Research ArticlePHYSICS

Surfactants and rotelles in active chiral fluids

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Science Advances  14 Apr 2021:
Vol. 7, no. 16, eabf8998
DOI: 10.1126/sciadv.abf8998
  • Fig. 1 Vibrot dimers suppress demixing of vibrot fluids.

    (A) Left-handed (black with white cross) and right-handed (white with black cross) vibrots manufactured by 3D printing (top). Scale bar, 10 mm. Vibrots can be connected by rigid bars that do not affect rotations (bottom). (B) Snapshots of equilibrated systems with increasing fractions of dimers. Connectors are highlighted by orange lines. Insets illustrate the particle geometry in experiments and simulations respectively. (C) Average number of equal neighbors per vibrot 〈Neq〉 and (D) number of chiral fluid domains Nd. The gray line corresponds to the hypothetical random state in which the handedness of all vibrots has been shuffled. Boxes indicate the 25th and 75th percentiles (p25 and p75). Whiskers show the range of observations from maximum to minimum. Points outside of [p25 − 1.5(p75p25), p75 + 1.5(p75p25)] are discarded as outliers. (E) Illustration of double-stranded and single-stranded chain configurations.

  • Fig. 2 Double-stranded vibrot chains have an affinity for chiral vibrot fluid interfaces.

    (A) Double-stranded vibrot chain of geometry 2 × 6. Strands are made from vibrots of opposite handedness. Vibrots are connected to their nearest neighbors in a square lattice to keep the chain semi-flexible. (B) Experimental snapshots with a 2 × 14 chain at three observation times. Vibrots are positioned initially in the mixed phase and then demixed. Orange lines are connectors. (C) Evolution of the distance between the centers of mass of the left-handed and right-handed fraction of vibrots (orange curve). Distance of each fraction from the chain’s center of mass (purple and green). All distances approach a constant. The distance between the fraction remains slightly below the confinement radius rsys = 150 mm.

  • Fig. 3 Demixing of a vibrot fluid in the presence of an active boundary.

    (A) Snapshots of the experiment at 0, 250, 500, and 3600 s. Left-handed vibrots are black with white crosses. Right-handed vibrots are white with black crosses. (B) Snapshot of the simulation after steady state has been reached. (C) Average distance of vibrots from the center of mass of the entire system for left-handed vibrots (orange) and right-handed vibrots (blue). Right-handed vibrots collect preferably at the boundary that consists of vibrots with the same handedness. (D) Snapshot of the experiment after steady state has been reached. Vibrots are found predominantly near boundary regions made from vibrots of opposite handedness. This is explained by the commensurability of the collective flow of the demixed domains (blue and orange circles) to the rotation direction of vibrots at the boundary. (E) Snapshot of the simulation after steady state has been reached. (F) Average distances of vibrots in the interior from vibrots in the boundary. Blue and red curves correspond to the distances for vibrots of equal and opposite handedness, respectively. Vibrots of opposite handedness show, on average (dashed lines), a smaller distance than vibrots of equal handedness.

  • Fig. 4 Double-stranded vibrot chains act as mixing agents for vibrot fluids.

    (A) Analysis of chain motion in a simulation with complete demixing (chain length N = 6, chain concentrations P = 6%). We identify the center of mass and the orientation of each chain (green arrow) and measure the total move distance from the start position (labeled as translation) and the total orientation change (labeled as rotation). Two modes of chain motion can be clearly distinguished in the translation versus rotation trajectory plot (bottom left): circular motion inside chiral fluids (top left; horizontal segments in trajectory plot) and superdiffusive motion along interfaces (bottom right; vertical segments). (B) The trajectory plot for a system with partial demixing (chain concentrations, 18%) has shorter straight segments indicating smaller chiral fluid domain sizes. Note the smaller axis ranges. (C) The trajectory plot for a system that remains mixed (chain concentrations, 30%) is evidence for free diffusion. Each trajectory plot contains the trajectories of 12 randomly chosen chains sampled over a time of 104 s. (D) Final simulation snapshots reveal complete demixing (dark blue frames), partial demixing (light blue frames), and no demixing (green frames) as a function of chain length N and chain concentration P. Vibrots are shown as disks for faster rendering.

  • Fig. 5 Rotelle formation in single-stranded vibrot block chains.

    (A) Single-stranded vibrot chains made from two blocks of opposite handedness can close around vibrot monomers and form a stable rotelle. (B) Rotelles appear in different sizes and can turn either of their blocks to the outside. The vibrots caught in the inside predominantly are of the handedness of the inside block. (C) More exotic but also much rarer rotelles observed in simulation. (D) Snapshots of a simulation with block-copolymer chains of varying chain length, N, and packing fraction, ϕ. We observe a concentrated rotelle solution at packing fraction ϕ = 46%. The chain concentration is kept constant at P = 50%. Vibrots are shown as disks for faster rendering. (E) Parameter space map. Rotelles form best at intermediate packing fractions (blue). “X” marks the snapshots shown in (D). A vector graphic is found in fig. S4.

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