Research ArticleMATERIALS SCIENCE

Dynamic and programmable self-assembly of micro-rafts at the air-water interface

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Science Advances  24 May 2017:
Vol. 3, no. 5, e1602522
DOI: 10.1126/sciadv.1602522
  • Fig. 1 The parametric design and characterization of one representative 3D printed micro-raft.

    (A) The essential features of the micro-raft include the number n (= 4) of cosinusoidal curve profiles around the edge, the arc angle θ (= 30°) of each profile’s span, and the amplitude A (= 4 μm) of each profile. (B) SEM image of a representative micro-raft. (C) An overlap of a laser confocal image and an optical image on the left, and the extracted edge-height profile on the right, demonstrating the fidelity of fabrication. (D) The phase image extracted from a digital holograph of the micro-raft floating at the air-water interface, showing the interfacial deformation caused by the micro-raft. (E) The schematic of the magnetic torque generation on a micro-raft at the air-water interface using a rotating permanent magnet and the linear relationship between the magnet rotation speed Ω and the micro-raft rotation speed ω.

  • Fig. 2 Studies of pairwise interactions between two micro-rafts.

    (A) Schematic showing magnet rotation speed Ω, individual micro-raft rotation speed ω, edge-to-edge distance d, and precession speed ωp. (B) Plots of d and ωp versus Ω for micro-rafts coated with 25-nm cobalt and 30-nm gold. Higher amplitudes create larger separations and induce capillary assembly (d = 0) at higher critical Ω’s. The dashed line in the ωp versus Ω plot corresponds to the line ωp = Ω. The zoomed-in region shows an increase in ωp for A = 2 to 4 μm before assembling, suggesting capillary coupling near the onset of assembling. The control micro-rafts with A = 0 assemble at 2500 rpm, because no capillary repulsion exists between them. (C) Plots of d and ωp versus Ω for micro-rafts coated with 100-nm cobalt and 30-nm gold. The overall magnetic potential created by the permanent magnet exerts stronger attractive interactions for micro-rafts with 100-nm cobalt than for micro-rafts with 25-nm cobalt. Therefore, the onsets of assembling shift to higher Ω’s for all A’s. (D) Plots of d and ωp versus Ω for micro-rafts coated with 25-nm cobalt and 30-nm gold and further functionalized by a layer of SAM of heptanethiol (HS-C7) to make the micro-raft surface hydrophobic. The general trend of surface hydrophobization is to push the onset of assembling toward lower Ω’s. (E) The first five images are the phase images obtained from a digital holographic microscope (DHM) for two micro-rafts of various amplitudes. All images were taken when the micro-rafts were spinning at 2500 rpm. The rightmost image is an optical microscope image showing a typical assembled structure. The arc angle θ is 30° for all micro-rafts in this figure.

  • Fig. 3 Dynamically self-assembled patterns formed by up to 40 micro-rafts.

    (A) Numbers of micro-rafts in each layer for up to 40 micro-rafts. The inset on the top left shows four distinct bands formed by the trajectories of 36 micro-rafts. The central band consists of the trajectory of only one micro-raft. (B) An example of experimentally observed polymorphism is the two polymorphs of 21 micro-rafts. The top row shows two micro-rafts in the innermost layer, whereas the bottom row shows only one micro-raft in the innermost layer. The number at the center of a raft is the raft number, and the numbering starts from the innermost layer and increases clockwise within one layer. (C) Experimental and simulated patterns for 36 to 40 micro-rafts. The number in italics at the bottom right of each raft indicates the number of its nearest neighbors. This analysis of nearest neighbors is based on Voronoi cell construction, and it shows that the micro-rafts in the inner layers contain 6 ± 1 neighbors.

  • Fig. 4 Assembly of three to four micro-rafts through change of spinning speeds and the translation of symmetry from individual micro-rafts to assembled structures.

    (A to D) Deterministic assembly of three to four micro-rafts with arc angle θ = 30°: (A) From the initial triangular positions in the dynamic self-assembly state, three micro-rafts formed a right angle in the assembled structure. (B) From the initial conditions of two assembled micro-rafts and one free micro-raft, three micro-rafts formed a line. (C and D) Similar right-angled structure and linear structure form for four micro-rafts, from an initial four free micro-rafts and one free micro-raft, respectively. (E) Nondeterministic assembly of four micro-rafts with arc angle θ = 90°. The assembled structures show both 90° and 45° bending angles. When the spinning speed was again increased, the structures could disassemble or reconfigure into either a diamond or a square configuration. The amplitude A is 1 μm for all the micro-rafts in this figure.

  • Fig. 5 Assembly of 40 micro-rafts.

