Artificial Chemotaxis of Self-Phoretic Active Colloids: Collective Behavior

Interplay of phoresis and self-phoresis in active particles: Transport properties, phoretic, and self-phoretic coefficients

Self-propelled synthetic particles have attracted scientific interest due to their potential applications as nanomotors in drug delivery and their insight into bacterial taxis. Research on their dynamics has focused on understanding phoresis and self-phoresis in catalytic Janus particles at both the nano- and microscale. This study explores the combined effects of self-diffusiophoresis and self-thermophoresis induced by exothermic chemical reactions on the surface of active particles moving in non-electrolyte media. We examine how these phoretic phenomena interact, influenced by the coupling between chemical reactions, heat generation, and the concentration and temperature fields at the particle interface. Using a theoretical framework based on the induction of surface tension gradients at the particle interface, we analyze the phoretic dynamics, quantifying parameters such as effective diffusivities, transport coefficients, and, most importantly, phoretic coefficients. Our findings provide insights into the conditions that dictate coupled or independent phoretic behaviors, with implications for drug delivery and nanomotor applications, enabling customized transport processes at the nanoscale.

Following Your Nose: Autochemotaxis and Other Mechanisms for Spinodal Decomposition in Flocks

We develop the hydrodynamic theory of dry, polar ordered, active matter ("flocking") with autochemotaxis; i.e., self-propelled entities moving in the same direction, each emitting a substance which attracts the others (e.g., ants). We find that sufficiently strong autochemotaxis leads to an instability to phase separation into one high and one low density band. This is very analogous to both equilibrium phase separation, and "motility induced phase separation" and can occur in flocks due to any microscopic mechanism (e.g., sufficiently strong attractive interactions) that makes the entities cohere.

Synchronized rotations of active particles on chemical substrates

Many microorganisms use chemical 'signaling' - a quintessential self-organizing strategy in non-equilibrium - that can induce spontaneous aggregation and coordinated motion. Using synthetic signaling as a design principle, we construct a minimal model of active Brownian particles (ABPs) having soft repulsive interactions on a chemically quenched patterned substrate. The interplay between chemo-phoretic interactions and activity is numerically investigated for a proposed variant of the Keller-Segel model for chemotaxis. Such competition not only results in a chemo-motility-induced phase-separated state, but also results in a new cohesive clustering phase with synchronized rotations. Our results suggest that rotational order can emerge in systems by virtue of activity and repulsive interactions alone without an explicit alignment interaction. These rotations can also be exploited by designing mechanical devices that can generate reorienting torques using active particles.

Clustering of chemically propelled nanomotors in chemically active environments

Synthetic nanomotors powered by chemical reactions have been designed to act as vehicles for active cargo transport, drug delivery, and a variety of other uses. Collections of such motors, acting in consort, can self-assemble to form swarms or clusters, providing opportunities for applications on various length scales. While such collective behavior has been studied when the motors move in a chemically inactive fluid environment, when the medium in which they move is a chemical network that supports complex spatial and temporal patterns, through simulation and theoretical analysis we show that collective behavior changes. Spatial patterns in the environment can guide and control motor collective states, and interactions of the motors with their environment can give rise to distinctive spatiotemporal motor patterns. The results are illustrated by studies of the motor dynamics in systems that support Turing patterns and spiral waves. This work is relevant for potential applications that involve many active nanomotors moving in complex chemical or biological environments.

Spinodal decomposition and phase separation in polar active matter

We develop and study the hydrodynamic theory of flocking with autochemotaxis. This describes large collections of self-propelled entities all spontaneously moving in the same direction, each emitting a substance which attracts the others (e.g., ants). The theory combines features of the Keller-Segel model for autochemotaxis with the Toner-Tu theory of flocking. We find that sufficiently strong autochemotaxis leads to an instability of the uniformly moving state (the "flock"), in which bands of different density form moving parallel to the mean flock velocity with different speeds. This instability is, therefore, completely different from the well-known "banding instability," in which bands form perpendicular to the mean flock velocity. The bands we find, which are reminiscent of ant trails, coarsen over time to reach a phase-separated state, in which one high-density and one low-density band fill the entire system. The same instability, described by the same hydrodynamic theory, can occur in flocks phase separating due to any microscopic mechanism (e.g., sufficiently strong attractive interactions). Although in many ways analogous to equilibrium phase separation via spinodal decomposition, the two steady-state densities here are determined not by a common tangent construction, as in equilibrium, but by an uncommon tangent construction very similar to that found for motility-induced phase separation of disordered active particles. Our analytic theory agrees well with our numerical simulations of our equations of motion.

