Crystallizing hard-sphere glasses by doping with active particles

Microscopic theory for nonequilibrium correlation functions in dense active fluids

One of the key hallmarks of dense active matter in the liquid, supercooled, and solid phases is the so-called equal-time velocity correlations. Crucially, these correlations can emerge spontaneously, i.e., they require no explicit alignment interactions, and therefore represent a generic feature of dense active matter. This indicates that for a meaningful comparison or possible mapping between active and passive liquids one not only needs to understand their structural properties, but also the impact of these velocity correlations. This has already prompted several simulation and theoretical studies, though they are mostly focused on athermal systems and thus overlook the effect of translational diffusion. Here, we present a fully microscopic method to calculate nonequilibrium correlations in two-dimensional systems of thermal active Brownian particles (ABPs). We use the integration through transients formalism together with (active) mode-coupling theory and analytically calculate qualitatively consistent static structure factors and active velocity correlations. We complement our theoretical results with simulations of both thermal and athermal ABPs which exemplify the disruptive role that thermal noise has on velocity correlations.

Dynamics of self-propelled particles in vibrated dense granular media

We study a system consisting of a few self-propelled particles (SPPs) placed among a crowd of densely packed granular particles that are vertically vibrated in a two-dimensional circular confinement. Our experiments reveal two important findings. First, an SPP exhibits a fractal renewal process within the dense granular medium, which induces a superdiffusive behavior whose diffusion exponent increases with its aspect ratio. Second, the SPPs eventually reach the boundary and form a moving cluster, which transitions from the moving state to the static state as the number of SPPs is increased. These results suggest a simple and effective method of modulating the fluidity and directionality of granular systems via controlling the shape and the number of SPPs.

Evidence for Enhanced Tracer Diffusion in Densely Packed Interfacial Assemblies of Hairy Nanoparticles

Nearly monodisperse nanoparticle (NP) spheres attached to a nonvolatile ionic liquid surface were tracked by in situ scanning electron microscopy to obtain the tracer diffusion coefficient Dtr as a function of the areal fraction ϕ. The in situ technique resolved both tracer (gold) and background (silica) particles for ∼1-2 min, highlighting their mechanisms of diffusion, which were strongly dependent on ϕ. Structure and dynamics at low and moderate ϕ paralleled those reported for larger colloidal spheres, showing an increase in order and a decrease in Dtr by over 4 orders of magnitude. However, ligand interactions were more important near jamming, leading to different caging and jamming dynamics for smaller NPs. The normalized Dtr at ultrahigh ϕ depended on particle diameter and ligand molecular weight. Increasing the PEG molecular weight by a factor of 4 increased Dtr by 2 orders of magnitude at ultrahigh ϕ, indicating stronger ligand lubrication for smaller particles.

Entropons as collective excitations in active solids

The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers.

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.

Pattern formation and flocking for particles near the jamming transition on resource gradient substrates

We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.

Binary Phases and Crystals Assembled from Active and Passive Colloids

Classic binary materials, ranging from polymer blends to table salts, contain equilibrium phases or crystals of two interacting components. Here, we report on the construction of binary colloidal materials out of equilibrium by employing active particles and passive particles that dynamically interact and organize. Key to our scheme is the introduction of photoactive microspheres whose activity can be precisely tuned. This allows us to leverage the complex nonequilibrium interplay between the constituent components for dynamic coassembly. A wide variety of binary structures have thus been realized, including the liquid-crystal phases and crystal-crystal phases via phase separation and, counterintuitively, the binary crystalline compounds. The obtained structures are validated by computer simulations, which reveal unexpected kinetic pathways that are unique for active systems. With these findings, our strategy could facilitate the design and fabrication of multicomponent materials beyond equilibrium.

