Living Clusters and Crystals from Low-Density Suspensions of Active Colloids

Abstract

Recent studies aimed at investigating artificial analogues of bacterial colonies have shown that lowdensity suspensions of self-propelled particles confined in two dimensions can assemble into finite aggregates that merge and split, but have a typical size that remains constant (living clusters). In this Letter we address the problem of the formation of living clusters and crystals of active particles in three dimensions. We study two systems: self-propelled particles interacting via a generic attractive potential and colloids that can move towards each other as a result of active agents (e.g. by molecular motors). In both cases fluid-like 'living' clusters form. We explain this general feature in terms of the balance between active forces and regression to thermodynamic equilibrium. This balance can be quantified in terms of a dimensionless number that allows us to collapse the observed clustering behaviour onto a universal curve. We also discuss how active motion affects the kinetics of crystal formation. PACS numbers:Active systems consume energy that keeps them in an out-of-equilibrium state [1,2]. This is typical for many biologically relevant systems which, by exploiting chemical energy, can self-organise into complex structures that lack any equilibrium counterpart. Examples are abundant and exist at different length-scales: from cytoskeleton remodulation during cell mitosis [3] to swarming phenomena in micro-swimmers or flocks of birds [4,5]. The similarity of the patterns displayed by these systems lead many to address the general principles behind their formation using simple models [6]. The reproducibility and robustness of the phenomena under a variety of external conditions motivated a large body of research on selfassembly of active particle as a possible strategy towards the fabrication of new functional nano-and mesoscopic structures [7]. In this respect there have been several efforts to study active self-organisation in a tightly controlled environment; the most studied systems being selfpropelled particles [6,[8][9][10][11] and active gels (e.g. [12]).Recently, two experimental groups have shown how two-dimensional suspensions of self-propelled (SP) colloids (moving through the consumption of an appropriate 'fuel') self-assemble into dynamic clusters that constantly join and split, recombining with each other to reach a steady-state [13,14]. A general understanding of active cluster formation is lacking, but different explanations have been proposed. The authors of Ref.[13] argued that a net attraction between colloids is responsible for clustering. This attraction is due to non-uniformity in the chemical fuel concentration between two colloids. This was confirmed by Ref. [14], that also found a 1/d 2 dependence of the particle-particle attraction ( d being the inter-particle distance). The formation of finite-size clusters has been also observed in low density bacteria/polymer suspensions, at intermediate polymer concentrations just before phase separation [10]. However, in other recent studi...

Light-activated self-propelled colloids

“…This behaviour arises from a self-trapping mechanism: self-propelled particles with a persistent time and colliding head on, arrest each other owing to the persistence of their orientation (figure 6a). Increasing the surface fraction of particles, this simple mechanism leads to a dynamic phase transition from a gas phase of hot colloids [10] to a dense state, resulting from the 'traffic jam' of the persistent self-propelled particles [46,[50][51][52][53][54][55][56][57]. The emergence of arrested phase owing to density-dependent mobility has been discussed theoretically in the context of bacteria by Tailleur & Cates [58].…”

Active microrheology in active matter systems: Mobility, intermittency, and avalanches

“…Examples of such systems include run-and-tumble bacteria [23][24][25][26] or self-mobile colloidal particles [27][28][29][30][31][32][33] , which are commonly modeled as self-mobile sterically interacting particles undergoing either active Brownian motion or runand-tumble dynamics. Such systems exhibit a transition from a uniform liquid state at low activities and densities to a cluster or phase separated state at higher activities and densities, where close-packed clusters are surrounded by a low density gas [32][33][34][35][36][37][38][39][40] . For monodisperse particles confined to two dimensions, the clusters have local triangular ordering, and the resulting crystallites can move, break apart, and re-form 32,33,[37][38][39][40] .…”

“…Such systems exhibit a transition from a uniform liquid state at low activities and densities to a cluster or phase separated state at higher activities and densities, where close-packed clusters are surrounded by a low density gas [32][33][34][35][36][37][38][39][40] . For monodisperse particles confined to two dimensions, the clusters have local triangular ordering, and the resulting crystallites can move, break apart, and re-form 32,33,[37][38][39][40] . A driven probe particle in an active matter system should show clear changes in mobility or velocity fluctuations depending on the spatio-temporal behavior exhibited by the active matter, and thus could serve as a powerful tool for understanding a wide range of active systems.…”

Effective Cahn-Hilliard Equation for the Phase Separation of Active Brownian Particles

“…At even higher densities, first steps have been taken to study glassy dynamics [20,21] and crystallization [22,23]. Another interesting question is the interplay of the propulsion with attractive forces [24][25][26].While the phase separation and nucleation in passive suspensions has been studied extensively, an open fundamental question is whether the clustering of active Brownian particles, which is an intrinsically nonequilibrium system, can be mapped on the phase separation dynamics of passive particles. In this Letter, we demonstrate for a simple model system of Brownian particles that this mapping exists on coarse-grained length and time scales.…”