Swimming to Stability: Structural and Dynamical Control via Active Doping

Orbits, Spirals, and Trapped States: Dynamics of a Phoretic Janus Particle in a Radial Concentration Gradient

A long-standing goal in colloidal active matter is to understand how gradients in fuel concentration influence the motion of phoretic Janus particles. Here, we present a theoretical description of the motion of a spherical phoretic Janus particle in the presence of a radial gradient of the chemical solute driving self-propulsion. Radial gradients are a geometry relevant to many scenarios in active matter systems and naturally arise due to the presence of a point source or sink of fuel. We derive an analytical solution for the Janus particle's velocity and quantify the influence of the radial concentration gradient on the particle's trajectory. Compared to a phoretic Janus particle in a linear gradient in fuel concentration, we uncover a much richer set of dynamic behaviors including circular orbits and trapped stationary states. We identify the ratio of the phoretic mobilities between the two domains of the Janus particle as a central quantity in tuning their dynamics. Our results provide a path for developing optimum protocols for tuning the dynamics of phoretic Janus particles and mixing fluid at the microscale. In addition, this work suggests a method for quantifying the surface properties of phoretic Janus particles, which have proven to be challenging to probe experimentally.

Restructuring a passive colloidal suspension using a rotationally driven particle

The interaction between passive and active/driven particles has introduced a new way to control colloidal suspension properties from particle aggregation to crystallization. Here, we focus on the hydrodynamic interaction between a single rotational driven particle and a suspension of passive particles near the floor. Using experiments and Stokesian dynamics simulations that account for near-field lubrication, we demonstrate that the flow induced by the driven particle can induce long-ranged rearrangement in a passive suspension. We observe an accumulation of passive particles in front of the driven particle and a depletion of passive particles behind the driven particle. This restructuring generates a pattern that can span a range more than 10 times the driven particles radius. We further show that size scale of the pattern is only a function of the particles height above the floor.

Kinetic temperature and pressure of an active Tonks gas

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.

Environmental memory boosts group formation of clueless individuals

The formation of groups of interacting individuals improves performance and fitness in many decentralised systems, from micro-organisms to social insects, from robotic swarms to artificial intelligence algorithms. Often, group formation and high-level coordination in these systems emerge from individuals with limited information-processing capabilities implementing low-level rules of communication to signal to each other. Here, we show that, even in a community of clueless individuals incapable of processing information and communicating, a dynamic environment can coordinate group formation by transiently storing memory of the earlier passage of individuals. Our results identify a new mechanism of indirect coordination via shared memory that is primarily promoted and reinforced by dynamic environmental factors, thus overshadowing the need for any form of explicit signalling between individuals. We expect this pathway to group formation to be relevant for understanding and controlling self-organisation and collective decision making in both living and artificial active matter in real-life environments.

Phase separation of passive particles in active liquids

The transport properties of colloidal particles in active liquids have been studied extensively. It has led to a deeper understanding of the interactions between passive and active particles. However, the phase behavior of colloidal particles in active media has received little attention. Here, we present a combined experimental and numerical investigation of passive colloids dispersed in suspensions of active particles. Our study reveals dynamic clustering of colloids in active media due to an interplay of activity and attractive effective potential between the colloids. The strength of the effective potential is set by the size ratio of passive particles to the active ones. As the relative size of the passive particles increases, the effective potential becomes stronger and the average size of the clusters grows. The simulations reveal a macroscopic phase separation at sufficiently large size ratios. We will discuss the effect of density fluctuations of active particles on the nature of effective interactions between passive ones.

Reconfiguration, Interrupted Aging, and Enhanced Dynamics of a Colloidal Gel Using Photoswitchable Active Doping

We study quasi-2D gels made of a colloidal network doped with Janus particles activated by light. Following the gel formation, we monitor both the structure and dynamics before, during, and after the activation period. Before activity is switched on, the gel is slowly aging. During the activation, the mobility of the passive particles exhibits a characteristic scale-dependent response, while the colloidal network remains connected, and the gel maintains its structural integrity. Once activity is switched off, the gel stops aging and keeps the memory of the structure inherited from the active phase. Remarkably, the motility remains larger than that of the gel, before the active period. The system has turned into a genuinely softer gel, with frozen dynamics, but with more space for thermal fluctuations. The above conclusions remain valid long after the activity period.

Ostwald-like ripening in the two-dimensional clustering of passive particles induced by swimming bacteria

Clustering passive particles by active agents is a promising route for fabrication of colloidal structures. Here, we report the dynamic clustering of micrometric beads in a suspension of motile bacteria. We characterize the coarsening dynamics for various bead sizes, surface fractions, and bacterial concentrations. We show that the time scale τ for the onset of clustering is governed by the time of first encounter of diffusing beads. At large time (t≫τ), we observe a robust cluster growth as t^{1/3}, similar to the Ostwald ripening mechanism. From bead tracking measurements, we extract the short-range bacteria-induced attractive force at the origin of this clustering.

Inertia changes evolution of motility-induced phase separation in active matter across particle activity

The effects of inertia in active matter and motility-induced phase separation (MIPS) have attracted growing interest but still remain poorly studied. We studied MIPS behavior in the Langevin dynamics across a broad range of particle activity and damping rate values with molecular dynamic simulations. Here we show that the MIPS stability region across particle activity values consists of several domains separated by discontinuous or sharp changes in susceptibility of mean kinetic energy. These domain boundaries have fingerprints in the system's kinetic energy fluctuations and characteristics of gas, liquid, and solid subphases, such as the number of particles, densities, or the power of energy release due to activity. The observed domain cascade is most stable at intermediate damping rates but loses its distinctness in the Brownian limit or vanishes along with phase separation at lower damping values.

Reinforcement learning reveals fundamental limits on the mixing of active particles

The control of far-from-equilibrium physical systems, including active materials, requires advanced control strategies due to the non-linear dynamics and long-range interactions between particles, preventing explicit solutions to optimal control problems. In such situations, Reinforcement Learning (RL) has emerged as an approach to derive suitable control strategies. However, for active matter systems, it is an important open question how the mathematical structure and the physical properties determine the tractability of RL. In this paper, we demonstrate that RL can only find good mixing strategies for active matter systems that combine attractive and repulsive interactions. Using analytic results from dynamical systems theory, we show that combining both interaction types is indeed necessary for the existence of mixing-inducing hyperbolic dynamics and therefore the ability of RL to find homogeneous mixing strategies. In particular, we show that for drag-dominated translational-invariant particle systems, mixing relies on combined attractive and repulsive interactions. Therefore, our work demonstrates which experimental developments need to be made to make protein-based active matter applicable, and it provides some classification of microscopic interactions based on macroscopic behavior.

Dynamic overlap concentration scale of active colloids

By introducing the notion of a dynamic overlap concentration scale, we identify additional universal features of the mechanical properties of active colloids. We codify these features by recognizing that the characteristic length scale of an active particle's trajectory, the run length, introduces a concentration scale ϕ^{*}. Large-scale simulations of repulsive active Brownian particles (ABPs) confirm that this run-length dependent concentration, the trajectory-space analog of the overlap concentration in polymer solutions, delineates distinct concentration regimes in which interparticle collisions alter particle trajectories. Using ϕ^{*} and concentration scales associated with colloidal jamming, the mechanical equation of state for ABPs collapses onto a set of principal curves that contain several overlooked features. The inclusion of these features qualitatively alters previous predictions of the behavior for active colloids, as we demonstrate by computing the spinodal for a suspension of purely repulsive ABPs. Our findings suggest that dynamic overlap concentration scales should help unravel the behavior of active and driven systems.

Active matter shepherding and clustering in inhomogeneous environments

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

Colloidal assembly manipulated by light-responsive Ag3PO4 nanoparticles

We report controllable assembly of polystyrene (PS) microspheres via a photocatalytically driven electroosmotic flow deriving from UV irradiation of Ag₃PO₄ nanoparticles in water. A series of assembly phases, including crystallites, chains and gels, are programmed by systematically modulating the UV intensity, the packing density of the PS microspheres and the concentration of the Ag₃PO₄ nanoparticles. Our findings demonstrate an important ability of light-responsive nanoparticles for colloidal assembly, which offers a new pathway toward effective manipulation of assembly at the microscale.

Collective excitations in active fluids: Microflows and breakdown in spectral equipartition of kinetic energy

The effect of particle activity on collective excitations in active fluids of microflyers is studied. With an in silico study, we observed an oscillating breakdown of equipartition (uniform spectral distribution) of kinetic energy in reciprocal space. The phenomenon is related to short-range velocity-velocity correlations that were realized without forming of long-lived mesoscale vortices in the system. This stands in contrast to well-known mesoscale turbulence operating in active nematic systems (bacterial or artificial) and reveals the features of collective dynamics in active fluids, which should be important for structural transitions and glassy dynamics in active matter.

Static-state particle fabrication via rapid vitrification of a thixotropic medium

Functional particles that respond to external stimuli are spurring technological evolution across various disciplines. While large-scale production of functional particles is needed for their use in real-life applications, precise control over particle shapes and directional properties has remained elusive for high-throughput processes. We developed a high-throughput emulsion-based process that exploits rapid vitrification of a thixotropic medium to manufacture diverse functional particles in large quantities. The vitrified medium renders stationary emulsion droplets that preserve their shape and size during solidification, and energetic fields can be applied to build programmed anisotropy into the particles. We showcase mass-production of several functional particles, including low-melting point metallic particles, self-propelling Janus particles, and unidirectionally-magnetized robotic particles, via this static-state particle fabrication process.

Universal reshaping of arrested colloidal gels via active doping

Colloids that interact via a short-range attraction serve as the primary building blocks for a broad range of self-assembled materials. However, one of the well-known drawbacks to this strategy is that these building blocks rapidly and readily condense into a metastable colloidal gel. Using computer simulations, we illustrate how the addition of a small fraction of purely repulsive self-propelled colloids, a technique referred to as active doping, can prevent the formation of this metastable gel state and drive the system toward its thermodynamically favored crystalline target structure. The simplicity and robust nature of this strategy offers a systematic and generic pathway to improving the self-assembly of a large number of complex colloidal structures. We discuss in detail the process by which this feat is accomplished and provide quantitative metrics for exploiting it to modulate the self-assembly. We provide evidence for the generic nature of this approach by demonstrating that it remains robust under a number of different anisotropic short-ranged pair interactions in both two and three dimensions. In addition, we report on a novel microphase in mixtures of passive and active colloids. For a broad range of self-propelling velocities, it is possible to stabilize a suspension of fairly monodisperse finite-size crystallites. Surprisingly, this microphase is also insensitive to the underlying pair interaction between building blocks. The active stabilization of these moderately sized monodisperse clusters is quite remarkable and should be of great utility in the design of hierarchical self-assembly strategies. This work further bolsters the notion that active forces can play a pivotal role in directing colloidal self-assembly.

Reverse osmotic effect in active matter

In nonequilibrium active matter systems, a spatial variation in activity can lead to a spatial variation in concentration of active particles satisfying, at steady state, the condition nU=const [Schnitzer, Phys. Rev. E 48, 2553 (1993)1063-651X10.1103/PhysRevE.48.2553; Tailleur and Cates, Phys. Rev. Lett. 100, 218103 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.218103], where n is the number density and U is the active (swim) speed. We show that this condition holds even when the variation is abrupt and when thermal Brownian motion is present provided that the Péclet number is large. This spatial variation in swim speed and concentration produces a fluid pressure distribution that drives a reverse osmotic flow-fluid flows from regions of high concentration to low.

Collective forces in scalar active matter

Large-scale collective behavior in suspensions of active particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.

Active binary mixtures of fast and slow hard spheres

We computationally studied the phase behavior and dynamics of binary mixtures of active particles, where each species had distinct activities leading to distinct velocities, fast and slow. We obtained phase diagrams demonstrating motility-induced phase separation (MIPS) upon varying the activity and concentration of each species, and extended current kinetic theory of active/passive mixtures to active/active mixtures. We discovered two regimes of behavior quantified through the participation of each species in the dense phase compared to their monodisperse counterparts. In regime I (active/passive and active/weakly-active), we found that the dense phase was segregated by particle type into domains of fast and slow particles. Moreover, fast particles were suppressed from entering the dense phase while slow particles were enhanced entering the dense phase, compared to monodisperse systems of all-fast or all-slow particles. These effects decayed asymptotically as the activity of the slow species increased, approaching the activity of the fast species until they were negligible (regime II). In regime II, the dense phase was homogeneously mixed and each species participated in the dense phase as if it were it a monodisperse system (i.e. not mixed at all). Finally, we showed that a weighted average of constituent particle activities, which we term the net activity, defines a binodal for the MIPS transition in active/active binary mixtures. We examined the critical point of the transition and found a critical exponent (β = 0.45) in agreement with similar studies on monodisperse systems, and distinct from equilibrium systems.

Microscopic origins of the swim pressure and the anomalous surface tension of active matter

The unique pressure exerted by active particles-the "swim" pressure-has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density-an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an "equivalent pressure" (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied.

Rheological implications of embedded active matter in colloidal gels

Colloidal gels represent an important class of soft matter, in which networks formed due to strong, short-range interactions display solid-like mechanical properties, such as a finite low-frequency elastic modulus. Here we examine the effect of embedded active colloids on the linear viscoelastic moduli of fractal cluster colloidal gels. We find that the autonomous, out-of-equilibrium dynamics of active colloids incorporated into the colloidal network decreases gel elasticity, in contrast to observed stiffening effects of myosin motors in actin networks. Fractal cluster gels are formed by the well-known mechanism of aggregating polystyrene colloids through addition of divalent electrolyte. Active Janus particles with a platinum hemisphere are created from the same polystyrene colloids and homogeneously embedded in the gels at dilute concentration at the time of aggregation. Upon addition of hydrogen peroxide - a fuel that drives the diffusiophoretic motion of the embedded Janus particles - the microdynamics and mechanical rheology change in proportion to the concentration of hydrogen peroxide and the number of active colloids. We propose a theoretical explanation of this effect in which the decrease in modulus is mediated by active motion-induced softening of the inter-particle attraction. Furthermore, we characterize the failure of the fluctuation-dissipation theorem in the active gels by identifying a discrepancy between the frequency-dependent macroscopic viscoelastic moduli and the values predicted by microrheology from measurement of the gel microdynamics. These findings support efforts to engineer gels for autonomous function by tuning the microscopic dynamics of embedded active particles. Such reconfigurable gels, with multi-state mechanical properties, could find application in materials such as paints and coatings, pharmaceuticals, self-healing materials, and soft robotics.

Activity-controlled annealing of colloidal monolayers

Molecular motors are essential to the living, generating fluctuations that boost transport and assist assembly. Active colloids, that consume energy to move, hold similar potential for man-made materials controlled by forces generated from within. Yet, their use as a powerhouse in materials science lacks. Here we show a massive acceleration of the annealing of a monolayer of passive beads by moderate addition of self-propelled microparticles. We rationalize our observations with a model of collisions that drive active fluctuations and activate the annealing. The experiment is quantitatively compared with Brownian dynamic simulations that further unveil a dynamical transition in the mechanism of annealing. Active dopants travel uniformly in the system or co-localize at the grain boundaries as a result of the persistence of their motion. Our findings uncover the potential of internal activity to control materials and lay the groundwork for the rise of materials science beyond equilibrium.