Light-controlled assembly of active colloidal molecules

Active Brownian information engine: Self-propulsion induced colossal performance

The information engine is a feedback mechanism that extorts work from a single heat bath using the mutual information earned during the measurement. We consider an overdamped active Ornstein-Uhlenbeck particle trapped in a 1D harmonic oscillator. The particle experiences fluctuations from an inherent thermal bath with a diffusion coefficient (D) and an active reservoir, with characteristic correlation time (τa) and strength (Da). We design a feedback-driven active Brownian information engine (ABIE) and analyze its best performance criteria. The optimal functioning criteria, the information gained during measurement, and the excess output work are reliant on the dispersion of the steady-state distribution of the particle's position. The extent of enhanced performance of such ABIE depends on the relative values of two underlying time scales of the process, namely, thermal relaxation time (τr) and the characteristic correlation time (τa). In the limit of τa/τr → 0, one can achieve the upper bound on colossal work extraction as ∼0.202γ(D+Da) (γ is the friction coefficient). The excess amount of extracted work reduces and converges to its passive counterpart (∼0.202γD) in the limit of τa/τr → high. Interestingly, when τa/τr = 1, half the upper bound of excess work is achieved irrespective of the strength of either reservoirs, thermal or active. Finally, we look into the average displacement of active Brownian particles in each feedback cycle, which surpasses its thermal analog due to the broader marginal probability distribution.

Localized Control of the Swarming of Kinesin-Driven Microtubules Using Light

The swarming of self-propelled cytoskeletal filaments has emerged as a new aspect in the field of molecular machines or robotics, as it has overcome one of the major challenges of controlling the mutual interaction of a large number of individuals at a time. Recently, we reported on the photoregulated swarming of kinesin-driven cytoskeletal microtubule filaments in which visible (VIS) and ultraviolet (UV) light triggered the association and dissociation of the swarm, respectively. However, systematic control of this potential system has yet to be achieved to optimize swarming for further applications in molecular machines or robotics. Here, we demonstrate the precise and localized control of a biomolecular motor-based swarm system by varying different parameters related to photoirradiation. We control the reversibility of the swarming by changing the wavelength or intensity of light and the number of azobenzenes in DNA. In addition, we regulate the swarming in local regions by introducing different-sized or shaped patterns in the UV light system. Such a detailed study of the precise control of swarming would provide new perspectives for developing a molecular swarm system for further applications in engineering systems.

Impact of non-reciprocal interactions on colloidal self-assembly with tunable anisotropy

Non-reciprocal (NR) effective interactions violating Newton's third law occur in many biological systems, but can also be engineered in synthetic, colloidal systems. Recent research has shown that such NR interactions can have tremendous effects on the overall collective behavior and pattern formation, but can also influence aggregation processes on the particle scale. Here, we focus on the impact of non-reciprocity on the self-assembly of a colloidal system (originally passive) with anisotropic interactions whose character is tunable by external fields. In the absence of non-reciprocity, that is, under equilibrium conditions, the colloids form square-like and hexagonal aggregates with extremely long lifetimes yet no large-scale phase separation [Kogler et al., Soft Matter 11, 7356 (2015)], indicating kinetic trapping. Here, we study, based on Brownian dynamics simulations in 2D, an NR version of this model consisting of two species with reciprocal isotropic, but NR anisotropic interactions. We find that NR induces an effective propulsion of particle pairs and small aggregates ("active colloidal molecules") forming at the initial stages of self-assembly, an indication of the NR-induced non-equilibrium. The shape and stability of these initial clusters strongly depend on the degree of anisotropy. At longer times, we find, for weak NR interactions, large (even system-spanning) clusters where single particles can escape and enter at the boundaries, in stark contrast to the small rigid aggregates appearing at the same time in the passive case. In this sense, weak NR shortcuts the aggregation. Increasing the degree of NR (and thus, propulsion), we even observe large-scale phase separation if the interactions are weakly anisotropic. In contrast, systems with strong NR and anisotropy remain essentially disordered. Overall, the NR interactions are shown to destabilize the rigid aggregates interrupting self-assembly and phase separation in the passive case, thereby helping the system to overcome kinetic barriers.

Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets

In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.

An Account on BiVO4 as Photocatalytic Active Matter

Photocatalytic materials are gaining popularity and research investment for developing light-driven micromotors. While most of the early work used highly stable TiO2 as a material to construct micromotors, mostly in combination with noble metals, other semiconductors offer a wider range of properties, including independence from high-energy UV light. This review focuses on our work with BiVO4 which has shown promise due to its small band gap and resulting ability to absorb blue light. Additionally, this salt's well-defined crystal structures lead to exploitable charge separation on different crystal facets, providing sufficient asymmetry to cause active propulsion. These properties have given rise to fascinating physical and chemical behaviors that show how rich and variable active matter can become. Here, we present the synthesis of different BiVO4 microparticles and their material properties that make them excellent candidates as active micromotors. A critical factor in understanding inherently asymmetric micromotors is knowledge of their flow fields. However, due to their small size and the need to use even smaller tracer particles to avoid perturbing the flow field, measuring flow fields at the microscale is a difficult task. We also present these first results, which allow us to demonstrate the correlation between chemical reactivity and the flow generated, leading to active motion. Due to the nontoxic nature of BiVO4, these visible-light-responsive microswimmers have been used to study the first steps toward applications, even in sensitive areas such as food technology. Although these initial tests are far from being realized, we have to face the fact that a single microswimmer will not be able to perform macroscale tasks. Therefore, we present the reader with the first simple studies of collective motion, hoping for many new contributions to the field. The one-step synthesis of BiVO4 clearly paves the way for studies requiring large numbers of particles. We predict that the combination of promising applications for a nontoxic material which is readily synthesized in large quantities will contribute pivotally to advance the field of active matter beyond the proof-of-concept stage.

Emergent Chirality and Hyperuniformity in an Active Mixture with Nonreciprocal Interactions

We investigate collective dynamics in a binary mixture of programmable robots in experiments and simulations. While robots of the same species align their motion direction, interaction between species is distinctly nonreciprocal: species A aligns with B and species B antialigns with A. This nonreciprocal interaction gives rise to the emergence of collective chiral motion that can be stabilized by limiting the robot angular speed to be below a threshold. Within the chiral phase, increasing the robot density or extending the range of local repulsive interactions can drive the system through an absorbing-active transition. At the transition point, the robots exhibit a remarkable capacity for self-organization, forming disordered hyperuniform states.

Self-organization of active colloids mediated by chemical interactions

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures.

Morphology-Tailored Dynamic State Transition in Active-Passive Colloidal Assemblies

Mixtures of active self-propelled and passive colloidal particles promise rich assembly and dynamic states that are beyond reach via equilibrium routes. Yet, controllable transition between different dynamic states remains rare. Here, we reveal a plethora of dynamic behaviors emerging in assemblies of chemically propelled snowman-like active colloids and passive spherical particles as the particle shape, size, and composition are tuned. For example, assembles of one or more active colloids with one passive particle exhibit distinct translating or orbiting states while those composed of one active colloid with 2 passive particles display persistent "8"-like cyclic motion or hopping between circling states around one passive particle in the plane and around the waist of 2 passive ones out of the plane, controlled by the shape of the active colloid and the size of the passive particles, respectively. These morphology-tailored dynamic transitions are in excellent agreement with state diagrams predicted by mesoscale dynamics simulations. Our work discloses new dynamic states and corresponding transition strategies, which promise new applications of active systems such as micromachines with functions that are otherwise impossible.