Self-Organization of Binary Colloidal Mixtures via Diffusiohporesis

Catalytic activity of the colloids and chemotactic response to gradients of the chemicals in the solution leads to effective interaction between catalytic colloids. In this paper, we simulate mixtures of active and passive colloids via a Brownian dynamics algorithm. These particles interact via phoretic interactions, which are determined by two independent parameters, surface activity and surface mobility. We find rich dynamic structures by tuning passive colloids’ surface mobility, size, and area fractions, which include schools of active colloids with exclusion zone, yolk/shell cluster, and stable active–passive alloys to motile clusters. Dynamical cluster can also be formed due to the nonreciprocity of the phoretic interaction. Increasing the size ratio of passive colloids to active colloids favors the phase separation of active and passive colloids, resulting in yolk/shell structure. Increasing the area fraction of active colloids tends to transfer from dynamical clusters into stable alloys. The simulated binary active colloid systems exhibit intriguing nonequilibrium phenomena that mimic the dynamic organizations of active/passive systems.

Activity-driven phase separation and ordering kinetics of passive particles

The steady state and phase ordering kinetics in a pure active Brownian particle system are studied in recent years. In binary mixture of active and passive Brownian particles passive particles are used as probe to understand the properties of active medium. In our present study, we study the mixture of passive and active Brownian particles. Here, we aim to understand the steady state and kinetics of small passive particles in the mixture. In our system, the passive particles are small in size and large in number, whereas ABPs are large in size and small in number. The system is studied on a two-dimensional substrate using overdamped Langevin dynamic simulation. The steady state and kinetics of passive particles are studied for various size and activity of active particles. Passive particles are purely athermal in nature and have dynamics only due to bigger ABPs. For small size ratio and activity, the passive particles remain homogeneous in the system, whereas on increasing size ratio and activity they form periodic hexagonal close pack (HCP) spanning clusters in the system. We have also studied the kinetics of growing passive particle clusters. The mass of the largest cluster shows a much slower growth kinetics in contrast to conserved growth kinetics in ABP system. Our study provides an understanding of steady state and kinetics of passive particles in the presence of bigger active particles. The mixture can be thought of as effect of big microorganism moving in passive medium.

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.

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.

Transport of self-propelled particles across a porous medium: trapping, clogging, and the Matthew effect

We study the transport of self-propelled particles from one free chamber to another across two stripe-like areas of dense porous medium. The medium is mimicked by arrays of obstacles. We find that active motion could greatly speed up the transport of particles. However, more and more particles become trapped in the obstacle arrays with the enhancement of activity. At high persistence (low rotational diffusion rate) and moderate particle concentration, we observe the Matthew effect in the aggregation of particles in the two obstacle arrays. This effect is weakened by introduction of randomness or deformability into the obstacle arrays. Moreover, the dependence on deformability shows the characteristics of first-order phase transition. In rare situations, the system could be stuck in a dynamic unstable state, e.g. the particles alternatively gather more in one of the two obstacle arrays, exhibiting oscillation of particle number between the arrays. Our results reveal new features in the transport of active objects in a complex medium and have implications for manipulating their collective assembly.

Anisotropic Exclusion Effect between Photocatalytic Ag/AgCl Janus Particles and Passive Beads in a Dense Colloidal Matrix

Synthetic nano- and micromotors interact with each other and their surroundings in a complex manner. Here, we report on the anisotropy of active-passive particle interaction in a soft matter system containing an immobile yet photochemical Ag/AgCl-based Janus particle embedded in a dense matrix of passive beads in pure water. The asymmetry in the chemical gradient around the Janus particle, triggered upon visible light illumination, distorts the isotropy of the surrounding electric potential and results in the repulsion of adjacent passive beads to a certain distance away from the Janus particle. This exclusion effect is found to be anisotropic with larger distances to passive beads in front of the Ag/AgCl cap of the Janus particle. We provide insight into this phenomenon by performing the angular analysis of the radii of exclusion and tracking their time evolution at the level of a single bead. Our study provides a novel fundamental insight into the collective behavior of a complex mixture of active and passive particles and is relevant for various application scenarios, e.g., particle transport at micro- and nanoscale and local chemical sensing.