Multifunctional Chiral Chemically-Powered Micropropellers for Cargo Transport and Manipulation

Practical applications of synthetic self-propelled nano and microparticles for microrobotics, targeted drug delivery, and manipulation at the nanoscale are rapidly expanding. However, fabrication limitations often hinder progress, resulting in relatively simple shapes and limited functionality. Here, taking advantage of 3D nanoscale printing, chiral micropropellers powered by the hydrogen peroxide reduction reaction are fabricated. Due to their chirality, the propellers exhibit multifunctional behavior controlled by an applied magnetic field: spinning in place (loitering), directed migration in the prescribed direction, capture, and transport of polymer cargo particles. Design parameters of the propellers are optimized by computation modeling based on mesoscale molecular dynamics. It is predicted by computer simulations, and confirmed experimentally, that clockwise rotating propellers attract each other and counterclockwise repel. These results shed light on how chirality and shape optimization enhance the functionality of synthetic autonomous micromachines.

Quorum sensing-induced transition from colloidal waves to Turing-like patterns in chemorepulsive active colloids

The study of active systems, especially in the presence of a chemical background field, is garnering significant attention. Traditionally, the self-propelled velocity of active colloids was assumed to be constant, independent of the local density of colloids. In this work, we introduce a chemotactic active system that features quorum sensing (QS), wherein particles act as chemorepellents. Interestingly, these particles lose their activity in regions of high local particle density. Our findings reveal that QS leads to a transition from an oscillatory colloidal wave to a Turing-like pattern, with the observation of an intermediate state. With the variation of the sensing threshold, both the mean oscillation frequency of the system and the number of clusters exhibit non-monotonic dependence. Furthermore, the QS-induced pattern differs markedly from systems without QS, primarily due to the competitive interplay between diffusion and chemotaxis. The dynamics of this phenomenon are explained using a coarse-grained mean field model.

Chemotactic Micro/Nanomotors for Biomedical Applications

In nature, many organisms respond chemotactically to external chemical stimuli in order to extract nutrients or avoid danger. Inspired by this natural chemotaxis, micro/nanomotors with chemotactic properties have been developed and applied to study a variety of disease models. This chemotactic strategy has shown promising results and has attracted the attention of an increasing number of researchers. This paper mainly reviews the construction methods of different types of chemotactic micro/nanomotors, the mechanism of chemotaxis, and the potential applications in biomedicine. First, based on the classification of materials, the construction methods and therapeutic effects of chemotactic micro/nanomotors based on natural cells and synthetic materials in cellular and animal experiments will be elaborated in detail. Second, the mechanism of chemotaxis of micro/nanomotors is elaborated in detail: chemical reaction induced chemotaxis and physical process driven chemotaxis. In particular, the main differences and significant advantages between chemotactic micro/nanomotors and magnetic, electrical and optical micro/nanomotors are described. The applications of chemotactic micro/nanomotors in the biomedical fields in recent years are then summarized, focusing on the mechanism of action and therapeutic effects in cancer and cardiovascular disease. Finally, the authors are looking forward to the future development of chemotactic micro/nanomotors in the biomedical fields.

Microscopic theory of a Janus motor in a non-equilibrium fluid: Surface hydrodynamics and boundary conditions

We present a derivation from the first principles of the coupled equations of motion of an active self-diffusiophoretic Janus motor and the hydrodynamic densities of its fluid environment that are nonlinearly displaced from equilibrium. The derivation makes use of time-dependent projection operator techniques defined in terms of slowly varying coarse-grained microscopic densities of the fluid species number, total momentum, and energy. The exact equations of motion are simplified using time scale arguments, resulting in Markovian equations for the Janus motor linear and angular velocities with average forces and torques that depend on the fluid densities. For a large colloid, the fluid equations are separated into bulk and interfacial contributions, and the conditions under which the dynamics of the fluid densities can be accurately represented by bulk hydrodynamic equations subject to boundary conditions on the colloid are determined. We show how the results for boundary conditions based on continuum theory can be obtained from the molecular description and provide Green-Kubo expressions for all transport coefficients, including the diffusiophoretic coupling and the slip coefficient.

