), h = 4.0 μm (movie S2). (B) Combined experiment (symbols) and simulation (colored regions) results of the location of the different transition paths in the (Φ, h) plane. (C and D) From simulations: Average cyclotron frequency of the dimers ν (C) and nearest neighbor separation distance 〈Δr〉 (D) versus driving frequency f. Both quantities can be used to classify the different transition paths observed.

  • Fig. 3 Colloidal current.

    (A) Microscope image with superimposed trajectories of up (blue) and down (orange) particles driven by an off-axis precessing field with B0 = 7.2 mT, θ = 26.9°, and f = 6 Hz in a cell of thickness h = 4 μm (movies S3 and S4). Scale bar, 10 μm. (B) Enlargement of this image with only two superimposed particle trajectories from experiments (left) and simulation (right). (C) Intensity I of the colloidal current versus shift angle δ for different values of the driving frequency (color bar) from simulations. High frequencies (blue lines) produce a smooth raise of I to the maximum flow, where all up and down particles contribute to the current. For f < 4 Hz (red lines), we observe a sharp increase from zero current to the maximum value at a fixed δ. (D) Schematic showing a shifted conical field obtained by adding a zenithal angle δ, which only rotates the static component of the magnetic field, Bs = sin (δ)ex+ cos (δ)ez. With this additional bias, the external field now reads as B(t) = B0[( sin (θ) cos (2πft) + cos (θ) sin (δ))ex + sin (θ) sin (2πft)ey + cos (θ) cos (δ)ez]. (E to G) Details on the exchange mechanism: (E) interparticle distance rij between two particles (i,j), from experiments and simulations. Only from simulations: (F) phase lag angle between the dimer and the field φ and (G) projection of the magnetic dipolar force F·r^ij versus rescaled time t. The pink shaded region indicates the time window of the dimer formation, rij = 2d.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/10/eaaz2257/DC1

    Single dimer stability analysis

    Fig. S1. Schematics showing a magnetic dimer in confinement.

    Fig. S2. Dynamical phases of a single magnetic dimer in a precessing field.

    Movie S1. Experimental realization of colloidal dimers and binary crystals.

    Movie S2. Different dynamic states of confined colloidal dimers under precessing field.

    Movie S3. Colloidal current generated by a precessing field.

    Movie S4. Trajectories of two particles producing the bidirectional current.

    Movie S5. Bidirectional colloidal current in a narrow slit from simulation.

  • Supplementary Materials

    The PDF file includes:

    • Single dimer stability analysis
    • Fig. S1. Schematics showing a magnetic dimer in confinement.
    • Fig. S2. Dynamical phases of a single magnetic dimer in a precessing field.
    • Legends for movies S1 to S5

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Experimental realization of colloidal dimers and binary crystals.
    • Movie S2 (.avi format). Different dynamic states of confined colloidal dimers under precessing field.
    • Movie S3 (.avi format). Colloidal current generated by a precessing field.
    • Movie S4 (.avi format). Trajectories of two particles producing the bidirectional current.
    • Movie S5 (.avi format). Bidirectional colloidal current in a narrow slit from simulation.

    Files in this Data Supplement:

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