Dynamical Crystallites of Active Chiral Particles

One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.

Figure 1

(a) Magnitude of average density-peak velocity $|⟨\mathbf{v}⟩|$ as a function of $M$, for ${\psi }_0=-0.3$ and $v_0=0.35$, 0.4, and 0.5. Dashed curves represent analytic results of Eq. (5) assuming ${\widehat{q}}_0\simeq q_0=1$. Inset: $⟨|\mathrm{\Omega }|⟩$ measuring particle self-spinning. (b)–(d) Snapshots of parts of the $\psi$ profiles in three characteristic regimes, with the density peaks shown in red, their velocities $\mathbf{v}$ indicated by large arrows, and the polarization field $\mathbf{P}$ by fine arrows. (e) Snapshot of migrating crystallites in an active melt (see Supplemental Material, Video S2 [49]). Inset: Enlarged portion of a two-grain impinged corner, with a penta-hepta dislocation.

Figure 2

Self-spinning-induced phase transformation of crystalline patterns with increasing $M$ (at $v_0=1$, ${\psi }_0=-0.4$).

Figure 3

(a) Averaged translational and rotational velocities ($|⟨\mathbf{v}⟩|$ and $⟨|\omega |⟩$ at $v_0=0.5$) as a function of $M$, containing translation- and rotation-dominated regimes for crystallites in a circular cavity and a transitional regime (shaded symbols) enlarged in the inset. (b)–(e) Snapshots of crystallite patterns simulated [as marked in (a)], with $\mathbf{v}$ vectors indicated.

Figure 4

Dynamical state diagrams in the $M-v_0$ space for three dynamical regimes in (a) bulk and (b) interfacial systems.

Figure 5

Interface-induced self-motion of crystalline layers at $v_0=0.5$, including (a) self-shearing ($M=0.5$, ${\psi }_0=-0.2$) and (b) frustrated motion ($M=0.19$, ${\psi }_0=-0.19$) for a slab crystallite, and (c) self-rotation of a ring crystallite ($M=0.25$, ${\psi }_0=-0.26$).