Open Questions of Chemically Powered Nano- and Micromotors

Chemically powered nano- and micromotors are microscopic devices that convert chemical energy into motion. Interest in these motors has grown over the past 20 years because they exhibit interesting collective behaviors and have found potential uses in biomedical and environmental applications. Understanding how these motors operate both individually and collectively and how environments affect their operation is of both fundamental and applied significance. However, there are still significant gaps in our knowledge. This Perspective highlights several open questions regarding the propulsion mechanisms of, interactions among, and impact of confinements on nano- and micromotors driven by self-generated chemical gradients. These questions are based on my own experience as an experimentalist. For each open question, I describe the problem and its significance, analyze the status-quo, identify the bottleneck problem, and propose potential solutions. An underlying theme for these questions is the interplay among reaction kinetics, physicochemical distributions, and fluid flows. Unraveling this interplay requires careful measurements as well as a close collaboration between experimentalists and theoreticians/numerical experts. The interdisciplinary nature of these challenges suggests that their solutions could bring new revelations and opportunities across disciplines such as colloidal sciences, material sciences, soft matter physics, robotics, and beyond.

Chemotactic Motility-Induced Phase Separation

Collectives of actively moving particles can spontaneously separate into dilute and dense phases-a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS-in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Pair Interaction between Two Catalytically Active Colloids

Due to the intrinsically complex non-equilibrium behavior of the constituents of active matter systems, a comprehensive understanding of their collective properties is a challenge that requires systematic bottom-up characterization of the individual components and their interactions. For self-propelled particles, intrinsic complexity stems from the fact that the polar nature of the colloids necessitates that the interactions depend on positions and orientations of the particles, leading to a 2d - 1 dimensional configuration space for each particle, in d dimensions. Moreover, the interactions between such non-equilibrium colloids are generically non-reciprocal, which makes the characterization even more complex. Therefore, derivation of generic rules that enable us to predict the outcomes of individual encounters as well as the ensuing collective behavior will be an important step forward. While significant advances have been made on the theoretical front, such systematic experimental characterizations using simple artificial systems with measurable parameters are scarce. Here, two different contrasting types of colloidal microswimmers are studied, which move in opposite directions and show distinctly different interactions. To facilitate the extraction of parameters, an experimental platform is introduced in which these parameters are confined on a 1D track. Furthermore, a theoretical model for interparticle interactions near a substrate is developed, including both phoretic and hydrodynamic effects, which reproduces their behavior. For subsequent validation, the degrees of freedom are increased to 2D motion and resulting trajectories are predicted, finding remarkable agreement. These results may prove useful in characterizing the overall alignment behavior of interacting self-propelling active swimmer and may find direct applications in guiding the design of active-matter systems involving phoretic and hydrodynamic interactions.

Alignment interaction and band formation in assemblies of autochemorepulsive walkers

Chemotaxis refers to the motion of an organism induced by chemical stimuli and is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular, autochemotaxis refers to chemotaxis mediated by a cue produced by the chemotactic particle itself. Here, we investigate the collective behavior of autochemotactic particles that are repelled by the cue and therefore migrate preferentially towards low-concentration regions. To this end, we introduce a lattice model inspired by the true self-avoiding walk which reduces to the Keller-Segel model in the continuous limit, for which we describe the rich phase behavior. We first rationalize the chemically mediated alignment interaction between walkers in the limit of stationary concentration fields, and then describe the various large-scale structures that can spontaneously form and the conditions for them to emerge, among which we find stable bands traveling at constant speed in the direction transverse to the band.

Optimal transport of active particles induced by substrate concentration oscillations

We show the existence of a stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport in cell membranes and tissues for medical treatments and soil remediation.