Clustering and Phase Separation in Mixtures of Dipolar and Active Particles in an External Field

Directing the assembly of colloidal particles through the use of external electric or magnetic fields shows promise for the creation of reconfigurable materials. Self-propelled particles can also be used to dynamically drive colloidal systems to nonequilibrium steady states. We investigate colloidal systems that combine both of these methods of directed assembly, simulating mixtures of passive dipolar colloids and active soft spheres in an external magnetic field using Brownian dynamics in two dimensions. In these systems, the dipolar particles align in the direction of the external field, but the active particles are unaffected by the field. The phase behaviors exhibited included a percolated dipolar network, dipolar string-fluid, isotropic fluid, and phase-separated state. We find that the external field allows the dipolar particles to form a percolated network more easily compared to when no external field is present. Additionally, the mixture phase separates at lower active particle velocity in an external field than when no field is present. Our results suggest that combining multiple methods of directing colloidal assembly could lead to new pathways to fabricate reconfigurable materials.

Clustering and phase separation in mixtures of dipolar and active particles

The self-assembly of colloidal particles in dynamic environments has become an important field of study because of potential applications in fabricating out-of-equilibrium materials. We investigate the phase behavior of mixtures of passive dipolar colloids and active soft spheres using Brownian dynamics simulations in two dimensions. The phase behaviors exhibited include dipolar percolated network, dipolar string-fluid, isotropic fluid, and a phase-separated state. We find that the clustering of dipolar colloids is enhanced in the presence of slow-moving active particles compared to the clustering of dipolar particles mixed with passive particles. When the active particle motility is high, the chains of dipolar particles are either broken into short chains or pushed into dense clusters. Motility-induced phase separation into dense and dilute phases is also present. The area fraction of particles in the dilute phase increases as the fraction of active particles in the system decreases, while the area fraction of particles in the dense phase remains constant. Our findings are relevant to the development of reconfigurable self-assembled materials.

Activity-modulated phase transition in a two-dimensional mixture of active and passive colloids

We study a two-dimensional binary mixture of active and passive colloids as an idealized model of an hybrid aggregate of living cells and inert particles. We perform molecular dynamics simulations of this system using two different thermostats, and we systematically investigate the effect of varying these two effective temperatures on the system behavior, as characterized by its density, structure and thermoelastic properties. Our results indicate that the presence of active colloids shifts the mixture towards the liquid state and renders it more deformable. Such system softening and melting effects due to the addition of active particles are larger than expected from a linear combination of temperatures of the active and passive components. This heightened effect becomes more pronounced as the effective temperature difference between the two components becomes larger. The binary mixture remains homogeneous for moderate colloidal activity, but segregation arises for large effective temperature difference. Our results provide insights to guide future experimental hybrid aggregate studies with promising biomedical applications.

Quorum-sensing active particles with discontinuous motility

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.

Active particles sense micromechanical properties of glasses

Understanding the mechanical properties of glasses is a great scientific challenge. A powerful technique to study the material response on a microscopic scale is microrheology, in which one analyses the translational dynamics of an externally driven probe particle. Here we show that the translational and rotational dynamics of a self-propelled probe particle with an unconstrained orientational motion can be used to gather information about the mechanical properties of a colloidal glassy system. We find that its rotational diffusion coefficient continuously increases towards the glass transition and drops down in the glassy state. Such unexpected behaviour demonstrates a strong coupling mechanism between the orientation of the active probe particle and the glassy structure, which can be well described by a simple rheological model. Our results suggest that active probe particles may be useful for the micromechanical characterization of complex materials.