Characterizing different motility-induced regimes in active matter with machine learning and noise

We examine motility-induced phase separation (MIPS) in two-dimensional run-and-tumble disk systems using both machine learning and noise fluctuation analysis. Our measures suggest that within the MIPS state there are several distinct regimes as a function of density and run time, so that systems with MIPS transitions exhibit an active fluid, an active crystal, and a critical regime. The different regimes can be detected by combining an order parameter extracted from principal component analysis with a cluster stability measurement. The principal component-derived order parameter is maximized in the critical regime, remains low in the active fluid, and has an intermediate value in the active crystal regime. We demonstrate that machine learning can better capture dynamical properties of the MIPS regimes compared to more standard structural measures such as the maximum cluster size. The different regimes can also be characterized via changes in the noise power of the fluctuations in the average speed. In the critical regime, the noise power passes through a maximum and has a broad spectrum with a 1/f^{1.6} signature, similar to the noise observed near depinning transitions or for solids undergoing plastic deformation.

Network Effects Lead to Self-Organization in Metabolic Cycles of Self-Repelling Catalysts

Mixtures of particles that interact through phoretic effects are known to aggregate if they belong to species that exhibit attractive self-interactions. We study self-organization in a model metabolic cycle composed of three species of catalytically active particles that are chemotactic toward the chemicals that define their connectivity network. We find that the self-organization can be controlled by the network properties, as exemplified by a case where a collapse instability is achieved by design for self-repelling species. Our findings highlight a possibility for controlling the intricate functions of metabolic networks by taking advantage of the physics of phoretic active matter.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Statistics of carrier-cargo complexes

We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.

Light, Matter, Action: Shining Light on Active Matter

Light carries energy and momentum. It can therefore alter the motion of objects on the atomic to astronomical scales. Being widely available, readily controllable, and broadly biocompatible, light is also an ideal tool to propel microscopic particles, drive them out of thermodynamic equilibrium, and make them active. Thus, light-driven particles have become a recent focus of research in the field of soft active matter. In this Perspective, we discuss recent advances in the control of soft active matter with light, which has mainly been achieved using light intensity. We also highlight some first attempts to utilize light's additional properties, such as its wavelength, polarization, and momentum. We then argue that fully exploiting light with all of its properties will play a critical role in increasing the level of control over the actuation of active matter as well as the flow of light itself through it. This enabling step will advance the design of soft active matter systems, their functionalities, and their transfer toward technological applications.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Active matter in space

In the last 20 years, active matter has been a highly dynamic field of research, bridging fundamental aspects of non-equilibrium thermodynamics with applications to biology, robotics, and nano-medicine. Active matter systems are composed of units that can harvest and harness energy and information from their environment to generate complex collective behaviours and forms of self-organisation. On Earth, gravity-driven phenomena (such as sedimentation and convection) often dominate or conceal the emergence of these dynamics, especially for soft active matter systems where typical interactions are of the order of the thermal energy. In this review, we explore the ongoing and future efforts to study active matter in space, where low-gravity and microgravity conditions can lift some of these limitations. We envision that these studies will help unify our understanding of active matter systems and, more generally, of far-from-equilibrium physics both on Earth and in space. Furthermore, they will also provide guidance on how to use, process and manufacture active materials for space exploration and colonisation.

Breaking action-reaction with active apolar colloids: emergent transport and velocity inversion

Artificial active particles are autonomous agents able to convert energy from the environment into net propulsion, breaking detailed balance and the action-reaction law, clear signatures of their out-of-equilibrium nature. Here we investigate the emergence of directed motion in clusters composed of passive and catalytically active apolar colloids. We use a light-induced chemophoretic flow to rapidly assemble hybrid self-propelling clusters composed of hematite particles and passive silica spheres. By increasing the size of the passive cargo, we observe a reversal in the transport direction of the pair. We explain this complex yet rich phenomenon using a theoretical model which accounts for the generated chemical field and its coupling with the surrounding medium. We exploit further our technique to build up more complex, chemically driven, architectures capable of carrying several passive or active species, that quickly assemble and disassemble under light control.