The interplay between chemo-phoretic interactions and crowding in active colloids

Many motile microorganisms communicate with each other and their environments via chemical signaling which leads to long-range interactions mediated by self-generated chemical gradients. However, consequences of the interplay between crowding and chemotactic interactions on their collective behavior remain poorly understood. In this work, we use Brownian dynamics simulations to investigate the effect of packing fraction on the formation of non-equilibrium structures in a monolayer of diffusiophoretic self-propelled colloids as a model for chemically active particles. Focusing on the case when a chemical field induces attractive positional and repulsive orientational interactions, we explore dynamical steady-states of active colloids of varying packing fractions and degrees of motility. In addition to collapsed, active gas, and dynamical clustering steady-states reported earlier for low packing fractions, a new phase-separated state emerges. The phase separation results from a competition between long-range diffusiophoretic interactions and motility and is observed at moderate activities and a wide range of packing fractions. Our analysis suggests that the fraction of particles in the largest cluster is a suitable order parameter for capturing the transition from an active gas and dynamical clustering states to a phase-separated state.

Utilizing passive elements to break time reversibility at low Reynolds number: a swimmer with one activated element

In the realm of low Reynolds number, the shape-changing biological and artificial matters need to break time reversibility in the course of their strokes to achieve motility. This necessity is well described in the so-called scallop theorem. In this work, considering low Reynolds number, a novel and versatile swimmer is proposed as an example of a new scheme to break time reversibility kinematically and, in turn, produce net motion. The swimmer consists of one sphere as a cargo or carried body, joined by one activated link with time-varying length, to another perpendicular rigid link, as the support of two passively flapping disks, at its end. The disks are free to rotate between their fixed minimum and maximum angles. The system's motion in two dimensions is simulated, and the maneuverability of the swimmer is discussed. The minimal operating parameters for steering of the swimmer are studied, and the limits of the swimmer are identified. The introduced swimming mechanism can be employed as a simple model system for biological living matters as well as artificial microswimmers.

Self-Regulatory Micro- and Macroscale Patterning of ATP-Mediated Nanobioconjugate

Directional interactions and the assembly of a nanobioconjugate in clusters at a specific location are important for patterning and microarrays in biomedical research. Herein, we report that self-assembly and spatial control in surface patterning of the surfactant-functionalized nanoparticles can be governed in micro- and macroscale environments by two factors, synergistic enzyme-substrate-nanoparticle affinity and the phoretic effect. First, we show that aggregation of cationic gold nanoparticles (GNP) can be modulated by multivalent anionic nanoparticle binding of an adenosine-based nucleotide and enzyme, alkaline phosphatase. We further demonstrate two different types of their autonomous aggregation pattern: (i) by introducing an enzyme gradient that modulates the synergistic nonequilibrium interactivity of the nanoparticle, nucleotide, and enzyme both in microfluidic conditions and at the macroscale; and (ii) the surface deposition pattern from evaporating droplets via the coffee ring effect. Here, temporal control over the width and site of the patterning area inside the microfluidic channel under catalytic and noncatalytic conditions has also been demonstrated. Finally, we show a change in capillary phoresis parameters responsible for the coffee ring due to introduction of ATP-loaded GNP in the blood serum, showing applicability in low-cost disease diagnostics. Overall, an enzyme-actuated surface nanobiopatterning method has been demonstrated that has potential application in controlled micro- and macroscale area patterning with a diverse cascade catalytic surface and spatiotemporal multisensory-based application.

Kinetic modeling of the chemotactic process in run-and-tumble bacteria

The chemotactic process of run-and-tumble bacteria results from modulating the tumbling rate in response to changes in chemoattractant gradients felt by the bacteria. The response has a characteristic memory time and is subject to important fluctuations. These ingredients are considered in a kinetic description of chemotaxis, allowing the computation of the stationary mobility and the relaxation times needed to reach the steady state. For large memory times, these relaxation times become large, implying that finite-time measurements give rise to nonmonotonic currents as a function of the imposed chemoattractant gradient, contrary to the stationary regime where the response is monotonic. The case of an inhomogeneous signal is analyzed. Contrary to the usual Keller-Segel model, the response is nonlocal, and the bacterial profile is smoothed with a characteristic length that grows with the memory time. Finally, the case of traveling signals is considered, where appreciable differences appear compared to memoryless chemotactic descriptions.

Spontaneous vortex formation by microswimmers with retarded attractions

Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback, implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that do not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as the key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric, phoretic, and hydrodynamic interactions. Our results demonstrate how even most simple retarded interactions can foster emergent complex adaptive behavior in small active-particle ensembles.

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.

Nonequilibrium thermodynamics of Janus particle self-assembly

We compute the energetic cost of formation of Janus particle structures. Using an approach that couples particle dynamics to the evolution of fuel concentration in the medium, which we consider to be initially inhomogeneous, we show the different types of emerging structures. The energy dissipated in the formation of such structures is obtained from the entropy production rate, which is a non-monotonic function of the fraction of assembled particles and, thus, different in each self-assembly regime. An analysis of the free energy of these particles allows us to establish a thermodynamic criterion of structure formation based on the behavior of chemical potential as a function of the fraction of assembled particles.

Reconfigurable assembly of colloidal motors towards interactive soft materials and systems

Due to the highly flexible reconfiguration of swarms, collective behaviors have provided various natural organisms with a powerful adaptivity to the complex environment. To mimic these natural systems and construct artificial intelligent soft materials, self-propelled colloidal motors that can convert diverse forms of energy into swimming-like movement in fluids afford an ideal model system at the micro-/nanoscales. Through the coupling of local gradient fields, colloidal motors driven by chemical reactions or externally physical fields can assembly into swarms with adaptivity. Here, we summarize the progress on reconfigurable assembly of colloidal motors which is driven and modulated by chemical reactions and external fields (e.g., light, ultrasonic, electric, and magnetic fields). The adaptive reconfiguration behaviors and the corresponding mechanisms are discussed in detail. The future directions and challenges are also addressed for developing colloidal motor-based interactive soft matter materials and systems with adaptation and interactive functions comparable to that of natural systems.

Cellular Sensing Governs the Stability of Chemotactic Fronts

In contexts ranging from embryonic development to bacterial ecology, cell populations migrate chemotactically along self-generated chemical gradients, often forming a propagating front. Here, we theoretically show that the stability of such chemotactic fronts to morphological perturbations is determined by limitations in the ability of individual cells to sense and thereby respond to the chemical gradient. Specifically, cells at bulging parts of a front are exposed to a smaller gradient, which slows them down and promotes stability, but they also respond more strongly to the gradient, which speeds them up and promotes instability. We predict that this competition leads to chemotactic fingering when sensing is limited at too low chemical concentrations. Guided by this finding and by experimental data on E. coli chemotaxis, we suggest that the cells' sensory machinery might have evolved to avoid these limitations and ensure stable front propagation. Finally, as sensing of any stimuli is necessarily limited in living and active matter in general, the principle of sensing-induced stability may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.

Confinement and Collective Escape of Active Particles

Active matter broadly covers the dynamics of self-propelled particles. While the onset of collective behavior in homogenous active systems is relatively well understood, the effect of inhomogeneities such as obstacles and traps lacks overall clarity. Here, we study how interacting, self-propelled particles become trapped and released from a trap. We have found that captured particles aggregate into an orbiting condensate with a crystalline structure. As more particles are added, the trapped condensates escape as a whole. Our results shed light on the effects of confinement and quenched disorder in active matter.

Chemotactic smoothing of collective migration

Collective migration—the directed, coordinated motion of many self-propelled agents—is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient—revealing a population-scale consequence of the manner in which individual cells transduce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.

Flocks of birds, schools of fish and herds of animals are all good examples of collective migration, where individuals co-ordinate their behavior to improve survival. This process also happens on a cellular level; for example, when bacteria consume a nutrient in their surroundings, they will collectively move to an area with a higher concentration of food via a process known as chemotaxis.

Several studies have examined how disturbing collective migration can cause populations to fall apart. However, little is known about how groups withstand these interferences. To investigate, Bhattacharjee, Amchin, Alert et al. studied bacteria called Escherichia coli as they moved through a gel towards nutrients.

The E. coli were injected into the gel using a three-dimensional printer, which deposited the bacteria into a wiggly shape that forces the cells apart, making it harder for them to move as a collective group. However, as the bacteria migrated through the gel, they smoothed out the line and gradually made it straighter so they could continue to travel together over longer distances.

Computer simulations revealed that this smoothing process is achieved by differences in how the cells respond to local nutrient levels based on their position. Bacteria towards the front of the group are exposed to more nutrients, causing them to become oversaturated and respond less effectively to the nutrient gradient. As a result, they move more slowly, allowing the cells behind them to eventually catch-up.

These findings reveal a general mechanism in which limitations in how individuals sense and respond to an external signal (in this case local nutrient concentrations) allows them to continue migrating together. This mechanism may apply to other systems that migrate via chemotaxis, as well as groups whose movement is directed by different external factors, such as temperature and light intensity.

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.

Collective self-optimization of communicating active particles

The quest for how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource-such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins-while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but, in general, it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared "resource field," the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal field-based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveil aspects of the communication rules which certain social groups use to maximize their survival chances.

Optimal Non-Markovian Search Strategies with n-Step Memory

Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a migrating cell that is repelled from the diffusive chemotactic signal that it secretes on its way, denoted as an autochemotactic searcher. To analyze the efficiency of this class of non-Markovian search processes, we present a general formalism that allows one to compute the mean first-passage time (MFPT) for a given set of conditional transition probabilities for non-Markovian random walks on a lattice. We show that the optimal choice of the n-step transition probabilities decreases the MFPT systematically and substantially with an increasing number of steps. It turns out that the optimal search strategies can be reduced to simple cycles defined by a small parameter set and that mirror-asymmetric walks are more efficient. For the autochemotactic searcher, we show that an optimal coupling between the searcher and the chemical reduces the MFPT to 1/3 of the one for a Markovian random walk.

Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment

pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of [Formula: see text] units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection-diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved [Formula: see text]. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer's immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.

Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids

Active colloidal particles that are propelled by a self-diffusiophoretic mechanism are often described by Langevin equations that are either postulated on physical grounds or derived using the methods of fluctuating hydrodynamics. While these descriptions are appropriate for colloids of micrometric and larger size, they will break down for very small active particles. A fully microscopic derivation of Langevin equations for self-diffusiophoretic particles powered by chemical reactions catalyzed asymmetrically by the colloid is given in this paper. The derivation provides microscopic expressions for the translational and rotational friction tensors, as well as reaction rate coefficients appearing in the Langevin equations. The diffusiophoretic force and torque are expressed in terms of nonequilibrium averages of fluid fields that satisfy generalized transport equations. The results provide a description of active motion on small scales where descriptions in terms of coarse grained continuum fluid equations combined with boundary conditions that account for the presence of the colloid may not be appropriate.

Self-Propelled Micro/Nanomotors for On-Demand Biomedical Cargo Transportation

Micro/nanomotors (MNMs) are miniaturized machines that can perform assigned tasks at the micro/nanoscale. Over the past decade, significant progress has been made in the design, preparation, and applications of MNMs that are powered by converting different sources of energy into mechanical force, to realize active movement and fulfill on-demand tasks. MNMs can be navigated to desired locations with precise controllability based on different guidance mechanisms. A considerable research effort has gone into demonstrating that MNMs possess the potential of biomedical cargo loading, transportation, and targeted release to achieve therapeutic functions. Herein, the recent advances of self-propelled MNMs for on-demand biomedical cargo transportation, including their self-propulsion mechanisms, guidance strategies, as well as proof-of-concept studies for biological applications are presented. In addition, some of the major challenges and possible opportunities of MNMs are identified for future biomedical applications in the hope that it may inspire future research.

Active Matter, Microreversibility, and Thermodynamics

Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature, active matter systems exist in nonequilibrium states. In this paper, the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collectively to form structures such as dynamic clusters. A general nonequilibrium thermodynamics framework for the description of such systems is presented that accounts for both self-diffusiophoresis and diffusiophoresis due to external concentration gradients, and is consistent with microreversibility. It predicts the existence of a reciprocal effect of diffusiophoresis back onto the reaction rate for the entire collection of colloids in the system, as well as the existence of a clustering instability that leads to nonequilibrium inhomogeneous system states.

Green Plasmonic Nanoparticles and Bio-Inspired Stimuli-Responsive Vesicles in Cancer Therapy Application

: In the past years, there is a growing interest in the application of nanoscaled materials in cancer therapy because of their unique physico-chemical properties. However, the dark side of their usability is limited by their possible toxic behaviour and accumulation in living organisms. Starting from this assumption, the search for a green alternative to produce nanoparticles (NPs) or the discovery of green molecules, is a challenge in order to obtain safe materials. In particular, gold (Au NPs) and silver (Ag NPs) NPs are particularly suitable because of their unique physico-chemical properties, in particular plasmonic behaviour that makes them useful as active anticancer agents. These NPs can be obtained by green approaches, alternative to conventional chemical methods, owing to the use of phytochemicals, carbohydrates, and other biomolecules present in plants, fungi, and bacteria, reducing toxic effects. In addition, we analysed the use of green and stimuli-responsive polymeric bio-inspired nanovesicles, mainly used in drug delivery applications that have revolutionised the way of drugs supply. Finally, we reported the last examples on the use of metallic and Au NPs as self-propelling systems as new concept of nanorobot, which is able to respond and move towards specific physical or chemical stimuli in biological entities.

Emergent collective dynamics of bottom-heavy squirmers under gravity

We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.

A practical guide to active colloids: choosing synthetic model systems for soft matter physics research

Synthetic active colloids that harvest energy stored in the environment and swim autonomously are a popular model system for active matter. This emerging field of research sits at the intersection of materials chemistry, soft matter physics, and engineering, and thus cross-talk among researchers from different backgrounds becomes critical yet difficult. To facilitate this interdisciplinary communication, and to help soft matter physicists with choosing the best model system for their research, we here present a tutorial review article that describes, in appropriate detail, six experimental systems of active colloids commonly found in the physics literature. For each type, we introduce their background, material synthesis and operating mechanisms and notable studies from the soft matter community, and comment on their respective advantages and limitations. In addition, the main features of each type of active colloid are summarized into two useful tables. As materials chemists and engineers, we intend for this article to serve as a practical guide, so those who are not familiar with the experimental aspects of active colloids can make more informed decisions and maximize their creativity.

Exact Phoretic Interaction of Two Chemically Active Particles

We study the nonequilibrium interaction of two isotropic chemically active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed point-a phenomenon that cannot be captured under the far-field approximation. We find that, due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects originate from a self-generated neighbor-reflected chemical gradient, similar to interactions of a self-propelling phoretic particle and a flat substrate.

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.

Temporal Light Modulation of Photochemically Active, Oscillating Micromotors: Dark Pulses, Mode Switching, and Controlled Clustering

Photochemically powered micromotors are prototype microrobots, and spatiotemporal control is pivotal for a wide range of potential applications. Although their spatial navigation has been extensively studied, temporal control of photoactive micromotors remains much less explored. Using Ag-based oscillating micromotors as a model system, a strategy is presented for the controlled modulation of their individual and collective dynamics via periodically switching illumination on and off. In particular, such temporal light modulation drives individual oscillating micromotors into a total of six regimes of distinct dynamics, as the light-toggling frequencies vary from 0 to 10³ Hz. On an ensemble level, toggling light at 5 Hz gives rise to controlled, reversible clustering of oscillating micromotors and self-assembly of tracer microspheres into colloidal crystals. A qualitative mechanism based on Ag-catalyzed decomposition of H₂O₂ is given to account for some, but not all, of the above observations. This study might potentially inspire more sophisticated temporal control of micromotors and the development of smart, biomimetic materials that respond to environmental stimuli that not only change in space but also in time.

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.

Linear and angular motion of self-diffusiophoretic Janus particles

We theoretically study the active motion of self-diffusiophoretic Janus particles (JPs) using the Onsager-Casimir reciprocal relations. The linear and angular velocity of a single JP are shown to respectively result from a coupling of electrochemical forces to the fluid flow fields induced by a force and torque on the JP. A model calculation is provided for half-capped JPs catalyzing a chemical reaction of solutes at their surface by reducing the continuity equations of the reacting solutes to Poisson equations for the corresponding electrochemical fields. We find that an anisotropic surface reactivity alone is enough to give rise to active linear motion of a JP, whereas active rotation only occurs if the JP is not axisymmetric. In the absence of specific interactions with the solutes, the active linear velocity of the JP is shown to be related to the stoichiometrically weighted sum of the friction coefficients (or hydrodynamic radii) of the reacting solutes. Our reciprocal treatment further suggests that a specific interaction with the solutes is required to observe far-field diffusiophoretic interactions between JPs, which rely on an interfacial solute excess at the JP surface. Most notably, our approach applies beyond the boundary-layer approximation and accounts for both the diffusio- and electrophoretic nature of active motion.

Self-assembly of colloids based on microfluidics

Self-assembly of colloids provides a powerful way for the construction of complex multi-scale materials. Microfluidic techniques possess great potential to precisely control the assembly of micro- and nano-scale building blocks via the rational design of various microfluidic environments. In this review, we first discuss the self-assembly of colloids without templates by using the laminar microfluidic technique. The self-assembly of colloids based on a droplet as a template was subsequently summarized and discussed via droplet microfluidic technique. Moreover, the evaporation-driven self-assembly of colloids in microfluidic channels has been discussed and analysed. Finally, the representative applications in this field have been pointed out. The aim of this review is to summarize the state-of-art on the self-assembly of colloids based on various microfluidic techniques, exhibit their representative applications, and point out the current challenges in this field, hoping to inspire and guide future work.

Confined 1D Propulsion of Metallodielectric Janus Micromotors on Microelectrodes under Alternating Current Electric Fields

There is mounting interest in synthetic microswimmers ("micromotors") as microrobots as well as a model system for the study of active matters, and spatial navigation is critical for their success. Current navigational technologies mostly rely on magnetic steering or guiding with physical boundaries, yet limitations with these strategies are plenty. Inspired by an earlier work with magnetic domains on a garnet film as predefined tracks, we present an interdigitated microelectrodes (IDE) system where, upon the application of AC electric fields, metallodielectric (e.g., SiO₂-Ti) Janus particles are hydrodynamically confined and electrokinetically propelled in one dimension along the electrode center lines with tunable speeds. In addition, comoving micromotors moved in single files, while those moving in opposite directions primarily reoriented and moved past each other. At high particle densities, turbulence-like aggregates formed as many-body interactions became complicated. Furthermore, a micromotor made U-turns when approaching an electrode closure, while it gradually slowed down at the electrode opening and was collected in large piles. Labyrinth patterns made of serpentine chains of Janus particles emerged by modifying the electrode configuration. Most of these observations can be qualitatively understood by a combination of electroosmotic flows pointing inward to the electrodes, and asymmetric electrical polarization of the Janus particles under an AC electric field. Emerging from these observations is a strategy that not only powers and confines micromotors on prefabricated tracks in a contactless, on-demand manner, but is also capable of concentrating active particles at predefined locations. These features could prove useful for designing tunable tracks that steer synthetic microrobots, as well as to enable the study of single file diffusion, active turbulence, and other collective behaviors of active matters.

Review: Interactions of Active Colloids with Passive Tracers

Collective phenomena existing universally in both biological systems and artificial active matter are increasingly attracting interest. The interactions can be grouped into active-active and active-passive ones, where the reports on the purely active system are still clearly dominating. Despite the growing interest, summarizing works for active-passive interactions in artificial active matter are still missing. For that reason, we start this review with a general introduction, followed by a short spotlight on theoretical works and then an extensive overview of experimental realizations. We classify the cases according to the active colloids’ mechanisms of motion and discuss the principles of the interactions. A few key applications of the active-passive interaction of current interest are also highlighted (such as cargo transport, flow field mapping, assembly of structures). We expect that this review will help the fundamental understanding and inspire further studies on active matter.

Osmosis, from molecular insights to large-scale applications

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression - the van 't Hoff perfect gas law - and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.