Response of active Brownian particles to boundary driving

We computationally study the behavior of underdamped active Brownian particles in a sheared channel geometry. Due to their underdamped dynamics, the particles carry momentum a characteristic distance away from the boundary before it is dissipated into the substrate. We correlate this distance with the persistence of particle trajectories, determined jointly by their friction and self-propulsion. Within this characteristic length, we observe counterintuitive phenomena stemming from the interplay of activity, interparticle interactions, and the boundary driving. Depending on the values of friction and self-propulsion, interparticle interactions can either aid or hinder momentum transport. More dramatically, in certain cases we observe a flow reversal near the wall, which we correlate with an induced polarization of the particle self-propulsion directions. We rationalize these results in terms of a simple kinetic picture of particle trajectories.

Assembly structures and dynamics of active colloidal cells

Many types of active matter are deformable, such as epithelial cells and bacteria. To mimic the feature of deformability, we built a model called an active colloidal cell (ACC), i.e. a vesicle enclosed with self-propelled particles (SPPs), which as a whole can move actively. Based on the model, we then study the role of deformability in the assembly structures and dynamics of ACCs by Langevin dynamics simulation. We find that deformability weakens the self-trapping effect and hence suppresses the clustering and phase separation of the deformable soft ACCs (sACCs). Instead of forming a large compact cluster like ordinary SPPs, sACCs pack into a loose network or porous structure in the phase-separation region. The condensed phase is liquid-like, in which sACCs are strongly compressed and deformed but still keep high motility. The interface between the gas and the condensed phases is blurry and unstable, and the effective interfacial energy is very low. Our work gives new insights into the role of deformability in the assembly of active matter and also provides a reference for further studies on different types of deformable active matter.

Tunable self-healing of magnetically propelling colloidal carpets

The process of crystallization is difficult to observe for transported, out-of-equilibrium systems, as the continuous energy injection increases activity and competes with ordering. In emerging fields such as microfluidics and active matter, the formation of long-range order is often frustrated by the presence of hydrodynamics. Here we show that a population of colloidal rollers assembled by magnetic fields into large-scale propelling carpets can form perfect crystalline materials upon suitable balance between magnetism and hydrodynamics. We demonstrate a field-tunable annealing protocol based on a controlled colloidal flow above the carpet that enables complete crystallization after a few seconds of propulsion. The structural transition from a disordered to a crystalline carpet phase is captured via spatial and temporal correlation functions. Our findings unveil a novel pathway to magnetically anneal clusters of propelling particles, bridging driven systems with crystallization and freezing in material science.

Activity often suppresses equilibrium ordering and crystallization in a group of driven or self-propelling colloids. Massana-Cid et al. show tunable self-healing process, where magnetic colloidal rollers are assembled to crystalline carpets upon a balance between magnetism and hydrodynamic interactions.

Swimming to Stability: Structural and Dynamical Control via Active Doping

External fields can decidedly alter the free energy landscape of soft materials and can be exploited as a powerful tool for the assembly of targeted nanostructures and colloidal materials. Here, we use computer simulations to demonstrate that nonequilibrium internal fields or forces-forces that are generated by driven components within a system-in the form of active particles can precisely modulate the dynamical free energy landscape of a model soft material, a colloidal gel. Embedding a small fraction of active particles within a gel can provide a unique pathway for the dynamically frustrated network to circumvent the kinetic barriers associated with reaching a lower free energy state through thermal fluctuations alone. Moreover, by carefully tuning the active particle properties (the propulsive swim force and persistence length) in comparison to those of the gel, the active particles may induce depletion-like forces between the constituent particles of the gel despite there being no geometric size asymmetry between the particles. These resulting forces can rapidly push the system toward disparate regions of phase space. Intriguingly, the state of the material can be altered by tuning macroscopic transport properties such as the solvent viscosity. Our findings highlight the potential wide-ranging structural and kinetic control facilitated by varying the dynamical properties of a remarkably small fraction of driven particles embedded in a host material.

Active apolar doping determines routes to colloidal clusters and gels

Collections of polar active particles have been unable to form stable and long-living structures due to the presence of self-propulsion. We solve this timely issue by introducing the concept of “active doping” and show that a few light-activated apolar, i.e., non–self-propelling, units can be used to rapidly trigger the formation of solid clusters and gels composed of passive colloidal particles. Our active doping can be used to assemble disparate microscopic objects, including synthetic or biological ones, paving the way toward the extension of fundamental concepts of gel and glass formation to active out-of-equilibrium systems.