    Assembly of 40 micro-rafts with arc angles of (A) 30° and (B) 90°. Note the difference between the mostly square-based tiling in (A) and random aggregates in (B). (C) Repeatedly decreasing and increasing the rotation speed of the permanent magnet Ω results in highly ordered, square-based tiling of micro-rafts at intermediate Ω (1000 to 1500 rpm). Some disruption of this order at low Ω (500 to 200 rpm) results in imperfections in the assembly, such as triangular or pentagonal shapes. The amplitude A is 1 μm for all the micro-rafts in this figure.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/5/e1602522/DC1

    table S1. Contact angles of noncoated and SAM-coated gold surface.

    fig. S1. Scaling analysis of various forces in the system.

    fig. S2. In-plane magnetization of cobalt thin films.

    fig. S3. Magnetic profile of a 5-mm cube magnet.

    fig. S4. Photos of the experimental setup.

    fig. S5. Pairwise interaction plots for micro-rafts used in Figs. 3 to 5.

    fig. S6. Preliminary quantitative studies of micro-raft pairwise interactions using the Surface Evolver program.

    fig. S7. Simulated pairwise interaction curves.

    fig. S8. Experimental and simulated dynamic patterns for 3 to 40 micro-rafts.

    fig. S9. Comparison between the digital holographical micrographs of micro-rafts with arc angles of 30° and 90°.

    fig. S10. Unstable and stable configurations of aggregates of four bubbles.

    movie S1. Examples of pairwise interactions.

    movie S2. Two polymorphs of the dynamic patterns formed by 21 micro-rafts.

    movie S3. Four examples of nearest-neighbor counts in dynamically self-assembled patterns.

    movie S4. The assembly of three free micro-rafts with an arc angle of 30°.

    movie S5. The assembly of one free and two attached micro-rafts with an arc angle of 30°.

    movie S6. The assembly of four free micro-rafts with an arc angle of 30°.

    movie S7. The assembly of one free and three attached micro-rafts with an arc angle of 30°.

    movie S8. The assembly of four free micro-rafts with an arc angle of 90°.

    movie S9. The disassembly of four assembled micro-rafts with an arc angle of 90°.

    movie S10. The rearrangement of four assembled micro-rafts with an arc angle of 90° into a diamond shape.

    movie S11. The rearrangement of four assembled micro-rafts with an arc angle of 90° into a square shape.

    movie S12. The assembly of 40 micro-rafts with an arc angle of 30°.

    movie S13. The assembly of 40 micro-rafts with an arc angle of 90°.

    movie S14. The local rearrangement of assembled structures of 40 micro-rafts with an arc angle of 30° at intermediate spinning speed.

  • Supplementary Materials

    This PDF file includes:

    • table S1. Contact angles of noncoated and SAM-coated gold surface.
    • fig. S1. Scaling analysis of various forces in the system.
    • fig. S2. In-plane magnetization of cobalt thin films.
    • fig. S3. Magnetic profile of a 5-mm cube magnet.
    • fig. S4. Photos of the experimental setup.
    • fig. S5. Pairwise interaction plots for micro-rafts used in Figs. 3 to 5.
    • fig. S6. Preliminary quantitative studies of micro-raft pairwise interactions using the Surface Evolver program.
    • fig. S7. Simulated pairwise interaction curves.
    • fig. S8. Experimental and simulated dynamic patterns for 3 to 40 micro-rafts.
    • fig. S9. Comparison between the digital holographical micrographs of micro-rafts with arc angles of 30° and 90°.
    • fig. S10. Unstable and stable configurations of aggregates of four bubbles.
    • Legends for movies S1 to S14

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mp4 format). Examples of pairwise interactions.
    • movie S2 (.mp4 format). Two polymorphs of the dynamic patterns formed by 21 micro-rafts.
    • movie S3 (.mp4 format). Four examples of nearest-neighbor counts in dynamically self-assembled patterns.
    • movie S4 (.mp4 format). The assembly of three free micro-rafts with an arc angle of 30°.
    • movie S5 (.mp4 format). The assembly of one free and two attached micro-rafts with an arc angle of 30°.
    • movie S6 (.mp4 format). The assembly of four free micro-rafts with an arc angle of 30°.
    • movie S7 (.mp4 format). The assembly of one free and three attached micro-rafts with an arc angle of 30°.
    • movie S8 (.mp4 format). The assembly of four free micro-rafts with an arc angle of 90°.
    • movie S9 (.mp4 format). The disassembly of four assembled micro-rafts with an arc angle of 90°.
    • movie S10 (.mp4 format). The rearrangement of four assembled micro-rafts with an arc angle of 90° into a diamond shape.
    • movie S11 (.mp4 format). The rearrangement of four assembled micro-rafts with an arc angle of 90° into a square shape.
    • movie S12 (.mp4 format). The assembly of 40 micro-rafts with an arc angle of 30°.
    • movie S13 (.mp4 format). The assembly of 40 micro-rafts with an arc angle of 90°.
    • movie S14 (.mp4 format). The local rearrangement of assembled structures of 40 micro-rafts with an arc angle of 30° at intermediate spinning speed.

    Download Movies S1 to S14

    Files in this Data Supplement: