Research ArticleBIOPHYSICS

Light-induced self-assembly of active rectification devices

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Science Advances  01 Apr 2016:
Vol. 2, no. 4, e1501850
DOI: 10.1126/sciadv.1501850
  • Fig. 1 Time-averaged local volume fraction ϕ(r) of interacting and noninteracting particles in a system with spatially patterned one-particle swim speed v(r), where v = vi = v0(1 – i/16) in the ith well and v = v0 between the wells.

    The solid lines show our predictions with a prefactor determined by least-squares fits, where we neglected the three highest density (ϕ > 0.5) data points for the interacting particles. Inset: Spatially resolved plot of ϕ(r) for the interacting particles; note the logarithmic scale on the color bar.

  • Fig. 2 Rectification through self-assembled funnels.

    (A) Time-averaged particle packing fraction ϕ(r) at steady state in a system of self-assembled funnels. Note the logarithmic scale on the color bar. (B) Magnification of one of the funnels showing the self-assembly process at three different times starting from a homogeneous particle distribution; τLJ is the Lennard-Jones time (see Methods). (C) Black curve: The packing fraction ϕ from (A) but now as a function of x and averaged over y; the pumping effect (rectification) is obvious. Red curve: For noninteracting particles, rectification is not possible.

  • Fig. 3 Steady-state packing fraction ϕ(x) (solid curves) in a system with a modulated speed v(x) composed of two opposing sawtooth profiles (dashed curves) obtained from particle-resolved simulations and our continuum model.

    For numerical reasons, the discontinuities of v(x) are smeared out over 10σ in the continuum calculations. The inset shows ϕ(x) with a magnified y scale, clearly demonstrating the rectification.

  • Fig. 4 Self-assembled active circuit.

    (A) Particle-resolved simulations of an annular circuit self-assembled through a prescribed speed profile v(r) with two similar sawteeth along the annulus and a very low speed outside of the annulus. The resulting dense particle packing outside of the annulus (not shown for clarity) confines the motile particles to the circuit. The color map shows the time-averaged steady-state local packing fraction ϕ(r), and vectors denote the rescaled local particle current J(r), with their colors indicating the absolute current density J(r) = |J(r)|. The logarithmic color bar applies both to the density plot and to the vector field plot. (B) Corresponding plot of the rescaled particle density ρ(r) ∝ ϕ(r) and particle current J(r) obtained from our continuum model.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/4/e1501850/DC1

    Particle leakage through the funnels

    Rectification mechanism

    Particle-resolved simulations

    Numerical solution of the continuum model

    Movie S1. Movie showing the self-assembly process of a single chevron-shaped obstacle.

    Fig. S1. Steady-state density profiles for funnel-wall systems with the funnel particles either mobile or fixed.

    Fig. S2. Local polarization around a sawtooth-shaped speed profile, obtained from particle-resolved simulations and the continuum model.

    Fig. S3. Polarization profiles obtained from the continuum model with w2 = 0 and w2 > 0.

    Fig. S4. Propulsion speed profiles used in simulations of “active circuits.”

  • Supplementary Materials

    This PDF file includes:

    • Particle leakage through the funnels
    • Rectification mechanism
    • Particle-resolved simulations
    • Numerical solution of the continuum model
    • Fig. S1. Steady-state density profiles for funnel-wall systems with the funnel
      particles either mobile or fixed.
    • Fig. S2. Local polarization around a sawtooth-shaped speed profile, obtained from particle-resolved simulations and the continuum model.
    • Fig. S3. Polarization profiles obtained from the continuum model with w2 = 0 and w2 > 0.
    • Fig. S4. Propulsion speed profiles used in simulations of “active circuits.”

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mov format). Movie showing the self-assembly process of a single chevron-shaped obstacle.

    Files in this Data Supplement:

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