Collections of interacting active particles, self-propelling or not, have shown remarkable phenomena including the emergence of dynamic patterns across different length scales, from animal groups to vibrated grains, microtubules, bacteria, and chemical- or field-driven colloids. Burgeoning experimental and simulation activities are now exploring the possibility of realizing solid and stable structures from passive elements that are assembled by a few active dopants. Here we show that such an elusive task may be accomplished by using a small amount of apolar dopants, namely synthetic active but not self-propelling units. We use blue light to rapidly assemble 2D colloidal clusters and gels via nonequilibrium diffusiophoresis, where microscopic hematite dockers form long-living interstitial bonds that strongly glue passive silica microspheres. By varying the relative fraction of doping, we uncover a rich phase diagram including ordered and disordered clusters, space-filling gels, and bicontinuous structures formed by filamentary dockers percolating through a solid network of silica spheres. We characterize the slow relaxation and dynamic arrest of the different phases via correlation and scattering functions. Our findings provide a pathway toward the rapid engineering of mesoscopic gels and clusters via active colloidal doping.

A random first-order transition theory for an active glass

How does nonequilibrium activity modify the approach to a glass? This is an important question, since many experiments reveal the near-glassy nature of the cell interior, remodeled by activity. However, different simulations of dense assemblies of active particles, parametrized by a self-propulsion force, [Formula: see text], and persistence time, [Formula: see text], appear to make contradictory predictions about the influence of activity on characteristic features of glass, such as fragility. This calls for a broad conceptual framework to understand active glasses; here, we extend the random first-order transition (RFOT) theory to a dense assembly of self-propelled particles. We compute the active contribution to the configurational entropy through an effective model of a single particle in a caging potential. This simple active extension of RFOT provides excellent quantitative fits to existing simulation results. We find that whereas [Formula: see text] always inhibits glassiness, the effect of [Formula: see text] is more subtle and depends on the microscopic details of activity. In doing so, the theory automatically resolves the apparent contradiction between the simulation models. The theory also makes several testable predictions, which we verify by both existing and new simulation data, and should be viewed as a step toward a more rigorous analytical treatment of active glass.

Effective equilibrium states in mixtures of active particles driven by colored noise

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

Driving dynamic colloidal assembly using eccentric self-propelled colloids

Designing protocols to dynamically direct the self-assembly of colloidal particles has become an important direction in soft matter physics because of promising applications in the fabrication of dynamic responsive functional materials. Here, using computer simulations, we found that in the mixture of passive colloids and eccentric self-propelled active particles, when the eccentricity and self-propulsion of active particles are high enough, the eccentric active particles can push passive colloids to form a large dense dynamic cluster, and the system undergoes a novel dynamic demixing transition. Our simulations show that the dynamic demixing occurs when the eccentric active particles move much faster than the passive particles such that the dynamic trajectories of different active particles can overlap each other while passive particles are depleted from the dynamic trajectories of active particles. Our results suggest that this is in analogy to the entropy-driven demixing in colloid-polymer mixtures, in which polymer random coils can overlap with each other while depleting the colloids. More interestingly, we find that by fixing the passive colloid composition at a certain value with increasing density, the system undergoes an intriguing re-entrant mixing, and the demixing only occurs within a certain intermediate density range. This suggests a new way of designing active matter to drive the self-assembly of passive colloids and fabricate dynamic responsive materials.

Demixing of active particles in the presence of external fields

Self-propelled active particles are inherently out of equilibrium as they collect energy from their surroundings and transform it into directed motion. A recent theoretical study suggests that binary mixtures of active particles with distinct effective diffusion coefficients exhibit dynamical demixing when their diffusion coefficients differ by more than one order of magnitude. Here, we show that this difference may be reduced drastically in the presence of external fields even when the response to the field is the same for both species. We investigate this demixing as a function of the ratio of the diffusion coefficients and discuss the implications of the results for active systems.

