Controlling active self-assembly through broken particle-shape symmetry

Many structural properties of conventional passive materials are known to arise from the symmetries of their microscopic constituents. By contrast, it is largely unclear how the interplay between particle shape and self-propulsion controls the meso- and macroscale behavior of active matter. Here we use large-scale simulations of homo- and heterogeneous self-propelled particle systems to identify generic effects of broken particle-shape symmetry on collective motion. We find that even small violations of fore-aft symmetry lead to fundamentally different collective behaviors, which may facilitate demixing of differently shaped species as well as the spontaneous formation of stable microrotors. These results suggest that variation of particle shape yields robust physical mechanisms to control self-assembly of active matter, with possibly profound implications for biology and materials design.

Figure 1

Actual and effective dynamical shapes of various microswimmers and simplified representation in the SPP model. (a) An L-shaped self-driven colloid [20]. (b) Superimposed phase-contrast micrographs (Zeiss Axiovert, 40$\times$, NA0.6) of swimming bull sperm. On time scales larger than the beat period $\sim 0.1$s, the cell mimics a forward-swimming cone. (c) A Chlamydomonas alga (63$\times$, NA1.3), confined to quasi-2D motion, resembles a backward-swimming triangle. (d) Nonconvex crescent-shaped Selenomonas bovis bacterium with flagella. (e) The SPP model approximates different shapes by combinations of rigidly linked spheres.

Figure 2

Simulation results for uniform systems of convex particles [34]. (a) and (b) Time-dependent speed $v$ in units of $v_0$ and trajectories (insets) of three colliding (a) $s^{+}$ SPPs and (b) $s^{-}$ SPPs. (c) and (d) The $s^{+}$ SPPs form aligned fronts, whereas $s^{-}$ SPPs exhibit clustering. Color encodes the horizontal velocity component $v_x$ ($N={10}^4$, $\left|p\right|=0.33$, and $\varphi =0.05$). (e) and (f) Static structure factor $S\left(q\right)$ at different volume filling fractions $\varphi$. The insets show a comparison of $S\left(q\right)$ for $s^{+}$ SPPs (red) and $s^{-}$ SPPs (blue) at two different filling fractions $\varphi$. (g) The peak of $S\left(0\right)$ at $p\approx -0.5$ indicates an optimal polarity for cluster formation. (h) Average velocity $\langle v\rangle$ for SPPs with $p=\pm 0.33$ (dashed lines with open symbols) and rotational diffusion coefficient $D_r$ of a tagged SPP (solid lines with closed symbols).

Figure 3

Demixing of $s^{+}$ SPPs and $s^{-}$ SPPs in an equimolar binary suspension [34]. (a) Snapshots of the center-of-mass positions for $N={10}^4$ SPPs with $\left|p\right|=0.67$ and $\varphi =0.05$. (b)–(d) Region enclosed by the dashed box in (a). Color in (c) and (d) encodes the translational speed $v$ and rotational velocity $\omega =|\partial \phi /\partial \tau |$ of each SPP.

Figure 4

Segregation and spontaneous self-assembly of $c^{-}$ rotors in an equimolar binary mixture of nonconvex SPPs [34]. (a) Snapshot of simulation with $N=2\times {10}^3$, $\kappa =0.2$, $\alpha =\pi$, and $\varphi =0.08$. (b) Enlarged view of the yellow-shaded area in (a). (c) Rotational velocity $\omega =\partial \phi /\partial \tau$ indicated by color coding. The insets depict snapshots of clusters composed of $c^{-}$ crescents rotating clockwise ($\omega <0$) or counterclockwise ($\omega >0$). (d) A pronounced peak of the structure factor signals the formation of $c^{-}$ rotors, which spin almost ballistically (lower left inset).