Strongly enhanced dynamics of a charged Rouse dimer by an external magnetic field

While the dynamics of dimers and polymer chains in a viscous solvent is well understood within the celebrated Rouse model, the effect of an external magnetic field on the dynamics of a charged chain is much less understood. Here, we generalize the Rouse model for a charged dimer to include the effect of an external magnetic field. Our analytically solvable model allows a fundamental insight into the magneto-generated dynamics of the dimer in the overdamped limit as induced by the Lorentz force. Surprisingly, for a dimer of oppositely charged particles, we find an enormous enhancement of the dynamics of the dimer center, which exhibits even a transient superballistic behavior. This is highly unusual in an overdamped system for there is neither inertia nor any internal or external driving. We attribute this to a significant translation and rotation coupling due to the Lorentz force. We also find that magnetic field reduces the mobility of a dimer along its orientation and its effective rotational diffusion coefficient. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.

Active colloidal molecules in activity gradients

We consider a rigid assembly of two active Brownian particles, forming an active colloidal dimer, in a gradient of activity. We show analytically that depending on the relative orientation of the two particles the active dimer accumulates in regions of either high or low activity, corresponding to, respectively, chemotaxis and antichemotaxis. Certain active dimers show both chemotactic and antichemotactic behavior, depending on the strength of the activity. Our coarse-grained Fokker-Planck approach yields an effective potential, which we use to construct a nonequilibrium phase diagram that classifies the dimers according to their tactic behavior. Moreover, we show that for certain dimers a higher persistence of the motion is achieved similar to the effect of a steering wheel in macroscopic devices. This work could be useful for designing autonomous active colloidal structures which adjust their motion depending on the local activity gradients.

Spontaneously rotating clusters of active droplets

We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while spinning around the plane normal. This effect exists for symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming an ordered cluster, the droplets cooperatively suppress their chaotic dynamics and turn the transient instability into a steady rotational state. We analyse the collective rotational dynamics as a function of droplet activity and cluster size and further propose that the stable collective rotation in the cluster is caused by a cooperative coupling between the rotational modes of individual droplets in the cluster.

Dynamics of active particles with space-dependent swim velocity

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

Efficiency of isothermal active matter engines: Strong driving beats weak driving

We study microscopic engines that use a single active particle as their "working medium." Part of the energy required to drive the directed motion of the particle can be recovered as work, even at a constant temperature. A wide class of synthetic active particles can be captured by schematically accounting for the chemical degrees of freedom that power the directed motion without having to resolve the exact microscopic mechanism. We derive analytical results for the quasistatic thermodynamic efficiency, i.e., the fraction of available chemical energy that can be recovered as mechanical work. While this efficiency is vanishingly small for colloidal particles, it increases as the dissipation is increased beyond the linear-response regime and goes through a maximum at large propulsion speeds. Our results demonstrate that driving beyond the linear-response regime has nontrivial consequences for the efficiency of active engines.

Optothermal pulling, trapping, and assembly of colloids using nanowire plasmons

Optical excitation of colloids can be harnessed to realize soft matter systems that are out of equilibrium. In this paper, we present our experimental studies on the dynamics of silica colloids in the vicinity of a silver nanowire propagating surface plasmon polaritons (SPPs). Due to the optothermal interaction, the colloids are directionally pulled towards the excitation point of the nanowire. Having reached this point, they are spatio-temporally trapped around the excitation location. By increasing the concentration of colloids in the system, we observe multi-particle assembly around the nanowire. This process is thermophoretically driven and assisted by the SPPs. Furthermore, we find such an assembly to be sensitive to the excitation polarization at the input of the nanowire. Numerically-simulated temperature distribution around an illuminated nanowire corroborates sensitivity to the excitation polarization. Our study will find relevance in exploration of SPP-assisted optothermal pulling, trapping and assembly of colloids, and can serve as a test-bed of plasmon-driven active matter.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

Metamachines of pluripotent colloids

Machines enabled the Industrial Revolution and are central to modern technological progress: A machine's parts transmit forces, motion, and energy to one another in a predetermined manner. Today's engineering frontier, building artificial micromachines that emulate the biological machinery of living organisms, requires faithful assembly and energy consumption at the microscale. Here, we demonstrate the programmable assembly of active particles into autonomous metamachines using optical templates. Metamachines, or machines made of machines, are stable, mobile and autonomous architectures, whose dynamics stems from the geometry. We use the interplay between anisotropic force generation of the active colloids with the control of their orientation by local geometry. This allows autonomous reprogramming of active particles of the metamachines to achieve multiple functions. It permits the modular assembly of metamachines by fusion, reconfiguration of metamachines and, we anticipate, a shift in focus of self-assembly towards active matter and reprogrammable materials.

Non-monotonic speed-dependence of microswimmers on wall distance

While substrates naturally occur in most microswimmer experiments, their impact on the swimming performance is not well understood. In the present study, we functionalize substrates with polymer brushes of varying swelling properties, grafting densities and brush lengths to systematically modify and explore the substrate-swimmer interactions. Notably, the swimming speed does not monotonically change with brush thickness, but shows a distinct maximum at a certain intermediate thickness, which results from two counteracting factors: surface charge and surface roughness. The results show that the speed of thermophoretic microswimmers does not only depend on the particle properties but is also strongly influenced by the properties of the underlying substrate. This provides a route to control the speed of microswimmers via the underlying substrate, which could be applied in the future e.g. to design complex motility landscapes by patterning substrates with polymer brushes. It is expected that similar effects would occur for diffusio- and electrophoretic particles.

Cooperative transport by flocking phototactic micromotors

Cargo delivery by micro/nanomotors provides enormous opportunities for micromanipulation, environmental cleaning, drug delivery, etc. However, due to the limited driving force, it is usually difficult for single micro/nanomotors to transport cargoes much larger or heavier than themselves. Here, we demonstrate that flocking phototactic TiO2 micromotors can cooperatively transport multiple and different types of large cargoes based on light-responsive diffusiophoresis. Utilizing spontaneous diffusiophoretic attraction, flocking TiO2 micromotors can load large cargoes. Under UV light navigation, flocking TiO2 micromotors cooperatively carry and transport cargoes via collective diffusiophoretic repulsion in open space or complex microenvironments. After reaching the destination, the carried cargoes can also be unloaded from the flock and be deployed at a predetermined destination by disassembling or reversing the flock. This study may pave the way for developing intelligent swarming micro/nanorobots for cooperative targeting micromanipulation and advancing their applications in drug delivery and microengineering.

Active droploids

Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, we take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. In experiments and simulations we observe that, under light-illumination, colloidal particles and their near-critical environment create mutually-coupled co-evolving structures. These structures unify in the form of active superstructures featuring a droplet shape and a colloidal engine inducing self-propulsion. We call them active droploids-a portmanteau of droplet and colloids. Our results provide a pathway to create active superstructures through environmental feedback.

Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects

Biomolecular condensates in cells are often rich in catalytically active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathway. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically active particles. We show that a Michaelis-Menten-like dependence of the particles' activities manifests itself as a screening of the interactions, and that a mixture of two differently sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.

Photothermally Reconfigurable Colloidal Crystals at a Fluid Interface, a Generic Approach for Optically Tunable Lattice Properties

Optically addressable colloidal assembly at fluid interfaces is a highly desired component to generate reconfigurable 2D materials but has rarely been achieved and only with specific interface engineering. Here we describe a generic method to get optically reconfigurable colloidal crystals at the air/water interface and emphasize a new mechanism to convert light into tunable lattice properties. We use light-absorbing anionic particles adsorbed at the air/water interface in the presence of minute amounts of cationic surfactant, which self-assembled into closely packed polycrystalline structures by collectively deforming the surrounding interface. Low-intensity irradiation of these colloidal crystals results in unprecedented control of the interparticle spacing in a preserved crystalline state while, at a higher intensity, cycles of melting/recrystallization with a controllable transition kinetics can be achieved upon successive on/off stimulations. We show that this photoreversible melting originates from an initial thermocapillary stress, expanding the colloidal assembly against the local confinement, and an increase in particles diffusivity imposing the transition kinetics. With this mechanism, local irradiation leads to highly dynamic patterns, including self-healing or self-fed "living" crystals, while multiresponsive assembly is also achieved by controlling particle organization with both light and magnetic stimuli.

Optimization of an active heat engine

Optimization of heat engines at the microscale has applications in biological and artificial nanotechnology and stimulates theoretical research in nonequilibrium statistical physics. Here we consider noninteracting overdamped particles confined by an external harmonic potential, in contact with either a thermal reservoir or a stochastic self-propulsion force (active Ornstein-Uhlenbeck model). A cyclical machine is produced by periodic variation of the parameters of the potential and of the noise. An exact mapping between the passive and the active model allows us to define the effective temperature T_{eff}(t), which is meaningful for the thermodynamic performance of the engine. We show that T_{eff}(t) is different from all other known active temperatures, typically used in static situations. The mapping allows us to optimize the active engine, regardless of the values of the persistence time or self-propulsion velocity. In particular, through linear irreversible thermodynamics (small amplitude of the cycle), we give an explicit formula for the optimal cycle period and phase delay (between the two modulated parameters, stiffness and temperature) achieving maximum power with Curzon-Ahlborn efficiency. In the quasistatic limit, the formula for T_{eff}(t) simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency. A point, which has been overlooked in recent literature, is made about the difficulty in defining efficiency without a consistent definition of effective temperature.

Phase separation of an active colloidal suspension via quorum-sensing

We present the Brownian dynamics simulation of an active colloidal suspension in two dimensions, where the self-propulsion speed of a colloid is regulated according to the local density sensed by it. The role of concentration-dependent motility in the phase-separation of colloids and their dynamics is investigated in detail. Interestingly, the system phase separates at a very low packing fraction (Φ≈ 0.125) at higher self-propulsion speeds (Pe), into a dense phase coexisting with a homogeneous phase and attains a long-range crystalline order beyond the transition point. The transition point is quantified here from the local density profiles and local and global-bond order parameters. We have shown that the characteristics of the phase diagram are qualitatively akin to the active Brownian particle (ABP) model. Moreover, our investigation reveals that the density-dependent motility amplifies the slow-down of the directed speed, which facilitates phase-separation even at low packing fractions. The effective diffusivity shows a crossover from quadratic rise to a power-law behavior of exponent 3/2 with Pe in the phase-separated regime. Furthermore, we have shown that the effective diffusion decreases exponentially with packing fraction in the phase-separated regime, while it shows a linear decrease in the single phase regime.

Control over self-assembled Janus clusters by the strength of magnetic field in [Formula: see text]

Colloidal Janus microparticles can be propelled by controlled chemical reactions on their surfaces. Such microswimmers have been used as model systems for the behavior on the microscale and as carriers for cargo to well-defined positions in hard-to-access areas. Here we demonstrate the propagation motion of clusters of magnetic Janus particles driven by the catalytic decomposition of [Formula: see text] on their metallic caps. The magnetic moments of their caps lead to certain spatial arrangements of Janus particles, which can be influenced by external magnetic fields. We investigate how the arrangement of the particles and caps determines the driven motion of the particle clusters. In addition, we show the influence of confining walls on the cluster motion, which will be encountered in any real-life biological system.

Fully Steerable Symmetric Thermoplasmonic Microswimmers

A cornerstone of the directed motion of microscopic self-propelling particles is an asymmetric particle structure defining a polarity axis along which these tiny machines move. This structural asymmetry ties the orientational Brownian motion to the microswimmers directional motion, limiting their persistence and making the long time motion effectively diffusive. Here, we demonstrate a completely symmetric thermoplasmonic microswimmer, which is propelled by laser-induced self-thermophoresis. The propulsion direction is imprinted externally to the particle by the heating laser position. The orientational Brownian motion, thus, becomes irrelevant for the propulsion, allowing enhanced control over the particles dynamics with almost arbitrary steering capability. We characterize the particle motion in experiments and simulations and also theoretically. The analysis reveals additional noise appearing in these systems, which is conjectured to be relevant for biological systems. Our experimental results show that even very small particles can be precisely controlled, enabling more advanced applications of these micromachines.

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.

Active Assembly of Spheroidal Photocatalytic BiVO4 Microswimmers

We create single-component photocatalytic bismuth vanadate (BiVO₄) microswimmers with a spheroidal shape that move individually upon irradiation without any asymmetrization step. These particles form active assemblies which we investigate combining an experimental approach with numerical simulations and analytical calculations. We systematically explore the speed and assembly of the swimmers into clusters of up to four particles and find excellent agreement between experiment and theory, which helps us to understand motion patterns and speed trends. Moreover, different batches of particles can be functionalized separately, making them ideal candidates to fulfill a multitude of tasks, such as sensing or environmental remediation. To exemplify this, we coat our swimmers with silica (SiO₂) and selectively couple some of their modules to fluorophores in a way which does not inhibit self-propulsion. The present work establishes spheroidal BiVO₄ microswimmers as a versatile platform to design multifunctional microswimmers.

Rapid-prototyping a Brownian particle in an active bath

Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length scales of usual active matter systems. A particle diffusing in a harmonic potential generated by an optical trap is kicked by programmed forces with time correlation at random intervals following the Poisson process. The model's generic simplicity allows us to find conditions for which displacements are Gaussian (or not), how diffusion is perturbed (or not) by kicks, and quantifying heat dissipation to maintain the non-equilibrium steady state in an active bath. The model reproduces experimental results of tracer mobility in an active bath of swimming algal cells. It can be used as a stochastic dynamic simulator for Brownian objects in various active baths without mechanistic understanding, owing to the generic framework of the protocol.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Dynamics of Magnus-dominated particle clusters, collisions, pinning, and ratchets

Motivated by the recent work in skyrmions and active chiral matter systems, we examine pairs and small clusters of repulsively interacting point particles in the limit where the dynamics is dominated by the Magnus force. We find that particles with the same Magnus force can form stable pairs, triples, and higher ordered clusters or exhibit chaotic motion. For mixtures of particles with opposite Magnus force, particle pairs can combine to form translating dipoles. Under an applied drive, particles with the same Magnus force translate; however, particles with different or opposite Magnus force exhibit a drive-dependent decoupling transition. When the particles interact with a repulsive obstacle, they can form localized orbits with depinning or unwinding transitions under an applied drive. We examine the interaction of these particles with clusters or lines of obstacles and find that the particles can become trapped in orbits that encircle multiple obstacles. Under an ac drive, we observe a series of ratchet effects, including ratchet reversals, for particles interacting with a line of obstacles due to the formation of commensurate orbits. Finally, in assemblies of particles with mixed Magnus forces of the same sign, we find that the particles with the largest Magnus force become localized in the center of the cluster, while for mixtures with opposite Magnus forces, the motion is dominated by transient local pairs or clusters, where the translating pairs can be regarded as a form of active matter.

Active colloidal molecules assembled via selective and directional bonds

The assembly of active and self-propelled particles is an emerging strategy to create dynamic materials otherwise impossible. However, control of the complex particle interactions remains challenging. Here, we show that various dynamic interactions of active patchy particles can be orchestrated by tuning the particle size, shape, composition, etc. This capability is manifested in establishing dynamic colloidal bonds that are highly selective and directional, which greatly expands the spectrum of colloidal structures and dynamics by assembly. For example, we demonstrate the formation of colloidal molecules with tunable bond angles and orientations. They exhibit controllable propulsion, steering, reconfiguration as well as other dynamic behaviors that collectively reflect the bond properties. The working principle is further extended to the co-assembly of synthetic particles with biological entities including living cells, giving rise to hybrid colloidal molecules of various types, for example, a colloidal carrousel structure. Our strategy should enable active systems to perform sophisticated tasks in future such as selective cell treatment.