Non-Equilibrium Assembly of Light-Activated Colloidal Mixtures

The collective phenomena exhibited by artificial active matter systems present novel routes to fabricating out-of-equilibrium microscale assemblies. Here, the crystallization of passive silica colloids into well-controlled 2D assemblies is shown, which is directed by a small number of self-propelled active colloids. The active colloids are titania-silica Janus particles that are propelled when illuminated by UV light. The strength of the attractive interaction and thus the extent of the assembled clusters can be regulated by the light intensity. A remarkably small number of the active colloids is sufficient to induce the assembly of the dynamic crystals. The approach produces rationally designed colloidal clusters and crystals with controllable sizes, shapes, and symmetries. This multicomponent active matter system offers the possibility of obtaining structures and assemblies that cannot be found in equilibrium systems.

Mode coupling theory for nonequilibrium glassy dynamics of thermal self-propelled particles

We present a mode coupling theory study for the relaxation and glassy dynamics of a system of strongly interacting self-propelled particles, wherein the self-propulsion force is described by Ornstein-Uhlenbeck colored noise and thermal noises are included. Our starting point is an effective Smoluchowski equation governing the distribution function of particle positions, from which we derive a memory function equation for the time dependence of density fluctuations in nonequilibrium steady states. With the basic assumption of the absence of macroscopic currents and standard mode coupling approximation, we can obtain expressions for the irreducible memory function and other relevant dynamic terms, wherein the nonequilibrium character of the active system is manifested through an averaged diffusion coefficient D[combining macron] and a nontrivial structural function S₂(q) with q being the magnitude of wave vector q. D[combining macron] and S₂(q) enter the frequency term and the vertex term for the memory function, and thus influence both the short time and the long time dynamics of the system. With these equations obtained, we study the glassy dynamics of this thermal self-propelled particle system by investigating the Debye-Waller factor f_q and relaxation time τ_α as functions of the persistence time τ_p of self-propulsion, the single particle effective temperature T_eff as well as the number density ρ. Consequently, we find the critical density ρ_c for given τ_p shifts to larger values with increasing magnitude of propulsion force or effective temperature, in good accordance with previously reported simulation work. In addition, the theory facilitates us to study the critical effective temperature T for fixed ρ as well as its dependence on τ_p. We find that T increases with τ_p and in the limit τ_p → 0, it approaches the value for a simple passive Brownian system as expected. Our theory also well recovers the results for passive systems and can be easily extended to more complex systems such as active-passive mixtures.

A framework for multi-scale simulation of crystal growth in the presence of polymers

We present a multi-scale simulation method for modeling crystal growth in the presence of polymer excipients. The method includes a coarse-grained (CG) model for small molecules of known crystal structure whose force field is obtained using structural properties from atomistic simulations. This CG model is capable of stabilizing the molecular crystal structure and capturing the crystal growth from the melt for a wide range of small organic molecules, as demonstrated by application of our method to the molecules isoniazid, urea, sulfamethoxazole, prilocaine, oxcarbazepine, and phenytoin. This CG model can also be used to study the effect of additives, such as polymers, on the inhibition of crystal growth by polymers, as exemplified by our simulation of suppression of the rate of crystal growth of phenytoin, an active pharmaceutical ingredient (API), by a cellulose excipient, functionalized with acetate (Ac), hydroxy-propyl (Hp) and succinate (Su) groups. We show that the efficacy of the cellulosic polymers in slowing crystal growth of small molecules strongly depends on the functional group substitution on the cellulose backbone, with the acetate substituent group slowing crystal growth more than does the deprotonated succinate group, which we confirm by experimental drug supersaturation studies.

Coarse-grained modeling of crystal growth and polymorphism of a model pharmaceutical molecule

We describe a systematic coarse-graining method to study crystallization and predict possible polymorphs of small organic molecules. In this method, a coarse-grained (CG) force field is obtained by inverse-Boltzmann iteration from the radial distribution function of atomistic simulations of the known crystal. With the force field obtained by this method, we show that CG simulations of the drug phenytoin predict growth of a crystalline slab from a melt of phenytoin, allowing determination of the fastest-growing surface, as well as giving the correct lattice parameters and crystal morphology. By applying meta-dynamics to the coarse-grained model, a new crystalline form of phenytoin (monoclinic, space group P2₁) was predicted which is different from the experimentally known crystal structure (orthorhombic, space group Pna2₁). Atomistic simulations and quantum calculations then showed the polymorph to be meta-stable at ambient temperature and pressure, and thermodynamically more stable than the conventional orthorhombic crystal at high pressure. The results suggest an efficient route to study crystal growth of small organic molecules that could also be useful for identification of possible polymorphs as well.

Classical Nucleation Theory Description of Active Colloid Assembly

Nonaligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods and analytic theory to examine the kinetics of formation of the dense phase. Despite the intrinsically nonequilibrium nature of the phase transition, we show that the kinetics can be described using an approach analogous to equilibrium classical nucleation theory, governed by an effective free energy of cluster formation with identifiable bulk and surface terms. The theory captures the location of the binodal, nucleation rates as a function of supersaturation, and the cluster size distributions below the binodal, while discrepancies in the metastable region reveal additional physics about the early stages of active crystal formation. The success of the theory shows that a framework similar to equilibrium thermodynamics can be obtained directly from the microdynamics of an active system, and can be used to describe the kinetics of evolution toward nonequilibrium steady states.

Active fluidization in dense glassy systems

Dense soft glasses show strong collective caging behavior at sufficiently low temperatures. Using molecular dynamics simulations of a model glass former, we show that the incorporation of activity or self-propulsion, f0, can induce cage breaking and fluidization, resulting in the disappearance of the glassy phase beyond a critical f0. The diffusion coefficient crosses over from being strongly to weakly temperature dependent as f0 is increased. In addition, we demonstrate that activity induces a crossover from a fragile to a strong glass and a tendency of active particles to cluster. Our results are of direct relevance to the collective dynamics of dense active colloidal glasses and to recent experiments on tagged particle diffusion in living cells.

Removing grain boundaries from three-dimensional colloidal crystals using active dopants

Using computer simulations we explore how grain boundaries can be removed from three-dimensional colloidal crystals by doping with a small fraction of active colloids. We show that for sufficient self-propulsion, the system is driven into a crystal-fluid coexistence. In this phase separated regime, the active dopants become mobile and spontaneously gather at the grain boundaries. The resulting surface melting and recrystallization of domains result in the motion of the grain boundaries over time and lead to the formation of a large single crystal. However, when the self-propulsion is too low to cause a phase separation, we observe no significant enhancement of grain growth.

Elasticity-induced force reversal between active spinning particles in dense passive media

The self-organization of active particles is governed by their dynamic effective interactions. Such interactions are controlled by the medium in which such active agents reside. Here we study the interactions between active agents in a dense non-active medium. Our system consists of actuated, spinning, active particles embedded in a dense monolayer of passive, or non-active, particles. We demonstrate that the presence of the passive monolayer alters markedly the properties of the system and results in a reversal of the forces between active spinning particles from repulsive to attractive. The origin of such reversal is due to the coupling between the active stresses and elasticity of the system. This discovery provides a mechanism for the interaction between active agents in complex and structured media, opening up opportunities to tune the interaction range and directionality via the mechanical properties of the medium.

Physics out-of-equilibrium is necessary to understand a variety of interactions, for example in biological systems. Here, the authors show that the interactions between non-Brownian active spinning particles can change from repulsive to attractive depending on the properties of the surrounding passive medium.

