Flocking transition in phoretically interacting active particles with pinning disorder

TL;DR

This paper investigates the flocking transition in a 2D system of phoretically interacting active colloids subject to quenched pinning disorder. A particle-based model with mobile and pinned particles, long-range chemo-repulsive interactions, torques, and diffusive chemical fields is simulated to map phase diagrams and quantify global polar and hexatic order. Key findings show that pinning destroys the crystalline flock while preserving a polar liquid phase; stronger translational repulsion can compensate pinning to sustain flocking, whereas removing chemo-repulsion makes order progressively fragile. The work reveals a disorder-induced solid-to-liquid transition driven by inert obstacles and provides a framework of observables and phase diagrams relevant for experiments and future studies of disorder in active matter.

Abstract

Recent studies in the collective behavior of active colloids have shown that a global polar order may emerge due to long-ranged chemo-repulsive interactions between them. Here, we report the role of pinning disorder in the flocking transition for such a system. To this end, we study the problem of chemically interacting active colloids with some fraction of the colloids randomly pinned over space such that they can only rotate while phoretically interacting with other particles. Using this model, we investigate the sustenance of global polar order in the presence of quenched disorder. We quantify the flocking transition by studying the global polarization, and the role of finite-size effects. We find that in the crystalline flocking phase, even a small fraction of pinning can destroy spatial crystalline order, although polar order in the form of a liquid phase is maintained. It is observed that polar order is sustained in a system with a higher pinning fraction if the long-ranged repulsive force is subsequently increased. However, in absence of chemo-repulsive forces between particles, polar order drastically decreases even with a smaller pinning fraction. Overall, this work suggests a novel route of solid-to-liquid transition that can be induced via "translationally inert" obstacles, that rotate but do not translate whilst interacting with the bulk.

Figures (5)

• Figure 1: (a) schematics for the interactions and dynamics of two active colloids (shown as orange circles with a black dot to indicate orientation). Solid red arrows show chemo-repulsive forces between particles while black curved arrows denote chemo-repulsive torques. Schematic of the model of active colloids with random pinning is show in (b). Pinned particles (grey colour) only rotate (no translational motion for pinned particles), while active particles rotate as well as translate.
• Figure 2: (a) Phase diagram in the $(n_p,\Lambda_t)$ plane, constructed via the order parameter $m$; three reference points on the diagram correspond to the phases are shown in (b) crystalline flock ($n_p=0$), (c) polar liquid ($n_p=0.15$) and (d) random ($n_p=0.36$). The total number of particles are taken as $N=1200$. Pinned particles are marked as Grey colour and direction of motion of the free particles follows the color scheme shown in (f); (e) Polarization $M$ versus time for (b)-(d) phases; (f) color scheme of moving particles, the angle is determined with respect to positive $x$-axis. (g) Order parameter $m$ versus $n_p$ for different system of sizes $L=32,64,128$ and $256$ (constant $\phi=0.36$). (h) Order parameter $m$ versus $n_p$ for different area fraction $\phi=0.12,0.24,0.36$ and $0.48$ ($L=128$ is constant).
• Figure 3: (a) Phase diagram of hexatic order in the $(n_p,\Lambda_t)$ plane. (b) Pair correlation $g(r)$ versus distance ($r$) plot for different pinning fraction $n_p=0$, $0.01$ and $0.15$. (c) $g(r, \varphi)$ plot with $n_p=0$, indicating a crystalline flock structure, (d) $g(r, \varphi)$ plot with $n_p=0.01$ indicating a liquid flock structure. Here, the total number of particles, $N=4000$.
• Figure 4: Phase diagram in ($n_p,\Lambda_t$) plane of spatial density variance $\sigma$ in (a) and susceptibility $\chi$ of polar order in panel (b). Phase diagram in the ($\Lambda_r$, $\Lambda_t$) plane: (c) Polar order parameter $m$ with constant $n_p=0.15$. Dotted curves indicate transition line of polar order with $n_p=0$ (marked as blue), and $n_p=0.5$ (marked as red) respectively. (d) Susceptibility $\chi$ of the order parameter with $n_p=0.15$, showing maximum values near the transition line. (e) Phase diagram of spatial density variance $\sigma$ with constant $n_p=0.15$.
• Figure 5: Case with $\Lambda_t =0$: Phase diagram in the $(n_p,\Lambda_r)$ plane for (a) polar order parameter $m$, (b) susceptibility $\chi$ of the order parameter. (c) density band with $n_p=0$, (d) liquid flock (no band forms) with $n_p=0.03$. The value of the parameters marked in (a) for these two steady-state configurations. The same colour scheme is followed as shown in Fig.\ref{['fig:phase_D1']}(f). Pinned particles in (d) are marked grey. Total number of particles taken as $N=1200$.