The assembly of active and self-propelled particles is an emerging strategy to create dynamic materials otherwise impossible. Here, the authors show the assembly of active colloidal molecules with a wide spectrum of new structures and dynamics, conferred to them by highly selective and directional interactions.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Swarm Hunting and Cluster Ejections in Chemically Communicating Active Mixtures

A large variety of microorganisms produce molecules to communicate via complex signaling mechanisms such as quorum sensing and chemotaxis. The biological diversity is enormous, but synthetic inanimate colloidal microswimmers mimic microbiological communication (synthetic chemotaxis) and may be used to explore collective behaviour beyond the one-species limit in simpler setups. In this work we combine particle based and continuum simulations as well as linear stability analyses, and study a physical minimal model of two chemotactic species. We observed a rich phase diagram comprising a “hunting swarm phase”, where both species self-segregate and form swarms, pursuing, or hunting each other, and a “core-shell-cluster phase”, where one species forms a dense cluster, which is surrounded by a (fluctuating) corona of particles from the other species. Once formed, these clusters can dynamically eject their core such that the clusters almost turn inside out. These results exemplify a physical route to collective behaviours in microorganisms and active colloids, which are so-far known to occur only for comparatively large and complex animals like insects or crustaceans.

Controlling the structure and mixing properties of anisotropic active particles with the direction of self-propulsion

In the search for advanced materials active particles could offer unique structural and functional properties, with tunable time-dependent characteristics. We demonstrate here that the direction of self-propulsion, relative to the particle orientation, may be as influential for the phase behavior as the pair interactions are for passive particles, and enable dynamic properties that are not available to passive systems. We perform simulations on ensembles of self-propelled squares, and find that squares that self-propel in the direction perpendicular to a side rapidly reach a steady state with a characteristic cluster distribution, positional order, and well-defined diffusion constant. After tuning the direction towards a corner, the particles form large and dense clusters that show a transient collective motion, and display remarkable fluctuations over long time scales, with a distinct periodicity. Clusters of these particles appear unstable beyond a critical size, and susceptible to a catastrophic disintegration. Directionality is found to effect equally sharp transitions in the mixing properties of active squares and passive squares, and the behavior of the passive ensemble. We relate directionality to the collision dynamics and the resulting reaction network of clusters, evolved by a Kinetic Monte Carlo algorithm, to correlate propulsion direction to the observed phase behavior. Understanding this behavior could offer new design rules for programmable materials, and grant further insights in the dynamic processes that nature employs for self-assembly.

Scalar activity induced phase separation and liquid-solid transition in a Lennard-Jones system

We report scalar activity induced phase separation and crystallization in a system of 3-d Lennard-Jones particles taken at state points spanning from the gas to the liquid regime using molecular dynamics simulation (MD). Scalar activity was introduced by increasing the temperature of half of the particles (labeled 'hot') while keeping the temperature of the other half constant at a lower value (labeled 'cold'). The relative temperature difference between the two subsystems is considered as a measure of the activity. From our simulations we observe that the two species tend to phase separate at sufficiently high activity ratio. The extent of separation is quantified by the defined order parameter and the entropy production during this process is determined by employing the two-phase thermodynamic (2PT) model and the standard modified Benedict-Webb-Rubin (MBWR) equation of state for a LJ fluid. We observe that the extent of the phase separation and entropy production increases with the density of the system. From a cluster analysis, we obtain the mean number of clusters ncl, and the mean size of the largest cluster n0 in the system, complementing each other. Bond orientation order parameters reveal that the so formed largest cluster also develops solid-like order consisting of both FCC and HCP packing. The presence of such crystalline order is also supported by a common neighbor analysis.

Photocatalytic TiO2 Micromotors for Removal of Microplastics and Suspended Matter

Environmental contamination is a major global challenge, and the effects of contamination are found in most habitats. In recent times, the pollution by microplastics has come to the global attention and their removal displays an extraordinary challenge with no reasonable solutions presented so far. One of the new technologies holding many promises for environmental remediation on the microscale are self-propelled micromotors. They present several properties that are of academic and technical interest, such as the ability to overcome the diffusion limitation in catalytic processes, as well as their phoretic interaction with their environment. Here, we present two novel strategies for the elimination of microplastics using photocatalytic Au@Ni@TiO₂-based micromotors. We show that individual catalytic particles as well as assembled chains show excellent collection and removal of suspended matter and microplastics from environmental water samples.