Fabricating large two-dimensional single colloidal crystals by doping with active particles

Using simulations we explore the behaviour of two-dimensional colloidal (poly)crystals doped with active particles. We show that these active dopants can provide an elegant new route to removing grain boundaries in polycrystals. Specifically, we show that active dopants both generate and are attracted to defects, such as vacancies and interstitials, which leads to clustering of dopants at grain boundaries. The active particles both broaden and enhance the mobility of the grain boundaries, causing rapid coarsening of the crystal domains. The remaining defects recrystallize upon turning off the activity of the dopants, resulting in a large-scale single-domain crystal.

Emergent ultra-long-range interactions between active particles in hybrid active-inactive systems

Particle-particle interactions determine the state of a system. Control over the range of such interactions as well as their magnitude has been an active area of research for decades due to the fundamental challenges it poses in science and technology. Very recently, effective interactions between active particles have gathered much attention as they can lead to out-of-equilibrium cooperative states such as flocking. Inspired by nature, where active living cells coexist with lifeless objects and structures, here we study the effective interactions that appear in systems composed of active and passive mixtures of colloids. Our systems are 2D colloidal monolayers composed primarily of passive (inactive) colloids, and a very small fraction of active (spinning) ferromagnetic colloids. We find an emergent ultra-long-range attractive interaction induced by the activity of the spinning particles and mediated by the elasticity of the passive medium. Interestingly, the appearance of such interaction depends on the spinning protocol and has a minimum actuation timescale below which no attraction is observed. Overall, these results clearly show that, in the presence of elastic components, active particles can interact across very long distances without any chemical modification of the environment. Such a mechanism might potentially be important for some biological systems and can be harnessed for newer developments in synthetic active soft materials.

Emergent self-organization in active materials

Biological systems exhibit large-scale self-organized dynamics and structures which enable organisms to perform the functions of life. The field of active matter strives to develop and understand microscopically driven nonequilibrium materials, with emergent properties comparable to those of living systems. This review will describe two recently developed classes of active matter systems, in which simple building blocks-self-propelled colloidal particles or extensile rod-like particles-self-organize to form macroscopic structures with features not possible in equilibrium systems. We summarize the recent experimental and theoretical progress on each of these systems, and we present simple descriptions of the physics underlying their emergent behaviors.

Formation, compression and surface melting of colloidal clusters by active particles

We demonstrate with experiments and numerical simulations that the structure and dynamics of a suspension of passive particles is strongly altered by adding a very small (<1%) number of active particles. With increasing passive particle density, we observe first the formation of dynamic clusters comprised of passive particles being surrounded by active particles, then the merging and compression of these clusters, and eventually the local melting of crystalline regions by enclosed active particles.

Activity-induced phase separation and self-assembly in mixtures of active and passive particles

We investigate the phase behavior and kinetics of a monodisperse mixture of active (i.e., self-propelled) and passive isometric Brownian particles through Brownian dynamics simulations and theory. As in a purely active system, motility of the active component triggers phase separation into a dense and a dilute phase; in the dense phase, we further find active-passive segregation, with "rafts" of passive particles in a "sea" of active particles. We find that phase separation from an initially disordered mixture can occur with as little as 15% of the particles being active. Finally, we show that a system prepared in a suitable fully segregated initial state reproducibly self-assembles an active "corona," which triggers crystallization of the passive core by initiating a compression wave. Our findings are relevant to the experimental pursuit of directed self-assembly using active particles.

Motility versus fluctuations in mixtures of self-motile and passive agents

Many biological systems consist of self-motile and passive agents both of which contribute to overall functionality. However, little is known about the properties of such mixtures. Here we formulate a model for mixtures of self-motile and passive agents and show that the model gives rise to three different dynamical phases: a disordered mesoturbulent phase, a polar flocking phase, and a vortical phase characterized by large-scale counter rotating vortices. We use numerical simulations to construct a phase diagram and compare the statistical properties of the different phases with observed features of self-motile bacterial suspensions. Our findings afford specific insights regarding the interaction of microorganisms and passive particles and provide novel strategic guidance for efficient technological realizations of artificial active matter.